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While traditional methods rely on manually labeled mistakes, our approach does not require mistake annotations, hence overcoming the need of domain-specific labeled data. Based on the observation that eye movements closely follow object manipulation activities, we assess to what extent eye-gaze signals can support mistake detection, proposing to identify deviations in attention patterns measured through a gaze tracker with respect to those estimated by a gaze prediction model. Since predicting gaze in video is characterized by high uncertainty, we propose a novel gaze completion task, where eye fixations are predicted from visual observations and partial gaze trajectories, and contribute a novel gaze completion approach which explicitly models correlations between gaze information and local visual tokens. Inconsistencies between predicted and observed gaze trajectories act as an indicator to identify mistakes. Experiments highlight the effectiveness of the proposed approach in different settings, with relative gains up to $+14\%$ , $+11\%$ , and $+5\%$ in EPIC-Tent, HoloAssist and IndustReal respectively, remarkably matching results of supervised approaches without seeing any labels. We further show that gaze-based analysis is particularly useful in the presence of skilled actions, low action execution confidence, and actions requiring hand-eye coordination and object manipulation skills. Our method is ranked first on the HoloAssist Mistake Detection challenge. + +# 1. Introduction + +Smart glasses are gaining more and more popularity, with various existing products capable of supporting the user + +![](images/2b811f6157ff7387f73370561628fd60c541e1af3163c949e215ce63515cce7e.jpg) + +![](images/88423628da16cfbcc6d22c29c3842120f9e4ba5404ec38b5b7218d68dfefcd4d.jpg) + +![](images/53ea10e3d6e253068726746521659c59f28488c3f634f1db3c46b5ae83cd539b.jpg) + +![](images/0e82c833cfef49cc015ef873f109c530f6011105b66c6a6cb49a04bcff1fb6a1.jpg) + +![](images/229aad7cc873cea7fba49158a9d1a4199fcdfb2f6db55f30d7134f60469de5e4.jpg) +Figure 1. Top: gaze trajectories of a correct and wrong execution of the "place water container" action, together with gaze fixation maps averaged across many action instances. Note the higher variability exhibited by wrong executions. Bottom: (a) The proposed unsupervised mistake detection method assumes as input a video with a partial gaze trajectory on the initial part of the video. (b) A gaze completion model predicts a gaze trajectory for the remaining part of the video, conditioned on the input video and the partial trajectory. (c) A mistake is detected if the predicted trajectory is significantly different from the observed one, suggesting a deviation from the expected attention patterns. + +![](images/a81329599ad5c1ad15a4d2395934fdbdb37ac92e091f6c4464007b6be92022ff.jpg) +(a) Input + +![](images/6db858edc082baff826b4290066ffefa0ec900c48eecda6c1319dddc378df6c0.jpg) +(b) Gaze Completion + +![](images/be34b4f706f53ddbf18917352027ed5236a0914ca03365faf1756c2d47de061d.jpg) +(c) Compare with GT + +through Augmented Reality. In order to provide timely assistance, wearable devices should be able to identify moments in which the user makes mistakes or is confused and requires help [7]. If such instances are properly detected, the AI system can proactively offer contextual information or suggestions on how to best carry out the task at hand [42]. + +Previous works tackled the problem of detecting mistakes from a fully supervised perspective, where mistake instances were labeled in egocentric video and machine learning algorithms were trained to discriminate between video segments of correct action executions and incorrect ones [34, 42]. Such a fully supervised approach has two main downsides: 1) It is domain-dependent, hence requiring an accurate characterization of what a mistake is, depending on the context (e.g., a mistake in a kitchen is different from + +a mistake in the assembly line); 2) It requires to collect and label a sufficient number of mistake instances, which may be difficult to observe and record, involve time consuming procedures, and require expert knowledge. Another class of methods [9, 33] aim to detect mistakes without relying on mistake annotations, but still requires domain-specific and costly temporal action annotations. Ideally, a wearable assistant should be able to infer when the behavioral patterns of the user deviate from the norm in order to determine if they need assistance in a scenario-independent setting, i.e., without making specific assumptions on how a mistake is defined and without requiring costly labels. To overcome the aforementioned limitations, we propose to detect mistakes in egocentric videos of human activity in an unsupervised way, learning from unlabeled video. + +Mistakes in task execution, in particular for tasks requiring hand-eye coordination and object manipulation skills, often involve abnormal attention patterns of the camera wearer [17, 18]. For instance, imagine a user operating a coffee machine without first adding water. As they press the brew button, they notice that no coffee is produced and start shifting their attention erratically between the cup, the water tank, and the LED indicator, deviating from the typical attention sequence of "button $\rightarrow$ cup $\rightarrow$ button." (See Figure 1(top)). This behavior is well-documented in psychology literature, which shows that gaze patterns are crucial for the execution of even the most repetitive daily activities (e.g., making tea) [20], and that they change in response to task complexity [30] and mistakes [29]. + +Following these observations, we study how the analysis of eye-gaze fixations can support mistake detection in egocentric video of skilled human activities. We hence propose to learn a model of "normal" attention patterns in the form of a gaze predictor producing likely eye gaze trajectories from a video at inference time. Since gaze prediction can be governed by high uncertainty, depending on the user's goals, we propose a novel "gaze completion" task in which a model takes as input a video and a partial gaze trajectory (Figure 1(a)) and is tasked to predict a likely continuation of the partial trajectory (Figure 1(b)). Gaze completion is tackled with a novel approach based on a Gaze-Frame Correlation module which explicitly models the correlation between gaze information and each local visual token. We expect videos of correct action executions to represent normal user behavior, and hence to be characterized by predictable gaze patterns, while human behavior will deviate from normality, and gaze will be unpredictable, when a mistake is made by the user. We hence signal a mistake by comparing the predicted gaze with the ground truth eye gaze trajectory obtained through a gaze tracker (Figure 1(c)). + +Experiments show the effectiveness of the proposed approach, both alone, or in combination with other techniques, when compared to one-class anomaly detection + +methods [8, 39], and various unsupervised mistake detection baselines, with relative gains up to $+14\%$ , $+11\%$ , and $+5\%$ in the on EPIC-Tent [15], HoloAssist [42] and IndustReal [32] datasets respectively, remarkably matching the results of supervised methods without any labels in one-class settings. Our analysis also shows that gaze is most effective in the presence of complex actions, low-confidence executions, and actions requiring hand-eye coordination and object-manipulation skills. + +In summary, the contributions of this work are as follows: 1) We investigate for the first time the problem of unsupervised mistake detection from egocentric video of human activity and provide an initial benchmark based on three datasets. 2) We define the novel "gaze completion" task where models predict gaze trajectories from video and partial gaze inputs, and introduce an approach based on a Gaze-Frame Correlation module; 3) We propose an approach to unsupervised mistake detection leveraging gaze completion to identify instances of unpredictable gaze patterns. Experiments analyze under which conditions gaze-based analysis is most useful and show the effectiveness of the approach, in one-class and unsupervised settings. + +We will publicly release the code and model checkpoints to support future research. + +# 2. Related Work + +Egocentric gaze estimation Literature on gaze estimation from egocentric video is rich, with previous works investigating simultaneous gaze prediction and action recognition [5], describing gaze prediction approaches incorporating egocentric cues [21], modeling task-dependent attention transition [13], leveraging vanishing point, manipulation point, hand regions [41], introducing specific architectures [1, 19], and proposing datasets to study egocentric gaze estimation and its applications in a variety of scenarios [12, 14, 22, 32, 42]. We propose a novel gaze completion task and show its application to the problem of unsupervised mistake detection in egocentric video. Differently from previous works, we define and tackle the novel task of gaze completion, with the aim to reduce the uncertainty associated with gaze prediction. + +Use of gaze in egocentric vision While many previous works focused on gaze estimation from video, few works investigated the use of gaze, estimated through a dedicated gaze tracker, as an input to support downstream egocentric vision applications. Specifically, previous investigations focused on discovering object usage [3], detecting privacy-sensitive situations [38], finding attended objects [27], assisting large language models in classification tasks [16], enhancing visual tasks [44, 46], improving egocentric human motion prediction [45], and aiding natural language processing tasks [36]. We show the effectiveness of gaze in mistake detection. Our method compares gaze trajectory + +ries predicted from visual data with gaze estimated through a gaze tracker to identify mistakes when predictions deviate from the ground truth. + +Mistake Detection in Egocentric Videos Mistakes naturally occur in human activities. The ability to automatically detect them from egocentric video can be beneficial for an AR assistant to offer support. Identifying mistakes usually entails modeling procedural knowledge [4, 9, 34], skill assessment [10], action segmentation [11] or detecting forgotten actions [37]. Notably, previous works tackled the task in a supervised fashion, training models to classify an action segment as "correct" or "mistake" in manually annotated instances [34, 42]. While this approach is feasible in a closed-world scenario, it requires 1) a definition of what a mistake is, depending on the domain (e.g., kitchens vs the assembly line), 2) significant amounts of manually labeled data, which is expensive and requires expert knowledge. In this work, we tackle an unsupervised mistake detection task, in which models observe unlabeled video at training time and are tasked to detect mistakes from video at test time. Our unsupervised scheme is possible through the analysis of gaze attention patterns, which provide a supervisory signal to create a joint video-gaze model of normal behavior. + +Video Anomaly Detection Our research also relates to the problem of Video Anomaly Detection (VAD), which involves recognizing abnormal or anomalous events within videos [23, 39]. A line of video anomaly methods are based on one-class classification, in which models are trained on normal videos and aim to identify divergence from the norm at test time [6, 8, 24, 25, 39, 40, 43]. Notably, anomaly detection in egocentric vision remains under-explored [26]. Similar to video anomaly detection, we aim to detect mistakes by determining video segments which deviate from statistics observed at training time [8]. Differently from previous works in video anomaly detection, we ground our predictions in an egocentric gaze estimation model, which acts as a proxy for modeling normal human behavior, hence effectively achieving mistake prediction detection when anomalous behavior is observed. Moreover, we go beyond the one-class assumption and show that our method can also be used in unsupervised settings where unlabeled correct and mistake examples are included at training time. + +# 3. Proposed Approach + +# 3.1. Mistake Detection Problem Setup + +The mistake detection task consists in highlighting those parts of the video in which the user is making a mistake during the execution of a given activity. In our setup, at each time-step $t$ , a model $\Phi$ takes as input a video $V$ observed up to time-step $t$ , $V_{1:t}$ , and a 2D gaze trajectory $T_{1:t}$ obtained with a gaze tracker, where the $i$ -th element of the trajectory $T_i^{(x,y)}$ is a 2D gaze fixation in frame $V_i$ . Given this input, + +the model has to return a score $s_t = \Phi(V_{1:t}, T_{1:t})$ indicating whether a mistake is happening at the current time $t$ . In this context, high $s_t$ scores indicate the occurrence of a mistake, while low $s_t$ scores indicate a correct action. We can hence see the mistake detection problem as a classification task, in which timestep $t$ is classified as a mistake if $s_t > \theta$ , where $\theta$ is a chosen threshold. We follow previous literature on anomaly detection [8, 39] and evaluate methods in a threshold-independent fashion by reporting the Receiver Operating Characteristics Area Under the Curve (ROC-AUC), where we consider "mistake" as the positive class1. For completeness, we also report the best $F_1$ score achieved considering the different thresholds, as well as its related precision and recall values. + +# 3.2. Proposed Approach + +At each timestep $t$ , we trim the input video $V_{1:t}$ and gaze trajectory $T_{1:t}$ to the last observed $F$ frames, hence considering $V_{t-F:t}$ and $T_{t-F:t}$ as inputs to our mistake detection method. (Figure 1(a)). Our method relies on two main components: a gaze completion model (Figure 1(b)), and a scoring function (Figure 1(c)). + +Gaze Completion Model Figure 2 illustrates the proposed gaze completion model. The model takes as input the video $V_{t - F:t}$ and the first half of the input gaze trajectory $T_{t - F:t - F / 2}$ and predicts a gaze trajectory $\hat{T}_{t - F / 2:t}$ aligned to the remaining part of the ground truth trajectory $T_{t - F / 2:t}$ . The goal of this model is to predict where the user is looking in the video, conditioned on the initial trajectory. As we show in the experiments, the conditioning allows to reduce the uncertainty on gaze predictions and give a prior into the intention and characteristics of the user. For instance, the model can notice that the user is a novice from the partial input trajectory or get an understanding of the performed activity and adapt its prediction accordingly. We build on [19] and propose an encoder-decoder transformer-based architecture, including two approaches to condition gaze prediction on the input partial trajectory: channel fusion and correlation fusion. + +Model Overview The input gaze trajectory $T_{t - F:t}$ is encoded into a stack of heatmaps $Q$ obtained by centering a Gaussian distribution of standard deviation $\sigma$ around the gaze points. The first half of the stack $Q_{1:F/2}$ , corresponding to the input half trajectory $T_{t - F:t - F/2}$ , is forwarded to the two trajectory fusion models (paths (1) and (2) in Figure 2), which inject information on the input trajectory at different semantic levels in the model. Input frames $V_{t - F:t}$ are processed by a token embedding layer which maps them to visual tokens with a convolution as in [19]. This mod + +![](images/d0cd36aaf41b121e6bd512cfe318be61b829619341c7a909c433087a5aaacdff.jpg) +Figure 2. The model takes as input $F$ RGB frames $V_{t - F:t}$ and a partial 2D gaze trajectory $T_{t - F:t - F / 2}$ on the first $F / 2$ input frames, and outputs a predicted trajectory $\hat{T}_{t - F / 2:t}$ from the input video, conditioned on the input trajectory. The input trajectory is encoded as a spatio-temporal heatmap $Q$ . Trajectory and RGB inputs are fused using two strategies, channel fusion, which adds gaze heatmaps as a separate channel (1), and correlation fusion, which uses a dedicated gaze-visual correlation module (2). We follow the design of [19] and process our inputs with a transformer encoder-decoder architecture which outputs a predicted gaze heatmap $\hat{Q}$ , supervised via a standard Kullback-Leibler divergence loss using the ground truth unobserved trajectory $T_{t - F / 2:t}$ . The output trajectory $\hat{T}_{t - F / 2:t}$ is recovered from $\hat{Q}$ using a peak finding operation. + +ule is also responsible for mapping the input heatmaps to a single trajectory token. Input tokens are then processed by the transformer encoder, by the gaze-visual correlation module and finally by the transformer decoder to output a likely completion of the gaze in the form of heatmaps $\hat{Q}$ , which are supervised with a standard Kullback-Leibler loss. Specifically, $\hat{Q}$ contains $F$ heatmaps related to the $F$ input frames $V_{t - F:t}$ . The final trajectory $\hat{T}$ is obtained by finding the global maxima of the predicted gaze heatmaps. Channel Fusion The channel fusion module (Figure 2(1)) adds the heatmaps in $Q_{1:F/2}$ to the first $F/2$ frames of the input video, $V_{t - F:t - F/2}$ as an additional channel. The values of this channel are set to zero for the remaining frames. This form of early fusion acts as a soft conditioning aiming to include information about the input gaze trajectory in the computation. Note that, in order to incorporate information about the relationships between haze and input frames, the model needs to learn how to compute suitable gaze representations from the additional input channel during training. Correlation Fusion This approach (Figure 2(2)) aims to fuse visual tokens with the gaze trajectory token computed by the token embedding layer. Inspired by global-local fusion originally proposed in [19], this is done in two stages. First, within the transformer encoder, where attention between all visual features and the gaze token is computed. In this stage, correlations between all visual tokens and across visual and gaze tokens are leveraged to obtain a strong representation. Second, within the dedicated gaze-visual correlation module. Here, attention is computed only between the gaze token and the visual tokens, thus learning a ded + +icated attention mechanism which explicitly enriches the representation of each visual token with gaze information. Note that this fusion mechanism operates both at the early (through the encoder) and mid (through the gaze-visual correlation module) levels, thus allowing to leverage low-level (co-occurrences of gaze and visual features) and more semantic (co-occurrences of gaze and semantic visual concepts) information. + +Scoring Function Our approach predicts the mistake confidence score $s_t$ by comparing the predicted trajectory $\hat{T}_{t - F / 2:t}$ with the ground truth one $T_{t - F / 2:t}$ which is obtained by the gaze tracker of the wearable device. We explore four different ways to compare the two trajectories: Euclidean distance, Dynamic Time Warping (DTW), Heatmap, and Entropy. + +Euclidean Distance This method consists in accumulating the Euclidean distances computed between corresponding points in each trajectory as the score $s_t$ : + +$$ +s _ {t} = \sum_ {i = F / 2 + 1} ^ {F} \| T _ {t - F + i} - \hat {T} _ {t - F + i} \|. \tag {1} +$$ + +Dynamic Time Warping This scoring function uses Dynamic Time Warping (DTW)[31] to measure the distance between trajectories: + +$$ +s _ {t} = \mathrm {D T W} (T, \hat {T}) \tag {2} +$$ + +Where $\mathrm{DTW}$ returns the cost of aligning $T$ to $\hat{T}$ according to + +the DTW algorithm2. + +Heatmap Differently from previous functions, this approach explicitly considers the probability values predicted by the model at each location. Specifically, we evaluate the likelihood of a ground truth eye fixation $T_{i}$ obtained by the device under the predicted heatmap $\hat{Q}_i$ , which can be computed as: + +$$ +P \left(T _ {i} \mid \hat {Q}\right) = \hat {Q} _ {i} \left(T _ {i} ^ {x}, T _ {i} ^ {y}\right) \tag {3} +$$ + +where $T_{i}^{x}$ and $T_{i}^{y}$ are the coordinates of the trajectory point $T_{i} = [T_{i}^{x}, T_{i}^{y}]$ . The score associated to the predicted trajectory $\hat{T}$ is computed as the sum of the likelihoods of each trajectory point, considering the predicted heatmap $\hat{Q}$ : + +$$ +s _ {t} = \sum_ {i = F / 2 + 1} ^ {F} P \left(T _ {t - F + i} | \hat {Q}\right). \tag {4} +$$ + +Entropy This is the only method which does not require ground truth gaze for computation. We consider this measure as a way to check whether mistakes are systematically characterized by uncertain gaze predictions. In this case, the score $s_t$ is set as the mean entropy of all predicted heatmaps for a given trajectory $\hat{T}$ . The entropy $H$ of a single heatmap $\hat{Q}$ is given by: + +$$ +s _ {t} = - \frac {1}{F / 2} \sum_ {i = F / 2 + 1} ^ {F} \sum_ {x, y} \hat {Q} _ {t - F + i} ^ {(x, y)} \log_ {2} \left(\hat {Q} _ {t - F + i} ^ {(x, y)}\right) \tag {5} +$$ + +$Q_{j}^{(x,y)}$ is the value at coordinates $(x,y)$ of heatmap $Q_{j}$ . + +# 4. Experiments and Results + +# 4.1. Datasets and Implementation Details + +We perform our experiments on three popular datasets. + +EPIC-Tent [14] includes 7 hours of egocentric video of 29 subjects wearing a head-mounded GoPro and an SMI eye tracker while assembling a camping tent. The dataset includes egocentric video, gaze and labels indicating video segments in which users make mistakes. Subjects also rated their level of confidence in action execution in each clip in the videos. EPIC-Tent contains 151,689 mistake frames and 384,558 frames of correct executions, hence with a 28:72 ratio between correct and mistake frames. Since no official train-test split is available, we randomly split videos in training, validation and test sets roughly following a 60:15:25 ratio, obtaining 86,099,27,613, and 37,977 mistake frames in the training, validation, and test sets respectively. Since the dataset contains a single video per subject, there is no subject overlap between the three sets. + +IndustReal [32] is designed for studying procedural tasks in industrial-like environments and consists of distinct training, validation, and test sets. The training set comprises + +78,902 frames, with $95.68\%$ frames labeled as correct and $4.32\%$ labeled as mistakes. The validation set includes 38,036 frames, with $95.18\%$ correct and $4.82\%$ mistaken frames. The test set contains 90,105 frames, with $92.53\%$ correct and $7.47\%$ mistaken frames. + +HoloAssist [42] focuses on a variety of scenarios in which users perform tasks with the assistance of an expert. The training set comprises 11,614,033 frames, with $94\%$ frames labeled as correct and $6\%$ labeled as mistakes. The test set contains 1,699,562 frames, with $95\%$ correct and $5\%$ mistake frames. + +Implementation Details We process input frames with a stride of 1 and set the batch size to 4 clips of 8 frames each. Weight decay is set to 0.07 to prevent overfitting. See the supplementary material for more details. + +# 4.2. Supervision Levels and Compared Approaches + +We compare the proposed approach to methods belonging to three different supervision levels: fully supervised, one-class classification, and unsupervised. All baselines described below are compared with a random baseline which assigns a random score to each input clip. + +Fully Supervised Methods are trained assuming the availability of mistake labels for all image frames. We consider this class of methods to provide an upper-bound to performance when assessing one-class and unsupervised methods. We consider two approaches in this class: a TimeSformer [2] action recognition model which classifies the input video clips without access to any temporal context from actions executed before or after the current one, and a C2F [35] temporal action segmentation model operating on DINOv2 [28] features, which naturally performs action segmentation taking into account the temporal context in which an action (or mistake) is executed. + +One-Class Classification Methods are trained only on videos of correct executions, following the standard setup of anomaly detection [8, 39]. In this context, we assume that the data is verified by an expert for correctness before being used for training. Note that this check does not require marking the temporal occurrence of mistakes, but only discarding any video which contains mistakes. For this class, we compare our method with respect to TrajREC [39] and MoCoDAD [8], two popular approaches for video anomaly detection based on the processing of human skeletal data. Since full human skeletons are not visible in egocentric videos, we replace skeletal data with hand joint keypoints3. We also adapt TrajREC and MoCoDAD to take a single gaze point instead of, or in addition to, the hand keypoints to assess the ability of such methods to leverage + +
ScoringFusionF1PrecisionRecallAUC
1Random//0.360.290.420.51
2Entropy//0.410.270.620.51
3Euclidean//0.420.290.600.55
4DTW//0.440.310.680.56
5Heatmap//0.450.320.700.57
6HeatmapCH0.450.320.740.63
7HeatmapCORR0.500.360.820.65
8HeatmapCH + CORR0.510.360.850.69
+ +eye-gaze information4. We compare these models to an instantiation of the proposed approach in which the gaze completion model is trained only on correct executions, hence effectively replicating a one-class scheme. We also compare with respect to a baseline which replaces the proposed gaze completion module with a simple gaze prediction component based on GLC [19]. Following the one-class setup, we train the GLC method of [19] on correct executions only and compare the predicted and ground truth gaze using the considered scoring functions. + +Unsupervised Methods assume no knowledge of which examples are correct executions and which are mistakes. Hence, models are trained on a natural mix of correct and incorrect action executions. This is the least constrained case in which the collected data is not verified by an expert prior to training. We compare our model with TrajREC and MoCoDAD adapted as discussed above and with the gaze-prediction baseline GLC [19]. + +# 4.3. Performance of Proposed Model and Ablations + +Table 1 reports the performance of the proposed approach in unsupervised settings, evaluating the considered scoring functions and gaze-video fusion strategies in the unsupervised mistake detection settings on EPIC-Tent. Rows 2-5 compare scoring functions when both fusion strategies are turned off and the model is not conditioned on previous trajectories. The entropy scoring function achieved an AUC of 0.51 and an F1 score of 0.41 (row 2), only marginally above the random baseline (F1 of 0.36), suggesting that high entropy in the predictions marginally correlates with the presence of a mistake. Alternative scoring functions improved the results, yielding an AUC of 0.55 and 0.56 when using Euclidean distance and DTW scoring functions, respectively (rows 3-4). The heatmap-based scoring function produced the best results, with an AUC of 0.57 and an F1 score of 0.45, significantly above random level (compare with the F1 score of 0.36 in row 1). The advantage of the heatmap scoring function is likely due to the better + +Table 1. Ablation of various scoring functions and fusion strategies on EPIC-Tent in the unsupervised setting. Best results per-block are underlined, while best global results are in bold. CH: channel fusion, CORR: correlation fusion. + +
MethodSup. LevelF1PrecisionRecallAUC
Random//0.360.290.420.51
TimeSformer [2]Fully Supervised0.490.350.800.67
C2F [35]Fully Supervised0.580.440.850.72
TrajREC (G) [39]One-Class0.400.260.880.51
MoCoDAD (G) [8]One-Class0.430.270.910.50
TrajREC (H) [39]One-Class0.440.310.760.55
MoCoDAD (H) [8]One-Class0.460.330.790.60
TrajREC (H+G) [39]One-Class0.420.290.750.53
MoCoDAD (H+G) [8]One-Class0.430.300.770.56
TrajREC (H+G)* [39]One-Class0.470.340.770.63
MoCoDAD (H+G)* [8]One-Class0.490.350.810.65
GLC [19]One-Class0.460.370.620.66
OursOne-Class0.520.370.850.69
Ours + MoCoDAD (H)*One-Class0.540.410.860.72
TrajREC (G) [39]Unsupervised0.270.160.940.50
MoCoDAD (G) [8]Unsupervised0.330.210.880.51
TrajREC (H) [39]Unsupervised0.400.270.790.58
MoCoDAD (H) [8]Unsupervised0.410.270.860.60
MoCoDAD (H+G)* [8]Unsupervised0.410.270.880.60
GLC [19]Unsupervised0.440.330.700.61
OursUnsupervised0.510.360.850.69
Ours + MoCoDAD (H)*Unsupervised0.520.370.880.70
+ +* Late fusion + +Table 2. Mistake detection results on EPIC-Tent. Best results are in bold, second best results are underlined. + +exploitation of the probability values computed by the gaze prediction model, as compared to other scoring functions. Hence, we adopted the heatmap-based scoring as our primary method in following comparisons. + +Rows 6-7 compare approaches using one of the two fusion strategies. While both fusion strategies improve results (compare rows 6-7 with 5), the proposed correlation strategy (CORR) systematically outperforms channel fusion, obtaining an AUC score of 0.65 and an F1 score of 0.50 and doubling the recall of the random baseline (0.82 vs 0.42) with better precision (0.36 vs 0.29). Combining the two fusion strategies (row 8) leads to an AUC of 0.69 and an F1 score of 0.51 (+0.12 and +0.06 compared to the standard heatmap method - row 5). This configuration is the one referred to as "ours" in future comparisons. $^{5}$ + +# 4.4. Comparison with the state of the art + +EPIC-Tent Table 2 compares the proposed mistake detection approach with competitors on EPIC-Tent, according to the three considered levels of supervision. C2F outperforms TimeSformer in all evaluated metrics, particularly in the F1 score (0.58 of C2F vs 0.49 of TimeSformer and 0.36 of the random baseline), suggesting that C2F is more adept at capturing temporal reasoning, which is crucial for identifying mistakes in dynamic activities. However, the reliance on fully labeled datasets poses limitations for both methods. One-class methods for anomaly detection adapted to take only gaze as input, namely, TrajREC (G) and MoCoDAD (G), show minor improvements over the random baseline in terms of AUC score (0.50 - 0.51 vs 0.51) and only small + +improvements in F1 score (0.40 - 0.43 vs 0.36). High recall values, paired with low precision, suggest that these methods tend to classify most clips as mistakes. Incorporating hand skeleton data instead of gaze, namely, TrajREC (H) and MoCoDAD (H), leads to slight improvements, as evidenced by F1 scores of 0.44 and 0.45, and AUC values of 0.55 and 0.60. Combining (H) and (G) models through late fusion (denoted with *) improves the results, with MoCoDAD $(\mathrm{H} + \mathrm{G})^{*}$ achieving an F1 score of 0.49 and an AUC of 0.65, suggesting that the signals captured by gaze-based and hand-based analyses are complementary. The one-class approach based on GLC [19] gaze prediction shows improved results compared to previous one-class methods, being only slightly less effective than the late fused method, despite not analyzing any hand-based information. This highlights the value of leveraging gaze analysis for mistake detection. + +Finally, the proposed method based on gaze completion obtains the best results, yielding an AUC of 0.69, an F1-score of 0.52, a precision of 0.37, and a recall of 0.85, which amount to relative improvements of $+5 / 13\%^6$ with respect to the best approach GLC and $+35 / 44\%$ with respect to the random baseline. Late-fusing our approach with MoCoDAD (H) achieves enhanced results with an AUC of 0.72 and an F1 score of 0.54, improving over compared approaches, suggesting that gaze analysis can further benefit from integration with approaches based on different cues. It is worth noting that our best method remarkably achieves the same AUC score of 0.72 as the best supervised approach and a comparable $F1$ score (0.54 vs 0.58) without access to labels during training. We compare unsupervised approaches in the bottom part of Table 2. Similarly to the one-class case, TrajREC (H) and MoCoDAD (H) slightly improve over the random baseline (e.g., 0.40 and 0.41 vs 0.36 of the random baseline in F1 score). GLC outperforms these former two methods obtaining an F1 score of 0.44 and an AUC score of 0.61, which are lower than the scores of 0.46 and 0.66 obtained in the one-class setting. In these settings, the proposed method achieves an F1 score of 0.51, which is comparable to the score obtained in one-class settings 0.52 with similar and recall values and the same AUC of 0.69, despite the unsupervised setting being more challenging. Late fusion with MoCoDAD (H) brings some additional improvements, with an F1 score of 0.52 and AUC of 0.70. + +Table 3 compares the proposed method with competitors on HoloAssist, which presents a more varied and expansive context than EPIC-Tent, making mistake detection more challenging. The random baseline achieves an F1 score of only 0.04. One-class methods like TrajREC and MoCoDAD improve over the baseline but tend to classify most clips as mistakes, with high recall values (0.96 and 0.94). Hand keypoint-based methods show improvements, with + +
MethodSup. LevelF1PrecisionRecallAUC
Random//0.040.020.390.50
TimeSformer [2]Fully Supervised0.210.350.130.58
C2F [35]Fully Supervised0.380.370.400.65
TrajREC (G) [39]One-Class0.090.040.960.50
MoCoDAD (G) [8]One-Class0.110.060.940.51
TrajREC (H) [39]One-Class0.190.110.720.56
MoCoDAD (H) [8]One-Class0.170.100.710.55
TrajREC (H+G) [39]One-Class0.130.070.680.52
MoCoDAD (H+G) [8]One-Class0.140.080.620.52
TrajREC (H+G)* [39]One-Class0.200.120.710.56
MoCoDAD (H+G)* [8]One-Class0.210.120.750.57
GLC [19]One-Class0.190.110.560.60
OursOne-Class0.220.140.590.61
Ours + MoCoDAD (H)*One-Class0.260.160.730.63
TrajREC (G) [39]Unsupervised0.050.030.920.50
MoCoDAD (G) [8]Unsupervised0.070.040.920.50
TrajREC (H) [39]Unsupervised0.110.070.320.56
MoCoDAD (H) [8]Unsupervised0.140.100.250.55
MoCoDAD (H+G)* [8]Unsupervised0.150.110.250.56
GLC [19]Unsupervised0.100.060.340.54
OursUnsupervised0.180.120.400.59
Ours + MoCoDAD (H)*Unsupervised0.210.150.400.60
+ +* Late fusion + +Table 3. Mistake detection result on HoloAssist. + +TrajREC (H) slightly outperforming MoCoDAD (H). GLC demonstrates better AUC and F1 scores, with more balanced precision and recall metrics. Our approach achieves an AUC of 0.61 and an F1 score of 0.22 in one-class settings, with the best results from late fusion with MoCoDAD, yielding an F1 score of 0.26 and an AUC of 0.63. In the unsupervised scenario, TrajREC (G) and MoCoDAD (G) show limited effectiveness, while the (H) approaches perform slightly better. Our method achieves an AUC of 0.59 and an F1 score of 0.18, showing robustness across evaluation settings and relative improvements over GLC, with gains of $+9\%$ and $+80\%$ , respectively. Combining with MoCoDAD (H) further enhances performance. + +Results on IndustReal, shown in Table 4, confirm the trends observed in HoloAssist. TrajREC and MoCoDAD bring small improvements over the random baseline in H, G, and $\mathrm{H + G}$ configurations. Our method outperforms competitors with improvements over GLC of $+5\%$ in AUC and $+14\%$ in F1 in one-class settings, and $+6\%$ in AUC in unsupervised settings, while late fusion with MoCoDAD (H) does not improve performance due to MoCoDAD's reduced effectiveness in this scenario. + +# 4.5. Contribution of gaze across scenarios + +In this section, we analyze the performance of our method with respect to scenarios in order to assess under which conditions gaze analysis is more or less predictive of mistakes. Action Complexity We investigated how action complexity correlates with gaze-predicted mistakes in procedural tasks. We asked 40 volunteers to rate the complexity of performing actions contained in HoloAssist without looking (1 = easy, 5 = difficult). We then compared the complexity of the action associated to a given video segment to the ability + +
MethodSup. LevelF1PrecisionRecallAUC
Random//0.120.060.620.51
TimeSformer [2]Fully Supervised0.200.120.350.58
C2F [35]Fully Supervised0.310.290.310.67
TrajRE(G) [39]One-Class0.170.090.900.53
MoCoDAD(G) [8]One-Class0.180.100.910.55
TrajREC(H) [39]One-Class0.210.120.880.57
MoCoDAD(H) [8]One-Class0.220.130.810.60
TrajREC(H+G) [39]One-Class0.180.100.860.55
MoCoDAD(H+G) [8]One-Class0.190.110.790.58
TrajREC(H+G)* [39]One-Class0.210.120.880.58
MoCoDAD(H+G)* [8]One-Class0.220.130.820.61
GLC [19]One-Class0.210.150.330.60
OursOne-Class0.240.180.350.63
Ours + MoCoDAD (H)*One-Class0.260.170.600.65
TrajREC (G) [39]Unsupervised0.110.060.920.51
MoCoDAD (G) [8]Unsupervised0.110.060.920.51
TrajREC (H) [39]Unsupervised0.150.110.280.55
MoCoDAD (H) [8]Unsupervised0.160.120.290.57
MoCoDAD (H+G)* [8]Unsupervised0.170.120.300.57
GLC [19]Unsupervised0.210.150.330.58
OursUnsupervised0.210.160.330.62
Ours + MoCoDAD (H)*Unsupervised0.200.150.320.61
+ +* Late fusion + +Table 4. Mistake detection result on IndustReal. + +of our model to make a correct prediction (which we term "success"). Results (see Figure 3a) showed a positive correlation between difficulty and prediction success, measured with a Point Biserial Correlation of 0.3843, with $p < 0.05^7$ . This suggests that our method is particularly effective in the case of complex actions which cannot be carried out without looking, while less effective in the case of trivial tasks. + +Confidence Level On the EPIC-Tent dataset, we compared if the self-rated confidence score reported by camera wearers was correlated to the success of our method. Results (see Figure 3b) obtained a Point Biserial Correlation of -0.1137, $p < 0.05$ indicating a small but significant negative correlation: our method is most effective when the self-rated confidence is higher. This suggests that gaze-based analysis is more effective in the case of novices, which reported lower confidence and probably rely more on visual observations when executing their tasks. + +Action Type We finally assess whether the type of the performed action affects the performance of our method. To this aim, we grouped actions contained in all three datasets in four categories (Hand-Eye Coordination, Object Manipulation, Task Preparation, Inspection/Verification) $^{8}$ . We hence computed the number of co-ocurrences between success or failure of our method and the different action classes. Results (see Figure 4) show a Cramer's V statistic of 0.27 (a moderate correlation of 0.27 in a $0 - 1$ scale) with a p-value $p < 0.05$ . Gaze-based analysis proves particularly useful in the case of actions requiring hand-eye coordination and object manipulation abilities, while less effective + +![](images/e5f3c971d3b69084ec2c9d6bc0d3444b19600ca5032cffafe9ccfb9fe2f4311f.jpg) +(a) + +![](images/f7b1186e8243bdc2e94bdbb2a47538d4f9aee1ab066e8da7c0914dd5a7ebdb2b.jpg) +(b) + +![](images/fbf016b1e60f7931fd9ecf02146d2faca3fda6bef54c8c9fb1eabdf7156d23a3.jpg) +Figure 3. Distributions of difficulty ratings (a) and execution confidence ratings (b) with respect to wrong and correct predictions. +Figure 4. Distributions of Correct/Wrong pred. by action type. + +for generic actions such as task preparation and inspection.[9] + +# 5. Conclusion + +We proposed to perform mistake detection in egocentric videos in an unsupervised way, leveraging gaze signals. We introduced a novel gaze completion task, where gaze trajectories are predicted based on observed video and partial gaze data, and an approach to tackle this task. 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Wolfe $^{6,7}$ + +Tat-Jen Cham + +Mengmi Zhang $^{1,2}$ + +Address correspondence to mengmi.zhang@ntu.edu.sg + +1College of Computing and Data Science, Nanyang Technological University, Singapore + +$^{2}$ Deep NeuroCognition Lab, I2R and CFAR, Agency for Science, Technology and Research, Singapore + +3Harbin Institute of Technology, Harbin, China 4Beijing Institute of Technology, Beijing, China + +5University of Virginia, USA 6Brigham and Women's Hospital, USA 7Harvard Medical School, USA + +# Abstract + +Imagine searching a collection of coins for quarters (0.25), dimes (0.10), nickels (0.05), and pennies (0.01)—a hybrid foraging task where observers look for multiple instances of multiple target types. In such tasks, how do target values and their prevalence influence foraging and eye movement behaviors (e.g., should you prioritize rare quarters or common nickels)? To explore this, we conducted human psychophysics experiments, revealing that humans are proficient reward foragers. Their eye fixations are drawn to regions with higher average rewards, fixation durations are longer on more valuable targets, and their cumulative rewards exceed chance, approaching the upper bound of optimal foragers. To probe these decision-making processes of humans, we developed a transformer-based Visual Forager (VF) model trained via reinforcement learning. Our VF model takes a series of targets, their corresponding values, and the search image as inputs, processes the images using foveated vision, and produces a sequence of eye movements along with decisions on whether to collect each fixated item. Our model outperforms all baselines, achieves cumulative rewards comparable to those of humans, and approximates human foraging behavior in eye movements and foraging biases within time-limited environments. Furthermore, stress tests on out-of-distribution tasks with novel targets, unseen values, and varying set sizes demonstrate the VF model's effective generalization. Our work offers valuable insights into the relationship between eye movements and decision-making, with our model serving as a powerful tool for further exploration of this connection. All data, code, and models are available at https://github.com/ZhangLab-DeepNeuroCogLab/visual-forager. + +# 1. Introduction + +![](images/5b8174584f725b8b8d6c11f79ab2d0c843ffe5ab4cc7be7a9e903e3070177f01.jpg) + +Counting down timer + +![](images/72354118862f531b94e75094cf3c457ea23bcf251613dc4ebcf0a9e5ec993721.jpg) + +Accumulative reward + +![](images/ee48eb6a74d0c229330a0b6196f4fe2ea26da38ce5f2bd607013aac80f0f3e32.jpg) + +Quarter ($0.25) + +![](images/368aaa1803058b9589b86e94d53de9ff554f8a67e5e4e4c5312d82294bb7e50a.jpg) + +Dime ($0.1) + +![](images/66baef91b0bcddad0b65fd21d4bd3d765731a54839b5f3887e5628e8ff9a893e.jpg) +Figure 1. Illustrative example of eye movements and decision-making in a hybrid visual foraging task. The image depicts a real-world scenario where the goal is to search piles of coins for multiple instances of target coins with varying monetary values in order to maximize the accumulative monetary reward, within a time-limited environment. Yellow dots and arrows represent the locations and order of eye movements during the search. Red bounding boxes show the target coins that are collected. Note that humans do not always collect every item they fixate on, highlighting the selective nature of the foraging process. + +Hybrid visual foraging is a ubiquitous challenge in our daily life, such as grocery shopping for a list of items, simultaneously scanning for traffic lights, parking spaces, and restaurants while driving, or looking for a specific amount of change among piles of coins (Fig. 1). These tasks involve searching for multiple instances of various target types stored in memory, where target values and prevalence can vary, and the exact number of target instances is often unknown. This raises a critical question about how to prioritize target selections during the search process. Understanding these dynamics is essential for optimizing search efficiency and decision-making in complex environments. + +To tackle this question, eye movements could offer a + +unique window into the underlying perceptual, cognitive, and evaluative processes involved in decision-making, such as sensory evidence sampling and accumulation [78, 87, 106, 140, 146], decision timing and temporal expectation [6, 10, 110, 120, 126], response inhibitions [24, 48, 65, 85, 88], and decision certainty and confidence [9, 23, 63, 96, 110], offering high temporal and spatial resolution [46, 49, 75, 103, 119]. In hybrid visual foraging, while neuroscience and psychology works [80, 133, 137-139] have primarily examined the sequence of target selections within the same environment and the timing of search transitions across different environments especially when target values and prevalence vary, there is a notable lack of studies focusing on eye movements. Here, we design and conduct human psychophysics experiments to examine how foraging strategies and eye movements are influenced by the prevalence and value of targets. + +Alongside studies in psychology and neuroscience, many AI models have been developed to predict eye movements during decision-making tasks, including visual search [2, 36, 51, 60, 86, 121, 128, 145], object recognition and detection [8, 91, 99, 130], and visual question answering [18, 59, 61]. Notably, existing visual search models integrate both bottom-up saliency [2, 36, 60] and top-down feature modulations [51, 86, 145]. However, these models assume idealized scenarios where either a single target type is present or multiple target types have equal values. As a result, they often overlook the need to prioritize target selections based on varying target prevalences and values during the search process. In this work, we introduce a computational model called Visual Forager (VF), a transformer-based architecture trained with reinforcement learning, designed to perform hybrid visual foraging efficiently across varying combinations of target prevalence and values. Unlike prior visual search models [19, 27, 122, 142], which often rely on human data for supervised training, our VF approximates human foraging behaviors and biases, despite zero training on human data. We highlight our key contributions: + +1. Drawing from psychology, we introduce hybrid visual foraging tasks for AI models. The predicted eye movements offer a unique window into the decision-making process with high spatial and temporal resolution. +2. We propose an AI model, Visual Forager (VF), for hybrid visual foraging tasks. VF uses actor-critic networks with a vision transformer backbone and integrates feature-based and value-based modulations to guide decision-making processes, determining where to fixate next and whether to collect currently fixated items during foraging tasks. +3. To benchmark AI model performances, we design and conduct human eye-tracking experiments for hybrid visual foraging tasks. Despite no training on human data, our VF achieves cumulative rewards comparable to human + +participants and approximates their foraging behaviors, including eye movements and decision biases toward highly valued and prevalent targets. + +4. Humans can flexibly adapt their foraging strategies to maximize total rewards under varying target values and prevalence. Remarkably, our VF also performs efficient foraging, under out-of-distribution conditions it was never trained on. This capability is attributed to our newly introduced data augmentations applied to target values. + +# 2. Related Work + +Eye movements as a window into decision making. Many psychology and neuroscience works have been using eye movements as a unique and non-invasive means [38, 41, 42, 62, 69, 75, 76, 79, 95, 101, 104, 105, 116, 117] to reflect how efficiently we interpret decision instructions [71, 140], the timing and duration of decision formation [6, 10, 110, 120, 126], expected rewards [43, 112, 125, 131, 143], decision accuracy [110], and our confidence in the outcome [9, 23, 63, 96]. Although multiple studies analyze the decision making in hybrid visual foraging tasks [15, 17, 35, 100, 144], there is a lack of research specifically examining eye movements and their relationships to decision making. To close this gap, we design and conduct eye-tracking experiments to investigate eye movements and their interactions with foraging behaviors. + +Computational models for goal-directed visual search. Eye movement in visual search is typically guided by five primary factors [136]: bottom-up saliency [66, 124, 135], top-down feature guidance [30, 34, 84], scene properties [12, 57, 123], prior history [32, 70, 132], and item values [3, 4, 82]. A range of computational models have been proposed to model human eye movements in each of these aspects during visual search [2, 13, 16, 21, 22, 44, 47, 51, 60, 67, 68, 74, 77, 86, 94, 118, 127-129, 145]. Recent deep learning models, such as [31, 40, 50, 51, 93, 141, 145, 146], have demonstrated success in searching for a single target in complex, naturalistic scenes by predicting a sequence of eye fixations and their durations. However, these models fail to look for multiple instances of multiple target types based on varying values and prevalence. To close this gap, we introduce Visual Forager (VF), capable of searching for multiple instances across different target types. Moreover, while models like GazeFormer [93], OAT [40], and IRL [141], rely on human data for training and struggle to generalize to unseen targets or unseen combinations of values and prevalence in out-of-distribution scenarios, VF can flexibly adapt its foraging strategy under these conditions. + +Deep reinforcement learning (RL) for value-guided decision-making. Deep RL models [1, 37, 52, 90, 92, 102, 109] have been applied to a wide range of decision-making + +![](images/09e7c9b7b8958f8fa6a77d788fc2872dcdf2c5b4550f6babb9ddc25882d84c67.jpg) +Figure 2. Schematic of the hybrid visual foraging experiment. Each foraging trial starts with a 2-second center fixation (omitted here for simplicity), followed by the presentation of target images and their associated values (e.g., a plant valued at 4). To ensure human participants memorize the targets and their values, they must pass a recognition test by selecting all targets among distractors and correctly matching their values. If they make errors, they repeat the target and value presentation phases. After another 2-second center fixation presentation, an object array is displayed. Both human and AI agents are tasked with collecting as many targets as possible through mouse clicks to maximize their total rewards, where rewards correspond to the values of the target objects, and a penalty of -1 is incurred for clicking on distractors. The trial ends either after 30 seconds or when 20 clicks are made. + +tasks, including video game playing [81, 89, 113], robotic control [5, 55, 107], and resource management [20, 83, 147]. These models learn to make sequential decisions by interacting with environments and receiving feedback through immediate or long-term reward [7, 26, 29, 39, 72]. Despite advancements in these decision-making models, they have not been specifically designed to model eye movements in hybrid foraging tasks. Here, we introduce a transformer-based network to learn optimal foraging and eye movement policies. This is in contrast to [54, 99, 111], where a transformer-based architecture is only used to extract visual features prior to decision-making. + +# 3. Hybrid visual foraging + +# 3.1. Human psychophysics experiments + +We conducted an in-lab psychophysics experiment for hybrid visual foraging, schematically illustrated in Fig. 2. The items were randomly arranged on a $16 \times 16$ grid, containing either 90, 105, or 120 items, with $20\%$ to $30\%$ of the squares filled with target instances. In each foraging trial, subjects searched for $N \in \{1, 2, 4\}$ target objects, each with a varying number of target instances. Targets and distractors in the search arrays were randomly selected from a pool of 2,400 unique items in [14]. A total of 15 subjects were recruited, yielding 750 trials, containing 50514 eye fixations and 12851 mouse clicks. All the experiments are conducted with the subjects' informed consent and according to the protocols approved by the Institutional Review Board of our institution. See Appendix Sec. S1.1 for more details. + +# 3.2. Foraging environments for AI models + +Humans have accumulated years of visual experiences, making them efficient zero-shot visual searchers without requiring prior training for hybrid visual foraging [138]. In contrast, AI models require task-specific training. Hence, we introduced procedural generation of diverse foraging environments, subsequently used to train AI models. As demonstrated in the human psychophysics experiments described above, the procedural generation of a foraging trial depends on several key experimental parameters: the total number of items on the object arrays within a $16 \times 16$ -sized grid, the number of target objects on the search arrays, the prevalence of target instances for each target object, the values assigned to the target objects, and the selection of target and distractor items from a pool of 2,400 unique items. It is evident that the decision-making processes of both humans and AI models may be influenced by any of these experimental parameters. We sub-sample various combinations of these experimental parameters for the procedural generation of foraging environments: the total number of items on the search array is fixed at 105. A fixed set of 4 items is randomly selected as targets with their values set at 2, 4, 8, and 16 and their prevalence randomly determined. See Appendix Sec. S1.2 for details. + +To benchmark AI model performance in hybrid foraging tasks, we introduce two in-domain hybrid foraging conditions that align with the distribution of the training environments that the AI models were optimized to solve. (1) In-domain Uneven Value, Equal Prevalence (UnValEqPre): the prevalence of all 4 targets is equal but their values vary. (2) In-domain Uneven Value, Unequal Prevalence (UnValUnPre): both target prevalence and values vary, with low-value targets being more common and high-value targets scarcer. To assess whether the AI models can generalize to out-of-distribution (OOD) hybrid visual search tasks, where experimental parameters differ from those encountered during training, we introduced five OOD conditions. (1) OOD - Even Value, UnEqual Prevalence (EqValUnPre): the 4 target types have the equal values with varying prevalence. (2) OOD - Unseen target objects (UTargets) The target images are unseen during testing. (3) OOD - Unseen value combinations (UVvalues) The target values exceeded the range used for training, with their values changing in either arithmetic or geometric series. (4) OOD - Unseen total item numbers (UItemNum): The total number of items on the search grid differs from the one used for training. (5) OOD - Unseen target object sizes (USetSize) The set size of target objects is manipulated. See Appendix Sec. S1.3 for details of each condition. + +Comparisons of foraging environments between humans and AIs. For a fair comparison between human and AI performance, we categorized the foraging trials from human psychophysics experiments into the same seven + +conditions above used for testing the AI models. We apply identical rewards and penalties to humans and all AI models for training and evaluation. Moreover, to interact with the foraging environments, both humans and AI models must decide where to move their eye fixations next and whether to click on the current item. In human psychophysics experiments, each trial ends either after 30 seconds or once 20 clicks are made. Unlike humans, AI models do not experience time delays in eye movements or motor responses for mouse clicks. To simulate these time constraints and allow for a fair comparison between the fixation and click sequences of AI models and humans, we impose constant time costs on the AI models: 776 milliseconds for one click and 336 milliseconds for one fixation. These time costs are calculated through linear regression based on human response data (Appendix Fig. S1 and Fig. S2). + +# 4. Our proposed Visual Forager (VF) + +We propose the Visual Forager (VF), a computational model for hybrid visual foraging (Fig. 3). At the current $t$ th fixation location $F_{t}$ , the model takes as input the search image $I_{S}$ and $N$ target images $I_{T}^{1:N}$ with their corresponding target values $V^{1:N}$ , processes them with foveated vision, and modulates the decision making with visual features of target images and their corresponding values. Our VF outputs the predicted $t + 1$ th fixation location $F_{t+1}$ and the mouse-click policies for the currently fixated item. VF comprises three modules: target feature modulation, target value modulation, and decision-making. + +# 4.1. Target feature modulation + +Our VF processes the $N$ input target images $I_T^{1:N}$ with a feed-forward convolution neural network (2D-CNN) to extract their feature maps $\phi_T^{1:N}$ at the last convolution layer. We used the VGG16 network [114], pre-trained on ImageNet [28] as the backbone of the feature extractor and froze its weights during training of hybrid foraging tasks. + +Receptive field sizes in the visual cortex increase progressively across brain areas [45]. This scaling is modeled in current visual recognition systems through eccentricity-dependent pooling operations [51]. Unlike uniform sampling in standard max pooling, receptive field size in eccentricity-dependent pooling layers grows with increasing distance from the current fixation $F_{t}$ . Following [51], we replace VGG16's standard max pooling layers $l_{10}, l_{14}$ , and $l_{18}$ with eccentricity-dependent pooling. We replicated the eccentricity-dependent pooling from [51], aligning it with neurophysiological recordings in macaque monkeys. See Sec. S1.4 for the detailed implementation of eccentricity-dependent pooling. This modified feature extractor produces feature maps $\phi_{S,t}$ for the search image $\mathcal{I}_S$ from the last convolutional layer, given the fixation + +location $F_{t}$ . For simplification of mathematical notations, we omit the subscript $t$ in $\phi_{S,t}$ for the rest of the text, unless specified. We use pre-trained ImageNet weights for VGG16 and freeze them for semantic feature extraction. Since pooling layers lack learnable weights, freezing the pre-trained weights of eccentricity-dependent VGG16 does not affect feature extraction quality. Note that we do not use eccentricity-dependent VGG16 to process feature maps of input target images $\mathcal{I}_T^{1:N}$ as these target images are often small and they can be processed in high resolution within the foveated region. + +Visual search or feature-based attention is often modulated by the visual features of the targets [51, 145, 146]. Similar to [145], we implement the attentional modulation by computing the similarity between the features $\phi_T^i$ of the $i$ th target image $I_T^i$ and the features $\phi_S$ of the search image $I_S$ : $M_F^i = \mathcal{M}(\phi_T^i, \phi_S)$ , where $\mathcal{M}(\cdot)$ is the 2D convolution of stride 2 with $\phi_T^i$ serving as a convolution kernel applied to $\phi_S$ . We repeat the same attentional modulation for each target image, resulting in $N$ similarity maps $M_F \in \mathbb{R}^{H \times W \times N}$ , where $H \times W = 16 \times 16$ denotes the grid size of the object arrays on $I_S$ . + +# 4.2. Target value modulation + +Values have proven to be a strong modulator of guidance in visual search [3]. To incorporate target values in our VF, we introduce a value encoder $\mathcal{E}_V(\cdot)$ consisting of two fully connected layers and a ReLU activation layer in between. $\mathcal{E}_V$ takes $N$ target values $V^{1:N} \in \mathbb{R}^N$ as input and produces a $D$ -dimensional value embedding $\mathcal{E}_V(V^{1:N})$ that encodes the target values. To embed $E_V$ into $M_F$ , we also introduce a 2D-CNN encoder $\mathcal{E}_F(\cdot)$ to extract feature maps $\mathcal{E}_F(M_F)$ of size $H \times W \times D$ from the similarity maps $M_F$ . The encoder comprises convolution blocks with ReLU activations, using $1 \times 1$ convolution kernels with stride 1 to maintain the spatial resolution of $M_F$ . No pooling layers are used. These convolution blocks facilitate feature fusion across all $N$ similarity maps within each location but not across $H \times W$ locations. + +Similar to the way that positional embeddings are added to each feature vector of the image patches in the vision transformer (ViT) [33], we duplicate the value embedding over all $H \times W$ locations and perform element-wise summation $\oplus$ on $\mathcal{E}_F(M_F)$ : + +$$ +M _ {V} = \mathcal {E} _ {F} \left(M _ {F}\right) \oplus \text {d u p l i c a t e} \left(\mathcal {E} _ {V} \left(V ^ {1: N}\right)\right) \tag {1} +$$ + +This results in the value-modulated feature maps $M_V \in \mathbb{R}^{H \times W \times D}$ , allowing the model to adapt the target similarity features based on target values. Note that the value-modulated feature maps $M_V$ is fixation-dependent, since $\phi_S$ changes based on the current fixation $F_t$ . Due to math simplifications, we omit the subscript $t$ for $M_V$ . + +![](images/8641355b4c196799bd87074afd6e9e8a46f85c0b3e64ff7caa3cbe33f329d3dd.jpg) +Figure 3. Architecture overview of our Visual Forager. VF consists of three modules elaborated in Sec. 4: visual feature modulation from target images with foveated vision mimicking eccentricity-dependent sampling in human vision (Sec. 4.1), modulation from various values of different targets (Sec. 4.2), and decision-making process with an actor-critic transformer architecture, outputting next fixation locations from predicted attention maps and the probability of clicking the currently fixated item (Sec. 4.3). + +# 4.3. Policy network for decision making + +Given $M_V$ at the current fixation $F_t$ as the state $s$ of the environment, VF must decide when to fixate next and whether to collect the currently fixated item. We model this as a Markov Decision Process with finite states and action spaces. Fixation locations are discretized to the $H \times W$ grid, corresponding to the search array size on $I_S$ . The mouse click is a binary decision of whether to collect the fixated item. Here, we introduce the architecture of the decision-making module, also known as the policy network. + +We employ the vision transformer (ViT) [33]) as the backbone for our decision-making network with its weights randomly initialized. We reshape the value-modulated similarity feature maps $M_V$ into a sequence of patches $x_{p}\in \mathbb{R}^{P\times D}$ , where $P = H\times W$ . To retain positional information for all the patches, we add the standard learnable 1D positional embeddings to all the patches. + +Similar to the role of the classification token in the original ViT, we introduce the extra click token to the patch sequence. A click action head is attached to the click token at the last layer of the transformer. The click action head is implemented with an average pooling layer over $D$ dimensions of the click token embedding followed by a sigmoid function, outputting the probability $P_{C}$ of the click. A click action $a_{c}$ is sampled based on $P_{C}$ . + +In parallel, we take the embeddings of all the patches from $x_{p}$ in the last layer of the ViT, apply average pooling over $D$ dimensions for every patch, and obtain the logit of fixation probability over total $P$ locations. Next, we use the softmax operation to normalize the logit map and reshape it to a 2D probabilistic attention map $P_{F} \in \mathbb{R}^{H \times W}$ indicating the most probable fixation location at $t + 1$ . The next fixation action $a_{f} = F_{t + 1}$ is sampled based on $P_{F}$ . + +# 4.4. Training Details + +To reduce overfitting and enhance the generalization of our VF, during training, we implement a channel augmentation technique that shuffles the input order of target images and their corresponding value pairs. We train VF with reinforcement learning (RL). The goal of RL is to jointly learn the fixation policy $\pi_f(\cdot |s)$ and the click policy $\pi_c(\cdot |s)$ , aiming to maximize the expected cumulative reward. Here, our VF uses the stochastic policy, where $\pi_f(a_f|s) = P_F$ and $\pi_c(a_c|s) = P_C$ . With these two separate policies, we can combine them into a joint probability over a multi-discrete action space $P_A = P_CP_F = \pi (a_c,a_f|s)$ . + +We specifically used the Proximal Policy Optimization (PPO) algorithm [109] with the Adam optimizer [64] for training $P_A$ . PPO is a policy gradient method designed to enhance the stability and efficiency of policy updates. Preliminaries on RL and PPO, as well as PPO hyperparameters, can be found in Appendix Sec. S2.1. + +In practice, PPO often employs an actor-critic network [109]. The actor network selects actions based on the current policy, while the critic network evaluates these actions by learning the value function, assessing the quality of the chosen actions. We use the policy network outlined in Sec. 4.3 as our actor network. To estimate the current state's value (or state-value in RL), we add a special state-value token to the token sequence in the policy network. A critic head, implemented as a single fully connected layer, is attached to this token embedding at the final transformer layer to output the state-value $V_{s}$ . + +Two-stage training with curricula. Hybrid visual foraging remains one of the challenges for decision-making due to the diversity of conditions in search scenes. Training VF for this task requires a large amount of interactions with the environments. To address this problem, similar to other + +curriculum learning works in RL [73, 97, 98], we introduce two-stage training with curricula where the transfer learning is applied to VF such that experience gained in an easy environment can be leveraged when starting to learn the next harder task. + +In the first training stage, we focus solely on training VF's fixation policy $\pi_f(\cdot |s)$ , omitting the click policy $\pi_c(\cdot |s)$ . VF receives a reward equal to the target value for accurate fixations and a penalty of -1 for fixations on distractors. This is consistent with the rewards and penalty setups for humans. Moreover, clicking on blank areas wastes time and reduces available clicks; thus, we also apply an intrinsic penalty of -0.01 to discourage suboptimal behaviors in VF. See Tab. S5 for the impact of this intrinsic reward via ablation studies. To further ease the task, we temporarily disable VF's eccentricity-dependent vision, allowing it full-resolution access to the search image. + +Without eccentricity-dependent vision, $M_V$ becomes independent of the fixation $F_t$ and remains static across all fixations, resulting in a fixed policy for a given state. Thus, $M_V$ must be modified to enable exploration and prevent VF from repeatedly choosing the same location. Like many other visual search models [58, 115, 145], we introduce an infinite inhibition-of-return (IOR) mechanism, which zeros out all previously visited cells of $M_V$ on the $16 \times 16$ grid. + +We proceed with the original hybrid foraging setup in the second training stage. We transfer all the weights pre-trained in stage one and freeze them. Only the positional embeddings and the weights responsible for the click policy $\pi_c(\cdot |s)$ are fine-tunable. The same scoring systems for humans are applied to train our VF. Our VF processes $I_{S}$ with eccentricity-dependent vision. + +In contrast to the infinite IOR in the first stage, we introduce a memory decay mechanism that approximates finite IOR, balancing the exploration of new locations and revisits of known ones. Although finite IOR reflects limitations in memory capacity, it also enhances vision by enabling strategic revisits in complex environments. For example, after exhausting high-value targets, returning to prior locations may help identify the next best options, thereby improving decision-making outcomes. Our VF employs a fixed finite IOR, independent of specific experimental conditions. The suppression of attention values on previously visited locations in $M_F$ decays over time. At the current $F_t$ , the suppression on past locations $\tilde{t} \in \{1, 2, \dots, t\}$ is given by: $m_{\tilde{t},t} = \eta^{t - \tilde{t}}$ , where $\eta = 0.8$ . This allows the inhibition of previously visited locations to gradually weaken, enabling VF to revisit those locations. + +# 4.5. Baselines and Evaluation Metrics + +We introduced six baseline models. (1) Chance: A sequence of eye fixations is generated through uniform random sampling on a 16x16 grid, with a mouse click + +(2) Visual Feature Modulation Only (FeatOnly): The method discards value modulations and predicts a sequence of eye fixations based solely on the items with the highest activation on the eccentricity-dependent similarity maps $M_F$ at $F_t$ . The sequence of clicks directly corresponds to the sequence of eye fixations. (3) Max Value First (MaxVal) Eccentricity-dependent feature similarity maps $M_F$ are modulated by multiplying each of its maps with the value of the corresponding target object in $V^{1:N}$ . A sequence of eye fixations, equivalent to mouse clicks, is predicted by selecting the items with the highest values from value-modulated $M_V$ . (4) Average Value First (AvgVal) We compute the average of value-modulated $M_V$ in MaxVal over all target objects. The items with the highest averaged values get fixated and collected by the model. (5) Deep-Q learning (DQN) Instead of modular designs in our VF with the transformer architecture, we use a classical 2D-CNN-based deep-Q network [92] and train it end-to-end. See Appendix Sec. S2.3 for implementation details. (6) Upper bound (UpperBound) It is an oracle model with perfect target localization and recognition abilities, capable of making globally optimal decisions by always selecting the target instances with the highest values in the search arrays and never clicking on a distractor. + +All the baseline models use infinite inhibition of return to track previous fixation locations and prevent revisiting them. This is accomplished by either masking the visited item locations in the action probability distribution for DQN or by removing the clicked or fixated items from the search arrays for the other baselines introduced above. + +We also include four more baseline models from the existing literature: IVSN [145] and its variant with value modulation and behavioral cloning, along with the pre-trained Gazeformer [93] and Gazeformer fine-tuned on our in-domain data. Since these models do not utilize foveated vision, direct comparisons with our VF model are not entirely equitable. Nevertheless, we include their results to provide a performance reference in Tab. S6. + +We propose two evaluation metrics. First, Normalized Score (Norm.Score) refers to the cumulative rewards as a function of the number of clicks within a foraging trial, normalized by the maximum score of UpperBound for that trial. The normalized score has an upper limit of 1, and a higher normalized score indicates that AI models or humans are more effective at making decisions to optimize cumulative rewards. Second, Click Bias Ratio (CBR) reflects the clicking biases of humans and AI models during foraging. We define the proportion of selections of target objects as Proportion Picked (PP) and the proportion of target objects left on the array as Proportion On-Screen (POS). CBR is then calculated as the normalized relative difference between PP and POS: $CBR = \frac{PP - POS}{PP + POS}$ . CBR + +![](images/ad8df476b357d9b2b152911aba2419f2027e9e64d66819604426976f5514b8c0.jpg) +A Uneven Value, Equal Prevalence + +![](images/df8f83ad2d370a2873284c373195378b1b18ecaeaeb00b64898c16626d1f0d34.jpg) +BUneven Value, Unequal Prevalence + +![](images/48cad82728db7a7b3b61cef88fb532feea4f52c0d0a77116e14f846ab4d56a70.jpg) +C Even Value, Unequal Prevalence +Figure 4. Humans and AI models are reward-seeking agents. We report the normalized scores (Norm. Score) as a function of click numbers for humans (red), our VF model (blue), and other baseline models (varying gray). Chance is in black. Three experimental conditions of foraging trials are included with varying prevalence and values of target objects. See Sec. 4.5 for evaluation metrics and baselines, and Sec. 3.2 for experimental conditions. + +can change over the course of clicks within a trial. If neither humans nor AI models exhibit clicking preferences, PP will equal POS, resulting in a CBR of 0. If either agent prefers one target object over others, PP will be greater than POS, yielding a positive CBR. If an AI model aligns with human clicking bias patterns in a given experiment, their CBR values will share the same signs. We also used scanpath similarity metrics, including ScanMatch [25] and Fixation Edit Distance (FED) [93], to compare the spatial and temporal dynamics of fixation sequences between humans and AI models. See Tab. S4 for the results and discussion on scanpath similarity. + +# 5. Results + +# 5.1. Humans and AI models are reward-seeking + +Humans and AI models are proficient foragers. We present the Norm.Score of humans and AI models under three conditions where target prevalence, value, or both vary, as shown in Fig. 4. Human subjects achieved Norm. Scores of $87.4\%$ , $84.1\%$ , and $93.1\%$ across these conditions, significantly exceeding chance levels. Notably, even at the first mouse click, the Norm. Score was already well above chance. Similarly, all competitive baselines and our VF model consistently outperformed chance across all click numbers. These results suggest that both human subjects and AI models are effective at hybrid visual foraging, with their mouse click decisions strongly influenced by the values of target objects. However, humans never reached the upper bound performance, indicating they are not perfect global optimizers. This may be due to imperfect object recognition [86], limited memory capacity [134], and foveated vision with restricted receptive fields [45]. We also present human and model scanpath visualizations in Fig. S6. These examples further support our analysis. + +Our VF model outperform all the baseline models. The Norm. Scores of our VF model are $72.6\%$ , $67.1\%$ , and $81.6\%$ across the three conditions, surpassing all baseline models. This indicates that our VF model + +effectively learns to optimize decision-making in foraging tasks and adapts well to variations in value and prevalence. Among the baseline models,FeatOnly achieved the highest Norm. Score, although it still underperformed VF. This highlights the importance of visual feature modulation in foraging tasks, but also reveals that feature modulation alone is insufficient for optimal decision-making. While both AvgVal and MaxVal models incorporate value-based guidance into their decision strategies, their lower performance compared toFeatOnly suggests that simply relying on explicit values is ineffective. Rather, value and feature modulations must interact in a more sophisticated manner to achieve optimal performance. + +# 5.2. Eye movements are effected by target values + +Eye fixations tend to be drawn to regions associated with higher rewards. Eye movements can serve as a valuable lens for examining the decision-making process [53]. Here, we analyzed eye fixation locations and their correlation with rewards in the corresponding areas. In Fig. S4, we present the average rewards of all target objects within the fixated areas, defined as those falling within a radius of 1.5 degrees of visual angle around each fixation. Surprisingly, we found that both humans and VF tend to fixate on regions associated with average rewards of 3.31 and 8.08, significantly higher than the averages derived from random fixations. This indicates that target values guide fixations during decision-making for both humans and VF. Despite limited visual coverage due to foveation, both agents can effectively explore more rewarding areas. We also conducted the human fixation duration analysis. Remarkably, we found that humans tend to spend more time fixating on higher-value targets compared to those with lower values (Appendix Sec. S3.3). + +# 5.3. Behavioral alignment between humans and VF + +Both humans and AI models tend to overpick high-valued targets and underpick low-valued targets. In this analysis, we examine the items selected by humans + +![](images/8f424ccd70cafa66ceb569032f8bce96a9f4ae5fbc9fd83cf3f52924f592a861.jpg) +Figure 5. (A) Our VF model has consistent clicking biases with humans. Humans (red) and our VF models (blue) share the same signs of CBR for most targets under UnValEqPre (a) and UnValUnPre (b). Chance (gray) has no preferences over target objects; hence, a CBR of 0. (B) Our VF model approximates humans in saccade size distributions. Saccade size distributions for humans (red), our VF model (blue), and our VF model with eccentricity removed (light blue) are presented. Vertical dash lines in colors indicate their mean saccade sizes in visual angle degrees. (C) Our VF model can generalize to out-of-distribution hybrid foraging tasks. Spider plot shows Norm.Score for humans (red), our VF (blue) and FeatOnly baseline (black dotted) under 7 experimental conditions. + +![](images/beae4ce86ab883fbd145b61398926fca76eedd6880be89840f41e61d2adbefe0.jpg) + +![](images/21dcc6d292c10e10c16edd55d42de27e03fe18dcefff92d3060b8b3e648e27fd.jpg) + +and AI models from the search arrays and report their click bias ratios (CBR) averaged over all click numbers under the UnValEqPre and UnValUnPre conditions, as shown in Fig. 5A. Consistent with [138], we find that humans tend to overpick the highest-valued targets, as indicated by a positive CBR, while they underpick the lowest-valued targets, reflected by a negative CBR. Interestingly, our VF exhibits similar signs and magnitudes of CBR on these targets, suggesting that it displays analogous click biases based on target values as humans. However, both humans and VF do not exclusively select the highest-valued targets, as their Proportion Picked (PP) for less-valued targets is not exactly zero. This suggests that both humans and VF occasionally select lower-valued targets during foraging. Moreover, we also noted a slight discrepancy in the signs of CBR when humans and VF select the second-highest-valued items. This indicates that VF is less sensitive to medium rewards compared to humans (Fig. S5). + +VF approximates the saccade size distributions of humans, without training on human eye movements. Human saccade sizes are restricted by physiological limitations of the eye muscles and oculomotor controls [45]. We aggregate all saccade sizes from humans and our VF model under 3 conditions and plot their distributions in Fig. 5B. Despite lacking prior training on human eye movements, VF yields a mean saccade size of 4.06 degree, closely approximating the mean saccade size of 4.05 degree for humans. Additionally, to investigate the mechanisms that constrain saccade sizes in VF, we present the distribution of saccade sizes with eccentricity-dependent layers replaced with standard max-pooling layers in the visual feature extractor. In line with [51], the saccade sizes increase, suggesting that smaller saccade sizes are partially due to foveal processing. + +# 5.4. VF generalizes to OOD conditions + +To assess the generalization performance of our VF model in out-of-distribution (OOD) hybrid foraging tasks, we + +benchmark humans, VF, and the best baseline model, FeatOnly, across five OOD conditions (Sec. 3.2). From Fig. 5C, VF outperforms FeatOnly in all experimental conditions, indicating that it learns generic decision-making strategies and adapts well to unseen foraging scenarios. However, VF still lags behind humans, suggesting that humans can more flexibly adjust their foraging strategies to maximize rewards based on the environments. + +# 6. Discussion + +In hybrid visual foraging, humans are proficient foragers, directing attention to regions with significantly higher rewards than chance. When there is an imbalance in target prevalence or values, humans tend to over-exploit the most prevalent or high-valued target types. To explain the characteristics of human behavior in hybrid visual foraging, we propose a transformer-based Visual Forager (VF) trained in reinforcement learning. We designed experiments using 2D grid worlds which provide precise control over experimental variables, minimize confounding factors, and make the analysis of cognitive processes more focused. VF's cumulative rewards match human performance and surpass other baseline models. Despite zero training on any human data, VF closely approximates human foraging behaviors, including foraging biases and eye movements. Remarkably, VF demonstrates exceptional generalization abilities, flexibly adjusting its foraging strategies to experimental conditions it has never encountered. We also clarify that novel stimuli for humans do not equate to an OOD task for AI since humans accumulate years of visual experiences which enables them to generalize effectively. However, we emphasize that while humans exhibit remarkable generalization based on prior experience and flexible cognition, AI models are still inferior to humans from our results. Our work paves the way for several new research directions in psychology, neuroscience, and AI. We discuss these future works in Appendix Sec. S4. + +# Acknowledgements + +This research is supported by the National Research Foundation, Singapore under its NRFF award NRF-NRFF15-2023-0001 and its AI Singapore Programme (AISG Award No: AISG2-RP-2021-025). 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Gen3DEval: A holistic ranking metric to assess the quality of generated 3D objects on appearance, surface quality and text fidelity using a vision large language model (vLLM) which is trained to choose the better out of two objects on the three evaluation dimensions (appearance, text fidelity or surface quality). + +![](images/8af0a7d610915b3f37972424dc8b0f0be11ee04d4b5902bbf3f65b909bf2c3f2.jpg) + +![](images/e452b601d94267c952fcd6c307865cc9c8a8dc225272e31ab6f7780740ee1b1e.jpg) + +# Abstract + +Rapid advancements in text-to-3D generation require robust and scalable evaluation metrics that align closely with human judgment, a need unmet by current metrics such as PSNR and CLIP, which require ground-truth data or focus only on prompt fidelity. To address this, we introduce Gen3DEval, a novel evaluation framework that leverages vision large language models (vLLMs) specifically finetuned for 3D object quality assessment. Gen3DEval evaluates text fidelity, appearance, and surface quality by analyzing 3D surface normals, without requiring ground-truth comparisons, bridging the gap between automated metrics and user preferences. Compared to state-of-the-art task-agnostic models, Gen3DEval demonstrates superior performance in user-aligned evaluations, placing it as a comprehensive and accessible benchmark for future research on text-to-3D generation. The project page can be found here: https://shalini-maiti.github.io/gen3deval.github.io/. + +# 1. Introduction + +The domain of text-to-3D generation has advanced significantly in recent years, driven by the rise of scalable architectures like diffusion models [43], neural radiance fields (NeRF) [36], and Gaussian splatting [25]. However, the field lacks standardized, human-aligned evaluation metrics that can reliably assess these assets and the methods that produce them. Existing metrics—such as CLIP [42] scores evaluate only limited aspects of the output like text fidelity and similarity-based measures like Peak-Signal-To-Noise Ratio (PSNR), SSIM [55], Chamfer Distance, and Fréchet Inception Distance (FID) [20] depend on ground-truth data making them inadequate and impractical for text-to-3D generation, where diverse outputs may correspond to a single prompt. In such cases, a unique, universally applicable reference does not exist, as multiple plausible 3D outputs can vary widely in style, appearance, and fidelity to the text. Meanwhile, FID computes a distributional similarity, which poses other challenges. Currently, there is no standardized large-scale validation set to serve as the ground-truth distri + +bution for 3D assets, making FID computation difficult and inconsistent. Moreover, generating sufficient 3D assets to estimate this distribution requires significant computational resources, casting FID as an expensive and time-intensive metric. As a result, these metrics fall short of capturing the nuanced requirements of evaluating text-to-3D generation, where a scalable, human-aligned approach is essential. + +While prior work such as GPT4VEval [57] has leveraged GPT-4V [38] for assessing 3D asset quality, GPT-4V is a general-purpose model not specifically trained for 3D quality assessment, which limits its effectiveness in this domain. Furthermore, it can be costly to deploy at scale, and in our experiments, we found that GPT-4o (which is the successor to GPT-4V) performed significantly worse than our method in aligning with human judgments of 3D asset quality. + +To bridge this gap, we introduce Gen3DEval, a vision-based large language model (vLLM) framework specifically fine-tuned to evaluate text-to-3D generation outputs in alignment with human preferences. Unlike existing metrics [42, 55, 63], Gen3DEval assesses not only text fidelity but also appearance and surface quality by analyzing rendered multi-view images. Supporting up to eight images as input, Gen3DEval enables comprehensive assessment by leveraging multi-view renderings, such as RGB and normal maps, of generated 3D objects. Using multi-view images as input allows for compatibility across diverse 3D representations [25, 36, 60]. + +Built upon the recent vLLM early fusion approaches [4, 5, 27, 29], our method processes these input renderings by first encoding each image through an image encoder, which translates them into visual tokens. These tokens are then integrated with text tokens and fed into a Llama3 model, allowing Gen3DEval to interpret both visual and textual features of the 3D objects holistically. To ensure robust performance, we curate data from human assessments and further enhance our training dataset with synthetically generated perturbations of artist-created 3D objects, incorporating artifacts like floaters, transparency errors, text fidelity inconsistencies, excessively smooth surfaces etc. + +A key component of our framework is Gen3DEval-Bench, a benchmark dataset designed to standardize text-to-3D evaluations across various quality dimensions. Comprising 80 diverse prompts, Gen3DEval-Bench facilitates consistent, human-aligned assessments of visual fidelity and aesthetic preferences. Our evaluation pipeline involves two main stages: first, it performs pairwise comparisons of 3D objects using multi-view renderings. Then it applies ELO rating metrics [13] to generate scores that closely align with human judgment. This process ensures robust and reliable evaluations across a broad range of 3D generative methods. To sum up, our contributions are: + +- A state-of-the-art holistic evaluation method for text-to-3D generation that ranks methods across appearance, sur + +face quality and text fidelity. + +- A vLLM fine-tuned on the Llama3 [2] model, using a synthetic dataset curated to reflect human preferences for evaluating generated 3D assets. +- A benchmark dataset, Gen3DEval-Bench, comprising 80 prompts for ranking existing and future text-to-3D generation methods in a standardized manner. + +# 2. Related Work + +Text-to-3D and Image-to-3D generation. In recent times, the landscape of text-to-3D generation has seen rapid growth with the advent of representations such as Neural Radiance Fields [36], occupancy fields [37], SDF [60] and Gaussian Splats [25], and the availability of large, publicly available datasets such as Objaverse [10, 11]. Some of the earlier methods in the space currently include [23, 28, 40, 41, 47, 48, 53, 56, 61, 64] that optimizes a randomly-initialized 3D model via gradient descent conditioned on sampled outputs of a text-to-image generation model. Another direction of work include methods such as [14, 21, 24, 31, 45, 46, 54] that use multi-view diffusion models to fine-tune text-to-image models to quickly generate highly consistent multiple views or videos simultaneously from a single input image. Notably, another family of methods [15, 22, 47] learns 3D priors from a large amount of data and a scalable architecture to directly output robust 3D outputs from text or image inputs. With such an impressive pace of growth in this research domain, it is imperative for the presence of robust evaluation metrics and benchmarks to ensure continued progress in this field, which is a gap that Gen3DEval attempts to bridge. + +3D Evaluation Metrics and benchmarks Classical 3D metrics like PSNR, Chamfer Distance, LPIPS [63] and SSIM [55] were developed to measure the quality of a generated 3D asset against a ground-truth asset. However, these are similarity metrics and measure the distance between generated and the ground-truth data. This is infeasible since a single text prompt can be mapped to many generated 3D outputs, with their quality or fidelity being independent of their similarity to any single generated asset. We propose that instead of measuring similarity, we need to inject 3D quality priors into the method itself for the purpose of evaluation, which is the foundation of Gen3DEval. + +Other metrics such as CLIP [42] scores have tried to measure alignment with text by using a standard benchmark of textual prompts and computing a corresponding score. However, they underwhelm with an increase in diversity of prompts. Another inadequacy is that only textual alignment is measured and not appearance or surface quality. Gen3DEval addresses both of these aspects. The work closest to ours in attempting to solve this problem is GPT-4V(ison) is a Human-Aligned Evaluator for Text-to-3D Generation [57]. However, it uses GPT4 [38] off the shelf, + +![](images/579ec440a56b8c43a8ac4fb915479b109fe3be64f5df935925b4708df36a5137.jpg) +Stage 1: Train the vLLM (Gen3DEval) in two stages: pre-training and supervised fine-tuning (SFT). +Figure 2. Gen3DEval framework: In stage 1, we train a vLLM to choose which object is better in terms of appearance, surface quality or text fidelity. This is further divided into 2 parts. In pre-training, we train the vision-to-language projector using image summary VQA. In the supervised fine-tuning (SFT) stage, we use comparison data to train for instruction following and preference evaluation. In stage 2, we compute a ranking metric for the set of methods by applying the trained vLLM from stage 1 pairwise on Gen3DEval-Bench prompts. + +![](images/863556af3f21163f09f38966cb71dc225e042725ff1338cbf6edf13c8f68a513.jpg) +Stage 2: Use the trained vLLM (Gen3DEval) to generate a ranking metric. + +which is a task-agnostic vLLM trained on half a trillion parameters whose API and checkpoints are not publicly available, making it costly to scale, whereas Gen3DEval has been specifically trained to evaluate text-to-3D objects, on 8.35 billion parameters and will be made available for public usage. Moreover, in our experiments, we found that Gen3DEval performed significantly better than GPT4-o in aligning with human judgments of 3D asset quality. + +In the absence of quantifiable metrics, user studies have been popularly employed as the gold standard to evaluate 3D generation methods. However, this is time-consuming, cost-effective and lacks a standard procedure. Certain benchmarks such as $\mathrm{T}^3$ Bench [17] and Dreamfusion prompts [40] have been created to reduce the lack of standardization in this process. Gen3DEval takes a step further in this direction by curating a benchmark Gen3DEval-Bench with diverse prompts in terms of types objects, length and compositionality. + +Large Multi-modal Models The past couple of years has seen great strides made in the development of Large languages models (LLMs) like Llama [52], GPT-4 [38], Claude [3], Gemini [49], and consequently, led to development of vLLMs such as LLaVA [29], BLIP [27], FUYU [5] and more [2, 3, 38]. They are powerful multimodal models that display strong image and language reasoning. However, since these are general purpose models, they do not perform well on evaluating generated 3D ob + +jects. [57] showcases capabilities of GPT4 [38] to be able to align with human preference for the assessment of 3D objects. Gen3DEval takes this effort further by fine-tuning a Llama3 [2] model using a curated synthetic dataset for the specific purpose of introducing 3D aesthetic preference into the vision-language space and transforming that into a ready-to-use evaluation ranking metric. + +# 3. Method + +The proposed method, Gen3DEval is a vision-based large language model (vLLM) that interprets and assesses the quality of 3D generated objects. We train Gen3DEval using a carefully curated Visual-Question-Answering (VQA) dataset, as detailed in Section 4.1. This training enables Gen3DEval to learn associations between visual cues in multi-view images and quality indicators such as text fidelity, surface detail, and appearance. We use up to eight multi-view RGB images—renderings that include RGB and normal maps—to capture comprehensive object details from multiple angles; see Figure 2 for an overview. + +# 3.1. Model Details + +The Gen3DEval training process builds upon the LLaVA architecture [29] and is organized into two sequential phases: pre-training and supervised fine-tuning. In the initial phase, each image is processed by an image encoder to produce visual embeddings $I_{emb}$ . These embeddings are transformed + +into language-compatible tokens $H_{i}$ via a linear projection matrix $W_{\theta}$ , enabling them to integrate seamlessly with the language-based representations. At the same time, a language tokenizer converts the natural language QuestionAnswer (QA) pairs into text tokens $H_{t}$ . The model $F_{\phi}$ then receives both the image and text tokens as input, learning to predict the next token $H_{y}$ by maximizing the likelihood of the correct token. + +For the image encoder, we initially consider CLIP [42], which is commonly used across various vision-language models [29, 40, 44]. However, since the input images are rendered views of 3D objects, we also evaluate two additional encoders: DinoV2 [39] and Fit3D [62]. DinoV2 generates visually consistent embeddings, while Fit3D is specifically designed to encode 2D images into features consistent with the underlying 3D scenes, making it particularly suited to our task. A comparison of these feature encoders is provided in Table 1 and discussed in Section 4.2. + +During the pre-training phase, the weights of both the LLM and the image encoder are frozen, and only the weights of the linear projection matrix $W_{\theta}$ are updated. This selective tuning establishes alignment between the visual embeddings and language tokens, forming a foundation for integrated visual-language comprehension. + +In the fine-tuning phase, we unfreeze both the projection matrix and the LLM, allowing them to be fine-tuned jointly, while keeping the image encoder's weights frozen. This stage further specializes the model for 3D quality assessment, enhancing its sensitivity to features such as surface texture, text fidelity, and overall visual coherence across various prompts and multi-view renderings. + +# 3.2. Multi-view Input + +To effectively evaluate the quality of generated 3D objects, Gen3DEval leverages multi-view input, using up to 8 rendered images uniformly panning each object. This approach is essential for capturing the complete appearance and surface consistency of 3D objects, as single-view images may overlook aspects like hidden surfaces and occlusions that become visible when observed from multiple viewpoints. + +In pre-training, the input images range from a set of 1 to 4 RGB images or rendered surface normals panning the object in a $360^{\circ}$ round-table manner alongside a short summary in a QA pair. In fine-tuning, we input two sets of images, for object 1 and object 2. Each set consists upto 4 multi-view images each, therefore training a VQA sample consists upto 8 images and QA capturing the preference for the preferred object. The number of tokens per image is 576 and approx. 250 for the text of the question. + +# 4. Training Details + +The following section provides an in-depth look at the Gen3DEval dataset, outlining its composition, structure, + +and the methodologies used to create a diverse and robust training set. We describe the dataset's sources and organization, the approach to rendering multi-view images, and the use of human judgment and synthetic perturbations to enhance model alignment with 3D quality standards. Each component of the dataset is designed to support the pre-training and fine-tuning stages, ensuring comprehensive coverage of key attributes like appearance, surface consistency, and text fidelity. + +# 4.1. Dataset + +Gen3DEval's training dataset is designed to train and evaluate the model's ability to assess 3D object quality across various dimensions, including appearance, surface consistency, and text fidelity. It comprises three subsets a) 3D artist-created meshes, b) human preference data on generative method outputs and c) synthetic 3D comparison data. + +3D Meshes: Comprising 140,000 high-quality 3D meshes created by artists, this internal dataset spans diverse semantic categories and provides a robust foundation for generalizing to different types of 3D content. Each asset comes with an accompanying text caption generated with Llama3.2 [2]. We render each 3D asset from multiple viewpoints, creating three types of visual inputs: RGB images, alpha masks, and surface normals. These multi-view renderings allow Gen3DEval to capture comprehensive visual cues necessary for accurate 3D evaluation. + +Human Annotations: To account for the nuances and irregularities inherent in 3D generative methods, we conducted a large-scale human preference study, collecting over 5K comparative data points across 13 different 3D generative methods [6, 8, 15, 16, 18, 30, 32-34, 46, 47, 51, 54]. Annotators viewed $360^{\circ}$ videos of two 3D assets side-by-side and selected the preferred asset based on appearance and alignment with the corresponding generation prompt. + +This preference data was incorporated into the Gen3DEval training dataset, enhancing the model's alignment with human aesthetics and text fidelity expectations. We conducted an in-depth analysis of these annotations to identify common artifacts in modern text-to-3D generation methods, including (1) disconnected components, (2) Janus artifacts, (3) opacity inconsistencies, (4) floating elements, (5) overly smooth or irregular surfaces, (6) texture seams. Based on these insights, we replicated these artifacts in the 3D mesh data to scale up our dataset and further improve Gen3DEval's performance. Examples of these artifacts are illustrated in the appendix. + +Synthetic Data: To expand the training dataset, we applied controlled perturbations using Blender, NeRF, and Gaussian splatting techniques, simulating common artifacts and misalignments found in text-to-3D generative outputs. For 3D meshes, we introduced perturbations such as Laplacian smoothing [19], beveling, random surface extrusions, + +![](images/81a1990578a191cd13030036222c7c74b45f35ab4e7b6e53444a80317e43d459.jpg) +Figure 3. Training Dataset We use single and multi-view RGB and surface normals renderings of a 3D object generated from a prompt. We take these objects and perturb them to simulate common appearance, surface and text-related artefacts in generative 3D methods. + +and texture map alterations like blurring and seam introduction. Additionally, we fitted NeRF and Gaussian splats to the renderings of the artist-created 3D assets, providing a broader foundation for synthetic training data. + +To further enrich this dataset, we introduced additional perturbations to the NeRF and Gaussian splatting by manually adding transparency artifacts, floating elements, and disconnected components, mimicking frequent issues observed in text-to-3D generative methods. + +To scale the text fidelity comparison dataset, we used the multi-view video diffusion model from IM-3D [33] and trellis [58] to generate single and multiple views of 3D objects with varied captions, focusing on changes to appearance attributes and composition of the objects. Textual perturbations were created with Llama3.2 [2] by prompting the model to modify the original captions, introducing subtle variations. This approach allowed us to generate a large, diverse synthetic dataset tailored for text fidelity comparison. To ensure high relevance and quality, we applied CLIP [42] to filter out examples with low image-text similarity, resulting in a refined synthetic dataset for evaluating text fidelity. Figure 3 showcases some samples of our SFT dataset. + +# 4.2. Image Encoders + +We evaluated 3 image encoders: CLIP [42], DinoV2 [39], Fit3D [62] and the combinations of CLIP with DinoV2 and CLIP with Fit3D; reshaping them to match the bigger of the two and adding the values. For CLIP embeddings, the effective resolution is $336 \times 336$ pixels and for both Dinov2 and Fit3D, which internally fine-tune the Dinov2 base model to introduce 3D awareness to image features, the model uses a ViT [12] backbone of patch size 14, effective resolution of $224 \times 224$ and embedding dimension 768. The results of these ablation experiments are reported in Table 1. + +We observe that Gen3DEval performs equally well on synthetic surface assessment in all the configurations with lowest accuracy score of 0.89 in the case of Gen3DEval + +w/ Fit3D whereas on user-annotated out-of-domain (OOD) benchmark, CLIP clearly outperforms the rest. On the synthetic appearance benchmark, described in Section 5.2, Gen3DEval w/ Fit3D reports the lowest accuracy of 0.8, with the rest between .85-.89. On the other hand, on the human evaluation appearance dataset (in-domain methods) described in Section 5.1, Gen3DEval w/ CLIP as well as a combination of Fit3D and CLIP report the best accuracy score of 0.9, followed by CLIP and DinoV2 (0.86), then Fit3D (0.81) and finally DinoV2 (0.77). In terms of generalization with OOD benchmarks, Gen3DEval with CLIP outperforms the rest by a large margin. + +On text fidelity benchmarks, in keeping with our earlier observation, the performance on OOD text fidelity benchmark is much better for Gen3DEval with CLIP (0.86) alone compared with the rest, with the nearest neighbour in CLIP and DinoV2 (0.74). Finally, on the synthetic text fidelity benchmark, Gen3DEval w/ DinoV2 alone underwhelms reporting 0.75. While standalone numbers for Fit3D is better, CLIP reports high scores by itself as well as in conjunction with Fit3D and DinoV2. + +Overall, we noticed that Gen3DEval with CLIP embedding consistently performs well across all evaluation dimensions. As a result of this, Gen3DEval uses CLIP encoder to extract image embeddings. + +# 4.3. Stage 1: Pre-training + +The objective of this training stage is to train the projection matrix to learn correlations between the image encoding space and the language description space. To train the projection matrix, we use the renderings of the 141,000 3D artist-created meshes and their accompanying text prompts. We sample 40K single view image, 40K two-view images, 40K four-view images, and 10K four-view rendered surface normal images and their corresponding captions. We also combine 11.4K of the four-view images mentioned above and combine them to form an image grid. In the case of + +surface normals, we process the captions to remove any aspect of appearance mentioned in them which is irrelevant to rendered normals. All multi-view images are sampled uniformly from a $360^{\circ}$ azimuth with a fixed elevation angle. + +The training process involved a batch size of 16, learning rate of $1\mathrm{e}^{-3}$ , a cosine learning rate scheduler with a warm-up ratio of 0.03, using the ADAM optimizer. We optimized the model using maximum likelihood for the next token prediction. Pre-training was conducted on 8 A100 GPUs over a period of 1 day, encompassing 8K iterations. + +# 4.4. Stage 2: Supervised Fine-tuning + +The objective of the supervised fine-tuning (SFT) stage is to jointly train the instruction-following large language model (LLM) and the pre-trained projection matrix for the task of selecting the best 3D object out of two based on text fidelity, 3D appearance and surface quality. For fine-tuning, we utilize the human-annotated data and the synthetically generated comparison data. The SFT dataset distribution is displayed in the appendix. + +The fine-tuning process involved a batch size of 4, a learning rate of $2\mathrm{e}^{-6}$ for the projector, and a learning rate of $1\mathrm{e}^{-5}$ for the vLLM, with a cosine learning rate scheduler and a warm-up ratio of 0.03, using the ADAM optimizer. We optimized the model by using maximum likelihood of next token prediction. This stage was trained on 16 A100 GPUs for 18 hours, for 4K iterations. + +# 5. Experiments + +We evaluated the performance of Gen3DEval using three distinct datasets. Their details are explained in the following subsections. We also performed ablation studies to explore the impact of different image encoders on the performance of Gen3DEval. This involved varying the types of image encoders and delineating their respective contributions to the overall performance of the model in Section 4.2. + +# 5.1. Human Evaluation Dataset + +The purpose of the human evaluation dataset is to assess the alignment of Gen3DEval with human preference on text fidelity, appearance and surface quality. We curated this dataset in the same way as we curated the human preference data for the supervised fine-tuning stage of training in Section 4.1 under Human Annotations. Post curation and processing, we split the total data by holding out $10\%$ of the total prompts (404) for the creation of this dataset and using the rest $(90\%)$ for the supervised fine-tuning stage of training. This dataset has 506 VQA comparison data samples for a total of 40 prompts, annotated on the basis of appearance. We also added 3 evaluation datasets, one each for appearance, surface and text fidelity generated from annotating pairwise evaluation and removing any ambiguities from methods as well as prompts that were not used as part + +of the training data. We use these to calculate out-of-domain (OOD) generalization performance of our Gen3DEval. + +# 5.2. Synthetic Dataset + +The second dataset is a synthetic evaluation dataset that includes objects generated by 3D artists along with their synthetically perturbed counterparts, enabling controlled experimentation in a low-noise environment. We created and processed this dataset in the same way as we processed the synthetic dataset for appearance, surface and textual perturbations detailed in Section 4.1 under Synthetic Data. Given that the VQA training is so diverse, we further ensured no overlap with training captions and objects by filtering the evaluation dataset using a sentence similarity threshold using sentence transformer embeddings [50]. We also curated a portion of the synthetic evaluation dataset by applying surface perturbations to artist-drawn meshes and rendering the surface normals of these pairs of objects. All the filtering mechanisms were similarly applied to this dataset. + +# 5.3. Benchmark Details + +We create a diverse set of 80 prompts, Gen3DEval-Bench, which considers the diversity of objects, textures, and levels of composition. We determine the size of this benchmark with the consideration that text-to-3D generation is a time- and computation-intensive process, aiming to make the benchmark easily accessible. It is split between 40 animate (humanoids, animals) objects and 40 inanimate objects, as well as into 43 single object and 37 composite object prompts, i.e., combining multiple objects. The average number of words per prompt is 12.863. Refer to the supplementary for comparison with other prompt benchmarks. + +# 5.4. Metric Computation + +To compute the metric, Gen3DEval compares two methods at a time using the following procedure. First, it samples four images from a $360^{\circ}$ RGB or surface normal video circling the object, at equal intervals covering a $360^{\circ}$ view of the 3D asset per prompt per method for a pair of methods. For each prompt in Gen3DEval-Bench and each pair of methods, Gen3DEval is applied to a pair of assets at a time. It takes 8 input images (4 per object) alongwith the relevant QA prompt and parses the natural language output using [2] to determine which 3D asset is better. Subsequently, it applies the ELO rating system to the parsed outputs and extracts an overall ranking metric. The generation prompt is only provided in the case of evaluation on text fidelity and not for appearance and surface. We treat them as separate tasks which enables us to compare any two generated assets, irrespective of the generated prompts. It also allows us to evaluate image-to-3D methods more effectively. + +![](images/80a145baa19f955c22487283a90590c97cb3ea484c0847c00ae867b423830708.jpg) +Figure 4. Qualitative Comparison of methods on samples of the evaluation dataset across text fidelity, appearance and surface evaluation. + +# 6. Results + +# 6.1. Gen3DEval and other evaluator methods + +We compare Gen3DEval against classical baseline metrics such as CLIP as well state-of-the-art vLLMs on evaluation datasets described in Section 5.1 and Section 5.2. We show that the model outperforms all the current methods on assessing appearance preference by a large margin on synthetic, user preference and out-of-domain evaluation data, demonstrating a strong correlation with human preference in the context of text-to-3D asset generation. In terms of text fidelity, Gen3DEval outperforms CLIP [42], which is the most popular metric for text fidelity evaluation. Gen3DEval also narrowly outperforms ImageReward [59] and PickScore [26] on the out-of-domain benchmark which has been curated to remove any ambiguous samples. We also outperform our baselines of surface comparisons data using only synthetically perturbed surface normals. + +Moreover, Gen3DEval is the first method that unifies text-to-3D generation metrics by incorporating appearance as well as text fidelity metrics in a holistic manner as evidenced in Table 1. We also provide a qualitative comparison of Gen3DEval with other methods on a few samples from the evaluation dataset in Figure 4. + +We also report results for ablation studies for choice of image encoders used for the instruction tuning stage in Table 1. We note from the ablations that CLIP embeddings have a more consistent performance across all dimensions for the purpose of our metric. + +Finally, we note that while user studies or user preference data is the current gold standard, it can be noisy and uncorrelated. For instance, when it comes to text fidelity comparison, sometimes, the preference is influenced by appearance. Moreover, with short or simple generation prompts, it is difficult to pick one over the other. In case of appearance comparison, sometimes, the background or scale can influence our choice. + +# 6.2. Generative 3D Methods on Gen3DEval-Bench + +Table 2 notes the results of Gen3DEval on Gen3DEval-Bench for a collection of 10 generative 3D methods, namely, Trellis [58], AssetGen [47], Fantasia3D [9], TripoSR [51], Magic123 [41], Magic3d [28], Vfusion-3d [15], Dreamfusion [40], LatentNerf [35] and Flex3D [16]. We rank them in the order of their performance for appearance, surface quality and text fidelity. The overall ranking is an average of the scores of appearance and text fidelity. + +# 6.3. Limitations + +Gen3DEval's assessment of objects with janus can be slightly erratic. There is room for improvement for out-of-domain performance for surface evaluation, because of limited availability of diverse, annotated surface comparison data. We also note that for image-to-3D generation methods, the performance of methods are inherently influenced by a text-to-image generation pipeline. Therefore, composing a strong and consistent image benchmark would be a logical next step. While Gen3DEval can be used for the pur + +
AppearanceSurfaceT-Fidelity
HumanSyntheticOODSyntheticOODSyntheticOOD
Classical
Avg. CLIP Score [42]0.30.40.170.30.450.780.8
Avg. Image Reward Score [59]0.730.60.660.70.540.650.85
Avg. PickScore [26]0.370.250.340.260.210.810.85
Vision Large Language models
Phi-3.5-Vision [1]0.530.470.540.490.50.640.65
LLaVA-Qwen-7B [29]0.540.460.540.510.460.680.58
LLaVA-Llama3-8b [29]0.50.50.470.470.480.490.5
Llama3.2-Vision-11B* [2]0.060.040.050.10.070.040.5
BLIP* [27]0.050.280.20.070.090.370.13
GPT-4o* [38]0.590.480.690.540.540.610.55
PaliGemma* [7]0.020.020.210.250.250.170.1
Gen3DEval (CLIP)0.90.850.890.990.670.980.86
Gen3DEval (CLIP + Fit3D)0.90.880.780.970.5710.53
Gen3DEval (CLIP + DinoV2)0.860.890.780.990.510.980.74
w/ Fit3D0.810.80.550.890.440.930.44
w/ DinoV20.770.870.540.970.610.750.58
+ +Table 1. We report accuracy for curated synthetic and out-of-domain human preference evaluation datasets for appearance, surface and fidelity to text. Additionally, for appearance, we compare methods on in-domain (unseen prompts from methods used for training data). We compare our method against classical metric methods as well as other vLLMs. For text fidelity, we do not provide prompts or pass empty strings for the classical methods. Methods with * next to their names do not currently support multi-image input and were passed either 4x2 grids composed of eight images or 8 input images in sequence in case of GPT-4o. + +
MethodsAppear.Surf.T-FidelityOverall
Trellis* [58]1111
AssetGen [47]2722
Flex3d* [16]4N/A33
Latentnerf [35]3N/A64
Magic123 [41]5445
Vfusion-3d* [15]6856
Magic3d [28]7577
Dreamfusion [40]8288
Fantasia3D [9]N/A3N/AN/A
TripoSR [51]N/A6N/AN/A
+ +Table 2. Gen3DEval applied to 3D generation methods on Gen3DEval-Bench. Methods are ranked (Best, Worst) on text fidelity, appearance and surface quality score (if available). Only appearance and text fidelity are used for the overall score. Imago-to-3D methods are denoted with * . + +pose of evaluating any given pair of generated 3D objects, for the purpose of being used as a standard evaluation metric, comprehensive application across numerous methods is relevant to its performance; examples in the appendix. + +# 7. Conclusion + +In this paper, we have laid out the lack of an existing metric in the text-to-3D domain that caters to all its necessary pa + +rameters and established the relevance for developing such a metric. It is a difficult problem to solve because of the many ways in which 3D generation is supported. Diverging from the trend of using similarity metrics, which is impractical in the case of text-to-3D generation, we propose introducing 3D aesthetic preference into the vision-language space and transforming that into a ready-to-use evaluation ranking metric using vLLMs. We demonstrate that Gen3DEval, a vLLM containing 8.35 billion parameters and trained using a synthetically curated 3D-object dataset coupled with user preference data establishes itself as a comprehensive, accessible and competitive evaluation method displaying strong performance on relevant metric dimensions, i.e., appearance, texture and text fidelity, in alignment with user 3D object preference. We hope that Gen3DEval will provide a standard benchmark and metric for the comparison of existing and future methods. + +# Acknowledgements + +We thank Antoine Toisoul for help in curating the synthetic data for our experiments. 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GenAssets takes in-the-wild camera image(s) and point cloud(s), and automatically reconstruct or generate $360^{\circ}$ assets. Our 3D assets are diverse and high-quality with complete geometry and appearance, allowing for realistic and scalable sensor simulation. + +![](images/6aa2a7b5d6f85b57ffc3ff3b89dcc1808f158827eafd55814053273210b66a20.jpg) + +# Abstract + +High-quality 3D assets for traffic participants are critical for multi-sensor simulation, which is essential for the safe end-to-end development of autonomy. Building assets from in-the-wild data is key for diversity and realism, but existing neural-rendering based reconstruction methods are slow and generate assets that render well only from viewpoints close to the original observations, limiting their usefulness in simulation. Recent diffusion-based generative models build complete and diverse assets, but perform poorly on in-the-wild driving scenes, where observed actors are captured under sparse and limited fields of view, and are partially occluded. In this work, we propose a 3D latent diffusion model that learns on in-the-wild LiDAR and camera data captured by a sensor platform and generates high-quality 3D assets with complete geometry and appearance. Key to our method is a "reconstruct-then-generate" approach that first leverages occlusion-aware neural rendering trained over multiple scenes to build a high-quality latent space for objects, and then trains a diffusion model that operates on the latent space. We show our method outperforms existing reconstruction and generation based methods, unlocking diverse and scalable content creation for simulation. Please visit https://waabi.ai/genassets for more details. + +# 1. Introduction + +Simulation environments enable testing the performance of autonomy systems in long-tail and safety critical scenarios safely, efficiently, and scalably [41, 61, 77, 97]. To test the complete autonomy stack, the virtual environments should simulate the sensor data (e.g., LiDAR, camera) of the robot. Realistic and consistent sensor simulation across multiple modalities depends on the availability of high-quality 3D assets that accurately represent the geometry and appearance of traffic participants such as cars and motorcycles. + +Commoditized simulation environments rely on artists to manually build such 3D assets [14, 59, 62]. This process is slow, costly, and requires precise specification of attributes such as geometry, UV mapping, and materials. As a consequence, existing methods utilize very limited content, failing to capture the full diversity of objects in the real world. + +An alternative and much more appealing approach that has gained traction is to reconstruct assets from real world data captured by the sensor platform, which enables diversity and realism. Reconstruction-based neural rendering methods have demonstrated impressive results by optimizing 3D representations that can render and match input sensor data for self-driving scenes [11, 15, 29, 70, 74, 86, 93, 94, 97, 103]. These approaches render high-quality data + +when the viewpoint is close to the training views, but can suffer from severe artifacts at novel viewpoints due to incomplete observations. Additionally, each asset must be observed in the real world and reconstructed via optimization, making it computationally expensive and limiting diversity. + +Recent 3D generative models [6, 7, 17, 47, 57, 63] have shown promise in generating complete assets and rendering novel views far from source. These methods leverage a combination of generative adversarial networks (GANs), diffusion models, and neural rendering, and train on large corpuses of images to learn shape and appearance priors. NeRF-based diffusion models that optimize via score-distillation sampling (SDS) [34, 52], or denoise in 3D space [9, 20, 45, 48, 85], have demonstrated particularly high-quality complete shape and appearance generation, and also offer controllability through text/image conditioning. However, such models usually rely on synthetic datasets with ground-truth 3D models to render the dense 2D views necessary to learn a 3D representation prior. They also primarily work on "clean" images that fully capture the object of interest. This reliance on clean synthetic data limits their ability to handle in-the-wild real data from a moving platform, where the data is typically captured from sparse viewpoints, under partial occlusions, limited resolution, and with sensor noise (e.g., lighting artifacts, rolling shutter). + +In this work, we propose a latent diffusion 3D generative model that learns directly from sparse, in-the-wild data, enabling high-quality asset generation at scale. We tackle the challenges of asset completion and generative modelling via a two-stage "reconstruct-then-generate" methodology. In the first stage, we learn a low-dimensional object latent space that generates complete assets by training across multiple scenes via neural rendering. To handle partial occlusion, we jointly learn a scene representation for both the static scene and dynamic actors, enabling occlusion-aware rendering during learning. In the second stage, we train a diffusion model to operate on the 3D latent space, enabling realistic asset generation that can be conditioned on individual views, day or night, or the actor class, enabling asset variations that are applicable to new scenes. We evaluate our model on the public self-driving dataset PandaSet [87], demonstrating its capability to reconstruct and generate high-quality assets from sparse, in-the-wild data. Additionally, we showcase applications such as conditional generation, as well as realistic rendering of our assets for downstream simulation systems, highlighting our approach's flexibility, scalability, and practical utility. + +# 2. Related Work + +3D Reconstruction in the Wild: Reconstructing objects from in-the-wild data is essential for creating 3D digital twins and simulations, but poses significant challenges due to the complexity (e.g., occlusions, sparse viewpoints, par + +tial observations) and noise (e.g., localization and calibration inaccuracies [99], sensor noise). Object-based reconstructions fall into optimizing explicit meshes [46, 78, 95] or implicit representations [27, 43, 49, 80, 96, 98, 100] methods via differentiable rendering. However, they rely on accurate object segmentation masks and struggle to handle complex occlusions. To address this issue, recent works propose compositional neural fields [35, 50, 53, 74, 97] or 3D Gaussians [11, 29, 93] to decompose 3D world into static background and dynamic actors. These works often involve costly per-scene optimizations and cannot generalize well to novel views with large shifts nor produce complete (i.e., 360-degree) objects. To mitigate these limitations, recent works propose generalizable reconstruction models [10, 23, 44, 56, 83] that generate a 3D representation with a single feed-forward network trained on many scenes. Another line of work aims to incorporate data-driven priors from pre-trained models (e.g., stable diffusion [58]) via score-distillation sampling (SDS) [25, 52, 81, 84]. However, existing methods either require object-centric synthetic training data [23, 83, 84] (e.g., Objaverse [12]) and/or perform poorly on in-the-wild sensor data [10, 25, 81]. Our approach builds high-fidelity and complete assets by directly learning on real-world data. + +GAN-based 3D Generation: Generative Adversarial Networks [19] (GANs) have shown great potential for 3D asset generation [17, 90], where the generator transforms random noise into the target 3D representation, and the discriminator is jointly trained using 2D images rendered from the generated representation and the ground truth. This paradigm allows generation without requiring explicit 3D ground truth. Specifically, $\pi$ -GAN [6] introduces a generative model for high-quality 3D-aware image synthesis based on neural radiance fields. GIRAFFE [47] further proposes to represent scenes as compositional generative neural feature fields, allowing for better object-background disentanglement and controllable scene generation. EG3D [7] and GET3D [17] further improve 3D generation efficiency and quality by integrating the triplane representation (for volume rendering or explicit mesh rendering) with a StyleGAN [28] architecture. Although they achieve robust and consistent 3D generation, they primarily focus on "clean" object-centric images with full coverage and no occlusions and have difficulties generalizing to in-the-wild driving data. Most recently, DiscoScene [90] and GINA-3D [63] learn 3D generative models from in-the-wild data. However, they often produce significant visual artifacts (e.g., floating particles, low-fidelity shapes and texture). In contrast, our method generates high-quality assets. + +Diffusion-based 3D Generation: Diffusion-based methods have achieved tremendous success in image generation + +[22, 51, 58, 67, 68], leveraging denoising diffusion probabilistic models [22] to transform white noise into high-quality outputs through iterative refinement. To bridge the gap between 2D and 3D generation, a common strategy involves lifting 2D images to 3D via score distillation sampling (SDS) [18, 25, 34, 52, 64, 71, 81, 84]. These methods rely on pre-trained or fine-tuned 2D diffusion models and optimize 3D representations with diffusion-prior guidance. The optimization is slow and the supervision can be multi-view inconsistent. To address this issue, recent works [32, 36, 37, 39, 64, 79] propose to synthesize multi-view consistent images via diffusion models and then perform 3D reconstruction with explicit meshes [89], neural radiance fields [32, 79] or 3D Gaussians [72, 92]. Another line of work performs diffusion directly in 3D, either by training 3D-aware diffusion model from posed 2D images without requiring explicit 3D supervision [1, 5, 9, 20, 45, 65, 69, 73, 91] or by operating directly on 3D data [38, 40, 75]. Inspired by latent diffusion models (LDM) [58], recent works diffuse within a latent space, where models like UNet [60] or VAEs [30, 76] map 3D data to a compressed latent representation for faster, higher-quality and more scalable synthesis of both objects [57, 85] and large-scale scenes [24, 42, 54, 55, 88, 101]. However, existing works primarily focus on synthetic objects [9, 42] or static scenes [24, 54, 55, 88] and cannot handle complex real-world scenarios. In contrast, we propose a latent diffusion 3D generative model with compositional radiance fields that learns directly from in-the-wild dynamic scenes, enabling high-quality 3D asset generation at scale. + +# 3. Method + +Our goal is to build a generative model that can create high-fidelity assets scalably for self-driving simulation. The model should enable unconditional generation of diverse assets for a variety of classes (e.g., cars, buses, trucks, pedestrians), and also support generating complete assets conditioned on new in-the-wild camera images and LiDAR point clouds for actors that may be occluded or far-away. Importantly, to avoid the quality degradation [9] that occurs when generative models trained on synthetic data are transferred to real data, our generative model should directly learn over a corpus of real-world driving scenes collected by a robot sensor platform. Towards this goal, we propose a two-stage "reconstruct-then-generate" framework. In the first stage, we jointly learn a set of latent codes through reconstruction-based neural rendering, where each latent code represents a foreground actor in our dataset. We devise a compositional scene representation that enables rendering of actors of driving scenes in an occlusion-aware manner, enabling us to decouple the foreground actors from the background (e.g., road, sky, vegetation). Fig. 2 provides an overview of this process. In the second stage, we train a diffusion model + +to learn generative priors in this asset latent space, enabling the generation of realistic and diverse neural assets. This enables both unconditional generation and conditional generation through score-based guidance. Fig. 3 shows the overview of our latent asset diffusion model. We first introduce our compositional scene representation (Sec. 3.1). We then describe how we compress the actor representations into a latent space to learn the set of latent codes via neural rendering (Sec. 3.2), and detail the diffusion process in the latent space and the training process (Sec. 3.3). + +# 3.1. Compositional Scene Representation + +We aim to learn a generative 3D asset model from real-world driving scenes. Unlike existing object-centric approaches [7, 9, 17, 18, 45, 48, 85], our sensor data contains many actors captured under different viewpoint, distances, and occlusions. To handle multiple instances and their occlusions, we leverage a compositional scene representation. Each scene is decomposed into a static background $\mathcal{B}$ and a set of dynamic actors $\{\mathcal{A}_i\}_{i=1}^K$ , with each actor enclosed within a 3D box and localized by a trajectory of $SE(3)$ poses. We model the static background and dynamic actors with separate neural feature fields parameterized by triplane representations [7]. Specifically, for each dynamic actor's volume, explicit features are aligned along three orthogonal planes, each with resolution $N_{\mathcal{A}} \times N_{\mathcal{A}} \times C$ , where $N_{\mathcal{A}}$ is the spatial resolution, and $C$ is the feature dimension. Similarly, triplane features of resolution $N_{\mathcal{B}} \times N_{\mathcal{B}} \times C$ represent the background volume. For a spatial query coordinate $\mathbf{x} \in \mathbb{R}^3$ , we project it onto each of the three feature planes $\mathbf{t} = (\mathbf{t}^{xy}, \mathbf{t}^{xz}, \mathbf{t}^{yz})$ and bilinearly interpolate the corresponding feature vectors. The interpolated features are concatenated with view direction $\mathbf{d} \in \mathbb{S}^2$ and processed by an MLP network $f_{\mathrm{feat}}$ to yield geometry as a signed-distance function (SDF) $s$ and a neural feature $\mathbf{f}$ . This querying process is defined by: + +$$ +s, \mathbf {f} = f _ {\mathrm {f e a t}} (\{\operatorname {i n t e r p} (\mathbf {x} ^ {p}, \mathbf {t} ^ {p}) \} _ {p \in \{x y, x z, y z \}}, \mathbf {d}), \quad (1) +$$ + +where $\mathbf{x}^p$ represents the 2D projection of $\mathbf{x}$ onto feature plane $p$ . To render the scene representation, we first transform the object-centric actor neural feature fields to world coordinates similar to [74, 97]. Then we compose the background and actor feature fields. The composited geometry and appearance features are then rendered into sensor observations through neural volume rendering. + +# 3.2. Learning Latent Asset Representations + +Encoding to a Latent Space: Per-scene reconstruction methods [74, 93, 97] train each scene separately, with its own set of actor and background triplanes. This prevents effective handling of ambiguities in occluded or unseen regions, resulting in actor representations that generalize poorly to unseen viewpoints. Naively training jointly over + +![](images/d6007d770690c8f517ec593fda1d3c06e079812fe73d3844f9b80cff4b5c756c.jpg) +Figure 2. Learning latent asset representation. We learn a low-dimensional object latent space that generates complete assets by training across multiple scenes via occlusion-aware neural rendering. The asset decoder is trained to map low-dimension latent codes into neural assets which are then composed with learnable per-scene background models to match real-world sensor observations. + +all the explicit triplanes for every actor in the dataset containing tens of thousands of objects requires vast amounts of GPU memory and still does not force the learned triplanes to have complete actor shape and appearance. To address these limitations, we propose learning a latent code $\mathbf{c}_i\in \mathbb{R}^{n_A\times n_A\times c}$ for each actor representation and a class embedding $\mathbf{e}_i\in \mathbb{R}^{n_A\times n_A\times c}$ , combined with a shared asset triplane decoder $f_{\mathrm{dec}}$ that maps the latent code into the triplane representation: + +$$ +f _ {\mathrm {d e c}}: \mathbf {e} _ {i}, \mathbf {c} _ {i} \in \mathbb {R} ^ {n _ {A} \times n _ {A} \times c} \rightarrow \mathbf {t} _ {i} \in \mathbb {R} ^ {N _ {A} \times N _ {A} \times 3 C}. \tag {2} +$$ + +The class embedding $\mathbf{e}_i$ has the same spatial resolution as the latent code and is shared among actors of the same class. We concatenate it with the actor latent code before passing it to the decoder. The decoder $f_{\mathrm{dec}}$ upsamples the latent code by a factor $f = N_{\mathcal{A}} / n_{\mathcal{A}}$ . The intuition is that different actors are observed from various viewpoints, so their feature planes $\mathbf{t}_i$ capture different informative regions. By compressing them into a latent code bottleneck, we enable learning shape and appearance priors, allowing inference of invisible parts from sparse observations. + +**Rendering Sensor Observations:** Now that we have decoded the asset neural fields $\{\mathbf{t}_i\}_{i=1}^N$ from the latent codes $\{\mathbf{c}_i\}_{i=1}^N$ , the next step is to compose them with the background neural fields $\mathbf{t_B}$ and render into the sensor data. In this work, we focus on camera images and LiDAR point clouds, as they are primary sensory modalities for SDVs. + +For camera rendering, we use a hybrid volume and neural rendering framework for both efficiency and realism. Given a camera ray $\mathbf{r}(t) = \mathbf{o} + h\mathbf{d}$ sent from the camera center $\mathbf{o}$ to the pixel in direction $\mathbf{d}$ , we sample 3D points along the ray, querying geometry $s_t$ and neural feature $\mathbf{f}_t$ via Eq. (1). We then aggregate these samples to obtain the pixel feature through volume rendering: + +$$ +\mathbf {f} (\mathbf {r}) = \sum_ {t = 1} ^ {N _ {t}} w _ {t} \mathbf {f} _ {t}, \quad w _ {i} = \alpha_ {t} \prod_ {j = 1} ^ {t - 1} (1 - \alpha_ {j}), \tag {3} +$$ + +where $\alpha_{t}$ is the opacity for the $t$ -th point, derived from the SDF $s_t$ following [74, 97]. We repeat this process to volume render all camera pixels, generating a 2D feature map $\mathbf{F} \in \mathbb{R}^{H_f \times W_f \times C_f}$ . Then we leverage 2D CNN network $f_{\mathrm{rgb}}$ [97] to convert this feature map into an image $\mathbf{I}_{\mathrm{rgb}}$ : + +$$ +f _ {\mathrm {r g b}}: \mathbf {F} \in \mathbb {R} ^ {H _ {f} \times W _ {f} \times C _ {f}} \rightarrow \mathbf {I} _ {\mathrm {r g b}} \in \mathbb {R} ^ {H \times W \times 3}. \tag {4} +$$ + +The CNN network $f_{\mathrm{rgb}}$ upsamples the rendered map from resolution $H_{f} \times W_{f}$ to $H \times W$ . This allows us to significantly reduce the number of neural feature field queries. This approach also enhances model capacity and improves image quality by capturing spatial relationships effectively. + +In addition to camera images, we use LiDAR rendering for additional geometry supervision. LiDAR sensors emit laser pulses and measure the time of flight to determine distances to reflective surfaces. This depth information provides valuable supervision for asset geometry. Using similar notation, we define $\mathbf{r}(t) = \mathbf{o} + h\mathbf{d}$ as a ray cast from the LiDAR sensor center $\mathbf{o}$ in the direction $\mathbf{d}$ . We render LiDAR depth similarly to Eq. (3) by aggregating sample depths via volume rendering: $D(\mathbf{r}) = \sum_{t=1}^{N_t} w_t h_t$ , where $h_t$ is the depth of the $t$ -th sampled point, and $w_t$ is the sample weight computed as in Eq. (3). + +Learning: We jointly optimize the asset code $\{\mathbf{c}_i\}_{i=1}^{N_c}$ , class embedding $\{\mathbf{e}_i\}_{i=1}^{N_e}$ , background neural fields $\mathbf{t}_B$ , asset decoder $f_{\mathrm{dec}}$ , neural feature fields MLP $f_{\mathrm{feat}}$ , and RGB CNN network $f_{\mathrm{rgb}}$ by minimizing the differences between rendered and observed sensor data. To achieve high-fidelity reconstruction and rendering, we incorporate perceptual and patch-based adversarial objectives. We also regularize the latent space by applying a Kullback-Leibler (KL) penalty. Our full objective is: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {r g b}} + \lambda_ {\text {p e r p}} \mathcal {L} _ {\text {p e r p}} + \lambda_ {\text {a d v}} \mathcal {L} _ {\text {a d v}} + \lambda_ {\text {l i d}} \mathcal {L} _ {\text {l i d}} + \lambda_ {\mathrm {K L}} \mathcal {L} _ {\mathrm {K L}}, \tag {5} +$$ + +where $L_{\mathrm{rgb}}$ and $L_{\mathrm{perp}}$ represent the $\ell_2$ photometric loss and the perceptual loss [102] between rendered and observed images, $\mathcal{L}_{\mathrm{adv}}$ is the adversarial objective using patchGAN [26], $\mathcal{L}_{\mathrm{lid}}$ is the $\ell_1$ depth loss between rendered and observed LiDAR points, and $\mathcal{L}_{\mathrm{KL}}$ is the injected KL penalty + +![](images/b7d4ce8951ce8b025cbe1ce6dc8230b5a4fed289b035b974b29e777dc2574251.jpg) +Figure 3. Left: Training asset diffusion model in latent space. Right: Sampling diffusion model for (un)conditional neural asset generation. + +![](images/e0fa0c0a58f2f98f78dc4b42b6a5420867851b5a1709a4384d428832d08d8ec4.jpg) + +guiding the latent space towards a standard normal distribution, similar to [30, 58]: $\mathcal{L}_{\mathrm{KL}} = \frac{1}{2}\| \pmb{\mu}_i^2 + \pmb{\sigma}_i^2 - 1 - \log (\pmb{\sigma}_i^2)\|_1$ , where $\pmb{\mu}_i$ and $\pmb{\sigma}_i$ represent the mean and standard deviation components of latent code $\mathbf{c}_i$ , i.e., $\mathbf{c}_i = \pmb{\mu}_i^2 + \pmb{\sigma}_i \odot \pmb{\epsilon}$ with $\pmb{\epsilon} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ . This regularization prevents overfitting and encourages the latent space to be compact, continuous, smooth, and low-variance, enabling easier learning of generative models. Similar to [16, 90], we introduce additional perceptual losses on object patches for enhanced object-level supervision, where the patches are obtained by projecting the 3D instance boxes onto the image plane. Please refer to supp. for more details. + +# 3.3. Latent Asset Diffusion Model + +Given our learned asset code library $\{\mathbf{c}_i\}_{i = 1}^N$ from the dataset, we aim to learn generative priors using a diffusion model. Diffusion models [22, 66] are probabilistic frameworks that model the data distribution by progressively denoising a Gaussian noise variable. In our approach, the diffusion model operates directly in the latent space and begins with Gaussian noise, progressively denoising it to recover the underlying latent distribution. The forward or diffusion process is a discrete-time Markov chain that iteratively adds Gaussian noise to the latent code $\mathbf{c}^{(0)}$ , producing progressively noisier codes following the transition probability $q(\mathbf{c}^{(t)}|\mathbf{c}^{(t - 1)}) = \mathcal{N}(\sqrt{1 - \beta^{(t)}}\mathbf{c}^{(t - 1)},\beta^{(t)}\mathbf{I})$ , according to a noise schedule $\beta^{(t)}$ . After $T$ steps, the code approximates pure Gaussian noise. This forward process can be directly sampled at timestep $t$ using closed-form expression: + +$$ +\mathbf {c} ^ {(t)} = \sqrt {\bar {\alpha} ^ {(t)}} \mathbf {c} ^ {(0)} + \sqrt {1 - \bar {\alpha} ^ {(t)}} \boldsymbol {\epsilon}, \tag {6} +$$ + +where $\bar{\alpha}^{(t)} = \prod_{s=1}^{t} \alpha^{(s)}$ with $\alpha^{(t)} = 1 - \beta^{(t)}$ , and $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ is drawn from a Gaussian distribution. The goal of the diffusion model is to learn the reverse process, progressively denoising the noisy code to recover a clean version. We parameterize the denoising network $f_{\mathrm{diff}}$ as a U-Net [60], which takes the noisy code $\mathbf{c}^{(t)}$ and timestep $t$ as inputs, predicting the noise estimate $f_{\mathrm{diff}}(\mathbf{c}^{(t)}, t)$ and removing it to yield a denoised code. The denoising network is trained with a weighted $\ell_2$ objective: + +$$ +\mathcal {L} _ {\text {d i f f}} = \mathbb {E} _ {\mathbf {c}, \boldsymbol {\epsilon}, t} \left[ \frac {1}{2} w ^ {(t)} \| f _ {\text {d i f f}} \left(\mathbf {c} ^ {(t)}, t\right) - \boldsymbol {\epsilon} \| _ {2} ^ {2} \right], \tag {7} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ is standard Gaussian noise, $t\sim \mathcal{U}(1,T)$ is uniformly sampled from the interval $[1,T]$ , and $\mathbf{c}^{(t)}$ is derived from $\mathbf{c}^{(0)}$ (Eq. (6)), where $\mathbf{c}^{(0)}\sim \{\mathbf{c}_i\}_{i = 1}^N$ is sampled from the asset code library. The term $w^{(t)}$ provides time-dependent weighting. Learning the diffusion process in the latent space, rather than in high-dimensional triplane space like prior work [2, 9, 45, 65, 85], offers key advantages for likelihood-based generative modeling by: (i) focusing on essential contents of the data and (ii) operating in a computationally efficient, compact space. + +Unconditional Asset Generation: Unconditional asset generation involves generating a latent code using the learned diffusion model $f_{\mathrm{diff}}$ and then decoding it into neural assets using the learned asset decoder $f_{\mathrm{dec}}$ . Sampling from the diffusion prior can be performed with various solvers (e.g., DDPM [22], DDIM [67]), similar to methods used in image generation. Taking DDIM [67] for example, we begin with a random Gaussian code $\mathbf{c}^{(T)} \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$ and iteratively denoise it over $T$ steps until reaching $t = 0$ : + +$$ +\mathbf {c} ^ {(t - 1)} = \sqrt {\alpha^ {(t - 1)}} \left(\frac {\mathbf {c} ^ {(t)} - \sqrt {\beta^ {(t)}} \tilde {\boldsymbol {\epsilon}}}{\sqrt {\alpha^ {(t)}}}\right) + \sqrt {\beta^ {(t - 1)}} \tilde {\boldsymbol {\epsilon}}, \tag {8} +$$ + +$$ +\text {s . t .} \tilde {\boldsymbol {\epsilon}} = f _ {\text {d i f f}} \left(\mathbf {c} ^ {(t)}, t\right), \tag {9} +$$ + +where $\tilde{\epsilon}$ is the noise estimate at timestep $t$ from the denoising network $f_{\mathrm{diff}}$ . The final denoised code $\mathbf{c}^{(0)}$ is a sample from the learned latent distribution. We then pass this code to the asset decoder to generate the asset neural fields, $\mathbf{t} = f_{\mathrm{dec}}(\mathbf{c}^{(0)})$ , for scene composition and rendering. + +Conditional / Guided Assets Generation: For conditional generation, we aim to model the conditional distribution of the latent space $p(\mathbf{c}|y)$ . This can be achieved with a conditional denoising network $f_{\mathrm{diff}}(\mathbf{c}^{(t)}, t, y)$ , with condition signals such as actor class and time-of-day. As shown in Fig. 1, classifier-free diffusion guidance enables effective control over asset generation. Alternatively, for some inverse problems such as image-to-3D, conditional generation can be approximated from an unconditional model using classifier guidance [13, 68], leveraging gradients of the rendering loss w.r.t. known observations. This flexibility re + +moves the need for separate models tailored to different inverse problems. Given camera image and/or LiDAR point cloud of a new actor to reconstruct, during the sampling process (Eq. (8)) we compute the gradient of the rendering loss with respect to the current code: $\mathbf{g} = \nabla_{\mathbf{c}^{(t)}}\left(\mathcal{L}_{\mathrm{rgb}} + \lambda_{\mathrm{lid}}\mathcal{L}_{\mathrm{lid}}\right)$ and then steer the sampling process by updating the noisy code similar to [9, 45]: + +$$ +\hat {\mathbf {c}} ^ {(t - 1)} \leftarrow \mathbf {c} ^ {(t - 1)} - \lambda \cdot \mathbf {g}, \tag {10} +$$ + +where $\mathbf{c}^{(t - 1)}$ is computed following Eq. (8) and $\hat{\mathbf{c}}^{(t - 1)}$ is the updated code; $\lambda$ is a small guidance weight. + +# 4. Experiments + +In this section, we first describe our experimental setup. We then compare our model to state-of-the-art reconstruction methods across multiple novel view synthesis settings. Next, we compare to SoTA generative models for 3D generation. Finally, we demonstrate conditional generation from different classes, single-image, and appearance (day/night), and show that the generated assets enhance downstream detection performance. Please refer to the supp. for implementation details and ablation of our model components. + +# 4.1. Experimental Setup + +Dataset: We conduct experiments on the PandaSet [87] dataset, which includes 103 driving scenes captured in San Francisco, with each scene spanning 8 seconds (80 frames at $10\mathrm{hz}$ ). The data collection platform features a $360^{\circ}$ mechanical spinning LiDAR, a forward-facing LiDAR, along with six $1920\times 1080$ cameras surrounding the vehicles. Object bounding boxes are provided with the dataset. As our focus is object reconstruction and generation, we extract object segmentation masks for metric evaluation. Specifically, we leverage 3D object boxes and LiDAR points to identify actor patches in the camera images, and then apply a visual foundation model [31] to generate instance masks for the actors. Our method does not require instance masks for learning. We employ them strictly to evaluate foreground-only metrics. Please see supp. for details. + +Baselines: We compare our method with several state-of-the-art reconstruction and generation approaches. For reconstruction, we benchmark against per-scene NeRF-based NeuRAD [74] and 3D Gaussian Splatting-based Street Gaussians [93], as well as generalizable reconstruction methods G3R [10] and PixelSplat [8]. During evaluation, these methods take as input all source views for the full scene, except for PixelSplat, which can only handle two views. For generation, we evaluate against the GAN-based EG3D [7] and DiscoScene [90], as well as diffusion-based SSDNeRF [9]. As EG3D and SSDNeRF are object-centric models, we train them on our object-centric benchmark with instance masks. + +# 4.2. Reconstruction Evaluation + +Evaluation Settings and Metrics: We evaluate our method across three challenging settings: (1) Sparse view synthesis: Using every 10th frame for training and the remaining frames for testing, with both training and testing frames captured from the front camera. (2) Novel camera synthesis: Training on frames from the front camera and evaluating on frames from the front-left camera. (3) $360^{\circ}$ View synthesis: Rotating actors $(0^{\circ} - 360^{\circ})$ to simulate various behaviors, evaluated on front camera views. We select 7 diverse scenes to assess reconstruction performance, with the remaining 96 scenes for learning generalizable priors. For sparse view synthesis and novel camera synthesis, we report PSNR, SSIM [82], and LPIPS [102]. For $360^{\circ}$ view synthesis, since no ground truth images are available, we report FID metrics [21]. As PixelSplat [8] is designed to reconstruct with two input views, we only evaluate it on the sparse view synthesis setting. + +Sparse View Synthesis: We first compare our method against state-of-the-art approaches for sparse view synthesis in Tab. 1. Our method outperforms the baselines across all metrics. Unlike prior methods that uses $90\%$ frames [11, 94], $75\%$ frames [93] or $50\%$ frames [10, 74, 97] for training, our setup is more challenging, relying on only $10\%$ of frames for training. We found that baseline methods struggle to learn robust geometry, leading to severe artifacts in novel viewpoints. Qualitative results in Fig. 4 (top) show that our method renders camera images more accurately. + +Novel Camera Synthesis: We compare our method against SoTA for novel camera synthesis in Tab. 1. A visual comparison is provided in Fig. 4 (middle). All baseline methods effectively reconstruct observed camera data (front camera). However, for new sensor poses (front-left camera), previously unobserved regions become visible, requiring the model to "hallucinate" these areas. For instance, the front-right part of the SUV in Fig. 4 (middle) is invisible in the front camera but becomes visible in front-left camera views. Reconstruction methods fail on these regions. Our method, by learning generative priors, is capable of rendering complete and high-quality simulations in this setting. + +$360^{\circ}$ View Synthesis: Sensor simulation requires not only simulating novel viewpoints but also synthesizing entirely new scenarios. Consider a four-way intersection with a car crossing in front of you from a perpendicular lane. To explore a situation where that car suddenly turns sharply into your lane, we must render actors in significantly different poses than those seen in the original scene. To that end, we investigate a $360^{\circ}$ view synthesis setting by rotating actors in the scene from $0^{\circ}$ to $360^{\circ}$ , simulating various + +![](images/0fe09ef11ca02842de980202ad0187a695aa53df72b458523891168a9da6aff0.jpg) +Figure 4. Top: Sparse view synthesis. GenAssets generalizes well on this extreme setting thanks to low-dimensional latent space learned across many scenes, while the SoTA reconstruction methods are less robust and produce noticeable visual artifacts (e.g., missing, blurry or distorted appearance). Middle: Novel camera synthesis. We train on frames from the front camera and evaluate on frames from the front-left camera. Our method generates assets that have better extrapolation results, while retaining high quality in the original view. Bottom: $360^{\circ}$ view synthesis. Through our multi-scene training and latent space, our method enables higher-fidelity asset completion for different object orientations compared to SoTA reconstruction-based methods. + +
MethodsSparse View SynthesisNovel Camera Synthesis360° View Synthesis
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓FID↓
PixelSplat* [8]17.670.7040.336----
G3R [10]18.370.7110.25517.400.7230.221191.92
Street Gaussian [93]20.010.7630.15617.810.7240.226162.37
NeuRAD [74]21.070.8250.12917.490.7230.214159.38
Ours21.340.8250.11318.360.8050.147100.28
+ +Table 1. Quantitative comparison with SoTA reconstruction approaches on PandaSet. We evaluate on sparse view synthesis (10% frames for training and remaining frames for testing), novel camera synthesis (training on front camera and testing on front-left camera), and $360^{\circ}$ view synthesis (rotating actors from $0^{\circ}$ to $360^{\circ}$ ). GenAssets outperforms existing SoTA per-scene or generalizable reconstruction approaches across all settings. PixelSplat* [8] (2 input views) only for sparse view synthesis evaluation. + +orientations. Since ground-truth images are unavailable, we report FID [21] in Tab. 1. Qualitative results in Fig. 4 (bottom) show that our method effectively hallucinates unseen parts of the actors, whereas all baselines struggle to do so. + +# 4.3. Generation Evaluation + +Evaluation Metrics: To evaluate the generation quality, we report both Fréchet Inception Distance (FID) [21] and Kernel Inception Distance (KID) [3] scores. The metrics are calculated by comparing distributions of 10K generated images with all available images in the validation set, providing a quantitative assessment of similarity in terms of perceptual quality and realism. FID measures the distance between the mean and covariance of feature representations from real and generated image distributions. KID complements FID by measuring differences in feature embeddings + +through a kernel-based approach. All generated objects are rendered at a resolution of $256 \times 256$ . + +Unconditional Generation: We compare our method against SoTA GAN-based method EG3D [7] and DiscoScene [90], as well as diffusion-based method SSDNeRF [9] in Tab. 2. All baselines struggle with occlusion, leading to suboptimal assets. In addition, EG3D and DiscoScene suffers from mode collapse, producing limited asset variety (mainly sedans). DiscoScene struggles to differentiate foreground and background and exhibits boundary artifacts, likely due to the absence of LiDAR or mask supervision. SSDNeRF yields blurry results, potentially due to challenges posed by our real-world sparse setting. Our model improves over these baselines across all metrics. Fig. 5 shows a visual comparison. + +![](images/0351ecbcc7f851e8d1a22eda20f12eaa410ba315b6536e27a47a1b96565979cf.jpg) +Figure 5. Qualitative comparison on unconditional generation. Our methods generate more diverse, complete and higher-quality 3D assets compared to SoTA 3D generative models. + +![](images/316ecfb449b4a3304e76b96382eaa40466e80128067c755e932a57ca3f4c572a.jpg) +Figure 6. Qualitative results on single-image to 3D. + +# 4.4. Applications + +Conditional Generation: The flexibility of our framework enables various conditional generation tasks. Specifically, we freeze the learned latent codes and train a conditional diffusion model $f_{\mathrm{diff}}(\mathbf{c}^{(t)}, t, y)$ using classifier-free guidance. We explore conditioning on fine-grained actor classes and time-of-day (day/night), with results presented in Fig. 1. We can generate complete assets for a variety classes, with intra-class shape and appearance variation. + +Single Image to 3D: Our approach also enables generating 3D assets from single-view images using a rendering-guided denoising process (Eq. (10)), where the denoising gradient is directed to minimize rendering loss against the observed image. Fig. 6 shows qualitative results of single-image reconstruction for three nearby vehicles, alongside comparisons to SoTA large reconstruction model MeshLRM [83]. MeshLRM produces distorted shapes and synthetic cartoon-ish appearance for unobserved views. Our approach generates higher quality completion and is consistent with the input. Please refer to supp. for more comparisons with other SoTA large models. + +Data Augmentation with GenAssets: We now showcase that our generated assets boost downstream performance when training a BEVFormer [33] 3D object detector (Tab. 3). Specifically, we augment the training dataset by swapping out existing actors with generated ones for the same scene layouts. Please see supp. for more details. + +
MethodsFID↓KID↓
SSDNeRF [9]191.30156.13
DiscoScene [90]138.48116.27
EG3D [7]80.5638.97
Ours59.5028.32
+ +Table 2. Unconditional generation evaluation on PandaSet. KID scores are multiplied by $10^{3}$ . GenAssets outperforms SoTA baselines on both metrics and generates higher-quality 3D assets. + +
mAP↑AP@1m↑AP@2m↑AP@4m↑
Real27.088.5826.9945.67
Real + Sim29.329.7829.1849.00
+ +Table 3. Data augmentation with GenAssets helps 3D detection. We report distance-based APs [4] at $1m$ , $2m$ and $4m$ . + +# 5. Conclusion + +In this work, we tackled the challenge of generating high-quality and complete assets from in-the-wild LiDAR and camera data captured by a moving sensor platform. Towards this goal, we developed a "reconstructthen-generate" approach where we first learn to reconstruct foreground actors over multiple scenes with compositional scene neural rendering and encode them to a latent space. We then train a diffusion model to operate within this latent space to enable generation. We show our method generates high-quality, complete assets for actors such as vehicles and motorcycles, outperforming both per-scene reconstruction methods and generative models. We also show that our approach can be conditioned for controllable asset generation such as on sparse sensor data, actor class, and time of day, enabling diverse and scalable content creation for simulation. Future work involves generating dynamic lighting and animation, intrinsic decomposition, and adopting more efficient scene representation and rendering techniques. + +Acknowledgement: We sincerely thank the Waabi team for their invaluable assistance and support. We also thank the anonymous reviewers for their insightful suggestions. + +# References + +[1] Titas Anciukevicius, Zexiang Xu, Matthew Fisher, Paul Henderson, Hakan Bilen, Niloy J Mitra, and Paul Guerrero. Renderdiffusion: Image diffusion for 3d reconstruction, inpainting and generation. In CVPR, 2023. 3 +[2] Miguel Angel Bautista, Pengsheng Guo, Samira Abnar, Walter Talbott, Alexander Toshev, Zhuoyuan Chen, Laurent Dinh, Shuangfei Zhai, Hanlin Goh, Daniel Ulbricht, et al. 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Paranjape and Vishal M. Patel +Johns Hopkins University + +{sambasa2,ngopala2，jparanj1，vpatel36}@jhu.edu + +# Abstract + +Deep learning-based models for All-In-One image Restoration (AIOR) have achieved significant advancements in recent years. However, their practical applicability is limited by poor generalization to samples outside the training distribution. This limitation arises primarily from insufficient diversity in degradation variations and scenes within existing datasets, resulting in inadequate representations of real-world scenarios. Additionally, capturing large-scale real-world paired data for degradations such as haze, lowlight, and raindrops is often cumbersome and sometimes infeasible. In this paper, we leverage the generative capabilities of latent diffusion models to synthesize high-quality degraded images from their clean counterparts. Specifically, we introduce GenDeg, a degradation and intensity-aware conditional diffusion model, capable of producing diverse degradation patterns on clean images. Using GenDeg, we synthesize over 550k samples across six degradation types: haze, rain, snow, motion blur, low-light, and raindrops. These generated samples are integrated with existing datasets to form the GenDS dataset, comprising over 750k samples. Our experiments reveal that image restoration models trained on GenDS dataset exhibit significant improvements in out-of-distribution performance as compared to when trained solely on existing datasets. Furthermore, we provide comprehensive analyses on implications of diffusion model-based synthetic degradations for AIOR. + +# 1. Introduction + +Image restoration is a well-studied computer vision problem that aims to reverse the effects of image corruptions or artifacts. It is important for numerous applications, including autonomous driving, imaging and surveillance. Early approaches focused on handling specific degradations such as haze [16, 58], rain [19, 47, 52, 53], + +![](images/159e8888c5326d708fd744fd1094cb8b7067a886e4c3831a39804903a62aeea2.jpg) +Figure 1. Out-of-distribution performance of three image restoration models when trained solely using existing datasets and our proposed GenDS dataset. Significant improvements can be observed across all degradations. Metric values reduce outward. + +snow [11, 59], blur [34, 42] etc. More recent methods such as Restormer [57], MPRNet [56] and SwinIR [27] proposed architectures capable of addressing any single restoration task. However, these approaches are limited to addressing one type of degradation at a time, making them inefficient for scenarios involving multiple types of corruptions. + +All-In-One Restoration (AIOR) methods overcome this limitation by employing a single model capable of handling multiple types of degradations. Recent approaches include PromptIR [35], DA-CLIP [32], DiffUIR [62], DiffPlugin [29], InstructIR [13] and AutoDIR [18]. Most AIOR methods are trained using a single dataset for each restoration task such as RESIDE [23] for dehazing, Snow100k [30] for desnowing, Rain13K [56] for deraining and GoPro [34] dataset for motion deblurring. Although these approaches perform well on degradations from these dataset distributions, they often exhibit poor generalization when confronted with new scenes or out-of-distribution (OoD) degradation patterns, which is very common in real-world scenarios. Recent studies have discussed the problem of generalization in image restoration models in great depth [17, 22]. We hypothesize that the limited generalization of these models is mainly due to two reasons: + +1. Lack of large datasets with real degradations under diverse scenes. We consider the degradations haze, snow, rain, raindrop, motion blur and low-light. Fig. 2 shows the number of synthetic and real images for each degradation from its existing publicly available datasets, along with the number of unique scenes. To the best of our knowledge, we have included most of the existing datasets. Firstly, the figure shows that existing restoration datasets are significantly smaller than those used to train generalizable models for other low-level vision tasks, such as SAM [21] for segmentation and Depth-Anything [51] for depth estimation ( $>1.5\mathrm{M}$ samples). This limited dataset size hinders the generalization of models to diverse real-world scenarios. Secondly, degradations such as haze, raindrop, low-light and snow have very few real images compared to synthetic ones due to challenges in capturing real images under these conditions. For instance, haze is an atmospheric phenomenon which is difficult to simulate in real scenarios. Conversely, motion blur and rain have more real-world examples as they can be generated from existing videos [15, 26, 34, 42, 47]. Thirdly, degradations such as haze, raindrop and low-light have very limited scene diversity which can further limit the generalization of models. Finally, the number of samples across different degradations is highly imbalanced. + +2. Lack of variety in degradation patterns within datasets. Previously, we analyzed the distribution of samples for each degradation. Examining individual datasets, especially synthetic ones, reveals that they contain degradations generated using only a particular model. For instance, the images in the RESIDE [23] dataset are generated by the atmospheric haze model [7] with specific parameters. Consequently, training a network on such a dataset can tailor it to work only for the degradation patterns of that dataset, limiting its generalization capability for real-world dehazing. + +Thus, AIOR methods often overfit to training distributions, limiting generalization to real-world samples. To address this, we aim to develop robust AIOR models capable of generalizing to OoD restoration. We define OoD samples as those from test sets, whose corresponding training sets are not used. Within-distribution test sets refer to test splits of the datasets used for training (also referred to as existing training data). To support these definitions, we compute the Wasserstein Distance (WaD) between DA-CLIP [32]'s degradation feature distributions for OoD test sets and the existing training datasets for each degradation (see Table 1). The mean WaD between within-distribution test sets and their training sets is 0.084, which is much lower than the WaD for OoD test sets, validating our definition. Achieving good OoD performance requires large-scale training data with diverse degradations. Since collecting real-world data + +![](images/080b864616fae45555c5b0c8debd856228f74a136c81024e4b1066985c79689b.jpg) +Figure 2. Analysis of real and synthetic image restoration datasets for various degradations. Existing datasets are small and less diverse, especially for haze, low-light, and raindrop. Our diffusion-generated synthetic data substantially increases the number of samples as well as scene diversity. + +Table 1. Wasserstein distance between the degradation feature distributions of DA-CLIP [32] for existing training data and OoD test sets. + +
DistanceHazeRainSnowMotionLow-lightRaindrop
Wasserstein0.2120.2870.2890.1730.3490.177
+ +for all the degradations is infeasible, we propose a novel degradation generation framework that leverages the generative capabilities of Latent Diffusion Models (LDMs) [40] to synthesize diverse degradations. Specifically, we introduce GenDeg, a Stable Diffusion-based model conditioned on text prompts, clean images and degradation intensity to produce images under various degradations. + +We train GenDeg by combining multiple existing datasets for each degradation type to ensure that it does not heavily rely on a specific degradation pattern or physical model. Thus, it can produce both synthetic and realistic degradations, thereby enriching the diversity of degradation patterns in the generated data. Furthermore, GenDeg offers fine-grained control over the intensity and spatial variations of generated degradations by conditioning on the mean $(\mu)$ and standard deviation $(\sigma)$ of the degradation map. Using GenDeg, we synthesize over 550k degraded images from roughly 120k clean images. We augment existing restoration datasets (used to train GenDeg) with our generated images to create a dataset, GenDS, with over 750k paired images under haze, rain, snow, motion blur, low-light and raindrop degradations. GenDS provides a significant boost in scene diversity and number of samples (see Fig. 2), resulting in substantial improvements in OoD performance of AIOR models (see Fig. 1). Fig. 3 illustrates that the diverse degradations in the GenDS dataset help bridge the domain gap between existing and OoD datasets (see Sec. 4.2 for + +![](images/fbebfd535215d8dbb6885a89275a25cd255005250687655f45ffb68f3afe9454.jpg) +DA-CLIP degradation features of hazy samples from training, GenDS and OoD datasets. +Figure 3. t-SNE visualization of degradation features obtained for hazy samples from existing training data, GenDS dataset and OoD test sets. The features were obtained using DA-CLIP [32]. + +more details). Additionally, GenDS consists of the same clean images under different degradations that, to the best of our knowledge, is the first such dataset. + +Finally, we train five models on the GenDS dataset, namely NAFNet [10], PromptIR [35], a Swin Transformer-based model that we propose, DA-CLIP [32] and Diff-Plugin [29]. Our experiments demonstrate that these models achieve significant improvements in their generalization performance when trained on our large-scale dataset. + +In summary, our contributions are as follows: + +1. We propose a novel diffusion model-based degradation generation framework, GenDeg, which is capable of producing diverse degradations on any clean image. +2. Using GenDeg, we synthesize over 550k degraded images which when combined with existing datasets forms the comprehensive GenDS dataset comprising approximately 750k samples across highly diverse scenes. Furthermore, each image in GenDS has multiple degraded versions, making it, to the best of our knowledge, the first restoration dataset of its kind. +3. Finally, we train restoration models on the GenDS dataset and demonstrate that incorporating our synthetic data significantly improves the out-of-distribution restoration capabilities of these networks. + +# 2. Related Works + +In this section, we discuss relevant works on all-in-one image restoration and diffusion models for synthetic data. Related works on diffusion models are given in supplementary. + +# 2.1. All-in-one image restoration + +All-In-One restoration (AIOR) methods employ a single model to address multiple corruptions. Early approaches include All-in-one [25], which used neural architecture search, and Transweather [46], which unified multiple encoders for efficient multi-weather restoration. Airtnet and [12] used contrastive loss to learn degradation repre + +sentations while PromptIR [35] utilized learnable prompts. Recent approaches have leveraged diffusion models for AIOR. DA-CLIP [32] used degradation information from CLIP [37] to guide diffusion-based image restoration. DiffPluginin [29] adopts task plugins to guide a latent diffusion model for restoration. DiffUIR [62] proposed selective hourglass mapping and AutoDIR [18] developed an automatic approach using vision-language models for degradation detection and restoration. InstructIR [13] utilized text guidance as instructions for AIOR while AWRaCLe [38] used visual in-context learning. Despite these advancements, no prior work (to the best of our knowledge) has explored using diffusion models to generate degradations. Our approach enables the creation of large datasets with realistic degradations to train generalizable AIOR models. + +# 2.2. Diffusion models for synthetic data + +Diffusion models have shown great potential for synthetic data generation. Methods such as Dreambooth [41] and Distribution Matching Distillation [54] focus on improving the generative process using diffusion-generated data, rather than creating paired synthetic data for downstream tasks. Sim2real techniques such as EPE [39] translate simulation images into realistic ones but do not synthesize degraded images for restoration. Recent research has focused on utilizing latent diffusion models for synthetic data generation tailored to specific tasks. [3, 4, 43, 44, 55] used diffusion-generated images to improve classification and zero-shot classification performance. However, classification tasks do not require preservation of intricate details in the generated images. Other approaches [33, 45, 49, 61] use diffusion-generated data for semantic and aerial segmentation, demonstrating promising directions. Nonetheless, these approaches generate segmentation masks which lack detailed scene content. In contrast, we generate high quality degraded images for image restoration, where preserving scene consistency is crucial for good performance. Our approach effectively addresses these challenges, leading to significant improvements in the generalization of image restoration models trained on our synthetic data. + +# 3. Proposed Method + +In this section, we detail GenDeg, our diffusion-based method for generating large-scale synthetic data for image restoration. We also discuss the process of data generation, curation and training of restoration models. + +# 3.1. Diffusion-based degradation generation + +Our goal is to leverage the generative priors of pre-trained diffusion models to produce diverse degradations on clean images while preserving scene semantics. We consider the synthesis of six degradations, namely, haze, rain, snow, low-light, motion blur and raindrops. To achieve this, we re + +![](images/64b024d08f44bc88faf51798e44a99e76ef47fe99f6390882f8c1d88a01cda78.jpg) +(a) + +![](images/9c070bbce19fd1b23d88e5f54a2ebb04470db1d8beaf137d5504372d13fbbeb9.jpg) + +![](images/a9b9c2c369eb6dd105b5d6e1f914e25c633e672dfcfa6afdbcf789f463d9d36f.jpg) +(c) +Figure 4. (a) Illustrates the training stage of the GenDeg model where it is trained to condition on the clean image, text prompt and mean intensity $(\mu)$ and variation $(\sigma)$ of the degradation pattern. (b) Shows the inference stage where the model generates a degraded image based on these conditions; and (c) Depicts the architecture of the Swin-transformer-based restoration network. + +require a diffusion model that conditions on an input clean image (that needs to be degraded) and a prompt specifying the desired degradation. One popular approach that aligns with our objectives is the InstructPix2pix [5] model. It is a text-based image editing framework that leverages the latent diffusion model (LDM), Stable Diffusion [40], to generate edited images that are consistent with the input image. LDM operates in the latent space of a pre-trained variational auto-encoder [20] whose encoder and decoder are denoted by $\mathcal{E}$ and $\mathcal{D}$ , respectively. Given an image $x_{\mathrm{in}}$ , image condition $c_{\mathrm{img}}$ and text condition $c_{\mathrm{text}}$ , the diffusion model $(\epsilon_{\theta})$ minimizes the following objective during training + +$$ +L = \mathbb {E} _ {\mathcal {E} (x _ {\text {i n}}), \mathcal {E} (c _ {\text {i m g}}), c _ {\text {t e x t}}, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, \mathcal {E} \left(c _ {\text {i m g}}\right), c _ {\text {t e x t}}\right) \| _ {2} ^ {2} \right], \tag {1} +$$ + +where $z_{t}$ is the noised version of $\mathcal{E}(x_{\mathrm{in}})$ at timestep $t$ of the forward diffusion process and $\epsilon$ is the added noise. + +In our adaptation, $x_{\mathrm{in}}$ is the degraded image from existing paired restoration datasets, $c_{\mathrm{img}}$ is the corresponding clean image, and $c_{\mathrm{text}}$ is a text-prompt describing the degradation to be produced. To train the diffusion model, we combine multiple synthetic and real image restoration datasets (see supplementary for details). This approach ensures that the diffusion model learns to produce diverse degradation patterns not specific to any single dataset. + +The text condition $c_{\mathrm{text}}$ includes high-level scene information along with degradation specifics. We obtain scene descriptions by processing clean images through the BLIP-2 [24] captioning model. We then append degradation-specific phrases such as "in hazy conditions." to these descriptions, forming the final text prompt. Incorporating scene descriptions provides initial guidance to Stable Dif + +fusion during training, helping it generate an image related to $c_{\mathrm{img}}$ . Examples of the text prompts are shown in Fig. 4. + +While this method produces degraded images effectively, we observed that using only the degradation type in the prompt causes the diffusion model to generate extreme degradation patterns during inference. For instance, the haze is excessively thick, or the rain is unrealistically heavy or minimal (see supplementary for examples). Such degradations could negatively impact the performance of a restoration model trained on this data, as the patterns differ significantly from typical real-world scenarios. To overcome this limitation, we introduce a conditioning on the level of the degradation, quantified by the mean intensity $(\mu)$ and standard deviation $(\sigma)$ of the degradation map $c_{\mathrm{map}}$ defined as $c_{\mathrm{map}} = |x_{\mathrm{in}} - c_{\mathrm{img}}|$ . $\mu$ represents mean intensity of degradation in the degraded image while $\sigma$ indicates its spatial distribution across the image. We fuse the conditioning information in the form of $\mu$ and $\sigma$ with the CLIP [37] embedding, $e_{\mathrm{text}}$ , of the prompt, $c_{\mathrm{text}}$ , as follows. First, we compute the range, $[a,b]$ of $\mu$ and $\sigma$ for each degradation type from all their respective datasets. We divide this range into 128 bins and obtain a one-hot encoding for the bins corresponding to particular $\mu$ and $\sigma$ values calculated from $c_{\mathrm{map}}$ during training. An additional bin is included for null-prompt conditioning [5], resulting in vectors of length 129. + +We then concatenate the one-hot vectors for $\mu$ and $\sigma$ to obtain $c_{\mathrm{stats}} \in \mathbb{R}^{2 \times 129}$ . $c_{\mathrm{stats}}$ is then projected to $c_{\mathrm{stats}}^{\mathrm{proj}} \in \mathbb{R}^{2 \times 77}$ . $c_{\mathrm{stats}}^{\mathrm{proj}}$ is then transposed to $\mathbb{R}^{77 \times 2}$ and concatenated with $e_{\mathrm{text}} \in \mathbb{R}^{77 \times 768}$ to obtain a vector of size $\mathbb{R}^{77 \times 770}$ . We project this vector back to the CLIP text embedding dimension. + +sion and obtain $e_{\mathrm{prompt}} \in \mathbb{R}^{77 \times 768}$ to be fed as conditioning to Stable Diffusion. All projection layers are learnable. This conditioning mechanism ensures that the diffusion model is aware of the degradation level to be added to the clean image, resulting in generated images, $x_{\mathrm{gen}}$ , with diverse and realistic degradation patterns. The effect of varying $\mu$ and $\sigma$ is given in Sec. 4.2. Fig. 4 (a) summarizes the above steps. + +Finally, we tackle the challenge of aligning the generated degraded images $(x_{\mathrm{gen}})$ precisely with the input clean images $(c_{\mathrm{img}})$ . The VAE encoding and decoding process in LDMs causes the loss of fine details in the image [9, 18]. To mitigate this issue, we draw inspiration from AutoDIR [18], which introduced a Structure Correction Module (SCM) to reverse VAE-induced distortions. In our framework, the SCM, denoted by $S$ , corrects $x_{\mathrm{gen}}$ as follows: + +$$ +x _ {S} = x _ {\text {g e n}} + S ([ x _ {\text {g e n}}, c _ {\text {i m g}} ]) \tag {2} +$$ + +The goal of $S$ is to reverse LDM and VAE artifacts while preserving the generated degradation. We train $S$ after the degradation generator has been trained (keeping generator frozen) using a one-step reverse diffusion process: + +$$ +z _ {\text {g e n}} = \frac {\left(z _ {t} - \sqrt {1 - \bar {\alpha} _ {t}} \cdot \epsilon\right)}{\sqrt {\bar {\alpha} _ {t}}} \tag {3} +$$ + +Here $\bar{\alpha}_t$ is the cumulative product of the noise schedule up to timestep $t$ , and $z_t$ is the noisy latent. We then obtain $x_{\mathrm{gen}} = \mathcal{D}(z_{\mathrm{gen}})$ . The loss function for training $S$ is given by + +$$ +L _ {S} = \sqrt {\bar {\alpha} _ {t - 1}} \cdot \sqrt {1 - \bar {\alpha} _ {t}} \cdot \| x _ {\text {i n}} - x _ {S} \| _ {2} ^ {2} \tag {4} +$$ + +The term $\sqrt{\bar{\alpha}_{t-1}} \cdot \sqrt{1 - \bar{\alpha}_t}$ weights the performance of $S$ for each timestep, recognizing that structure correction is easier near the initial timesteps ( $t \approx 0$ ) and quite challenging near the final timesteps ( $t \approx T$ ). This weighting reduces the influence of these extreme cases during training. + +We found that $S$ works well for degradations that possess smooth characteristics such as haze, raindrops and motion blur. However, for degradations such as rain and snow, $S$ blurs out the rain streaks and snowflakes in the generated image. Similarly, for low-light conditions, the SCM can produce blurry outputs due to the low pixel intensities. Thus, for rain, snow and low-light degradations, we omit the usage of $S$ . Instead, we pass the clean image through the VAE encoder and decoder to obtain a slightly altered version $\hat{c}_{\mathrm{img}}$ that is better aligned with the generated image than the original clean image $(c_{\mathrm{img}})$ . Visual results showcasing the effect of $S$ can be found in the supplementary. + +# 3.2. Dataset creation + +GenDeg enables synthesizing diverse degradations on any clean image. We generate degradations on unique clean images taken from the training datasets of GenDeg. Since we use a large number of training datasets, we obtain approximately 120k distinct scenes. For each clean image, we produce degradations that were not present in its original training set, resulting in five degradations per image. This + +strategy supplements existing restoration datasets with our synthetic data, enhancing the generalization capabilities of restoration models when trained on them. + +To generate a particular degradation, we randomly select a dataset associated with that degradation type. We sample $\mu_{\mathrm{gen}}$ from the histogram of $\mu$ values in the selected dataset, which is created by the same binning strategy used during training. Subsequently, we sample $\sigma_{\mathrm{gen}}$ from a similar histogram of $\sigma$ values obtained from images belonging to the sampled $\mu_{\mathrm{gen}}$ bin. This process ensures that the value of $\sigma_{\mathrm{gen}}$ is meaningfully correlated with the chosen $\mu_{\mathrm{gen}}$ , resulting in realistic degradation patterns. To further enhance diversity, for every 1 in 20 images, we select a random value of $\sigma_{\mathrm{gen}}$ (within acceptable limits) for a chosen $\mu_{\mathrm{gen}}$ . The clean image is then degraded using the chosen $\mu_{\mathrm{gen}}$ and $\sigma_{\mathrm{gen}}$ values. After generation, we filter images based on the mean value of the generated degradation map to discard poor quality images (see Fig. 4(b)). The filtering thresholds are empirically determined for each degradation type (given in supplementary). In total, after filtering, we create approximately $550\mathrm{k}$ degraded images which are combined with samples from existing datasets to obtain the GenDS dataset. + +# 3.3. Training image restoration models + +Transformer-based architectures have demonstrated enormous potential in learning generalizable image features. However, the usage of pre-trained transformers for image restoration remains limited. We hypothesize that transformer encoders pre-trained on large datasets such as ImageNet [14] can serve as effective feature encoders for improving generalization in restoration tasks. Hence, we choose a pre-trained Swin transformer encoder [50] for extracting generalizable features from degraded images. We specifically choose the Swin transformer [31] over the standard Vision Transformer (ViT) as it provides hierarchical features at multiple resolutions, which is crucial for preserving fine details in restored images. To reconstruct the restored image from the features extracted by the Swin transformer, we employ a lightweight convolutional decoder. This decoder aggregates information from different hierarchical levels of the encoder to produce a high-quality image. The overall architecture is depicted in Fig. 4 (c). The usage of $3 \times 3$ convolutions in the decoder helps to overcome a major limitation of patch border artifacts [28] that occur when using transformer models for image restoration. The effect is more exacerbated when using vision transformers due to its large patch size. In addition to training the above Swin transformer-based architecture, we also train two other non-generative restoration networks: NAFNet [10] and PromptIR [35], on the GenDS dataset. To show that the GenDS dataset benefits generative image restoration, we also include two recent diffusion-based restoration models, namely, DA-CLIP [32] and Diff-Plugin [29]. + +Table 2. Quantitative comparisons of NAFNet [10], PromptIR [35], Swin transformer, DA-CLIP [32] and Diff-Plugin [29] models using LPIPS and FID metrics (lower is better), trained with and without our GenDS dataset. Performance is evaluated on OoD test sets. The table also includes the performance of existing state-of-the-art (SOTA) approaches. Training with the GenDS dataset significantly enhances OoD performance. (R) indicates real images and (S) indicates synthetic images. Diff-Plugin# is the publicly available pre-trained model. + +
MethodREVIDE [60]O-Haze [1]RainDS [36]LHP [15]RSVD [8]GoPro [34]LOLv1 [48]SICE [6]RainDS [36]
Degradation TypeHaze (R)Haze (R)Rain (S)Rain (R)Snow (S)Motion Blur (R)Low-light (R)Low-light (R)Raindrop (R)
DiffUIR0.268/58.50.334/147.20.088/31.20.187/26.50.176/26.10.144/25.20.148/65.10.442/102.9-
Diff-Plugin#0.281/72.90.377/164.70.194/45.00.178/30.20.207/22.50.217/32.80.195/70.50.233/69.2-
InstructIR0.313/65.40.341/154.50.117/29.20.139/21.2-0.146/21.10.132/57.30.234/65.2-
AutoDIR0.247/57.90.315/144.10.105/30.60.181/27.0-0.157/22.20.116/43.70.249/74.00.157/52.4
PromptIR0.262/62.00.333/150.90.111/49.30.186/29.30.128/15.80.186/32.90.258/111.80.391/99.30.208/106.8
PromptIR GenDS0.212/56.00.160/89.00.096/34.40.182/28.10.119/13.90.191/31.90.178/87.90.375/90.70.182/79.8
Swin0.242/62.90.254/109.90.182/38.80.189/27.10.143/21.70.198/31.70.241/112.00.293/88.30.232/82.6
Swin GenDS0.209/54.30.165/74.60.116/35.80.162/24.10.121/14.10.170/36.20.167/73.10.241/72.10.197/70.7
NAFNet0.211/71.30.183/99.20.107/34.40.200/29.30.131/14.30.155/28.20.167/78.80.304/83.50.178/73.4
NAFNet GenDS0.151/52.50.143/76.70.100/31.50.180/27.10.110/11.30.149/28.70.147/63.70.278/78.50.170/60.5
DA-CLIP0.300/59.70.369/154.60.153/49.10.194/39.70.177/39.00.187/39.10.332/100.80.331/91.70.254/85.1
DA-CLIP GenDS0.215/51.40.251/113.70.140/45.90.178/35.90.148/30.70.146/33.50.250/81.60.285/76.10.246/78.9
Diff-Plugin0.273/63.90.320/130.30.197/49.30.214/36.40.207/24.30.174/27.10.276/103.30.256/79.50.287/93.0
Diff-Plugin GenDS0.230/57.10.278/110.80.186/45.20.197/33.30.186/21.00.163/26.00.252/90.90.223/68.00.223/64.9
+ +# 4. Experiments + +In this section, we provide detailed results and analysis of our method. Implementation details and dataset details can be found in the supplementary. + +# 4.1. Results + +To assess the impact of the GenDS dataset, we first trained NAFNet [10], PromptIR [35], the Swin model (Sec. 3.3), DA-CLIP [32] and Diff-Plugin [29] solely on existing restoration datasets, without incorporating our synthetic data. We then evaluated their performance on both within-distribution and out-of-distribution (OoD) test sets. Subsequently, we retrained the same models using the GenDS dataset and evaluated the performance. Additionally, we compared their performance against state-of-the-art (SOTA) AIOR models, namely, DiffUIR [62], Diff-Plugin [29] (pre-trained model), InstructIR [13] and AutoDIR [18]. + +Quantitative comparisons. Due to space constraints, we present quantitative comparisons using only the LPIPS and FID metrics (following [29]). Table 2 presents these scores for OoD test sets across all six degradations. We observe that PromptIR, NAFNet, the Swin model, DA-CLIP and Diff-Plugin exhibit significant improvements in OoD performance when trained on the GenDS dataset. Motion blur performance remains nearly the same even after training with the GenDS dataset. Since motion blur already contains sufficient real data with diverse scenes (see Fig. 2), introducing more synthetic data does not impact performance on real OoD samples. This highlights the importance of diverse high-quality data for generalizable AIOR. + +Furthermore, the results indicate that the synthetic data generated by GenDeg aids in bridging the domain gap with OoD samples. In certain instances, SOTA methods (upper portion of Table 2) outperform our models on specific OoD datasets (e.g., AutoDIR raindrop removal on RainDS). However, it is important to note that our models serve as simple baselines compared to the more complex SOTA architectures, and that SOTA methods do not consistently perform well for OoD datasets across degradations. Furthermore, SOTA architectures could further enhance their OoD performance by training with our GenDS dataset, as evidenced by the improvements observed for Diff-Plugin. + +Table 3 presents the mean within-distribution performance for each degradation. Interestingly, the performance remains almost identical even after training with our GenDS dataset. Moreover, the within-distribution performance shows substantial improvements for haze, lowlight and raindrop degradations. This improvement is likely due to the GenDS dataset effectively addressing the limited scene diversity present in existing datasets for these degradations. Detailed quantitative results (including PSNR and SSIM metrics) are available in the supplementary material. + +Qualitative comparisons. Fig. 5 shows qualitative results from one OoD test set per degradation for three top-performing models (PromptIR, NAFNet and the Swin model). Comparisons with SOTA are in the supplementary. Models trained with GenDS dataset consistently yield the best results. Notably, the enhanced images often contain richer colors than the ground truth (see first row), which can lower PSNR and SSIM scores. Thus, LPIPS and FID + +Table 3. Quantitative comparisons of mean LPIPS and FID scores (lower is better) across within-distribution datasets for each degradation. Comparisons are shown for PromptIR [35], NAFNet [10], Swin transformer, DA-CLIP [32] and Diff-Plugin [29] models trained with and without our GenDS dataset, along with SOTA models. Diff-Plugin# is the publicly available pre-trained model. + +
MethodHazeRainSnowMotion BlurRaindropLow-light
DiffUIR0.329/141.460.175/53.530.305/23.670.182/42.89-0.551/260.26
Diff-Plugin#0.351/154.120.205/47.100.227/26.860.218/50.57-0.464/180.67
InstructIR0.355/158.810.144/35.03-0.148/31.86-0.402/157.74
AutoDIR0.306/136.270.139/38.12-0.161/33.340.195/68.090.420/155.14
PromptIR0.309/141.050.097/32.610.100/18.340.163/35.790.189/84.480.421/189.87
PromptIR GenDS0.210/112.540.080/27.950.091/16.190.171/34.930.188/74.650.354/168.59
NAFNet0.190/118.220.074/21.840.067/8.200.136/28.720.085/39.910.349/172.36
NAFNet GenDS0.171/104.430.077/22.130.069/8.560.136/29.310.069/29.920.316/148.65
Swin0.244/121.920.092/24.500.080/10.800.194/40.690.097/47.090.420/187.65
Swin GenDS0.182/105.2420.090/24.480.083/11.440.189/42.170.092/39.630.368/166.13
DA-CLIP0.344/147.150.114/33.320.128/43.610.198/50.030.101/40.820.538/208.47
DA-CLIP GenDS0.267/109.110.102/30.500.072/26.480.140/37.820.094/36.030.434/182.16
Diff-Plugin0.340/143.660.165/39.710.178/18.080.147/37.680.185/60.640.466/167.63
Diff-Plugin GenDS0.302/128.010.164/39.220.176/17.700.142/35.990.133/42.520.456/156.18
+ +![](images/c261a0723fa926e6c6002c91b7881c85138be0356a9fa3fc26f59552a2632042.jpg) +Figure 5. Qualitative comparisons of image restoration models trained with and without our GenDS dataset. The suffix GD represents training with the GenDS dataset. Zoomed-in patches are provided for viewing fine details. + +scores are more reliable for testing the OoD performance. These results demonstrate that the synthetic data generated by GenDeg enhances the generalization of AIOR models. + +# 4.2. Analysis + +In this section, we use our generated synthetic data to conduct various insightful analyses. + +Synthetic Data Scaling. We analyze the impact of progressively adding synthetic data generated by GenDeg to existing real data on out-of-distribution (OoD) performance, utilizing the Swin transformer model. Fig. 6 illustrates the variation in mean OoD LPIPS and FID scores with increasing synthetic data. There is substantial OoD performance improvements with the addition of up to $100\mathrm{k}$ syn + +![](images/24f65c4a03d6f5085b787ab4ae3304d35c5456c0011e6ecb8befaf76909f7ebe.jpg) +Figure 6. Effect of scaling number of GenDeg samples augmented with real data on OoD performance (LPIPS and FID). + +thetic samples, after which the performance improvement is reduced. Due to limited computational resources, we were unable to scale the synthetic dataset beyond 500k samples. + +Generated degradation diversity. GenDeg-generated data significantly aids in improving OoD performance of restoration models. This improvement is primarily due to the enhanced scene diversity (as shown in Fig. 2) in our dataset and the variety of degradation patterns produced by GenDeg. To illustrate the diversity in degradation patterns, we utilize degradation-aware CLIP (DA-CLIP [32]), a robust CLIP model trained to extract degradation-specific features from images. Fig. 3 presents a t-SNE visualization of the DA-CLIP degradation embeddings obtained from hazy samples in existing training datasets, our GenDS dataset, and the OoD test sets. The visualization reveals a clear gap between features of the training dataset and OoD test sets. This indicates that the degradation patterns in these datasets are different, hindering generalization. GenDS dataset bridges this gap by introducing numerous samples that resemble those in the OoD test sets, thereby enhancing generalization. Note that GenDeg was never trained on the OoD test sets. Furthermore, the t-SNE plot showcases the diversity of degradation patterns produced by our model, as evidenced by our samples spanning a wide area. + +Domain gap with real data. We examine the domain gap between existing datasets and GenDeg-generated data by training the Swin model exclusively on GenDeg synthesized data. Table 4 provides the mean LPIPS and FID scores for both within-distribution and OoD testing across all degradations. Training solely with GenDeg data lowers within-distribution performance compared to training on existing datasets due to the domain gap caused by factors such as alignment discrepancies between diffusion-generated samples and corresponding clean samples. However, utilizing both existing and GenDeg synthesized data, i.e., GenDS dataset, enhances performance as the restoration model benefits from diverse degradation patterns and scenes while maintaining performance on existing data. + +Table 4. LPIPS/FID scores for analyzing the performance difference between training on solely existing data, solely GenDeg data, and both existing and GenDeg data (GenDS dataset). + +
SettingExisting dataGenDeg dataGenDS data
Within-distribution0.1879/72.100.2358/81.080.1669/64.84
OoD0.211/59.360.207/61.710.1694/47.99
+ +Image, $\sigma :0.12$ $\mu :0.1$ $\mu :0.2$ $\mu :0.27$ + +![](images/26a7019e1b05229581f3ffd3a28df81af068a5298eb41620e180525356cee879.jpg) + +Image, $\mu :0.15$ $\sigma :0.15$ $\sigma :0.17$ $\sigma :0.2$ + +![](images/917a9824473871896f8e4bf9923f077fd2ea282d7af03eb9563dbbb581736be3.jpg) +Figure 7. Effect of varying $\mu$ and $\sigma$ in our GenDeg framework for the degradation of haze. + +![](images/6e37e4bff60b475e86e5d6b5d6845ef8e231aca56d03a792bd8c395bee6a933d.jpg) + +![](images/04719e1ea5371bb060f237e29e1cf5769df683e1988d3a03d867de9a89b5578e.jpg) + +The model trained only on existing datasets performs worse on OoD data than within-distribution. Training solely on GenDeg data improves OoD performance demonstrating that the diversity in scenes and degradation patterns enhances generalization. Nevertheless, the best performance is achieved when training on the GenDS dataset. + +Effect of $\mu$ and $\sigma$ . GenDeg enables control over the intensity and variations in the generated degradations, thereby enhancing diversity. In Fig. 7, we illustrate the effect of varying $\mu$ and $\sigma$ on two images for the synthesized degradation of haze. When $\mu$ is increased, the intensity of haze in the image expectedly increases. $\sigma$ controls the variation of haze in the image. For $\sigma = 0.15$ , the non-homogenous haze (similar to NH-Haze [2]) is spread throughout the image. As $\sigma$ increases, the spread of haze becomes more localized with higher intensity as seen from the figure. + +# 5. Conclusions + +In this paper, we addressed the important problem of generalization in All-In-One Restoration (AIOR) models. Toward this aim, we introduced GenDeg, a novel diffusion model-based framework for synthesizing diverse degradations on clean images, offering fine-grained control over degradation characteristics. Utilizing GenDeg, we generated over 550k degraded samples encompassing a wide range of scenes and degradations. Training AIOR models with both existing and GenDeg data yielded significant improvements in out-of-distribution performance. Our work suggests a promising research direction for addressing generalization challenges in AIOR, aiding in the development of more robust restoration models. + +# Acknowledgments + +This work is supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0076. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. 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GenFusion introduces a reconstruction-driven generative model to enable artifact-free 3D asset generation and view synthesis for both view interpolation and extrapolation. + +![](images/58e9a611600b5fedc1125e27078b96df4941414b3b97e234b1d5734a06b3eeae.jpg) + +![](images/a4ba9a74185910edef6d1ef8881d31def3e0dee8ce84eafdd98af3fc93bf1324.jpg) + +# Abstract + +Recently, 3D reconstruction and generation have demonstrated impressive novel view synthesis results, achieving high fidelity and efficiency. However, a notable conditioning gap can be observed between these two fields, e.g., scalable 3D scene reconstruction often requires densely captured views, whereas 3D generation typically relies on a single or no input view, which significantly limits their applications. We found that the source of this phenomenon lies in the misalignment between 3D constraints and generative priors. To address this problem, we propose a reconstruction-driven video diffusion model that learns to condition video frames on artifact-prone RGB-D renderings. Moreover, we propose a cyclical fusion pipeline that iteratively adds restoration frames from the generative model to the training set, enabling progressive expansion and addressing the viewpoint saturation limitations seen in previous reconstruction and generation pipelines. Our evaluation, including view synthesis from sparse view and masked input, validates the effectiveness of our approach. + +# 1. Introduction + +Generating 3D assets is a fundamental task in computer vision and computer graphics, with broad applications in AR/VR, autonomous driving and robotics. Recent advances in Neural Radiance Fields (NeRF [36], Mildenhall et al. + +in 2020) and Gaussian Splatting (GS [27], Kerbl et al. in 2023) have enabled high-fidelity 3D scene reconstruction and novel view synthesis. They employ MLP or Gaussian primitives to represent scenes and optimize 3D representation through photometric loss. However, this line of work inherits a key limitation: faithful reconstruction relies on abundant viewpoint coverage; under-observed regions or viewpoints may lead to significant artifacts or missing content. + +This is primarily because reconstructing NeRFs or GSs from multi-view images is inherently underconstrained, as an infinite number of photo-consistent explanations may exist for the input images [40, 63]. Consequently, reconstruction models tend to generate "floaters" or "background collapse" artifacts to fake view-dependent effects, even when supplied with dense and well-captured high-quality images [46]. This observation has motivated a series of regularization techniques to constrain neural field training, including sparsity regularizers [22, 56], smoothness losses [37, 55, 62] and monocular geometric cues [61]. For example, ReconFusion [48] regularizes a NeRF-based 3D reconstruction pipeline by introducing a sample loss between novel random camera poses and images predicted by a PixelNeRF-style image diffusion model, yielding significant performance improvements over previous NeRF reconstruction methods in sparse setting. In contrast, feedforward reconstruction methods [5, 6, 10, 14, 57, 60] learn + +inductive biases directly from the dataset. While recent advances enable 3D reconstruction from as few as a single image, existing feedforward reconstruction methods exhibit performance saturation when processing more than 4-8 images. This limitation arises primarily from the architectural constraints of conventional feedforward networks in effectively aggregating and utilizing information from multiple viewpoints. + +Meanwhile, generative methods have demonstrated the potential of obtaining 3D assets without multi-view capture. Leveraging large-scale datasets and scalable architectures, models like Stable Diffusion (SD) have achieved remarkable progress in image and video generation [3, 21, 23]. Recent work has applied these approaches to generate 3D assets. For example, DreamFusion [39] introduces Score Distillation Sampling (SDS) to perform text-to-3D synthesis using a pre-trained 2D text-to-image diffusion model, while another line of research [4, 30, 59] explores single-view scene extrapolation by progressively in/outpainting layered depth image. + +Despite these advances in 3D reconstruction and generation, a notable conditioning gap remains: scalable 3D reconstruction typically requires dense view coverage, whereas generation methods often operate with single or even no input view. Our paper explores how 3D reconstruction and generation can complement each other in a scalable manner, relaxing the constraints on the number of input views. + +We introduce GenFusion, a novel reconstruction method that leverages video generative model to achieve artifact-free 3D scene reconstruction and content expansion along novel trajectories by leveraging the proposed reconstruction pipeline, as illustrated in Figure 2. The core of our approach is a simple and scalable reconstruction-driven video generation architecture that predicts realistic video from artifact-prone renderings. Specifically, we first fine-tune Dynam-iCrafter [51] using RGB-D videos reconstructed from a large-scale, real-world scene-level video dataset [34]. We patchify the capture videos into patches, then randomly select a patch sequence to perform 3D scene reconstruction, rendering full-frame RGB-D videos as input to our video diffusion model, which is subsequently supervised by the original video capture and its monocular depth. Our key insight is that masked 3D reconstruction enables flexible pre-training of video models. As shown in Figure 3, masking $75\%$ of the input pixels during 3D reconstruction produces artifacts and missing regions sharing similar artifact patterns with far-field viewpoint rendering. The resulting artifact-prone video is encoded into latent space, with diffusion guided by a scene description token processed by a CLIP model on a randomly sampled frame. In addition, the baseline video diffusion model, conditioned only on text and RGB, lacks sequence input handling and geometry + +constraints for view consistency. To address this, we embed input views as latent sequences and incorporate depth by replacing the RGB VAE with an RGB-D VAE. Once trained, we introduce a cyclic reconstruction-generation fusion scheme for scalable 3D scene generation with artifact correction. + +Our GenFusion learns very high-capacity models that generalize well, we make the following contributions: + +- We introduce a reconstruction-driven video diffusion model that efficiently repairs reconstruction artifacts and generates new content in invisible regions. +- We design a masked 3D reconstruction for artifact-GT video pair generation, serving as a new novel view synthesis evaluation protocol for far-field viewpoints. +- Experiments on challenging benchmark datasets [1, 28, 34] demonstrate the effectiveness of GenFusion in synthesizing views distant from the training views. +- Our approach to bridging 3D reconstruction and generation through videos is principled and straightforward, picking the best of these two fields. + +# 2. Related Work + +Regularization Techniques: Optimizing 3D scene representations, e.g., NeRF [36] and 3DGS [27], from 2D images inherently involves an ill-posed inverse problem, where multiple solutions may exist for a given set of observations. To address these challenges, various techniques have been proposed to constrain the optimization of scene representations. In general, unsupervised regularization techniques are based on the assumption that the 3D representation should be sparse [22, 56], smooth [37, 55, 62], low rank [7-9]; rendering weights to be compact [1]; or geometry/texture to be consistent with nearby views in image space [15, 16, 18]. In addition to the multitude of regularization strategies available, many optimization techniques have been proposed to enhance training procedures. For example, gradient scaling [38] is applied for NeRF to address the issue of high-magnitude gradients in regions close to the camera, where more points are sampled, often leading to artifacts known as floaters. One of the most impactful approaches is the "coarse-to-fine" training [31, 32], which modulates the frequency band of positional encodings or hash grid resolution. Another line of research leverages pseudo-observations by using off-the-shelf models to predict cues that enhance reconstruction quality, such as sparse point clouds [17] and monocular depth/normal maps [61]. These approaches are also employed in 3DGS representations [29, 64]. Recently, combining generation models to generate novel views as regularization has proved to be effective in reconstruction objects [54] and scene [35, 48]. Our work aligns closely with ReconFusion [48] and the concurrent 3DGS-Enhancer [35], both of which utilize genera + +![](images/77626ef12fce8a7c0fd56b0ef9ddc254b88a7cb7dd505a78e42467fcbf01b349.jpg) +Video Diffusion Training +Figure 2. GenFusion pipeline. Our approach contains two stages: video diffusion pre-training (left) and zero-shot generalization (right). In pre-training, we first fine-tune DynamiCrafter [51] on RGB-D videos from a large-scale real-world scene video dataset [34]. Captured videos are patched, and a random patch sequence is selected for 3D scene reconstruction, rendering full-frame RGB-D videos as input to our video diffusion model, supervised by the original video capture and its monocular depth. During generalization, we treat reconstruction and generation as a cyclical process, iteratively adding restoration frames from the generative model to the training set for artifact removal and scene completion. + +![](images/f8a93bfbe62bcf8cda76a7737c28b6c250b00ebd307ede0d894095aa31ed7149.jpg) +Zero-shot Generalization + +tive priors to guide the optimization of 3D representations. Despite these methods achieve impressive view interpolation results in sparse-view scenarios, they still struggle with rendering trajectories that deviate significantly from the input views. + +Feed-forward 3D Reconstruction: In contrast to the per-scene optimization required by neural fields, recent research has explored feed-forward architectures capable of regressing 3D scene representations from a sparse set of input images. These methods learn 3D representations from input images and directly predict novel views in a feed-forward manner. PixelNeRF [58] predicts neural radiance representations from input images, using a convolutional network for efficient feature extraction. MVSNeRF [6] pioneers the paradigm of leveraging cost volumes to regress realistic images from novel viewpoints. Subsequent works [12, 26, 33, 52] further improve performance through enhanced feature matching architectures. In the context of 3DGS, pixelSplat [5] directly regresses scene-level 3D representations from paired images, incorporating an epipolar transformer module to effectively capture view-dependent geometric correspondences. MVSplat [14] builds a cost volume representation to learn cross-view feature similarity, achieving high-quality scene generation with improved efficiency. Recently, DepthSplat [53] further boosts the performance using a pre-train multi-view depth estimator, and Long-LRM [65] utilizes Mamba2 blocks to handle many input views. To handle single view inputs, Flash3D [44] extend monocular depth estimation to 3D shape and appear + +ance reconstruction. Recently, SplatFormer [13] proposes a learning-based model to refine Gaussian splats, enabling out-of-distribution novel-view synthesis. However, existing feed-forward methods are limited to a small number of views - typically fewer than 10 - which significantly restricts their application. + +View-Conditioned Generation: Generative models have emerged as a promising solution to synthesize plausible content for regions without observations. Thanks to their success in image generation, diffusion models are widely used for multi-view synthesis. Early work 3DiM [47] trains a pose-conditional image-to-image diffusion model for object-centric novel view synthesis. Follow-up research Zero-1-to-3 [20] advanced this approach by finetuning large-scale pre-trained diffusion models on synthetic datasets. SSDNeRF [11] jointly optimize diffusion and NeRF auto-decoder to synthesize novel views for object. Recently, ZeroNVS [41] and CAT3D [19] extended the paradigm by training diffusion models with camera pose and multi-view image conditioning. Nevertheless, relying solely on 2D features proves insufficient for maintaining 3D consistency across generated views. Several works [43, 50] inject 3D information into diffusion models for improved geometric understanding. For instance, ViewCrafter [60] explicitly utilizes 3D information from point clouds and expands it iteratively, facilitating consistent interpolation between two views. To enable generating long sequences of 3D scenes from a single input image, InfiniteNatureZero [30] and following work [4, 45, 59] explore single + +view scene extrapolation by progressively in/outpainting layered depth images predicted by a monocular estimator. While these generative methods achieve visually appealing 3D asset generation, their reconstruction quality and view coverage, particularly at scene scale, remains far from that of 3D scenes reconstructed from densely captured multiview data. + +# 3. GenFusion + +Our goal is to construct artifact-free 3D scenes with content augmentation given conditioning views $\{\mathbf{I}_i\} (i > = 1)$ . The core idea to align 3D reconstruction and generation through video renderings. Specifically, we propose a cyclic fusion approach where 3D reconstruction and generation benefit each other in a virtuous cycle: during the reconstruction process, we iteratively leverage information from the generative model to improve reconstruction quality; meanwhile, more accurate reconstruction results help the generative model produce more realistic and consistent content. This bidirectional enhancement mechanism creates a positive feedback loop. + +In the pre-training stage, we aim to train a model that learns from large-scale scenes, which then serves as guidance for optimizing general ill-posed 3D lifting tasks, such as reconstructing 3D from sparse views. We use a video diffusion model as guidance, pre-trained on video captures and their artifact-prone renderings of 3D reconstructions. Specifically, we train a generative model $G_{\phi}$ by maximizing the expected log-likelihood of generating the complete image given the reconstruction from a masked input: + +$$ +\arg \max _ {\phi} \mathbb {E} \left[ \log p _ {\phi} \left(I \mid R _ {\theta} (\tilde {I})\right) \right] \tag {1} +$$ + +where $R_{\theta}$ denotes a reconstruction and rendering function (e.g., NeRF or 3DGS) and $\tilde{I}$ denotes the masked version of target image $I$ . To make the generation process 3D aware, our video diffusion model learns to capture the underlying distribution of images by conditioning on artifact-prone rendering video $R_{\theta}(\tilde{I})$ in our case. + +With the video diffusion model, we propose optimizing the 3D scene representation, $\theta$ , guided by both input image conditions and generated video for a new scene. Specifically, we maximize the similarity between the novel view videos rendered from 3D representation and the videos generated from our pre-train diffusion model, therefore the gradient of 3D representation is propagated from the photometric loss: + +$$ +\arg \min _ {\theta} \mathbb {E} \left[ \left| G \phi (\hat {I} _ {k + 1} \mid R _ {\theta} (\tilde {I} _ {k})) - R _ {\theta} (\hat {I} _ {k + 1}) \right| _ {2} \right] \tag {2} +$$ + +where $k$ denotes the iteration index. + +In the following sections, we first introduce our reconstruction-driven generation architecture, i.e. + +![](images/0ec8d7e63ab548a37ee589b90fb8eb77c4247066e186921eb83b55dfb76c1cbf.jpg) +(a) Artifacts in GS reconstruction + +![](images/e6139527273d74168c3df76774200cc9d6a3553a348ef332f8dcb56dd8fe9420.jpg) +(b) Masked reconstruction +Figure 3. Artifact-GT video pair generation using masked reconstruction. a) current SOTA Gaussian Splitting methods render accurately near training views but produce artifacts for distant views due to limited angular supervision, like the red trajectory. b) we propose a masked reconstruction scheme to replicate such artifact patterns for training video diffusion models by masking $75\%$ of pixels during 3D reconstruction and re-rendering the scene along the original trajectory, including the masked pixels. + +$G_{\phi}(I|R_{\theta}(\tilde{I}))$ , in Sec. 3.1. Next, we detail our cyclic generation and reconstruction fusion process in Sec. 3.2. + +# 3.1. Reconstruction-driven Generation + +We generate view-consistent video by conditioning the current fragment's generation on previous corrupted reconstructions. To generate corrupted reconstructions, we propose a masked 3D reconstruction approach for generating training data, along with a new video diffusion model that facilitates 3D-aware generation and regularization. + +Masked 3D Reconstruction. We now discuss how to learn novel view generalization capability in a reconstruction paradigm from open-world large-scale videos. Given video captures of a scene, a straightforward approach is to downsample frames at uniform intervals or split the input sequence at the midpoint into train/test segments for scene reconstruction, then render the reconstructed scene from the testing camera viewpoints to generate artifact-prone data. These rendered sequences and original video captures then serve as input and output pairs for video diffusion model training. However, we observe that these sampling schemes limit models to either view interpolation or pure generation. Specifically, scenes are often fully covered by sampled views, with target views located adjacent to these, while the alternative approach often leaves most content unseen in the training segment. Our work aims to learn regularization and generate new content in trajectories that deviate significantly far from the capture trajectories. + +To this end, we propose a masked 3D reconstruction technique to obtain corrupted 3D scenes from observations + +![](images/a6303b4c821141fc09e9ee26d13e02cef6074fb8bdaff2f893d83af7f18c81f2.jpg) +Figure 4. Reconstruction-driven Video Generation. Our video diffusion model is able to generate realistic RGB-D video from artifact-prone RGB-D renderings, which is then used as photometric guidance in our cyclic fusion period. + +across both spatial and temporal dimensions, then render images for the full input sequence to generate the training dataset. In specific, we divide input image captures into 4 regular non-overlapping patches, i.e. top-left, top-right, bottom-left and bottom-right, as shown in Figure 3. Then we sample the top-left or bottom-right patch region and mask out (i.e., remove) the remaining three for each scene. The sampled patch sequence is used to conduct 3D reconstruction using the standard approaches, i.e. 2D Gaussian Splatting (2DGS) [25] in this paper. Note that the mask is applied per scene rather than per view, forcing the reconstruction process to have limited view coverage. In practice, since we use open-world large-scale video sequence captures I for training, which further increases sparsity - views are dense only on the trajectory but extremely sparse in angle coverage - unlike standard multi-view datasets such as Mip-NeRF 360 [1]. + +With masked reconstruction, we render full-view videos along the same camera poses as the input to form real capture and reconstruction rendering pairs for our video diffusion model training. Our insight is that reconstructing from masked images simulates a narrower field-of-view camera, requiring that context outside the mask be inferred from views deviating from the current viewpoint, which promotes view extrapolation. Moreover, rendering to full view introduces unconstrained regions with extensive black backgrounds, facilitating content outpainting. + +# Video Diffusion. + +In essence, we build our video generation model upon the foundation of pre-trained DynamiCrafter [51] - an image-to-animation model - and adapt the model to reconstruction-related video restoration tasks. + +More specifically, we enhance frame consistency by incorporating geometric information into the generation pro + +cess. This is achieved by replacing the VAE in the baseline model with a pre-trained RGB-D VAE, where encoder and decoded are denoted as $\mathcal{E}$ and $\mathcal{D}$ respectively. It allows depth to be integrated without altering the diffusion architecture. In the training process, the ground truth RGBD video $I_{RGB - D}$ are encoded into latent space $z\coloneqq \mathcal{E}(I_{RGB - D})$ , which we add noise in different timestep $t$ and obtain $z_{t}$ . To guide the generation process under reconstruction result, We provide two conditions $c$ . The artifact-prone RGB-D video $I_{RGB - D}^{\prime}$ is encoded and concatenated with per-frame initial noise to support sequence conditioning. This allows rich visual details from the rendered videos to condition the generation process effectively. Additionally, we select the input view closest to the rendering trajectory and embed its ground-truth image into the CLIP feature space. This high-level conditioning provides global information about the scene content. Thus the video denoising network $\epsilon_{\theta}$ is optimized by: + +$$ +\mathcal {L} = \mathbb {E} _ {\mathcal {E} (x), c, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, t, c\right) \| _ {2} ^ {2} \right], \tag {3} +$$ + +The refined latent is subsequently decoded into the final RGB-D video through a pre-trained VAE decoder $\hat{V} = \mathcal{D}(z)$ [43]. + +# 3.2. Cyclic Fusion + +We build our fusion process upon the popular 2D Gaussian Splatting and use a number of 2D oriented planar Gaussian disks to represent 3D scenes. Gaussian disks are parameterized by center position $p \in \mathbb{R}^{3 \times 1}$ , opacity (scale) $\alpha \in [0,1]$ , two principal tangential vectors $\mathbf{t}_u$ and $\mathbf{t}_v$ for orientation, a calling vector $\mathbf{S} = (s_u, s_v)$ , and Spherical Harmonices (SH) coefficients. We refer the reader to the original paper for representation and splatting details [25]. In the follow- + +ing, we introduce how to initialize and progressively update the Gaussian primitives by fusing the 3D reconstruction and video diffusion output. + +Fusion. We follow the original 3DGS approach by reusing the calibration point cloud for initialization. We initialize Gaussians and their attributes, which are then updated end-to-end based on rendering losses. The optimization process operates as a reconstruction and generation cycle, supervising Gaussians with both input conditioning and novel generated views. More concretely, for every $K$ iteration, we begin with sample new trajectories and render RGB-D videos based on the current reconstruction. We feed these rendering sequences to our video diffusion model to generate artifact-free videos, which are then added to the supervision set, as shown in Figure 2. The cyclic process enables artifact correction in under-observed regions and generates new content for areas that are invisible within the input views. + +Among these, we find that novel trajectory sampling is the most critical component. To ensure comprehensive view and angle coverage, we employ two types of trajectories: view interpolation between neighboring input views and a spiral/spherical path generated across all input camera poses. + +Content Expansion. Large unobserved areas can appear as black or noisy pixels when the sampling trajectories are away from the input views. Although we use generation outputs as supervision for these regions, we found it challenging to split and clone new Gaussians [27] due to the absence of surrounding Gaussians. We solve this issue by adaptively adding new Gaussian points to the scene during optimization, using an unreliable depth-based mapping. Pixels are considered unreliable when + +$$ +T < \tau_ {T} \text {o r} | D - \hat {D} | > \tau_ {D} \tag {4} +$$ + +where $T$ is cumulative opacity, $D$ and $\hat{D}$ are rendered depth and aligned generated depth D respectively. $\tau_{T}$ and $\tau_{D}$ are hyperparameter thresholds. + +For these unreliable areas, we add new Gaussians by back-projecting the generated RGB-D points into 3D space, similar to the initialization stage. Note that for the newly added Gaussians, position and color values are directly obtained from the RGB-D video, while other attributes are initialized as in 2DGS. + +Loss function. During cyclic fusion, we freeze the video diffusion model and optimize the 3D representation end-to-end, using simple photometric losses between rendered RGB-D images and input (i.e. $\mathcal{L}_{\text {recon }}$ ) and generated views (i.e. $\mathcal{L}_{\text {gen }}$ ): + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c o n}} + \lambda \mathcal {L} _ {\text {g e n}} \tag {5} +$$ + +where $\mathcal{L}_{\text{recon}} = \lambda_{l_1} \cdot \mathcal{L}_{l1} + \lambda_{SSIM} \cdot \mathcal{L}_{SSIM} + \lambda_{mono} \cdot \mathcal{L}_{mono}$ , and the $\mathcal{L}_{mono}$ is a scale-invariant depth loss, as used in [61] that enforces consistency between our rendered rendered depth $\hat{D}$ and the monocular depth $D$ predicted by our video diffusion model. The generation loss $\mathcal{L}_{gen}$ shares components but is instead applied to generated images. + +To stabilize the optimization process, we use an Sinusoidal warm-up and annealing strategy for the generation loss weight $\lambda$ , which is defined as: + +$$ +\lambda (k) = 1. 0 \cdot \sin \left(\frac {k - K _ {\text {s t a r t}}}{K _ {\text {e n d}} - K _ {\text {s t a r t}}} \cdot \pi\right) \tag {6} +$$ + +where $k$ is the iteration, and $K_{\mathrm{start}}$ and $K_{\mathrm{end}}$ are the start and end iteration of the diffusion term. + +# 4. Experiments + +We begin with the experimental setup for training and evaluating our GenFusion. Next, we present our reconstruction-driven video diffusion model and compare it quantitatively/qualitatively with state-of-the-art methods for sparse-view 3D reconstruction and view synthesis. Finally, we demonstrate the generative capabilities of our method with scene completion. + +# 4.1. Experimental Setup + +Training set: We train our diffusion model on DL3DV10K [34], a large-scale dataset containing 10,510 videos, including 140 benchmark scenes. To prepare reconstruction-gt video pairs for diffusion model training, we optimize each scene for 7K steps using our masked 3D reconstruction scheme introduced in Section 3.1. The number of training views are uniformly downsampled to $1/4$ frames for each video to ensure sufficient sparsity, and we render the reconstructed scenes along the original trajectories at a resolution of $960 \times 540$ and augment the dataset with depth information using the current SOTA monocular depth estimator [24]. + +Evaluation Dataset: We evaluate our method on diverse scenes from three datasets, including 24 scenes from the DL3DV-Benchmark [34], 7 scenes from Tanks and Temples (TnT) [28], and 9 scenes from the Mip-NeRF360 [1] dataset, see supplement for details. + +Implementation Details: In this work, we adopt Dynami-Crafter [51] as the video diffusion backbone and fine-tune the model on artifact-GT RGB-D video pairs. The finetuning includes both coarse and fine stages: in the coarse stage, the video resolution is set to $16 \times 320 \times 512 \times 4$ with a latent space dimension of $16 \times 40 \times 64 \times 4$ . We train this stage for 30K steps with a learning rate of $1 \times 10^{-5}$ and a batch size of 2 on four H100 GPUs. The model is then finetuned to a higher resolution of $16 \times 512 \times 960 \times 4$ for another + +
MethodRGB VAERGB-D VAERGB-D VAERGB-D VAE
Frames16164816
Resolution512×320512×320512×320960×512
FID↓26.160725.400629.354522.5526
+ +Table 1. Analysis on reconstruction-driven video diffusion model. + +
PSNR ↑SSIM ↑LPIIS ↓
3-view6-view9-viewAvg.3-view6-view9-viewAvg.3-view6-view9-viewAvg.
Zip-NeRF [2]12.7713.6114.3013.560.2710.2840.3120.2890.7050.6630.6330.667
DiffusioNeRF [49]11.0512.5513.3712.320.1890.2550.2670.2370.7350.6920.6800.702
FreeNeRF [55]12.8713.3514.5913.600.2600.2830.3190.2870.7150.7170.6950.709
SimpleNeRF [42]13.2713.6715.1514.030.2830.3120.3540.3160.7410.7210.6760.713
ZeroNVS [41]14.4415.5115.9915.310.3160.3370.3500.3340.6800.6630.6550.666
ReconFusion [48]15.5016.9318.1916.870.3580.4010.4320.3970.5850.5440.5110.547
3DGS [27]13.0614.9616.7914.940.2510.3550.4470.3510.5760.5050.4460.509
2DGS [25]13.0715.0216.6714.920.2430.3380.4230.3350.5800.5060.4490.512
FSGS [62]14.1716.1217.9416.080.3180.4150.4920.4080.5780.5170.4680.521
GenFusion (Ours)15.2917.1618.3616.930.3690.4470.4960.4370.5850.5000.4650.517
+ +34K steps in the fine stage. To handle the RGB-D format, we use a frozen RGB-D VAE from LDM3D [43]. During inference, we apply DDIM sampling with 25 steps and set the classifier-free guidance scale to 3.2. + +For zero-shot generalization, we use 2DGS as the 3D representation and initialize with the COLMAP point cloud. In our experiments, views are masked and frames are downsampled; we filter and retain only the points visible from the training views for point cloud initialization. + +# 4.2. Video Generation + +In this paper, we introduce a reconstruction-driven video diffusion architecture that enables novel view regularization and content generation. We report the VAE design and its impact on video resolution in Table 1. Surprisingly, we find that our model fine-tuned with RGB-D VAE achieves a better FID score than the RGB VAE, even though the diffusion backbone was originally pre-trained on the RGB VAE latent space. Significant improvement can be observed when increasing the spatial resolution from $512 \times 320$ to $960 \times 512$ . We show the visualization results of our diffusion model in Figure 4, our video diffusion model effectively removes "floaters" from the input video while generating realistic content in black-pixel regions. + +# 4.3. View Interpolation + +Next, we evaluate our method in a view interpolation scenario where the target scene is fully covered by the input views, and testing views lie between these inputs—a common setup in prior regularization evaluations. We compare our method with previous regularization techniques on the Mip-NeRF 360 test set using 3, 6, and 9 input views, as + +![](images/31cf64e6e3fa054b8b21c3126339c93d42519344459f32e88234493a624830a9.jpg) +Figure 5. Qualitative comparison of novel view synthesis using sparse view input on Mip-NeRF360 scenes [1]. + +Table 2. Quantitative evaluation of sparse view 3D reconstruction methods on Mip-NeRF360 dataset. Our approach demonstrates strong performance across a variety of domains, surpassing baseline methods in most cases. We color each column as: best, second best, and third best. The NeRF baseline results above are taken from Reconfusion. + +
DL3DV 1/2 fps.TnT 1/2 fps.DL3DV 1/4 fps.TnT 1/4 fps.
PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
3DGS [27]17.220.7400.31415.950.6530.41416.900.7280.32114.750.6090.440
2DGS [25]16.560.7170.32315.460.6400.40916.020.6930.33614.380.5890.440
FSGS [62]18.250.7220.36216.720.6250.46517.830.7100.37016.040.6070.473
Ours20.470.7880.28417.450.6620.42720.010.7800.29216.290.6300.447
+ +Table 3. Quantitative comparison on DL3DV [34] and TnT [28] datasets. Each method is trained for 7,000 steps. Our method outperforms baselines by a significant margin. + +shown in Table 2. + +Our results demonstrate that our method achieves more realistic novel view synthesis than the 3DGS and 2DGS baselines, as well as recent FSGS, by a significant margin. It is worth noting that Gaussian Splatting is known to be more challenging to train than NeRF, especially in sparse view settings. We significantly narrow this gap, and, for the first time, show that Gaussian Splatting achieves performance comparable to state-of-the-art NeRF on the challenging Mip-NeRF360 dataset in sparse view settings.(see Table 2 and Figure 5). + +# 4.4. View Extrapolation + +Unlike sparse view reconstruction, our paper focuses on a more practical scenario: generating complete, artifact-free 3D scenes from video captures. In reality, video offers dense sampling along the trajectory but highly sparse viewpoint coverage. While video is easy to capture and calibrate, it's challenging for 3D reconstruction, even reconstruction with state-of-the-art reconstruction methods can easily overfit to training views and produce serious artifacts + +![](images/9c286058a67af75c4c8a0a4dfbfc996fe06115cf258ed2a2792790b2e0df7a11.jpg) +3DGS [27] +Figure 6. Qualitative comparison of novel view synthesis using masked input on DL3DV scenes [34]. Gaussian Splatting methods can easily overfit to training views, producing holes and needle-like artifacts when viewed from distant viewpoints. Our method effectively repairs these artifacts while augmenting invisible regions. + +![](images/5ea6027a08400dc894de1e22f9325cc900b31a759b77dc229aab02ca12a4a6d9.jpg) +2DGS [25] + +![](images/a8d3deef5dbefe4ef5ae0e61d49d4076acc296ae996d61e10dc93c571e0ebe48.jpg) +FSGS [64] + +![](images/487b666be0f3eb05f7706e59855b05496830054cc741f3da3d734a3b5634dca6.jpg) +Ours + +![](images/9152ea40024264087e3d275ba67316664ec3f113395e642a7afe24ee8f521380.jpg) +GT + +for the viewpoints that are far away from the training views, see Figure 3. Therefore, we care about the novel view synthesis quality from the far field. + +To this end, we propose a new evaluation protocol and reuse the masked reconstruction to mime the far-field rendering while preserving the reference, as introduced in Section 3.1. Specifically, we downsample the video sequence at different time ratios for the train/test split (e.g., $1/2$ and $1/4$ in Table 3) and select a patch covering about $25\%$ of the pixels in the training viewpoint for reconstruction, while evaluating on the full field of view of test viewpoints. Note that fixing the path location can result in many invisible and black regions, leading to bias in our generative methods, where the baselines may have significant errors in these areas. To ensure a reasonable comparison, we assign a trajectory to the masking path to provide more complete content coverage, see supplementary video. + +Table 3 and Figure 6 show quantitative and qualitative results comparing our method with baselines on the DL3DV-benchmark and TnT scenes. GenFusion achieves significantly better rendering quality than the baselines, thanks to the strong prior from the diffusion model. It effec + +tively removes needle-like artifacts and augments realistic 3D content for the invisible regions. + +Scene Completion. Furthermore, GenFusion not only provides content augmentation at the 3D scene boundary but also achieves scene-level completion, as shown in Figure 1. Please refer to our webpage for more results. + +# 5. Discussion + +We have presented GenFusion, a novel model for artifact-free 3D asset generation. First, we adapt an existing well-trained 2D video diffusion model to drive a powerful 3D guidance with minimal modifications. Second, cyclical fusion enables scalable and robust 3D lifting, efficiently closing the loop between 3D reconstruction and generation through video synthesis. Several limitations are evident: our method requiring additional denoising steps and slightly increasing training time (about 40 minutes per scene). Additionally, filling large invisible regions can cause blurriness due to inconsistency between video fragments. Modeling and addressing this inconsistency in the fusion module will be a key step toward achieving the next level of quality. + +Acknowledgements: This work was supported by the Westlake Education Foundation, supported by the Natural Science Foundation of Zhejiang province, China (No. QKWL25F0301), by the ERC Starting Grant LEGO-3D (850533), by the DFG EXC number 2064/1 - project number 390727645. + +# References + +[1] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Mip-nerf 360: Unbounded anti-aliased neural radiance fields. In Proc. IEEE Conf. on Computer Vision and Pattern Recognition (CVPR), 2022. 2, 5, 6, 7 +[2] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. Srinivasan, and Peter Hedman. Zip-nerf: Anti-aliased grid-based neural radiance fields. 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Long-lrm: Long-sequence large reconstruction model for wide-coverage gaussian splats. arXiv preprint 2410.12781, 2024. 3 \ No newline at end of file diff --git a/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/images.zip b/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..8a84cdb5547078a5662658d042f25c052704cdc5 --- /dev/null +++ b/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:f041e85d7961c2efc8b42b62d16190823b02ca3e315a0d916c3c98485b30f195 +size 788379 diff --git a/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/layout.json b/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..6b6ab39d1ceaff5f3da4d7d188e42b8a807e7cfd --- /dev/null +++ b/CVPR/2025/GenFusion_ Closing the Loop between Reconstruction and Generation via Videos/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:a41cbc1e29f969bf79806b8f5128f2ff62f1185693ca0c700cce2a2e4986f0c1 +size 381461 diff --git a/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_content_list.json b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..e5c1155fd58fb3f23b36557750ef7371e2cc02f9 --- /dev/null +++ b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:444a6b6b3e77877f37b83aac47141346bb6e0281548c7ffcbb18bca233716605 +size 75677 diff --git a/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_model.json b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_model.json new file mode 100644 index 0000000000000000000000000000000000000000..a41be354305e22ebee783f665c85917274e466bb --- /dev/null +++ b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:1f83b2dd0fef82ac7a2b93c33f893f9138a58bdfba4dc5157610e27b39cb0f53 +size 95485 diff --git a/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_origin.pdf b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..ae45b18e54a12985fed6eedfaf62b6bf20fe58bf --- /dev/null +++ b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/33065446-96bd-487f-842a-0ad7ebde7571_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5eb675935cf104c78569a393b30d8ec33326bb17c1c49cbbeb5523219f295ee6 +size 3850681 diff --git a/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/full.md b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/full.md new file mode 100644 index 0000000000000000000000000000000000000000..e577f5b3283a8bb2d57919f7f539af7cbb4bce87 --- /dev/null +++ b/CVPR/2025/GenPC_ Zero-shot Point Cloud Completion via 3D Generative Priors/full.md @@ -0,0 +1,281 @@ +# GenPC: Zero-shot Point Cloud Completion via 3D Generative Priors + +An Li† Zhe Zhu† Mingqiang Wei‡ Nanjing University of Aeronautics and Astronautics + +{lian, zhuzhe0619, mqwei}@nuaa.edu.cn* + +# Abstract + +Existing point cloud completion methods, which typically depend on predefined synthetic training datasets, encounter significant challenges when applied to out-of-distribution, real-world scans. To overcome this limitation, we introduce a zero-shot completion framework, termed GenPC, designed to reconstruct high-quality real-world scans by leveraging explicit 3D generative priors. Our key insight is that recent feed-forward 3D generative models, trained on extensive internet-scale data, have demonstrated the ability to perform 3D generation from single-view images in a zero-shot setting. To harness this for completion, we first develop a Depth Prompting module that links partial point clouds with image-to-3D generative models by leveraging depth images as a stepping stone. To retain the original partial structure in the final results, we design the Geometric Preserving Fusion module that aligns the generated shape with input by adaptively adjusting its pose and scale. Extensive experiments on widely used benchmarks validate the superiority and generalizability of our approach, bringing us a step closer to robust real-world scan completion. Our code is available at https://github.com/liannuaa/GenPC. + +# 1. Introduction + +Point clouds, as an essential form of 3D representation, are widely used in various applications. However, due to factors such as self-occlusion, camera viewpoint limitations, and sensor resolution, the acquired point clouds are often incomplete. This issue significantly hinders downstream tasks. Therefore, developing effective and robust methods for completing real-world partial point clouds is crucial for achieving a comprehensive understanding of the real world. + +In recent years, numerous deep learning-based point cloud completion methods [18, 40, 45, 47-49, 55] have shown remarkable success. These approaches utilize carefully designed neural networks to extract shape patterns from + +![](images/8cebc50b1fcf759fd32dc7144ec1075ed34979684af2839a34d0bf2e14f75504.jpg) + +![](images/d07657684eeedc27924e359dba48eeb87ce379e79c1793826197ddd3a7003aa7.jpg) +Figure 1. Difference between our GenPC with previous zero-shot point cloud completion method [19]. (a) SDS-Complete [19] uses the SDS loss to directly extract prior knowledge from a 2D diffusion model, featuring time-consuming optimization and suboptimal completion results. (b) The proposed GenPC leverages explicit priors provided by a 3D generative model, achieving improved completion quality with significantly reduced inference time. + +input point clouds, enabling them to generate detailed geometric structures to complete missing portions of the point cloud. Although these techniques perform well on trained or similar categories, they rely on labeled 3D training data and exhibit limited generalization to categories unseen during training. Moreover, constrained by domain gaps between synthetic training data and real-world scans, these models tend to perform poorly when applied to downstream tasks. + +With the impressive zero-shot generation capabilities of pre-trained 2D diffusion models [31], numerous studies [24, 27, 33] have emerged that utilize these models for 3D generation tasks. Enlightened by these successes, sdscomeplete [19] first utilized 2D priors for zero-shot shape completion. This method fits the input partial point cloud surface using Signed Distance Functions (SDF) and leverages Score Distillation Sampling (SDS) [27] to extract 2D diffusion priors for completion. Later, Huang et al. [17] proposed a similar SDS-based framework, but used 3D Gaussian splatt ing [21] to initialize the partial point cloud as 3D Gaussians. Although these methods demonstrate improved zero-shot completion capabilities compared to training-based counterparts, they are time-consuming, as they require training a radiance field from scratch for each incomplete point cloud. + +![](images/a971c585b243cdbf8747ded4469ae7d174b538df321c186983dcae28a871c9bc.jpg) +Figure 2. The architecture of GenPC. The Depth Prompting module first prompts the depth-guided 2D generative model with the partial input and generates an RGB image, which is fed into an image-to-3D generative model, producing a 3D shape. The Geometric Preserving Fusion module then integrates the generated shape with the partial point cloud. + +Additionally, SDS loss often leads to coarse geometric details, limiting their reconstructing quality. + +Recently, scalable network architectures and large-scale 3D datasets have propelled the success of feed-forward 3D generative models [15, 16, 43]. Once trained, these models achieve impressive zero-shot generation quality within seconds. This raises an intriguing question: "Can we leverage this 3D generative capability for point cloud completion?" To answer it, we introduce a novel zero-shot point cloud completion framework, GenPC. Unlike previous 2D diffusion-based approaches [17, 19], GenPC utilizes explicit 3D priors from an image-to-3D generative model to enhance zero-shot completion quality, significantly improving inference speed. + +As illustrated in Figure 2. To leverage the powerful zero-shot generation capabilities of the image-to-3D generative model, we first need an image input. To address the issue of partial point clouds not directly providing image input for these models, we introduce a Depth Prompting module. This module estimates the scanning viewpoint of the partial point cloud and extracts depth, effectively bridging the modality gap between the point cloud and the generative model. After generating the 3D shape, a significant issue arises: the generated 3D shape may differ from the input partial point cloud in terms of scale, pose, and shape. To align it with the input point cloud and retain the original geometric structure, we introduce the Geometric Preserving Fusion module. This module first dynamically adjusts the scale and pose using a scaling factor at both geometric and semantic levels. In addition, we can further refine the point cloud using the SDS loss, minimizing shape detail discrepancies caused by multi-stage error accumulation. By leveraging explicit geometric priors offered by the 3D generative model, our approach avoids the need for optimization from scratch, enabling faster inference and superior completion quality. + +In summary, our contributions are as follows: + +- We design a novel zero-shot completion framework called GenPC, which significantly improves real-world scan completion by prompting a pre-trained 3D generative model. +- We propose a Depth Prompting module to bridge the + +modality gap between partial scans and generative models by utilizing depth images as a stepping stone. + +- We introduce the novel Geometric Preserving Fusion module for refining the initial generated results. It adaptively aligns the generated content with partial input, ensuring that the final result is both semantically accurate and structurally faithful. +- Extensive experiments demonstrate that GenPC achieves state-of-the-art performance on real-world datasets while significantly reducing completion time. + +# 2. Related Work + +# 2.1. Point cloud completion + +Early methods [8, 13, 34, 42] primarily used voxels as intermediate representations and performed completion using 3D convolutions. However, they are often limited by the resolution of the voxels. With the development of point-based networks like PointNet [28], various point cloud tasks can be handled by end-to-end networks [2, 29, 30, 46, 54]. Among them, PCN [49] is the first work that directly generates high-resolution complete point clouds in a coarse-to-fine manner for point cloud completion. A similar generation strategy is also adopted in a series of following works [18, 23, 36, 37, 39]. Transformer [35] has also been leveraged in recent works. PointTr [47] treats the point cloud as a token sequence, using transformer encoder-decoder to predict the missing parts. SnowflakeNet [40] designs a transformer decoder with skip connections to refine the point cloud. Another line of works [53, 56] enhances completion performance using 2D information. Different from the above approaches, SVDFormer [55] and GeoFormer [45] project point clouds into 2D depth images, requiring information from only partial input. + +Although these methods perform well on synthetic datasets, their reliance on training data causes performance degradation on out-of-distribution real-world scans and previously unseen categories. Recent unsupervised [4, 38, 41, 51] and self-supervised approaches [6, 14, 26] have allevi + +ated this issue to some extent; however, the completion results remain suboptimal. To address these limitations, SDS-Complete [19] formulates point cloud completion as a test-time optimization problem, introducing a zero-shot method that fits a Signed Distance Function (SDF) to the input partial point cloud. It leverages Score Distillation Sampling (SDS) to extract 2D priors from the Stable Diffusion [31] model to complete the missing regions. Subsequently, Huang et al.[17] propose initializing the partial point cloud as 3D Gaussians and distilling prior knowledge from zero123[24]. Although these methods exhibit impressive zero-shot completion capabilities, they require optimization from scratch for each incomplete point cloud, making them time-intensive. Moreover, reliance on implicit 2D diffusion priors limits the reconstruction of fine geometric details. In this work, we leverage explicit priors from a pre-trained 3D generative model to enhance zero-shot point cloud completion quality while significantly reducing processing time. + +# 2.2.3D Generation + +DreamFusion [27] is the first method to use 2D priors for 3D generation, introducing Score Distillation Sampling (SDS) to extract 2D priors from a pretrained diffusion model and guide the 3D generation process, inspiring numerous impressive works. Magic3D [22] adopts DMTet [32] as the 3D representation instead of NeRF [25] and then performs optimization using SDS. Fantasia3D [3] decouples the optimization of geometry and material properties. With the emergence of 3D Gaussian Splatting [21], a highly expressive 3D representation, the optimization time for 3D generation with SDS has been significantly reduced. DreamGaussian [33] firstly attempts to use SDS optimization for 3D Gaussians, reducing the optimization time to just a few minutes while achieving excellent results. GaussianDreamer [44] initializes 3D Gaussians using point cloud priors, yielding impressive results. Although the above methods are effective, they require several minutes or even hours for optimization. The emergence of large-scale datasets [9, 10] has driven the development of faster feed-forward methods. Once trained, these methods can generate 3D objects within seconds through a single forward inference. Recently, LRM [16] demonstrated that a regression model can predict a NeRF from a single image within seconds. Based on this, InstantMesh [43] generates additional multi-view images from a single image and then reconstructs the mesh. However, both methods are limited by resolution. To address this, LGM [15] introduces an efficient representation of multi-view Gaussian features, enabling the prediction of high-resolution 3D Gaussian models. + +These feed-forward methods can generate high-quality 3D objects from a single image in a very short time while demonstrating strong generalization ability. We are motivated to leverage this advantage for point cloud completion, aiming to achieve superior zero-shot completion results + +![](images/5be1b9d989215545a5fe58cfc1bbe902ac272ed371f84f1a5ab065c6f15f360f.jpg) +Figure 3. Illustration of Depth Prompting. (a) Overview. First, we uniformly position cameras around the partial point cloud $P_{in}$ to select a scanning viewpoint. From this viewpoint, we project to obtain depth and the corresponding mask, and then apply mask inpainting to achieve high-quality depth. (b) Viewpoint Selection: For each viewpoint $V_{i}$ , we perform a spherical flip on $P_{in}$ for each camera to obtain a mirrored point cloud $\vec{P_{in}}$ , then create a convex hull around $\vec{P_{in}} \cup V_{i}$ , identifying the points on this hull as visible points. The camera with the greatest number of visible points is chosen as the scan viewpoint $V_{scan}$ . The top of (b) is a true viewpoint, all points lie on the convex hull. The bottom of (b) is the opposite viewpoint, only two lie on the convex hull. + +![](images/162ab0d8ba61e30050330e7e3421fc2d0018ac17bac869354c3a98f8cfc54601.jpg) + +while reducing optimization time. + +# 3. Method + +The input of GenPC consists of a partial point cloud $P_{in} \subseteq \mathbb{R}^{N \times 3}$ and a corresponding text prompt $T_{in}$ , where $N$ represents the number of points in $P_{in}$ . Our goal is to obtain a complete shape $P_{out}$ that preserves the original structure in input. As illustrated in Figure 2, our method seamlessly incorporates an image-to-3D generative model into the point cloud completion process through the introduction of two innovative modules. First, current image-to-3D models are designed to accept only 2D images as input. To adapt them for point cloud completion, we introduce the Depth Prompting module, which leverages depth images as a stepping stone to bridge the modality gap between partial point clouds and generative models. After generating a 3D shape from the image-to-3D model, a key challenge arises: the original points in $P_{in}$ are not retained in the generated shape. To address this, we propose the Geometric Preserving Fusion module, which further aligns the initial generated shape with $P_{in}$ , ensuring that the final result is both semantically accurate and structurally faithful. + +# 3.1. Depth Prompting + +Figure 3 describes the proposed Depth Prompting module. This module generates an RGB image from the input partial point cloud $P_{in}$ by first projecting it to a coarse depth map $D_{raw}$ as an intermediary. Through masked inpainting of missing areas, a smooth depth map $D_{c}$ is produced to enhance robustness to point cloud sparsity. Finally, $D_{c}$ and + +the text prompt $T_{in}$ are input into a depth-conditioning ControlNet [52] to produce the corresponding RGB image. To project a high-quality depth image from an incomplete point cloud, we propose to find the viewpoint from which the point cloud was captured. Although Huang et al. [17] employs a distance-based method for viewpoint estimation, this approach can sometimes result in issues such as depth reversal. To address these problems, we follow the approach proposed by [20], framing the viewpoint estimation as a hidden point removal task. As illustrated in Figure 3(a), We start by evenly positioning $M$ cameras $V_{i}$ (where $i = 1,2,\dots ,M$ ) around the input point cloud $P_{in}$ . For each camera, as shown in Figure 3(b), we perform a spherical flip on $P_{in}$ to obtain a mirrored point cloud $\hat{P_{in}}$ . We then create a convex hull around $\hat{P_{in}}\cup V_i$ , identifying the points on this hull as visible points. The camera with the greatest number of visible points is chosen as the scan viewpoint $V_{scan}$ . By constructing the convex hull, our approach effectively prevents depth reversal and projects $P_{in}$ to an initial depth map $D_{raw}$ . + +However, some partial point clouds, such as cars in the KITTI dataset, are extremely sparse, leading to sparse depth projections that hinder subsequent completion. To address this issue, we use a pre-trained 2D inpainting diffusion model [11] to fill the missing holes in the sparse depth $D_{raw}$ , resulting in a complete, high-quality depth image $D_{c}$ . To create an inpainting mask, we first project the point cloud with a large pixel size to obtain $M_{FULL}$ . We then apply an XOR operation between $M_{FULL}$ and the inverted depth map $(\neg D_{raw})$ , which generates the required mask for inpainting. Using this mask, the inpainting model fills the missing depth regions and smooths any irregular edges, producing $D_{c}$ . Note that any inpainting model capable of filling masked areas can be applied here. Finally, we use $D_{c}$ as conditioning input, along with the text prompt $T_{in}$ , to generate the image $I_{gen}$ corresponding to the partial input. This is achieved by leveraging a pre-trained depth-conditional image generation model, such as ControlNet [52]. + +# 3.2. Geometric Preserving Fusion + +In the Dynamic Scale Adaptation stage, we first colorize the input point cloud $P_{in}$ using the generated image $I_{gen}$ , resulting in $P_{partial}$ . Then, $P_{partial}$ and $P_{gen}$ are aligned at dynamic scales, producing an initial, completed point cloud $P_{all}$ . Then, we apply an optional Refining stage. In this stage, $P_{all}$ is initialized as 3D Gaussians $G_{all}$ , with different regions having distinct Gaussian parameter settings to preserve the original geometric details of the input point cloud while optimizing the shape of missing areas. This step helps to eliminate error accumulation and enhance overall completion quality. + +# 3.2.1 Dynamic Scale Adaptation + +We first use the generated image $I_{gen}$ to obtain the 3D shape $P_{gen}$ through the Image-to-3D generation model. Thanks to the powerful zero-shot generation performance of the pre-trained models, the generated $I_{gen}$ and $P_{gen}$ are highly consistent in category and shape with the input point cloud. Next, we use $P_{gen}$ to fill in the missing areas of the input point cloud, as shown in Figure 4. To improve the fusion process, we color $P_{in}$ using the RGB information from $I_{gen}$ , creating a colored partial point cloud $P_{partial}$ . Since different parts of the object exhibit distinct colors, these colors can be regarded as semantic cues, enriching the fusion with additional contextual information for more accurate integration. Both $P_{partial}$ and $P_{gen}$ are then normalized to a unified scale within the range [-0.5, 0.5], reducing the search space for subsequent integration. + +To eliminate the impact of both scale and pose differences, we scale $P_{gen}$ within the range [0.8, 1.2] at intervals of 0.1, and perform ICP [1] alignment at each scale, using the Chamfer Distance to evaluate the alignment results. We treat the color of the point cloud as semantic information, which allows us to not only supervise the alignment geometrically but also consider color information as an additional supervision signal. During the iterative registration, we calculate both the Euclidean and RGB Chamfer Distance between $P_{partial}$ and $P_{gen}$ . The Chamfer Distance ensures accurate geometric alignment, while the RGB Chamfer Distance supervises the alignment of the semantic information, thereby improving the overall quality of the fusion. Together, they form the following objective: arg $\min_{s\in [0.8,1.2]}(\alpha \cdot CD_{XYZ}(P_{partial},s\cdot P_{gen}) + \beta \cdot CD_{RGB}(P_{partial},s\cdot P_{gen}))$ + +where $\alpha$ and $\beta$ are regularization terms, and $s$ represents the scaling factor. Finally, we select the registration result that minimizes the combined XYZ and RGB Chamfer distances and remove points from $P_{\mathrm{gen}}$ that are adjacent to $P_{\mathrm{partial}}$ to avoid point cloud overlap, resulting in the missing portion of the point cloud $P_{\mathrm{miss}}$ . Together, $P_{\mathrm{miss}}$ and $P_{\mathrm{partial}}$ form the preliminary complete point cloud $P_{\mathrm{all}}$ . + +# 3.2.2 Refining + +To further enhance the accuracy of point cloud completion and reduce error accumulation, we optimize the preliminarily completed point cloud, as shown in Figure 4. First, the point cloud is initialized as 3D Gaussians, and then distinct parameter configurations are applied to different parts of the 3D Gaussian. This approach maintains the integrity of the original part $G_{\text{partial}}$ while optimizing the geometry of the missing part $G_{\text{miss}}$ , thereby improving the overall quality and consistency of the point cloud completion. + +Partial setup: For the partial point cloud $P_{\text{partial}}$ , we initialize it as a 3D Gaussians $G_{\text{partial}}$ . To preserve the original geometry, we fix parameters such as the coordinates, color, + +![](images/1e0eb2b780dbbfcdbe8ffe93aca5ac32e11041a1b018f4778f72d7996a560465.jpg) +Figure 4. Illustration of Geometric Preserving Fusion. In the Dynamic Scale Adaptation stage, an optimal scale factor is selected to align $P_{\text{partial}}$ and $P_{\text{gen}}$ , producing an initial completed point cloud $P_{\text{all}}$ . Then, to reduce the accumulated error in the previous steps, an optional Refining operation can be performed, where $P_{\text{all}}$ is initialized as 3D Gaussians and optimized by the SDS loss. + +scale, and opacity, making them non-trainable. This ensures that the geometric of the partial point cloud remains unaffected during the optimization process, thereby maintaining consistency with the original input. + +Miss setup: For the missing point cloud $P_{miss}$ , we initialize it as a 3D Gaussians $G_{miss}$ . The scale remains fixed, as these points are uniformly sampled from the mesh surface and already have a reasonable scale. Opacity is set to 1 and remains non-trainable to ensure the stability of the Gaussian points on the surface. The color parameters are not fixed, but the learning rate is set relatively low because color carries semantic information. This allows for adjustments to the color during optimization while preserving its semantic characteristics as much as possible. The Gaussian coordinates are the main focus of the optimization, ensuring that the missing point cloud fits the shape of the partial input. + +SDS Guidance Optimization: Next, under the viewpoint $V_{\text{scan}}$ , we render an image $I_{\text{optim}}$ and a depth map $D_{\text{optim}}$ from $G_{\text{partial}}$ . We then incorporate both $G_{\text{miss}}$ and $G_{\text{partial}}$ , and render an image $\tilde{I}_{\text{optim}}^i$ from a random viewpoint. This process is iterated multiple times, where in each iteration, we apply SDS to extract 2D priors from the pre-trained novel view synthesis diffusion model Zero123 [24], refining $G_{\text{miss}}$ based on $I_{\text{optim}}$ until satisfactory completion is achieved. The SDS Loss can be formulated as: + +$$ +\nabla_ {G _ {a l l}} \mathcal {L} _ {\mathrm {S D S}} = \mathbb {E} _ {t, p, \epsilon} \left[ (\epsilon_ {\phi} (I _ {\mathrm {o p t i m}}; t, \tilde {I} _ {\mathrm {o p t i m}} ^ {i}, \Delta p) - \epsilon) \frac {\partial I _ {\mathrm {o p t i m}}}{\partial G _ {a l l}} \right] +$$ + +where $\epsilon_{\phi}(\cdot)$ is the predicted noise from the 2D diffusion prior $\phi$ , $t$ is the time step, $\epsilon$ is the standard noise and $\Delta p$ represents the relative camera pose change from the scan viewpoint $V_{scan}$ , respectively. + +Additionally, to prevent other 3D Gaussians in the optimization process from affecting the geometric information + +of the input in the $G_{\text{partial}}$ region, we also render images $I_{\text{optim}}^i$ and depth maps $D_{\text{optim}}^i$ under the viewpoint $V_{\text{scan}}$ during the optimization iterations, and set a preservation loss $L_{\text{Presv}}$ for the partial region: + +$$ +L _ {P r e s v} = w _ {1} \cdot \mathrm {M S E} (I _ {o p t i m}, I _ {o p t i m} ^ {i}) + w _ {2} \cdot \mathrm {M S E} (D _ {o p t i m}, D _ {o p t i m} ^ {i}) +$$ + +where MSE is the Mean Squared Error between the optimized and reference images $I_{optim}^{i}$ and $I_{optim}$ , as well as the depth maps $D_{optim}^{i}$ and $D_{optim}$ . $w_{1}$ and $w_{2}$ are weights that balance the importance of image and depth losses. By incorporating $L_{Presv}$ and $L_{SDS}$ , our method preserves the geometry of the partial point cloud while optimizing the missing areas, reducing multi-stage error accumulation and improving the overall completion quality. + +# 4. Experiment + +# 4.1. Dataset and Evaluation Metric + +We validate our method on three real-world datasets Redwood [5], ScanNet [7], and KITTI [12]. For the Redwood [5] dataset, we follow prior approaches [19], using single-view scans as partial inputs and multi-frame aggregations as ground truth. Since previous deep learning-based methods were trained on standardized synthetic datasets, we normalize the Redwood dataset point clouds to the range [-0.5, 0.5] and set the elevation angle to $0^{\circ}$ to ensure a fair comparison with their input requirements. For the ScanNet dataset, which contains partial point clouds extracted from RGB-D scans, we focused on tables and chairs due to their complex structures and additional supports that introduce challenging self-occlusion cases for our method. For each category, we select 16 objects for validation. In addition, we used the + +Table 1. Quantitative results on the Redwood [5] [19] dataset. Ours* represents our results without Refining ( $\ell^1$ CD and $\mathrm{EMD} \times 10^{2}$ ). + +
Objects MetricsTable CD/EMDSwivel-Chair CD/EMDArm-Chair CD/EMDChair CD/EMDSofa CD/EMDVase CD/EMDOff-Can CD/EMDVespa CD/EMDWheelie-Bin CD/EMDTricycle CD/EMDAvg↓ CD/EMD
PoinTr [47]1.86/3.504.08/8.491.95/4.222.69/5.382.96/5.024.05/7.284.82/6.922.00/4.062.78/3.511.70/3.992.89/5.24
SnowflakeNet [40]3.44/6.923.40/7.582.15/4.452.35/5.282.64/5.004.63/7.694.36/6.752.07/4.423.14/5.031.44/3.322.96/5.64
Adapointr [48]5.20/6.445.09/8.033.67/4.534.40/5.963.59/5.186.23/7.566.04/7.693.21/4.654.13/7.632.90/4.254.45/6.19
SDS-Complete [19]1.67/2.922.24/3.092.18/3.162.62/3.612.95/4.563.26/5.894.03/4.363.46/5.942.69/3.212.11/3.872.72/4.06
Ours*1.41/2.241.69/2.371.38/1.761.47/2.481.61/2.933.15/5.243.04/4.621.59/2.832.65/3.641.79/3.521.98/3.16
Ours1.28/2.071.43/2.291.16/1.681.36/2.201.58/2.782.86/4.852.72/4.361.36/2.472.31/3.171.38/2.971.74/2.88
+ +![](images/ccfcac8fa469835c50376103717c005a9bb30847676e35309c98099cfd945ce8.jpg) +Figure 5. Visual comparisons with recent methods [40, 47, 48] on the Redwood dataset. + +Table 2. Quantitative results on ScanNet $\left( {{\ell }^{1}\mathrm{{CD}}\text{and}\mathrm{{EMD}} \times {10}^{2}}\right)$ . + +
Methods MetricsSnowflakeNet CD/EMDAdaPoinTr CD/EMDOurs CD/EMD
Table1.80/4.782.34/6.121.67/3.86
Chair1.68/3.762.07/3.091.57/3.24
Avg1.74/4.272.21/2.381.62/3.55
+ +Table 3. Performance of ablation variant C (w/o depth inpainting) on different datasets. Variant C performs relatively well on Redwood's dense point clouds but shows significant performance drops with the sparse point clouds in ScanNet ( $\ell^1$ CD and EMD $\times 10^2$ ). + +
Methodsvariant COurs
MetricsCD/EMDCD/EMD
Redwood2.23/3.601.74/2.88
ScanNet3.57/6.101.62/3.55
+ +Table 4. Performance of ablation variants on the Redwood dataset $(\ell^1$ CD and EMD $\times 10^{2}$ + +
MethodsCD↓EMD↓
A: w/o Viewpoint Selection2.443.79
B: w/o ControlNet4.316.80
C: w/o Depth Inpainting2.233.60
D: w/o 3D Generative Model4.656.13
E: w/o Dynamic Scale Adaptation4.384.52
F: w/o SDS Optimization1.983.16
Ours1.742.88
+ +ground truth provided by [50], consisting of 2048 points for quantitative evaluation. + +For quantitative evaluation, we followed prior methods by sampling 16,384 points from the Redwood dataset and 2,048 points from the ScanNet dataset using Farthest Point Sampling (FPS) to enable direct comparison with the ground truth. To assess the quality of point cloud completion, we used the widely adopted Chamfer Distance (CD) and Earth Mover's Distance (EMD) metrics, scaling the loss values by a factor of 100 for clearer interpretation. We also conduct a qualitative evaluation on KITTI [12] to assess the performance on sparse LiDAR scans. + +# 4.2. Results on the Redwood dataset + +The quantitative and qualitative results are presented in Table 1 and Figure 5. With or without the SDS Refining step, GenPC consistently achieves state-of-the-art performance across the entire dataset. These results indicate that existing learning-based methods [40, 47, 48] struggle to complete + +![](images/7a30ba357cd2dc3e91d13aad2d32633566571091e09ac912d64e7724b6918aac.jpg) +Figure 6. Visual comparisons with recent methods [40, 48] on the ScanNet dataset. + +![](images/e081dcc43dbac5e0e92c97b7d453683622ea60af1726ebd4fb8a884c5f193f7e.jpg) +Figure 7. (Top) Visual comparisons with AdaPoinTr [48] on KITTI [12]. (Bottom) We display the point clouds in different colors: blue for the Partial Input, red for AdaPoinTr, and gray for Ours. Our result maintains a consistent scale with the input. + +out-of-distribution data, even when these data belong to categories seen during training (e.g., chairs and couches). Additionally, these methods are sensitive to scale variations, leading to inconsistent outputs when the input scale changes. Compared with the only zero-shot method, SDS-Complete [19], GenPC achieves an average reduction in CD by $36\%$ and EMD by $29\%$ . Furthermore, Figure 5 clearly illustrates that GenPC outputs finer structure details than SDS-Complete, attributed to the rich geometric priors provided by the pre-trained 3D generative model. + +# 4.3. Results on the ScanNet dataset + +Comparison with two cutting-edge learning-based methods [40, 48] are presented in Table 2 and Figure 6. Our method demonstrates advanced performance in completion quality, maintaining reliable results even when dealing with sparse and noisy point clouds. As shown in Figure 6, our method generates completion outputs with high fidelity to the + +# Variant A + +Our $D_{c}$ Reversed $D_{c}$ + +![](images/d6b05be0608ff8201b2abdf614b9dcd539097c59ae63fc1dad36382a5f085f28.jpg) + +![](images/ee84b57e1bf6d683e1f5f0b7fe71f347f4322cdfee91b8f8722f5e996ca119ed.jpg) +$I_{gen}$ +Figure 8. Depth and RGB images produced by variant A (w/o Viewpoint Selection) and Variant C (w/o Depth Inpainting). (Left) The above is the complete depth $D_{c}$ obtained from the scanning viewpoint and the opposite viewpoint, and below are the corresponding generated images $I_{gen}$ . (Right) The above are the sparse depth $D_{\mathrm{raw}}$ and the complete depth $D_{c}$ , and below are the generated corresponding images $I_{gen}$ . + +# Variant C + +![](images/956a0d176db7b1dd347ebaf8f2c64a44f4481bc61541e82ed8025e3b7854eca1.jpg) +$D_{raw}$ + +![](images/7c82c68b4b46dbe8b95d3f9c41af2c0b7001af81dec771bebd2c52d16e703203.jpg) +$D_{c}$ + +![](images/e308330ea192c8c4e73dc28216707a622d52d37dbba851946ad2c490a1739831.jpg) +$I_{gen}$ + +![](images/d72b9937d45a28869daf2fd93bb97b78dd7c9f3cdce9dcdcbbc6cf42c8d6598e.jpg) + +input point cloud and rich geometric details, while learning-based methods are affected by domain gaps, leading to numerous noisy points in their results. + +# 4.4. Results on KITTI + +A qualitative comparison on the KITTI dataset is presented in Figure 7, which shows that GenPC produces results with a complete and realistic shape without any extraneous noise. In contrast, previous methods trained on ShapeNet produce completed point clouds that are smaller in scale than the original, as shown in the bottom of 7. The proposed Dynamic Scale Adaptation allows the completed results to maintain scale consistency with the original point cloud. + +# 4.5. Ablation Study + +# 4.5.1 Ablation on Depth Prompting Module + +To investigate the impact of the depth extraction method, we compare three variants of Depth Prompting. In variant A, we replace our viewpoint selection with a distance-based method similar to [17], leading to significantly increased CD and EMD values. Meanwhile, as shown in Figure 8, although this method correctly identifies the viewpoint in some cases, it may select the reverse viewpoint, causing depth flipping. This flipped depth map disrupts accurate image generation and severely impacts completion quality. In variant B, ControlNet is removed, and the inpainted depth $D_{c}$ is used as input to the image-to-3D generative model to examine the effects of color information on subsequent processes. In some cases, experimental observations show + +that, even with high-quality depth, the generated 3D shapes are reasonable but lack color, rendering them unsuitable for SDS optimization in the second stage. In variant C, we skip the depth inpainting step to evaluate the effect of low-quality depth on downstream processes. As shown in Figure 8, depth maps projected from sparse point clouds fail to generate accurate images, resulting in a significant drop in performance. Therefore, while this variant performs well on dense point cloud datasets like Redwood, it struggles on sparse point cloud datasets like ScanNet, as shown in Table 3. + +# 4.5.2 Ablation on 3D Generative Model + +To examine the effect of the image-to-3D generative model in our pipeline, we form variant D by replacing the generated 3D shape with a set of Gaussian noise point clouds. The Refine step is then applied, optimizing over 5000 iterations in an attempt to complete the missing regions. The results in Table 4, the absence of explicit geometric priors significantly impacts the completion performance. + +# 4.5.3 Ablation on Geometric Preserving Fusion Module + +In variant E, we directly align the generated 3D shape $P_{\mathrm{gen}}$ with $P_{\mathrm{partial}}$ without using Dynamic Scale Adaptation to validate the effectiveness of this process. Due to scale inconsistency, the direct alignment fails to properly match the two point clouds, thereby wasting the rich geometric priors provided by the 3D shape. In variant F, we omit the Refining process and use the merged point cloud $P_{\mathrm{all}}$ directly as the completion result. While quantitative metrics show that the Refining process can further enhance the overall completion quality, our experiments reveal that the merged point cloud $P_{\mathrm{all}}$ often performs competitively in both visualization and quantitative metrics. Therefore, we make the Refining process optional to improve completion speed. + +# 5. Conclusion + +In this study, we make the first attempt to leverage a pretrained 3D generative model for zero-shot point cloud completion and introduce GenPC. To capitalize on the generative model's inherent generalization ability, our framework consists of two key components: Depth Prompting and Geometric-Preserving Fusion. 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Kim $^{3}$ Siddhartha Chaudhuri $^{3}$ Qixing Huang $^{1}$ Zhiqin Chen $^{3}$ + +1The University of Texas at Austin 2Simon Fraser University 3Adobe Research + +# Abstract + +We introduce the first method for generating Vector Displacement Maps (VDMs): parameterized, detailed geometric stamps commonly used in 3D modeling. Given a single input image, our method first generates multi-view normal maps and then reconstructs a VDM from the normals via a novel reconstruction pipeline. We also propose an efficient algorithm for extracting VDMs from 3D objects, and present the first academic VDM dataset. Compared to existing 3D generative models focusing on complete shapes, we focus on generating parts that can be seamlessly attached to shape surfaces. The method gives artists rich control over adding geometric details to a 3D shape. Experiments demonstrate that our approach outperforms existing baselines. Generating VDMs offers additional benefits, such as using 2D image editing to customize and refine 3D details. Code and data are available at https://yyuezhi.github.io/GenVDM/. + +# 1. Introduction + +Generative neural models for 3D shape synthesis is a rapidly advancing research area [61]. However, they are still not widely adopted in artistic workflows for two main reasons. First, synthesizing fine geometric details is challenging due to the heterogeneity of 3D representations and the lack of detailed 3D training data. Second, existing neural tools lack the precise spatial and compositional controls needed by 3D artists. To address these limitations, instead of reinventing the 3D modeling stack to accommodate generative AI, we draw inspiration from an existing workflow in which an artist starts with a base mesh and "stamps" the desired details onto the 3D surface (see Figure 1). These smaller stamps are easier to generate than full-scale 3D models, fit seamlessly into existing workflows, eliminate artists' dependence on expensive and limited third-party stamp libraries, and provide full artistic control over spatial arrangement and composition. + +We chose the vector displacement map or VDM as our + +![](images/4371f7a74f8be93a42fda36749e98ec7184d50548c96a61f6da29ed5945ceb5e.jpg) +Figure 1. We introduce GenVDM, a method that can generate a highly detailed Vector Displacement Map (VDM) from a single input image. The generated VDMs can be directly applied to mesh surfaces to create intricate geometric details. Note that the thumbnails represent plain 2D RGB image sources. + +stamp representation. A VDM assigns an arbitrary 3D displacement to every point in a 2D rectangle, warping the sheet to form a curved surface with complex geometric features, such as overhangs and cavities. It is widely supported in 3D software [1-4] and compactly stored as a vector field over a UV image domain. While using VDMs is commonplace, authoring them is extremely challenging, and artists usually depend on packs of VDMs created by third parties (analogous to brushes in digital painting tools), with limited customization or generality. Image or text-driven stamp generation could drastically expand the scope of VDM usage by providing artists with custom stamps on demand. + +In this paper, we propose the first neural pipeline to generate a VDM from a single RGB image. To achieve this, we address two main technical challenges. The first challenge is that existing generative models are not suitable for VDM generation: generating a 3D object usually does not also produce a parametric 2D domain for stamp application, and predicting a depth map from a single image does not capture complex high-amplitude variations, overhangs, + +and occlusions; see Figure 6. Thus, we develop a three-step method. First, given an input RGB image (which can also be generated with existing text-to-image models), we predict normal maps from multiple viewing directions to resolve occlusions that may be hidden in a single view. Second, we reconstruct a mesh (which need not have disk topology) by fitting a neural SDF to the multi-view normal maps and polygonizing the result. Third, we use a neural deformation model to displace points on a 2D rectangle to fit the mesh, forming the final VDM. + +The second challenge in training a generative VDM model is the absence of training data. We tackle it by building an interactive tool to segment interesting semantic and geometric regions from Objaverse 3D models [19], and then develop a geometry processing pipeline for converting these regions into a VDM representation, creating a dataset of 1,200 VDM patches used for training. Our pipeline is robust enough to analyze polygon soups in the wild, which we achieve by re-sampling the selected regions and reconstructing a single connected surface after removing outliers. We then deform the resulting mesh to obtain a co-planar boundary that can be seamlessly attached to a flat base tile over which the VDMs are typically defined. The processed shapes can then be rendered and used to finetune the multiview normal generation model. + +We compare our method to state-of-the-art shape generation techniques [27, 42, 54], as well as to reconstructing a heightfield (i.e. a scalar displacement map) from estimated depth [84]. We use a collection of images depicting parts commonly used in VDMs (e.g., facial elements, decorations), and evaluate using visual fidelity [57] and semantic similarity [55] metrics. Our method outperforms others due to its ability to handle smaller VDM-like regions. Note also that other mesh generation methods do not produce a displacement map – which can have both “outward” and “inward” displacements – and thus their output can only be additively combined with the base shape, e.g., they are not able to introduce cavities like an eye or a mouth in Figure 1. + +To summarize, our contributions are: + +- The first generative ML pipeline for VDMs; +- A robust method to reconstruct VDMs from multi-view normal maps produced by image diffusion models; +- A novel VDM extraction pipeline to efficiently extract and process patches from 3D objects to produce VDMs; +- The first public dataset of VDMs for academic research. + +# 2. Related work + +Vector Displacement Maps. Texture mapping [10, 26] is the dominant solution in the industry to add complex surface details to shapes without increasing mesh complexity. Accompanying it are many techniques that hallucinate complex geometric details, such as bump mapping [9], horizon + +mapping [46], and parallax mapping [31]. Unlike those techniques that do not change the geometry of the shape, displacement mapping [17, 18, 64] adds geometric details by subdividing the original geometry into finer polygons and then displacing each vertex in its normal direction by a height value indexed from the displacement map (although some versions of displacement mapping can be done in the pixel space without changing the original geometry [69]). + +While a displacement map can be considered as a single-channel image or heightfield, a vector displacement map (VDM) can be seen as a three-channel image, where each pixel contains a 3D displacement vector. VDMs naturally support representing more complex geometries with less distortion compared to displacement maps, and both are used in 3D modeling tools to create geometric details. Research on displacement maps and VDMs has focused on texture synthesis from examples [85], and synthesis of human body and face meshes for shape reconstruction [6, 83]. VDMs conceptually resemble Geometry Images [23], and some recent works adopt image diffusion models for generating Geometry Images to synthesize 3D shapes [20, 82]. To our knowledge, there is no prior work on generative models of VDMs, nor a public research dataset for VDMs. + +Image-to-3D. Early works on single-view 3D reconstruction [15, 16, 22, 48, 70, 81, 86] mostly adopt feed-forward neural networks trained on limited data [11]. More recent work [30, 49, 88, 90] trained on large 3D datasets [19] has shown significantly improved generalizability to novel shape categories. With the introduction of text-to-image diffusion models [52, 56], a line of work [47, 66] achieved zero-shot single-image-to-3D with score distillation sampling (SDS) [53] by distilling 2D diffusion priors into 3D representations with per-shape optimization. + +Another line of work [40, 74] utilizes image diffusion models for novel view synthesis conditioned on an input image and a relative camera pose. Such models produce images of the object from different views, therefore 3D object can be reconstructed by SDS-based optimization [54] or a feed-forward reconstruction network [39]. These methods inspired a series of subsequent work that finetunes pretrained image diffusion models to directly generate 3D-consistent multi-view images of target output shape given a single-view image, where output shape can be reconstructed from generated multi-view images via optimizing a neural field or mesh [41, 42, 60], a 3D diffusion reconstruction network [38], or a feed-forward large reconstruction model powered by Transformers [27, 36, 67, 71, 73, 77, 79, 89, 91]. Most recently, image diffusion models have been replaced by video diffusion models to achieve better 3D consistency of generated views [24, 68]. + +Modeling by Parts. The use of small building components to compose complex shapes has been widely studied + +![](images/73381186bf4901715ffa5746788d1e9fb2ceeba60c9096be69386dc66bf6a281.jpg) +Figure 2. Overview of our image-to-VDM pipeline. Given an input image, we first add a gray square behind the object/part in the image as background, so the image resembles a textured VDM applied to a square mesh, as in (a). Then we utilize a multi-view image diffusion model to generate six normal maps with pre-defined camera poses, as in (b). The multi-view normal maps effectively represent the geometry of the VDM when applied to a square mesh, and thus we can reconstruct the VDM from these normal maps, as in (c). The reconstructed VDM can then be applied to various surfaces as in (d). + +in modeling-by-assembly systems [21, 34]. Before generative AI rose to prominence, these systems relied on part databases [12] (or shape databases from which parts could be cut out), and focused on building tools to help users find the right parts [7, 13, 59, 78] and assemble them meaningfully [29, 63, 80]. As a variation, methods were developed to extract and transfer detailed patches from a shape to another [65]. A few papers studied joint synthesis and layout of parts [37], but the synthesis was conditioned only on the layout and not on user input, and the focus was on whole-shape generation and not adding detail to existing ones. + +Relying on existing part datasets or part generation without user control, and on complex, non-standard, topologysensitive mesh fusion algorithms limits the utility of these older methods. Our approach generates detailed complementary geometry in-situ from the image prompt, and our generated VDMs are defined over parameterized 2D domains which are suitable for seamlessly blending onto 3D models, with industry-wide support. + +# 3. Method + +Our image-to-VDM pipeline is shown in Figure 2. Similar to other methods in the literature, we follow an approach that first generates multi-view images of the target object with an image diffusion model and then reconstructs the object from the generated images. In particular, we only generate normal maps of the object as we are only interested in the geometric details. Details of the multi-view normal generation are described in Section 3.1. Next, we reconstruct the VDM from the multi-view normals. As VDMs have specific properties and constraints, reconstructing them is highly non-trivial. We report our attempts and solutions in Section 3.2. Finally, as there is no publicly available dataset for VDMs, we designed an efficient tool for extracting shape patches from Objaverse [19], and devised algorithms to process those patches for use as training data. We describe the data processing pipeline in Section 3.3. + +# 3.1. Multi-View Normal Map Generation + +We opt to finetune an image diffusion model to generate multi-view images, as the pretrained image diffusion model offers strong generalizability. As will be shown in our experiments, our model, trained on a small dataset of 1,200 examples, works on a large variety of shapes. + +Specifically, we adopt Zero123++ [60] as the backbone for our multi-view diffusion model. Zero123++ is an image-to-multiview model based on Stable Diffusion [56]. Given an input image, Zero123++ generates a $960 \times 640$ image representing six multi-view images in a $3 \times 2$ grid, where the six images have pre-defined camera poses so they can be easily used for 3D reconstruction. However, the pre-defined camera poses in Zero123++ fully surround the object, e.g., there are front views and back views of the object. In our pipeline, since we are aiming to generate VDMs, the back views of the object are unnecessary. Therefore, we re-designed the camera poses of the six images. As shown in Figure 2 (b), assuming that the front view (see (a) for an example) has (elevation angle, azimuth angle) = $(0^{\circ}, 0^{\circ})$ , we define the six camera poses as $(0^{\circ}, -60^{\circ})$ , $(0^{\circ}, -30^{\circ})$ , $(0^{\circ}, 30^{\circ})$ , $(0^{\circ}, 60^{\circ})$ , $(45^{\circ}, 0^{\circ})$ , $(-45^{\circ}, 0^{\circ})$ . We also adopt orthographic cameras to reduce distortion, and let the model generate a normal map of the object for each camera pose. To train the model, we render single-view RGB images as input and multi-view normal maps as ground truth output. Details about training data are described in Section 3.3. Note that the input image does not have to be a front view; we render random views for training so the model can handle images from various viewpoints. We fine-tuned the checkpoint provided by Zero123++ [60] on 8 NVIDIA A100 GPUs for 3 days. + +# 3.2. VDM Reconstruction + +Reconstructing 3D shapes from multi-view images has been well studied in the text/image-to-3D literature. Most recent + +![](images/53266734ec5a430b766ffd5a5c374a98c8d4f70904f64a66275f5f5091510acb.jpg) +Figure 3. Reconstructing VDM from multi-view normal maps. We adopt a two-step approach. First, we reconstruct an accurate (but perhaps noisy) mesh (b) from the multi-view normals (a) with differentiable rendering and neural SDF representation. Then we parameterize the mesh by fitting a deformable square to it with a neural deformation field, as in (c). An VDM image can thus be obtained by discretizing the square into pixels and infer each pixel's displacement from the neural deformation field. The whole reconstruction pipeline takes about 6 minutes for each shape on an NVIDIA A100 GPU, where each step takes about 3 minutes. + +methods adopt a feed-forward large reconstruction model (LRM) to directly generate a 3D shape from multiple input images of different viewpoints [27, 36, 67, 71, 75, 89]. Therefore, a straightforward way for reconstructing VDMs is to train a similar LRM to take the normal maps as input and directly regress a VDM image. However, given limited VDM training shapes, our LRM trained on a small dataset is unlikely to generalize as well as other LRM models trained on larger datasets, therefore leading to suboptimal results. + +Given the above discussions, we adopt a slower but more robust per-shape optimization approach. Given the six normal maps with pre-defined fixed camera poses, we want to optimize a 3D representation to converge to the target 3D shape with supervision provided by differentiable rendering. A naive approach would be to initialize with a discretized square mesh and optimize with mesh-based differentiable rendering. However, as has been shown in other methods [35, 50], differentiable rendering on meshes is often problematic and requires careful design of regularization losses and tuning of hyperparameters. As we will show later, even with ground truth 3D supervision, optimizing a discretized mesh to fit the target shape is not an easy task. + +Therefore, we devise a two-step approach, as shown in Figure 3, to first optimize a neural SDF field to reconstruct a 3D shape from the multi-view normal maps, and then parameterize the 3D shape into a VDM image. We utilize the method proposed in Wonder3D [42] for the first step, with the only modification being that we removed $L_{rgb}$ , the loss term to punish the difference between rendered RGB images and the ground truth, as we do not predict multiview RGB images. Since we always put a grey square as background in our input images, the shape we obtained via optimization has a solid plane-like primitive where the object/part is attached to, see Figure 3 (b); then we can extract a mesh from the neural SDF field and easily separate a single layer of mesh that represents the VDM. + +![](images/324dc1c7f680ca78e19d3e8d11e5e6caba939d3e5dbf683ae7c7108a9860a70a.jpg) +Figure 4. Comparison of different approaches for parameterizing a shape into VDM. (a) Topology fixing and Tutte embedding with classic tools leads to noise and distortion. (b) Fitting a plane mesh to the target mesh leads to large distortion. (c) Our approach by applying a neural deformation field to a parametric square leads to clean and high-quality reconstruction. + +The next step is to parameterize the mesh into a VDM image. Since the mesh is reconstructed from sparse-view images, its geometry is often noisy and riddled with small holes and large gaps, see Figure 4 (a) left. To convert it into a VDM, we will need to fix its topology so that it is topologically equivalent to a plane; and then we will apply a mesh parametrization method to obtain its Tutte embedding on a square, so that each pixel on the square can be assigned with a displacement vector. However, as shown in Figure 4 (a), although the state-of-the-art topology fixing algorithms [87] can fix the topology, the result is often not satisfactory, e.g., a gap that should have been filled is being cut, see Figure 4 (a) middle where the helix of the ear is cut in half. As a result, after applying [58] to obtain its + +![](images/e23c681f70db97182d74cf3355ff5b0ad26dbe72d5ce24a99c719381bd8c678a.jpg) +Figure 5. Data preparation. For each interesting object (a), we use a 3D lasso tool to segment out interesting parts. For each part, we densely sample points on the part's surface and then perform Screened Poisson Surface Reconstruction [32] to obtain a single connected mesh (b). We then stitch the mesh to a square mesh with an algorithm inspired by Poisson Image Editing [51] (c). Afterwards, we can color the part and render RGB images (d) and normal maps (e) for training the image diffusion model. + +embedding on a plane, we see large distortions and noise in the final VDM, see Figure 4 (a) right where the upper part of the ear is missing due to distortion. + +An alternative is to initialize with an estimable square mesh and optimize it using a reconstruction loss with respect to the target mesh, as shown in Figure 4 (b). However, as mentioned, it is often required to have carefully designed regularization losses when a mesh is to be optimized. When adopting a naive optimization method proposed in [14], the resulting mesh exhibits large distortion. + +Therefore, instead of tuning the mesh optimization algorithm, inspired by AtlasNet [22] and Deep Geometric Prior [76], we propose to deform the square mesh with a neural deformation field parameterized by a Multilayer Perceptron (MLP). The MLP acts as a natural regularizer, as its inductive smoothness bias encourages smoothness of the deformation. We define the square as $\{p\mid p\in [0,1]^2\}$ , and the MLP $\phi_{\theta}$ with estimizable parameters $\theta$ . Then, given any 2D point $p$ in the square, we obtain its corresponding 3D point $p^{\prime} = \phi_{\theta}(p)$ in the deformed shape. Therefore, for each optimization step, we sample a grid of 2D points in $[0,1]^2$ , apply $\phi_{\theta}$ to obtain the deformed 3D points, and then compute the symmetric Chamfer Distance between the deformed 3D points and the ground truth points sampled from the target mesh. We also include a loss to maintain the square boundary. Therefore our optimization objective is + +$$ +\begin{array}{l} \underset {\theta} {\operatorname {a r g m i n}} \mathbb {E} _ {P, Q} \frac {1}{| P |} \sum_ {p \in P} \underset {q \in Q} {\min } \| \phi_ {\theta} (p) - q \| _ {2} ^ {2} + \frac {1}{| Q |} \sum_ {q \in Q} \underset {p \in P} {\min } \| \phi_ {\theta} (p) - q \| _ {2} ^ {2} + \tag {1} \\ \frac {1}{| \partial P |} \sum_ {p \in \partial P} \| \phi_ {\theta} (p) - \operatorname {p r o j} (p) \| _ {2} ^ {2}, \\ \end{array} +$$ + +where $P$ and $Q$ are sets of sampled points from $[0,1]^2$ and the target mesh, respectively. $\partial P$ contains all the boundary points in $P$ and $\mathrm{proj}(p)$ maps $p$ to a corresponding 3D point in a pre-defined square boundary. After optimization, we can sample a regular grid of points in $[0,1]^2$ and compute their 3D displacement vectors from $\phi_{\theta}$ to obtain the VDM image, as shown in Figure 4 (c). + +# 3.3. Data Preparation + +To the best of our knowledge, there is no publicly available dataset for VDMs. Therefore, we developed a data processing pipeline so we can efficiently annotate interesting parts from objects and then convert the parts into VDMs. In fact, our data processing pipeline does not produce true VDMs, but rather, shapes that look like VDMs, which are good enough to train our multiview generation model, see Figure 5. If needed, our VDM reconstruction method in Section 3.2 can be used to obtain readily usable VDMs. + +To construct our VDM training dataset, we crop parts from the Objaverse [19] dataset. We first create a keyword filtering list and apply the filter on Objaverse shape captions [43, 44]. As VDMs are mostly used to model organic parts, we select objects likely to contain such parts, e.g., animals and characters. + +We then developed a UI to precisely crop a part from a 3D object. This is achieved by a 3D lasso tool, where the user only needs to select a ring of points along the cutting boundary of the desired part. Our algorithm connects the points to form a cut and extracts the part from the object. Note that the part may not be a single connected mesh – it may comprise several sub-meshes. Hence, we remesh the part into a single connected mesh. We first densely sample points on the part, and then remove interior points by computing winding numbers [8]. For the remaining points, we performed screen Poisson surface reconstruction [32] to obtain a single connected mesh (Figure 5 (b)). Our 3D lasso tool has proven to be quite efficient. Annotating our entire dataset with 1,200 parts took only 24 man-hours. + +After obtaining the parts, we will then stitch each part to a square mesh to mimic the appearance of a VDM applied to a plane. Note that in almost all cases, the vertices on the boundary of each part are not coplanar, therefore, additional steps are required to make them coplanar. We first determine the plane via least squares plane fitting with respect to + +the boundary vertices. Then we project the boundary vertices to the plane, and adopt a method similar to Poisson Image Editing [51] to deform the part so that it follows the new coplanar boundary. Denote the set of all boundary vertices in the part (before projection) as $B$ and non-boundary vertices as $A$ ; also denote the set of all edges as $E$ . Denote the coplanar boundary vertices after projection as $B'$ , and the non-boundary vertices after deformation as $A'$ . For each point $p$ in $A$ or $B$ , denote its corresponding point in $A'$ or $B'$ as $p'$ . Then our new vertices after mesh deformation can be obtained by solving a quadratic error function + +$$ +\operatorname {a r g m i n} _ {A ^ {\prime}} \mathbb {E} _ {(p, q) \in E} \| \left(p ^ {\prime} - q ^ {\prime}\right) - (p - q) \| _ {2} ^ {2}. \tag {2} +$$ + +The minimization objective is to ensure that the gradients on the mesh are preserved after deformation, while the target coplanar boundary points $B'$ are also strictly followed. + +We then place the deformed part on a square mesh so that the boundary vertices and the square mesh vertices are coplanar. Once the part is attached to the square mesh, we perform one additional Laplacian smoothing step on the vertices close to the boundary to remove boundary noise, see Figure 5 (c). We always keep the square mesh gray and assign a random color to the part. We also perform translation, scaling, and rotation augmentation to the part to enrich the diversity of the dataset. Finally, for each shape, we render several RGB images from different viewpoints to serve as the training input to the multi-view normal generation model, and six normal maps in pre-defined camera poses as the ground truth output, see Figure 5 (d, e). + +# 4. Experiments + +In this section, we verify the effectiveness of our method by comparing it with various state-of-the-art methods. We also validate our design choices in ablation studies. Finally, we present additional results produced by our method, show applications of VDMs on adding details to geometry, and demonstrate how users can customize VDMs by simply editing the input images. We will make our code, trained model weights, and dataset available to the public. + +# 4.1. Vector Displacement Map Generation + +Baselines. Since there is no prior work on generating VDMs from single view images, we compare our method with methods that perform a similar task, namely, single-view image to 3D reconstruction. Specifically, we compare our method with Wonder3D [42], Magic123 [54], Large Reconstruction Model (LRM) [27], as well as a scalar displacement map (scalar DM) reconstruction method based on DepthAnything [84]. Given an input image, Wonder3D [42] generates multi-view RGB and normal images and optimizes a neural SDF field to reconstruct the 3D shape from the multi-view images. Magic123 [54] uses + +
MethodCLIPImg↑CLIPText↑3D-FID↓
Wonder3D [42]0.82460.2542199.5
Magic123 [54]0.82930.2510213.2
LRM [27]0.81440.2510239.9
Scalar DM0.82230.2564213.0
Ours0.85200.2701192.7
+ +Table 1. Quantitative comparison with baselines. Scalar DM is scalar displacement map produced from DepthAnything [84]. + +
MethodCLIPImg↑CLIPText↑3D-FID↓
Recon. Mesh0.84400.2636198.0
Topo. Fix(a)0.84010.2617209.9
Mesh Opt.(b)0.82450.2525217.2
Ours(c)0.85210.2701192.7
+ +Table 2. Quantitative ablation on VDM Reconstruction. + +the SDS loss [53] to optimize the 3D shape while applying a reconstruction loss on the input view. LRM [27] generates multi-view RGB images and trains a Transformer-based feed-forward model to reconstruct the 3D shape from the multi-view images. To validate the necessity of generating vector displacement map instead of regular scalar displacement map, we also compare with a state-of-the-art depth prediction method, DepthAnything [84], by converting the predicted depth of the object into a scalar DM. We run these baseline models with official implementation and pretrained weights; except that LRM does not release the official code, so we use open-source implementation OpenLRM [25] instead. For all reconstructed shapes, we render textureless images for visualization and evaluation. For Wonder3D, Magic123, and LRM, as they generate complete objects and not VDMs, we put a square plane behind their generated shapes to make the visualization more consistent and to have a fair quantitative comparison. + +Evaluation Dataset and Metrics. As there is no existing benchmark dataset for VDMs, we collected a dataset of 50 RGB images from the Internet and a text-to-image model [5] for evaluation. All images depict common VDM categories used by artists such as facial elements and decorations. For quantitative evaluation, we measure CLIP similarity [55] and 3D-FID score [72] between the input image and the rendered images of the generated shapes from different views, denoted as CLIPImg and 3D-FID, respectively. For CLIP, we additionally assess semantic alignment by measuring CLIP similarity between rendered images and texts describing the categories of the input images, denoted as CLIPText. We use public implementation of CLIP [62] and 3D-FID [57] for computing the metrics. + +The quantitative results are summarized in Table 1 and qualitative results are presented in Figure 6. Quantitatively, our method outperforms others by a significant margin. The closest competitors to our method are Wonder3D and scalar DM, which is also reflected in the qualitative results in Fig- + +![](images/5138cc15103b67126f122acae3eac9a6a2b0aed98f4557bdcc5d018d1e723781.jpg) +Figure 6. Qualitative results compared with baseline methods. As Magic123 [54], LRM [27], and Wonder3D [42] generate complete objects and not VDMs, we put a square plane behind their generated shapes to make the visualization more consistent. + +![](images/14e669df05dbd11aab9e849d2782754d44ee6a86d9fc3684cac0e951ee31c60c.jpg) +Figure 7. Qualitative results of ablation study. + +![](images/2b02f7029cff4d050475fa0124972ba7676bb4e2b92b8ea93f09b195854c1ff1.jpg) + +![](images/65d26152ff24b20dae1613f1fb33afe8dc585d9fdd1e5c28ad1253db12ed066a.jpg) + +![](images/92e33ce3121f4a5f92c3251a6b443f6a605df46bae47ad948b9d425a0f9f1c4f.jpg) + +![](images/fd60045fb3b2cc2d01cd65eb7d89cfa030d3dee51b838727506e17a3a0ba3ecd.jpg) +(a) Original + +![](images/80db3d25e6f604a9b12bf80a6de5c75d97dc907503ee98399e516ca1633ef3a9.jpg) +(b) Edition 1 + +![](images/d8309018fe4755ba2baaf1a2394f1a17f2a47d5cc129d0b68d4403cc3255391e.jpg) +(c) Edition 2 +Figure 8. Customizing VDMs by editing images. Here we show original input images and generated VDMs in (a) and edited images and their generated VDMs in (b)(c). + +ure 6. Magic123 and LRM lack geometric detail as they rely heavily on textures which often hallucinate details in geometry. Wonder3D has a shape generation pipeline similar to ours, yet it was designed to generate complete objects. Therefore, it struggles to generate partial shapes, e.g., noses and ears. Although the results of scalar DM look reasonable from the front view, its side view suffers as scalar DM cannot represent unseen regions of the front view. + +# 4.2. Ablation Study + +As discussed in Section 3.2, we compare the following settings for parameterizing the reconstructed mesh into a VDM image: (a) Topology fixing and Tutte embedding, (b) fitting a square mesh into reconstructed mesh, and (c) our approach; see Figure 4. We also include the reconstructed mesh before parameterization as a reference baseline. Table 2 summarizes the quantitative results and Figure 7 shows the qualitative comparisons. Topological fixing and Tutte embedding suffer when the topology of the reconstructed mesh is complex due to noisy reconstruction results, as shown in Figure 7 (a). This is because the topological fixing algorithm does not consider the distortion after parameterization as one of its optimization goals, thus some topological fixes may significantly increase distortion. Figure 7 (b) shows that mesh optimization is not reliable in our setting and is likely to fall into local minima during optimization. In contrast, our method, shown in Figure 7 (c), not only reconstructs high quality VDMs with correct topology, but also smooths out noise induced in neural SDF reconstruction, leading to visually more pleasing results. + +# 4.3. Application + +Shape modeling. With our method, users can generate parts of the shape from single-view images or text prompts (via text-to-image to obtain input to our method). Compared with methods that generate complete shapes, our method naturally provides more controllability, as users can + +![](images/6b63c3bc07b2c6ba6e1529e930bee6224e0aa183b15dd8fac7dfc9d4bde04005.jpg) +(a) Input image + +![](images/761b9fdf732dceaca134460cb34ad5955c8222489db8f32bfc1821d8c5a96bd0.jpg) +(b) Normal maps +Figure 9. Failure case. + +![](images/5ab6abf955625a12b4174d88e9bc914ae75024bbb3a347d9cedf83d28481f9dd.jpg) +(c) Reconstructed mesh + +![](images/9f677fc7799a22578a756d6a363bf3ac9347fcf45e84892c0802ec9f9fdfc9dc.jpg) +(d) Final VDM + +start with a coarse shape and add customization details and shape parts, see Figure 1. We also show a video in the Supplementary Material to demonstrate the modeling process with VDMs generated by our method. + +Part editing. With our image-to-VDM, one can perform editing in 2D image space and change the appearance of the part in 3D, see Figure 8. Editing in image space is typically much more convenient than sculpting 3D shapes, therefore allowing users to customize their parts with ease. + +# 5. Conclusion, Limitation, and Future Work + +In this work, we propose a method to generate a VDM from an input single-view image. Our method first finetunes a pretrained image diffusion model to generate multi-view normal maps from the input image, and then reconstructs a VDM image from the multi-view normals. The generated VDMs can be used directly in shape modeling, which provide more freedom to the users on the appearance and position of each part on the shape. We also propose an efficient pipeline for creating a VDM dataset from 3D objects. Our method outperforms state-of-the-art image-to-3D models and scalar displacement map baseline, proving that our approach is more suited for VDM generation. + +As discussed in Section 3.2, our VDM reconstruction involves per-shape optimization, making its inference time significantly slower than the current image-to-3D methods with feed-forward LRM. Investigating the possibility of a VDM-LRM with limited training data is of great interest to us. For certain shapes with thin structures, our method cannot produce plausible results, while the generated normals look reasonable, see Figure 9. We suspect it is due to the multi-view images being inconsistent across different views, as observed by many other works [24, 68]. + +VDMs are predominantly used for modeling organic shapes, yet the idea of modeling-by-parts can be applied to the majority of 3D shapes. There are exciting further avenues for part-based 3D generative models. + +Acknowledgment. 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It is challenging for existing keypoint localization methods because their limited training data cannot provide generalizable shape and semantic cues, leading to inferior performance and generalization capability. Instead of relying on large scale training data, this work tackles this challenge by exploiting the rich priors from large generative models. We propose a data-efficient generalizable localization method named GenLoc. GenLoc extracts the generative priors from a pre-trained image generation model by calculating the correlation map between image latent feature and condition embedding. Those priors are hence optimized with our proposed heatmap expectation loss to perform object keypoint localization. Benefited by the rich knowledge of generative priors in understanding of object semantics and structures, GenLoc achieves superior performance on various object keypoint localization benchmarks. It shows more substantial performance enhancements in cross-domain, few-shot and zero-shot evaluation settings, e.g., getting $20\% + AP$ enhancement over CLAMP [43] in various zero-shot settings. + +# 1. Introduction + +The rapid progress in deep learning and computer vision has pushed the object visual perception from coarse detection to fine-grained structure analysis. Typically, the object structure can be represented as a set of pre-defined keypoints, e.g., shoulder, elbow, or tail and root. As an important step for object structure analysis, general object keypoint localization has attracted increasing attention. Existing keypoint localization methods typically utilize powerful neural networks, e.g., Convolutional Neural Network (CNN) [28, 35] or Vision Transformer (ViT) [21, 38] to either directly regress keypoint coordinates [15] or estimate the keypoint heatmaps [28, 35] to perform localization. Those methods learn keypoint priors purely from training + +![](images/2e5bf25942dcf5e0f12ad60a152c0b60e747fad5b8fa6df6aca700aa3e81189e.jpg) +Figure 1. Upper: The pre-trained image generation model LDM [25] has shown the correlation between input image latent feature and different text condition through the cross attention mechanism. Bottom: We aim to optimize the correlation map to locate the object keypoint by learning a specific condition embedding. Directly optimizing the cross attention map in LDM cannot produce well-localized heatmap. Our method can address this issue and produce more accurate results. + +set, i.e., training backbone from scratch on a specific keypoint localization dataset and test it on corresponding test set. This pipeline is limited to the narrow domain defined by the training data, making those methods hard to generalize to different domains or various objects, resulting in poor generalization capability. + +Designing a generalizable keypoint localization method is important but challenging. The generalization capability of neural network is inseparable from large scale training data, which is demonstrated by recent generative models in language and vision area, e.g., Large Language Model (LLM) [2] and Latent Diffusion Model (LDM) [25] show remarkable generation performance across a wide range of + +domains. Therefore a straightforward way to pursue generalization capability is to collect large scale data on a specific task and train model. For instance, SAM [12] and Depth Anything [39] involve a training-annotation-loop to automatically generate image-mask/depth pair to train a powerful segmentation/depth estimator. These methods are effective but not efficient and will consume large resources. + +Different from those efforts, this work is motivated to exploit whether a generative model trained on large scale data can be transferred to generalizable keypoint localization task. In depth estimation task, Marigold [9] proposes to fine-tune the U-Net of LDM to generate depth map from noise and input image. This pipeline is efficient and effective as it only requires a small amount of labeled data to achieve satisfied performance. However, directly transferring this pipeline into object keypoint localization is not trivial. Different from depth map containing only single channel, keypoint heatmaps contains more channels than image to reflect keypoint type information, making it infeasible to fine-tune U-Net to get desired outputs with a frozen VAE decoder. Therefore how to transfer LDM into keypoint localization is still a challenging problem. + +To tackle this challenge, as well as to achieve generalizable keypoint localization, we utilizes the controllability of LDM to get desired keypoint heatmaps, instead of directly fine-tuning LDM U-Net to output target. Specifically, current LDM performs image generation under the condition guidance such as text, image or semantic maps, the condition plays an important role in generation model to inject the semantic information. As shown in Fig. 1, pre-trained LDM can produce different response map for different input condition. This motivates us to encode the keypoint type information into condition and extract the response map through the controllable mechanism of LDM to exploit the generative priors for keypoint localization. + +The above intuition leads to our proposed GenLoc, a generalizable object keypoint localization method. GenLoc performs keypoint localization by exploiting the correlation map between keypoint condition and image latent feature, which is extracted by the Condition-guided Keypoint Heatmap Extraction (CKHE) module. To fully utilize the property of keypoint distribution in the extracted correlation map, we also introduce the Heatmap Expectation Loss (HEL) to effectively optimize the whole model in an end-to-end manner. As shown in Fig. 1, compared with related work [3, 10, 24, 44] on optimizing cross attention map in LDM to find targets, GenLoc models the keypoint distribution over image spatial dimension, which can produce more localized heatmap and achieve better performance. + +Our proposed GenLoc can effectively leverage the potential of generative prior in pre-trained image generation model, thus achieving superior performance in various object keypoint localization benchmarks. GenLoc achieves + +$80.1\%$ AP on animal keypoint localization, outperforming previous SoTA model by $2.3\%$ . Moreover, exploiting generative priors makes GenLoc a data-efficient method. For instance, in few-shot setting, GenLoc achieves $62.8\%$ AP with only 5 images per category, which is higher than previous ScarceNet [14] by $9.5\%$ . In zero-shot keypoint localization setting, GenLoc also shows superior performance. + +In summary, GenLoc performs keypoint localization by extracting the correlation map between image feature and keypoint condition. This design can effectively exploit the generative priors in pre-trained LDM and make GenLoc a data-efficient generalizable keypoint localization method. Benefited by the proposed CKHE and HEL, GenLoc achieves superior performance on various keypoint localization datasets, especially in cross-domain, few-shot and zero-shot settings. + +# 2. Related Work + +# 2.1. Keypoint Localization + +keypoint localization aims to locate the keypoints of various objects from input RGB images, and existing keypoint localization methods can be divided into regression-based and heatmap-based methods. + +Regression-based keypoint localization directly outputs keypoint coordinates via powerful neural network [1, 32]. Due to the high non-linear mapping between input image and numerical coordinates, many works have been proposed to improve the performance of direct regression, including: i) regressing via integration, such as Soft-armgax [29] and Sampling-argmax [16], ii) proposing proposing new loss functions like RLE [15], and iii) designing more powerful backbones to improve the performance of direct regression, such as TokenPose [17] and PETR [26]. + +Heatmap-based keypoint localization encodes keypoint location with a probability map [31]. This type of methods estimates heatmaps and retrieves keypoint coordinates with a post-processing operation. Currently, heatmap-based methods dominate the field of keypoint localization because heatmap is easy to learn by CNN or Vision Transformer. Pioneer works [22, 28, 35, 38] design powerful CNN or Transformer models to estimate high resolution heatmaps for human/animal/face keypoint localization. + +All above methods train model on a narrow domain training data, which leads to limited generalization capability. In contrast, our method exploits generative priors encoded in LDM from large scale data, making it more generalizable to detect keypoints from various image domain and objects. + +# 2.2. Generative Models for Visual Perception + +Generative model, e.g., Latent Diffusion Model (LDM) [25] aims to reconstruct data, e.g., image, from random noise without manual annotation, making them effectively uti + +lize large scale unlabeled data to enhance its generalization capability. Therefore, researchers try to transfer the generative models into other areas such as visual perception to boost performance. A line of work utilizes the architecture of generative model, e.g., diffusion model to effectively capture the task-specific data distribution. DDP [6] adopts the multi-step denoising framework into segmentation and depth estimation task and achieves superior performance over conventional architecture. SODA [5] adopts the diffusion framework for representation learning. However, directly transferring generative architecture cannot fully utilize the generative priors trained from large scale data, these methods still have limited generalization capability. + +Another line of work exploits how to transfer the generative model with pre-trained weights into downstream tasks. Directly fine-tuning LDM on specific task is a way to achieve this goal. Marigold [9] fine-tunes the U-Net of LDM to estimate the depth map, achieving superior generalization performance in depth estimation. DMP [13] adopts LoRA [4] to fine-tune the U-Net for dense prediction tasks. GED [45] simplifies the multiple denoising steps in LDM by directly predicting the latent edge map. Recently some methods show that optimizing the condition of LDM can also get desired outputs. SLiMe [10] optimizes the condition to perform few-shot segmentation. Diff-Tracker [44] learns prompts to represent object for tracking. Hedlin et al. [3] optimizes text embedding for unsupervised learning of keypoints and landmarks. However, these methods simply adopt cross attention map to find targets, which is not effective in keypoint localization. As demonstrated in Sec. 4, optimizing cross attention map like Hedlin et al. [3] cannot achieve satisfied performance in standard keypoint localization tasks. Our proposed method can accurately model the keypoint distribution, thus achieves better performance. + +# 3. Method + +# 3.1. Overview + +The object structure can be represented by a set of keypoints $\{\mathcal{K}_i\}_{i=1}^n$ , where $\mathcal{K}_i$ denotes the coordinates of the $i$ -th type keypoint, e.g., person shoulder or animal tail root, $n$ is the total type of keypoint defined in this object. The goal of object keypoint localization is to estimate the coordinates of target keypoints from input image, i.e., + +$$ +\left\{\mathcal {K} _ {i j} \right\} _ {i = 1} ^ {n} = \operatorname {l o c a t e} (\mathcal {I}), \tag {1} +$$ + +where $\mathcal{I}$ denotes the input image contains a specific object. + +We adopt the heatmap technology [31] to locate keypoint, which encodes keypoint into a 2D probability distribution map $\mathcal{H}_i$ and estimates it with a neural network, i.e., + +$$ +\left\{\mathcal {H} _ {i} \right\} _ {i = 1} ^ {n} = \Phi (\mathcal {I}), \tag {2} +$$ + +where $\Phi (\cdot)$ can be implemented by Convolutional Neu + +ral Network (CNN) [28, 35] or Vision Transformer [38]. Once the model is learned, keypoints can be decoded by finding the maxima in each channel of heatmap $\mathcal{H}$ , i.e., $\mathcal{K}_i = \arg \max (\mathcal{H}_i)$ . Typical object keypoint localization methods learn the model $\Phi (\cdot)$ purely from training data, i.e., training on a specific domain. This pipeline makes them restricted to a specific image domain or object category and leads to inferior performance and generalization capability. + +Instead of learning $\Phi(\cdot)$ from a specific domain, we aims to exploits the rich prior in image generative models to perform localization. Image generative models, e.g., latent diffusion model (LDM) [25], trained on large scale image data have shown promising performance in understanding scene structure and are successfully transferred to depth estimation [9] or edge detection [45] tasks. This motivates us to learn a generalizable localization model $\Phi(\cdot)$ by exploiting the generative priors from LDM. Given an input image $\mathcal{I}$ , LDM adopts a pre-trained VAE encoder $\mathcal{E}$ to encoder $\mathcal{I}$ into a latent vector $\mathbf{z} = \mathcal{E}(\mathcal{I})$ , from which the original data can be reconstructed via a decoder $\mathcal{D}$ by $\bar{\mathcal{I}} = \mathcal{D}(\mathbf{z}) \approx \mathcal{I}$ . LDM performs generation in latent space, i.e., training a denoising U-Net $\mathcal{U}$ to predict the noise from current input $z_{t}$ , time step $t$ and condition $\mathbf{c}$ , i.e., + +$$ +\epsilon = \mathcal {U} (\mathbf {z} _ {t}, t, \mathbf {c}). \tag {3} +$$ + +LDM freezes $\mathcal{E}(\cdot)$ and only trains $\mathcal{U}(\cdot)$ by minimizing the $\ell_2$ distance between the predicted noise with its ground truth. Therefore, the generative priors are embedded in $\mathcal{U}(\cdot)$ . However, how to extract such information from LDM remains a problem. Previous work [9, 45] shows that directly fine-tune $\mathcal{U}(\cdot)$ on specific tasks can achieve satisfied performance, but directly transferring this approach to keypoint localization is not trivial. Keypoint localization needs to output multiple types of keypoints for single object, which is larger than image channel, making it infeasible to adopt decoder $\mathcal{D}(\cdot)$ to recover latent feature $\mathbf{z}$ to image-level representation. + +We propose the GenLoc to extract the generative prior in $\mathcal{U}(\cdot)$ to implement $\Phi (\cdot)$ and perform generalizable keypoint localization. Instead of fine-tuning $\mathcal{U}(\cdot)$ to output corresponding heatmaps, GenLoc exploits the correlation map $C_i$ between latent feature map $\mathbf{z}$ with condition $\mathbf{c}_i$ to generate final heatmap, this is achieved by the proposed Conditionguided Keypoint Heatmap Extraction (CKHE) module, i.e., + +$$ +\left\{\mathcal {C} _ {i} \right\} _ {i = 1} ^ {n} = \operatorname {C K H E} (\mathcal {U} (\cdot), \mathbf {z}, \left\{\mathbf {c} _ {i} \right\} _ {i = 1} ^ {n}). \tag {4} +$$ + +In this way, keypoint type is encoded into condition $\mathbf{c}_i$ , allowing us flexibly to locate arbitrary type of keypoints. + +We train CKHE module with our proposed Heatmap Expectation Loss (HEL), which computes the loss by taking the extracted correlation map $\{\mathcal{C}_i\}_{i=1}^n$ and its corresponding ground truth heatmap $\{\mathcal{H}_i^*\}_{i=1}^n$ as inputs. The computed + +![](images/f3d4a0523be8661861d076f95bd40808c56b0ae499d880abbabe3d9cfd17a2a3.jpg) +Figure 2. The proposed GenLoc for generalizable keypoint localization by exploiting generative priors from LDM [25]. GenLoc takes object image as input and initializes a set of keypoint condition to extract generative priors. The image input is processed by a frozen VAE encoder to get the latent image feature. The denoising U-Net takes the latent feature and keypoint condition as input and generates corresponding updated output features. Latent feature and keypoint condition are passed to our proposed CKHE module to obtain the keypoint distribution map. The whole pipeline is optimized by our proposed Heatmap Expectation Loss in an end-to-end manner. + +loss $\mathcal{L}_{HEL}$ can be represented as, + +$$ +\mathcal {L} _ {\mathrm {H E L}} = \sum_ {i = 1} ^ {n} \mathcal {D} \left(\mathcal {C} _ {i}, \mathcal {H} _ {i} ^ {*}\right), \tag {5} +$$ + +where $\mathcal{D}(\cdot)$ computes the loss by comparing the difference between the extracted correlation map and its ground truth. + +We supervise CKHE with HEL to perform localization, Fig. 2 shows the pipeline of the proposed GenLoc. During training we freeze the VAE encoder $\mathcal{E}$ , U-Net $\mathcal{U}(\cdot)$ and only adjust condition c and a small set of LoRA [4] parameters to extract the generative prior. This strategy allows us to keep the rich knowledge in $\mathcal{U}(\cdot)$ and accurately locate the target keypoints. Compared with directly fine-tuning $\mathcal{U}(\cdot)$ in previous work, our method GenLoc is more effective in maintaining and exploiting the generative prior for keypoint localization. Implementations to CKHE and HEL can be found in the following parts. + +# 3.2. Localization from Generative Priors + +Given an input image $\mathcal{I}$ and pre-trained LDM U-Net $\mathcal{U}(\cdot)$ , GenLoc aims to optimize a set of keypoint condition $\mathbf{c} = \{\mathbf{c}_i\}_{i=1}^n$ to locate the target keypoint coordinates. The core components of GenLoc are the Condition-guided Keypoint Heatmap Extraction (CKHE) module to extract generative prior from $\mathcal{U}(\cdot)$ and Heatmap Expectation Loss (HEL) to supervise the whole model training. + +Condition-guided Keypoint Heatmap Extraction. Different from previous work that direct fine-tuning U-Net to estimate heatmap, we exploit the controllable generation mechanism in LDM for heatmap generation. Current most generative models implement controllable mechanism via condition input, e.g., text or image. Condition is injected into generation process via the widely adopted attention mechanism in Transformer [33]. Specifically, given the latent feature $\mathbf{z} \in \mathbb{R}^{m \times d}$ and condition embedding $\mathbf{c} \in \mathbb{R}^{n \times d}$ , + +we pass them to $\mathcal{U}(\cdot)$ to get the updated latent feature and condition, the cross attention can be computed by, + +$$ +\mathcal {S} = \operatorname {s o f t m a x} _ {\mathbf {n}} \left(\frac {\mathbf {z} \cdot \mathbf {c} ^ {T}}{\sqrt {d}}\right), \tag {6} +$$ + +where $S \in \mathbb{R}^{m \times n}$ denotes the attention score between latent feature $\mathbf{z}$ and condition $\mathbf{c}$ , $m$ and $n$ denotes the number of image tokens and keypoint condition embeddings, $d$ indicates the dimension of features. Note that the softmax is performed along different keypoint conditions, this indicates that each token from latent $\mathbf{z}$ independently finds the similar keypoint condition and aggregates its feature. An illustration of cross attention in LDM is shown in Fig. 3. + +Although $S$ in Eq. (6) can be interpreted as heatmap to perform localization, directly adopting it has several drawbacks. First, the similarity computation in $S$ is independent among $m$ image latent tokens, which does not satisfy the property of heatmap that only has high response at target spatial position, leading to inaccurate keypoint distribution estimation. Second, different conditions are correlated in $S$ and it is hard to differentiate spatial adjacent keypoints as each image token can only produce high response to only one type of keypoint. Therefore we propose the CKHE to avoid above limitation. Different from cross attention in Eq. (6), CKHE considers to compute correlation map between latent feature $\mathbf{z}$ and keypoint condition $\mathbf{c}$ such that each token in $\mathbf{z}$ is correlated but different condition in $\mathbf{c}$ is independent. To achieve this goal, we exchange the computation order in Eq. (6) and compute the softmax over latent tokens, not keypoint condition, i.e., + +$$ +\mathcal {C} = \operatorname {s o f t m a x} _ {\mathbf {m}} \left(\frac {\mathbf {c} \cdot \mathbf {z} ^ {T}}{\sqrt {d}}\right), \tag {7} +$$ + +where $\mathcal{C} \in \mathbb{R}^{n \times m}$ denotes the estimated heatmap by CKHE. Besides Eq. (7), we also need to fine-tune corresponding attention layer parameters to adapt the changed computation + +![](images/9770a4fe864b326158c17449b3b7fa65843639515488410001564549977d06b6.jpg) +Figure 3. Illustration the different interaction mechanism between image latent feature and keypoint condition. (a) LDM adopts cross attention to aggregate condition information into latent feature, which is not suitable for keypoint localization and leads to inferior heatmap results. (b) Our proposed CKHE models the keypoint distribution over image latent features and decouple the keypoint condition, which generates more localized heatmaps and can differentiate spatial adjacent keypoints. + +way, which is implemented by LoRA. Note that although Eq. (7) is similar to Eq. (6), they are different in many aspects. As state above, Eq. (7) adopts keypoint condition as query to compute similarity score, therefore the tokens in latent $\mathbf{z}$ are naturally correlated, namely only a small number of tokens have high probability in the estimated correlation map $\mathcal{C}$ . Moreover, Eq. (7) also de-correlates the keypoint condition, making it feasible to detect spatial adjacent keypoints. As shown in Fig. 3, CKHE can model keypoint distribution more accurately and generate more localized heatmap, achieving better performance. + +Heatmap Expectation Loss. We aims to optimize the condition $\mathbf{c}$ so that the obtained correlation map $\mathcal{C}$ can be used to accurately locate the target keypoint. To achieve this goal we compute loss by measuring the difference between $\mathcal{C}$ and target ground truth $\mathcal{H}^*$ . A straightforward approach is to adopt the widely used $\ell_2$ distance, i.e., + +$$ +\mathcal {L} _ {\mathrm {M S E}} = \ell_ {2} \left(\mathcal {C} _ {i}, \mathcal {H} _ {i} ^ {*}\right). \tag {8} +$$ + +However, adding element-wise supervision in Eq. (8) is not effective because $\mathcal{H}^*$ is manually defined unnormalized Gaussian distribution with fixed variance, which cannot reflect the underlying true distribution and will hinder the model to learn a accurate distribution to model the target + +keypoint, which is also observed in previous work [15, 20]. + +Although the underlying distribution of target keypoint is unknown, it should have large overlap with $\mathcal{H}^*$ to produce high response at the target location. Therefore we instead model the overlap between $\mathcal{C}$ and $\mathcal{H}^*$ and propose a Heatmap Expectation Loss (HEL) to address above limitation. Inspired by Integral Pose [29], we compute the expectation score by integral the target $\mathcal{H}_i^*$ over the estimated distribution $\mathcal{C}_i$ to model the overlap between $\mathcal{C}$ and $\mathcal{H}^*$ . The goal of HEL is to maximize the expectation score, i.e., + +$$ +\mathcal {L} _ {\mathrm {H E L}} = - \log \left(\sum_ {j = 1} ^ {m} \mathcal {C} _ {i} [ j ] \cdot \mathcal {H} _ {i} ^ {*} [ j ]\right), \tag {9} +$$ + +where $m$ denotes the number of image tokens. As illustrated in Fig. 2 right, higher expectation score indicates larger overlap between $\mathcal{C}_i$ and $\mathcal{H}_i^*$ , leading to sharper heatmap in Fig. 3. Compared with $\mathcal{L}_{\mathrm{MSE}}$ , $\mathcal{L}_{\mathrm{HEL}}$ can fully utilize the normalization property of $\mathcal{C}$ to producing more effective gradients during training, thus achieves better performance. + +To better show the advantage of the proposed HEL, we give a detailed gradient analysis of Eq. 8 and Eq. 9 and show how them different in optimizing the correlation map $\mathcal{C}$ to its target $\mathcal{H}^*$ . Specifically, the gradient of the loss function to each image latent token $\mathcal{C}_i[j] \in \mathcal{C}_i$ can be computed as, + +$$ +\frac {\partial \mathcal {L} \left(\mathcal {C} _ {i} [ j ] , \mathcal {H} _ {i} ^ {*} [ j ]\right)}{\partial \mathcal {C} _ {i} [ j ]} = \left\{ \begin{array}{c l} - 2 \left(\mathcal {H} _ {i} ^ {*} [ j ] - \mathcal {C} _ {i} [ j ]\right) & \text {f o r} \mathcal {L} _ {\mathrm {M S E}} \\ - \mathcal {H} _ {i} ^ {*} [ j ] / \left(\sum_ {j} \mathcal {C} _ {i} [ j ] \cdot \mathcal {H} _ {i} ^ {*} [ j ]\right) & \text {f o r} \mathcal {L} _ {\mathrm {H E L}} \end{array} \right. \tag {10} +$$ + +For positive samples in $\mathcal{C}_i$ (i.e. $\mathcal{H}_i^*[j] = 1$ ), the gradient of HEL and MSE loss is small when $\mathcal{C}_i[j] \to 1$ . Their difference is reflected on hard samples. When a positive position is predicted with a low probability, HEL will produce larger gradient than MSE loss for the model training, thus is more effective for model training. This strategy is also adopted in other loss functions such as focal loss in object detection and triplet loss with hard mining in metric learning. + +# 3.3. Discussions + +Compared with conventional keypoint localization methods trained on a specific domain, GenLoc exploits the rich generative priors in LDM, which is pre-trained on large scale image dataset. Equipped with our proposed CKHE and HEL, GenLoc can accurately locate keypoint and show superior performance on various localization benchmarks. + +GenLoc share some similarity with several works like SLiMe [10], Diff-Tracker [44] and Hedlin et al. [3] in optimizing condition to find desired targets. However, as illustrated in CKHE, all previous methods directly optimize cross attention map to find targets, which is not suitable for keypoint localization, as it requires accurately modeling the keypoint distribution over spatial dimension. Our proposed CKHE and HEL boost the cross attention baseline by a large margin, producing more localized heatmap in Fig 3. More quantitative results can be found in Sec. 4. + +# 4. Experiments + +# 4.1. Datasets and Evaluation Metrics + +We evaluate GenLoc on several widely used keypoint localization benchmarks, e.g., COCO Keypoint [19] and HumanArt [8] for human keypoint localization, AP-10K [40] for animal keypoint localization. + +COCO Keypoint [19] is a large scale human keypoint localization dataset with 17 annotated keypoints, e.g., nose, left ear, etc. It contains more than 200,000 images and 250,000 person instances. COCO Keypoint is divided into three parts: 57k images for training set, 5k images for validation set and 20k images for test-dev set. + +Human-Art [8] is a large scale human keypoint localization containing both natural scenes such as sports or outdoor, and artificial scenes including cartoon, digital art, ink painting and etc. We adopt it to evaluate the cross-domain localization performance of different methods. Similar to COCO, Human-Art is also annotated with 17 keypoints and contains $35\mathrm{k}$ images for training set and $5\mathrm{k}$ images for validation set. In this paper we only adopt its validation set. + +AP-10K [40] is a large scale animal keypoint localization dataset contains 10,015 images collected and filtered from 23 animal families and 54 species. 17 keypoints are annotated in the dataset. AP-10K splits the train, validation, and test sets with a ratio of 7:1:2 per animal species. + +Evaluation metrics. We follow the standard evaluation metric and use OKS-based metrics for keypoint localization. We report average precision with different thresholds and object sizes: AP, $\mathrm{AP}^{50}$ , $\mathrm{AP}^{75}$ , $\mathrm{AP}^M$ and $\mathrm{AP}^L$ . + +# 4.2. Implementation Details + +All experiments are implemented based on PyTorch [23]. We utilize Stable Diffusion v1.5 [25] as the pre-trained image generative model. The dimension of condition embedding of SD1.5 is set to 768. We additionally fine-tune LDM by LoRA, with hidden dimension $r = 16$ . We insert CKHE into all cross attention layers in U-Net up-blocks. The condition embedding and LoRA modules are optimized by Adam optimier [11] with 1e-2 and 1e-3 learning rate, respectively. We train GenLoc with batch size of 200 through gradient accumulation and 10 epochs on AP-10k for ablation study. For final comparison, we train model 100 epochs on AP-10K and 14 epochs for COCO Keypoints. + +# 4.3. Ablation Study + +This section aims to investigate the contribution of each proposed components in GenLoc, including the CKHE module and proposed Heatmap Expectation Loss. We also present training analysis in our method. + +Effectiveness of CKHE. We first show the effectiveness of the proposed CKHE on keypoint localization. The results are shown in the top rows of Table 1. LDM adopts + +
ComponentAP\( AP^{50} \)\( AP^{75} \)\( AP^M \)\( AP^L \)
Heatmap generation
Cross Attention60.992.365.849.761.2
CKHE70.794.378.553.471.0
Loss function
MSE Loss70.794.378.553.471.0
HEL73.396.880.955.173.7
Fine-tuning strategy
Only condition + LoRA60.193.164.637.960.7
73.396.880.955.173.7
Noise time step selection
High noise(t = 601)15.441.38.57.015.7
Low noise(t = 21)71.394.979.057.171.6
No noise73.396.880.955.173.7
+ +Table 1. Ablation study on each proposed component on AP-10K. + +cross attention to aggregate the information from condition to image latent feature, which is inconsistent with the goal of keypoint localization. In contrast, our proposed CKHE regards condition as query and computes the condition and image latent feature along spatial token dimension, thus can better estimate the distribution of keypoints. As shown in Table 1, CKHE significantly outperforms cross attention by a large margin under the same setting, e.g., higher than $9.8\%$ . In Fig. 3 we also can observe that CKHE produces more localized heatmaps, leading to better performance. + +Effectiveness of HEL. In the middle rows of Table 1 we also show the effectiveness of the HEL over traditional MSE loss. As stated in Sec. 3, MSE loss is not effective in learning accurate keypoint distribution from the manually defined ground truth heatmap. Our proposed HEL can fully utilize the normalization property of correlation map and produce more effective gradient to train model. As shown in Table 1, HEL outperforms MSE loss by $2.6\%$ , indicating its advantages in learning accurate keypoint distribution. + +Fine-tuning with LoRA. We also verify the necessity of fine-tuning the model with LoRA. Previous methods [3, 10, 44] only optimizing condition to find targets, which cannot achieve superior performance in keypoint localization, i.e., only obtaining $60.1\%$ . This may be that LDM does not need a well-localized correlation map for image generation, which is exactly required by keypoint localization. By fine-tuning LDM with LoRA, we achieve a balance between the localization performance and the generalization capability, outperforming baseline by $13.2\%$ AP. + +Noise time step selection. LDM performs generation from noisy input and previous work [30] extracts features from U-Net by adding noise to input image. Therefore we investigate how to add noise to input image for keypoint localization. We evaluate model performance under high + +
MethodAP\( AP^{50} \)\( AP^{75} \)\( AP^M \)\( AP^L \)
SimplePose [35]69.9----
Hourglass [22]72.9----
HRNet-W32 [28]72.293.578.955.772.9
HRNet-W48 [28]72.893.680.257.773.5
ViPNAS [37]67.1----
HRFormer-S [41]71.7----
HRFormer-B [41]73.5----
RTMPose [7]72.293.978.856.972.8
CLAMP-B [43]74.3----
CLAMP-L [43]77.8----
Ours80.197.387.659.380.5
+ +noisy, low noisy and clean input (namely no noise is added to image), and results are shown in the bottom of Table 1. It can be observed that a low noise is preferred by model to extract image feature and we find that adopting clean image as input achieves the best performance. Therefore in the following experiments we adopt clean image as input. + +# 4.4. General Object Keypoint Localization + +The section aims to demonstrate the effectiveness of the proposed GenLoc on various object keypoint localization tasks. We compare GenLoc with recent methods on animal keypoint localization benchmark AP-10K and human keypoint localization benchmark COCO Keypoint. The results are shown in Table 2 and Table 3. + +Animal Keypoint Localization. We first compare GenLoc with other methods on animal keypoint localization task and report performance on AP-10K. As shown in Table 2, existing animal keypoint localization methods are belong to heatmap-based method, e.g., SimplePose [35], HRNet [28] and HRFformer [41]. Compared with these conventional methods, GenLoc achieves superior performance, e.g., $80.1\%$ AP on AP-10K, which is higher than HRFformer by a large margin. Recent CLAMP [43] embeds language information into animal keypoint localization, which improves the localization performance. Compared with CLAMP, our method can fully utilize the large LDM pre-trained on large scale image data, outperforming CLAMP by $2.3\%$ AP. All this indicates the superior performance of GenLoc on animal keypoint localization task. + +Human Keypoint Localization. We then show that GenLoc can also locate person keypoint and compare on COCO Keypoint. As shown in Table 3, existing methods can be divided into heatmap-based method: SimplePose [35], HRNet [28] and ViTPose [38], and regression-based methods: DeepPose [32] and RLE [15]. All of them learn the keypoint prior purely from training data. Compared with these works, our method can exploit the generative priors in LDM and achieving better performance. + +Table 2. Comparison on AP-10K in animal keypoint localization. + +
MethodAP\( AP^{50} \)\( AP^{75} \)\( AP^M \)\( AP^L \)AR
DeepPose [32]53.882.659.252.257.366.8
RLE [15]74.091.581.670.978.576.8
SimplePose [35]74.492.682.571.579.277.6
HRNet [28]76.893.683.674.081.579.6
SimCC [18]76.593.283.173.681.579.7
ViTPose [38]77.493.684.874.781.980.2
Ours77.694.685.774.882.680.7
+ +Table 3. Comparison on COCO in human keypoint localization. + +
MethodAP\( AP^{50} \)\( AP^{75} \)\( AP^M \)\( AP^L \)AR
SimplePose [35]48.473.050.727.250.752.8
SimCC [18]51.775.254.826.254.357.0
HRNet [28]53.476.356.530.455.957.5
ViTPose [38]53.877.957.431.456.658.7
LocLLM [34]64.887.470.440.967.469.3
Ours67.087.972.543.269.970.8
+ +Table 4. Comparison on Human-Art in cross-domain keypoint localization. All models are trained on COCO Keypoint. + +
Method510152025
Labeled data + additional unlabeled data
UDA [36]0.4290.5190.5660.5800.628
FixMatch [27]0.4780.5440.5890.6010.631
FlexMatch [42]0.4660.5550.5960.6180.646
ScarceNet [14]0.5330.5970.6320.6540.681
Only labeled data
HRNet [28]0.3600.4630.5110.5470.588
Ours0.6280.6680.6880.6920.711
+ +Table 5. Comparison on AP-10K in few-shot localization. We train model when 5, 10, 15, 20, 25 images per species are labeled. + +# 4.5. Cross-Domain Keypoint Localization + +In this section we aims to demonstrate the generalization capability of GenLoc by comparing with other methods in cross-domain keypoint localization, i.e., training model on one dataset and test it on other domain dataset without fine-tuning. Human-Art [8] dataset contains different image domain from COCO Keypoint, therefore we adopt it as test set to evaluate models trained on COCO Keypoint. + +As shown in Table 4, although previous methods achieve superior performance in COCO Keypoint, they obtain inferior performance over Human-Art benchmarks. This is because limited training data in COCO Keypoint cannot provide rich prior for these model to locate keypoint from different image domain. Our method utilizes the prior in pretrained LDM, which is trained on large scale data to ensure its domain diversity. It achieves $67.0\%$ AP on Human-Art, outperforming previous methods. + +![](images/d15a4756978006a73458a58270919d4f64a6d3b921e55d85709c6b6a0e1e104c.jpg) +Figure 4. Visualization of keypoint localization results from COCO Keypoint (left), Human-Art (middle) and AP-10K (right). + +
MethodTrainTestAPAP50AP75AR
SimplePose [35]BovidaeCanidae41.379.436.449.1
CLAMP [43]BovidaeCanidae46.984.445.653.8
OursBovidaeCanidae72.897.482.475.8
SimplePose [35]BovidaeEquidae41.971.840.346.6
CLAMP [43]BovidaeEquidae46.675.647.551.2
OursBovidaeEquidae76.095.783.180.7
SimplePose [35]BovidaeFelidae22.052.415.028.4
CLAMP [43]BovidaeFelidae28.767.618.936.3
OursBovidaeFelidae64.394.769.269.2
SimplePose [35]CanidaeFelidae39.674.134.546.6
CLAMP [43]CanidaeFelidae48.485.744.055.1
OursCanidaeFelidae73.495.880.977.4
SimplePose [35]CanidaeCricetidae16.141.710.126.0
CLAMP [43]CanidaeCricetidae22.051.114.131.6
OursCanidaeCricetidae50.284.251.055.8
SimplePose [35]CanidaeEquidae20.543.916.625.3
CLAMP [43]CanidaeEquidae28.459.123.134.1
OursCanidaeEquidae61.285.461.566.0
+ +Table 6. Comparison on AP-10K in zero-shot localization. + +# 4.6. Few-shot Keypoint Localization + +In this section we aims to show that GenLoc is a highly data-efficient generalizable keypoint localization method, e.g., it only requires a small set of labeled data to achieve satisfied performance. We follow the ScarceNet [14] setting to randomly select 5, 10, 15, 20, 25 labeled images of each species from original AP-10K training set to train the model, and directly test it on the complete test set. + +As shown in Table 5, existing methods in few-shot setting can be divided into two categories. The first is semi-supervised methods, e.g., UDA [36] and ScarceNet [14], these methods require additional unlabeled data to boost the model performance. The second kind of methods only use labeled data to train model like HRNet [28]. However, limited training data cannot provide rich prior to perform keypoint localization, thus HRNet achieves much worse performance than semi-supervised methods like ScarceNet. Different from previous methods, our method exploits the rich generative priors from image generation model to perform keypoint localization, and achieves superior performance over semi-supervised methods when only using la + +beled data. For instance, GenLoc achieves $62.8\%$ AP in 5-shot setting, which is higher than ScarceNet by $9.5\%$ AP and HRNet by $26.8\%$ AP, respectively. + +# 4.7. Zero-shot Keypoint Localization + +In the final section we further evaluate the generalization capability of GenLoc on unseen objects in zero-shot keypoint localization. We follow CLAMP [43] setting to conduct experiments by testing model on unseen animal species on AP-10K, e.g., training model on one animal species and test it on another species. This setting is more challenging because the appearance, size and background environment are quite different for different animal species. + +We follow CLAMP [43] to conduct different zero-shot keypoint localization experiments according to whether the animal during training and test belong to the same animal order or not. As shown in Table 6, we compare our method with previous methods SimplePose [35] and CLAMP [43]. It can be observed that our method significantly outperform these methods by a large margin. For instance, when training on Bovidae specie and testing on Canidae specie, our GenLoc achieves $72.8\%$ AP, which is higher than CLAMP by $25.9\%$ AP. When training and testing species belong to different orders, e.g., training on Canidae and testing on Felidae, our method can get more improvement, outperforming CLAMP by $35.6\%$ AP. Such large improvement comes from the rich generative priors from large scale data pretrained LDM, which can provide more prior than a narrow domain training data. Our method can fully utilize the generative prior to achieve generalizable keypoint localization in zero-shot setting. + +# 5. Conclusion + +This paper proposes GenLoc, a generalizable object keypoint localization method. GenLoc exploits the generative priors in image generation model to perform keypoint localization. It first adopts the proposed CKHE to extract the correlation map between condition and latent image feature, then optimizes the correlation map by our Heatmap Expectation Loss to perform localization. Experiments on various keypoint localization benchmarks demonstrate the strong generalization capability of the proposed method. + +# Acknowledgement + +This work is supported in part by Guanghua Talent Project of Southwestern University of Finance and Economics and Sichuan Science Foundation project (Grants No. 2024ZDZX0002 and 2024NSFTD0054), in part by CCF-Baidu Open Fund (No. 202422) and open research fund of Key Laboratory of Machine Intelligence and System Control, Ministry of Education (No. MISC-202406), in part by Grant No. 2023-JCJQ-LA-001-088, in part by Natural Science Foundation of China under Grant No. U20B2052, 61936011, 62402013, in part by the Okawa Foundation Research Award, in part by the Ant Group Research Fund, and in part by the Kunpeng&Ascend Center of Excellence, Peking University. + +# References + +[1] Joao Carreira, Pulkit Agrawal, Katerina Fragkiadaki, and Jitendra Malik. Human pose estimation with iterative error feedback. 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This task remains challenging due to complex variations in real-world applications. Recently, diffusion models have demonstrated remarkable capabilities in diverse scene generation, which inspires us to explore their potential for improving DG tasks. Instead of generating images, our method extracts multi-step intermediate features during the diffusion process to obtain domain-invariant features for generalized detection. Furthermore, we propose an efficient knowledge transfer framework that enables detectors to inherit the generalization capabilities of diffusion models through feature and object-level alignment, without increasing inference time. We conduct extensive experiments on six challenging DG benchmarks. The results demonstrate that our method achieves substantial improvements of $14.0\%$ mAP over existing DG approaches across different domains and corruption types. Notably, our method even outperforms most domain adaptation methods without accessing any target domain data. Moreover, the diffusion-guided detectors show consistent improvements of $15.9\%$ mAP on average compared to the baseline. Our work aims to present an effective approach for domain-generalized detection and provide potential insights for robust visual recognition in real-world scenarios. The code is available at Generalized Diffusion Detector + +# 1. Introduction + +Object detection stands as a fundamental task in computer vision and has achieved remarkable technological breakthroughs in recent years. Most object detection methods, including CNN [41, 51, 52, 62] and transformer-based [5, 83] + +detectors assume consistent distributions between training and testing data. However, in practice, detectors face significant challenges from domain shifts and environmental variations, and the performance often deteriorates substantially when deployed in unseen scenarios [9, 78]. + +Domain generalization [34, 35, 65] and adaptation [3, 13, 26, 40] methods have been developed to address these challenges. Mainstream approaches include semi-supervised learning with pseudo-labels [3, 6, 13, 40], feature alignment via adversarial training [9, 40, 57, 68], and style transfer techniques [18, 81]. However, these adaptation methods require target domain data during training, limiting their practical applications. This has led to increased interest in domain generalization through data augmentation [12, 24, 33, 77], adversarial training [36, 82], and meta-learning [1, 15]. While recent advances in foundation models like ClipGap [63] have shown promising results, building robust detectors remains challenging. + +Inspired by the remarkable capabilities of diffusion models [23, 54, 59] in handling visual variations, we propose to leverage them for domain-generalized detection. We extract and fuse multi-timestep intermediate features during the diffusion process to construct a diffusion-based detector that learns domain-invariant representations. However, directly applying these models introduces significant computational overhead due to the multi-step feature extraction process, limiting their practical deployment. + +To address this limitation while preserving their strong generalization advantages, we develop an efficient knowledge transfer framework that enables lightweight detectors to inherit capabilities from diffusion-based detectors. Specifically, our framework consists of feature-level alignment using correlation-based matching and object-level alignment through shared region proposals, allowing conventional detectors to learn both domain-invariant features and robust detection capabilities. Through feature and object-level alignment, conventional detectors can achieve + +![](images/238f64dc3183f36e1c4529636e8daf6e6db76a334c56140212db0d8828fe8f7a.jpg) +Figure 1. Left: Six DG benchmarks used in our paper. The sample images demonstrate substantial domain shifts between source and target distributions. Right: Compared with previous SOTA methods, our approach achieves superior performance across all 13 datasets from six benchmarks. + +![](images/b78cfce992d16d755cdcccbc8827616aa2203df58121c74bb0c01ddc5bedf7b5.jpg) + +![](images/1f6709f990f0fbd1ed71115ee06ab534e8dc6d0e3e658b53ce9b214121191150.jpg) + +improved generalization without increasing inference time. Our work pioneers the application of diffusion models in domain-generalized detection, demonstrating their potential in enhancing detector generalization through knowledge distillation. + +We conduct comprehensive experiments on six challenging DG benchmarks as shown in Fig. 1: Cross Camera, Adverse Weather, Synthetic to Real, Real to Artistic, Di-verse Weather Benchmark, Corruption Benchmark. Experimental results demonstrate that our diffusion-based detector achieves consistent improvements across these benchmarks, with average performance gains of $\{18.6, 15.0, 27.2, 16.4, 2.3, 4.7\}\%$ mAP compared to previous methods, even outperforming most domain adaptation methods that have access to target domain data. Moreover, through our proposed feature-level and object-level learning framework, diffusion-guided detectors obtain significant improvements of $\{20.8, 21.4, 24.6, 9.9, 5.3, 13.8\}\%$ mAP compared to their baselines. These results validate the effectiveness of leveraging diffusion models for domain-generalized detection and provide a promising direction for building robust detectors in real-world scenarios. + +The main contributions of this work can be summarized as follows: + +- This work introduces diffusion models into domain-generalized detection. The inherent denoising mechanism and powerful representation capabilities of diffusion models are utilized to extract domain-invariant features for robust detection. +- To address the computational overhead, we propose a simple yet effective knowledge transfer framework. + +This framework enables detectors to inherit strong generalization capabilities through feature-level alignment and object-level learning, maintaining efficient inference time. +- Comprehensive experiments on six DG benchmarks demonstrate significant improvements over previous approaches in various scenarios. The findings provide valuable insights for robust visual recognition tasks. + +# 2. Related Work + +# 2.1. Domain generalization for object detection + +Domain adaptation methods for object detection focus on adversarial feature alignment [9, 40, 57, 68] and consistency-based learning with pseudo labels [3, 6, 13, 40]. However, these approaches inherently require target domain data during training. Domain generalization methods have been explored through data augmentation [11, 12, 24, 77], adversarial training [36, 82], and meta-learning [1, 15] to enhance model robustness through style transfer and domain shift simulation. Recent works [12, 33, 43, 67, 79] extend these strategies to domain-generalized detection through multi-view learning, specialized augmentation and causal learning. Additionally, ClipGap [63] demonstrates the potential of foundation models by leveraging CLIP [48]. These advances inspire us to explore diffusion models as foundation models, harnessing their inherent generalization capabilities for domain-generalized detection. + +# 2.2. Diffusion models and applications + +Recent studies demonstrate that diffusion models [16, 23, 49, 54, 56, 59] not only excel in image generation but + +also exhibit unique advantages in representation learning [2, 19, 69]. The noise-adding and denoising mechanism enables effective handling of visual perturbations like noise, blur, and illumination changes [46, 61]. These properties suggest the potential of diffusion models in addressing domain generalization challenges. Specifically, the intermediate features during diffusion contain rich semantic information [46], while the denoising process naturally builds robustness against various perturbations [61]. Recent works like [2, 19, 30] further demonstrate the effectiveness of diffusion-based representations in various vision tasks. These promising properties motivate us to leverage diffusion models for domain-generalized detection, and further inspire us to explore transferring their superior capabilities to other detectors. + +# 3. Method + +# 3.1. Overview + +In this section, we introduce our approach for domain generalization detection. The proposed method leverages a diffusion model as feature extractor to learn domain-robust representations through its iterative process. A two-level alignment mechanism is designed to transfer knowledge from the diffusion model to standard detectors: feature-level alignment for domain-invariant patterns and object-level alignment for accurate detection across domains. The overall framework is illustrated in Fig. 3. + +In the following subsections, we first present the problem formulation and introduce the diffusion model basics in Sec. 3.2. The feature extraction and fusion strategy from diffusion models is described in Sec. 3.3. Our two-level alignment approach, including feature-level alignment (Sec. 3.4) and object-level alignment (Sec. 3.5), guides standard detectors to learn robust representations while maintaining accurate detection. The overall training objectives integrating detection losses with alignment constraints are detailed in Sec. 3.6. + +# 3.2. Preliminaries + +DG for detection: Let $S = \{\mathbf{x}_s^i, \mathbf{y}_s^i\}_{i=1}^{N_s}$ denote the source domain with $N_s$ labeled samples, where $\mathbf{x}_s^i$ represents an image and $\mathbf{y}_s^i$ represents the corresponding bounding box annotations. Let $\mathcal{T} = \{\mathbf{x}_t^j\}_{j=1}^{N_t}$ denote the target domain with $N_t$ unlabeled images. The source and target samples are drawn from different distributions $P_S$ and $P_T$ , with discrepancies in image distributions (e.g., style, scene), label distributions (e.g., shapes, density), and sample sizes. The goal is to learn robust representations from the labeled source domain that generalize well to the unseen target domain. + +Diffusion Model: The diffusion process gradually converts source domain images $\mathbf{x}_s^i$ into pure noise through a fixed + +Markov chain of $T$ steps. At each time step $t \in [0, T]$ , Gaussian noise is progressively added to obtain the noisy samples $\mathbf{x}_t$ . The forward process is formulated as: + +$$ +\mathbf {x} _ {t} = \sqrt {\bar {\alpha} _ {t}} \mathbf {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon} \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(0,\mathbf{I})$ , and $\bar{\alpha}_t$ represents the cumulative product of noise schedule $\{\alpha_t\}_{t=1}^T$ controlling the noise magnitude. During training, a neural network $\mathcal{F}_{\theta}$ learns to estimate the added noise from noisy observations $\mathbf{x}_t$ conditioned on time step $t$ . The network is optimized to minimize the discrepancy between predicted and actual noise. At inference, the model reverses this process by iteratively denoising pure noise through refinement steps until obtaining the final output $\hat{\mathbf{x}}_0$ . + +# 3.3. Multi-timestep Feature Extraction and Fusion + +![](images/df5d28167da63369300839f411bca6702e21df557a5281de90040c8d9ddd0f59.jpg) +Figure 2. Overview of multi-timestep feature extraction and fusion. Multi-scale features are extracted from a frozen diffusion model at different timesteps, then processed through trainable bottleneck structures and weighted aggregation module to obtain the final hierarchical features. + +Feature Extraction via Diffusion: The inherent characteristics of diffusion models' intermediate representations make them particularly suitable for domain-invariant feature learning. During the denoising process, the noise predictor $\mathcal{F}_{\theta}$ accumulates multi-scale semantic information by modeling data variations at different noise levels. + +To leverage these properties, we extract and aggregate intermediate features from a sequence of time steps during the forward diffusion process. Specifically, given a source image $\mathbf{x}_s^i$ , we progressively add noise following $\mathbf{x}_s^i \to \mathbf{x}_1 \to \dots \to \mathbf{x}_t$ , where $t \in \{1, 2, \dots, T\}$ . At + +each time step $t$ , we extract features from the four upsampling stages of $\mathcal{F}_{\theta}$ , denoted as $\mathbf{s}_t \in \mathbb{R}^{C_{l,k} \times H_{l,k} \times W_{l,k}}$ , where for each layer $l \in \{1,2,3,4\}$ , we extract three intermediate features ( $k = 1,2,3$ ) from the middle of the layer. The feature dimensions are defined as $C_{l,k}$ , $H_{l,k}$ , and $W_{l,k}$ based on the corresponding layer architecture. This process captures the representation of the transition $\mathbf{x}_{t-1} \rightarrow \mathbf{x}_t$ and generates a multi-timestep feature sequence $\{\mathbf{s}_t\}_{t=1}^T$ for each input image. + +Multi-timestep Feature Fusion: For each timestep, features first go through individual bottleneck structures to align dimensions. A weighted aggregation module then combines features across timesteps with learnable weights as shown in Fig. 2. The fused features form a feature pyramid containing four levels with increasing channel dimensions $C_l \in \{C_1, C_2, C_3, C_4\}$ where $C_l = 256 \times 2^{l-1}$ , and corresponding spatial resolutions $H_l \times W_l$ where $H_l = H/2^{l+1}$ and $W_l = W/2^{l+1}$ for $l \in \{1, 2, 3, 4\}$ , with $H$ and $W$ being the height and width of input image respectively. + +# 3.4. Feature level imitation and alignment + +We construct our detector based on the features extracted from the diffusion model as described above. Specifically, we employ Faster R-CNN [52] with all default parameters unchanged and train it exclusively on the source domain to obtain $\mathcal{F}_{\mathrm{diff}}$ . + +Motivation: Common detectors $\mathcal{F}_{\mathrm{comm}}$ tend to overfit source domain data, limiting their generalization to unseen domains. To address this, we propose leveraging knowledge from diffusion-based detector $\mathcal{F}_{\mathrm{diff}}$ through a two-level alignment approach. Through aligning both feature distributions and object predictions, we expect $\mathcal{F}_{\mathrm{comm}}$ to learn more domain-invariant representations while preserving its detection capability. + +Feature alignment: Due to the inherent feature distribution differences between diffusion-based and standard detectors, we adopt PKD [4] for feature alignment, which enables robust cross-architecture knowledge transfer through correlation-based matching. + +We extract FPN features $\mathcal{M}_{\mathrm{comm}}^l$ and $\mathcal{M}_{\mathrm{diff}}^l$ from the ResNet [20] of $\mathcal{F}_{\mathrm{comm}}$ and the multi-timestep diffusion feature extraction network in $\mathcal{F}_{\mathrm{diff}}$ respectively. Both features have dimensions $\mathbb{R}^{B\times C\times H_l\times W_l}$ at pyramid level $l$ , where $B$ is the batch size, $C$ is the number of channels, and $H_{l}\times W_{l}$ represents the spatial dimensions. With $\hat{\mathcal{M}}$ denoting normalized features, the alignment loss is defined as: + +$$ +\mathcal {L} _ {\text {a l i g n}} = \sum_ {l = 1} ^ {L} \frac {1}{N _ {l}} \| \hat {\mathcal {M}} _ {\mathrm {c o m m}} ^ {l} - \hat {\mathcal {M}} _ {\mathrm {d i f f}} ^ {l} \| _ {2} ^ {2} \tag {2} +$$ + +Cross feature adaptation: To address the potential instability of direct feature alignment between heterogeneous models, we propose to feed $\mathcal{M}_{\mathrm{diff}}$ into $\mathcal{F}_{\mathrm{comm}}$ ’s detection + +heads, enabling stable adaptation while preserving the original detection pipeline. The cross feature loss is defined as: + +$$ +\mathcal {L} _ {\text {c r o s s}} = \mathcal {L} _ {\text {c o m m}} ^ {\text {r p n}} \left(\mathcal {M} _ {\text {d i f f}}; \theta_ {\text {c o m m}}\right) + \mathcal {L} _ {\text {c o m m}} ^ {\text {r o i}} \left(\mathcal {M} _ {\text {d i f f}}; \theta_ {\text {c o m m}}\right) \tag {3} +$$ + +where $\mathcal{L}_{\mathrm{comm}}^{\mathrm{rpn}}$ combines objectness classification and box regression losses for RPN, and $\mathcal{L}_{\mathrm{comm}}^{\mathrm{roi}}$ combines classification and box regression losses for ROI head, following the standard Faster R-CNN detection losses. + +# 3.5. Domain-invariant Object-level Knowledge Transfer + +Beyond feature-level alignment, we aim to enhance $\mathcal{F}_{\mathrm{comm}}$ 's object detection capability in unseen domains by transferring task-relevant knowledge from $\mathcal{F}_{\mathrm{diff}}$ . However, this presents two challenges: (1) target domain data is unavailable during training under the DG setting, and (2) traditional knowledge distillation methods are not directly applicable due to the heterogeneous architectures between $\mathcal{F}_{\mathrm{comm}}$ and $\mathcal{F}_{\mathrm{diff}}$ . + +Shared RoI Feature Propagation: Inspired by CrossKD [64], we propose to align object-level predictions through shared region proposals. We first generate candidate regions $\mathcal{R}_{\mathrm{roi}} \in \mathbb{R}^{N \times 4}$ using the RPN of $\mathcal{F}_{\mathrm{comm}}$ where $N$ is the number of proposals. These regions are used to pool features from both detectors, yielding fixed-size features $\mathcal{M}_{\mathrm{comm}}^{\mathrm{roi}}$ and $\mathcal{M}_{\mathrm{diff}}^{\mathrm{roi}} \in \mathbb{R}^{N \times d}$ , where $d$ is the feature dimension. The spatially aligned features are then fed into diffusion detector's branches: + +$$ +\mathbf {P} _ {\text {c a t}} = \mathcal {F} _ {\text {d i f f}} ^ {\text {c l s}} \left(\mathcal {M} _ {\text {d i f f}} ^ {\text {r o i}}\right), \quad \mathbf {P} _ {\text {b b o x}} = \mathcal {F} _ {\text {d i f f}} ^ {\text {r e g}} \left(\mathcal {M} _ {\text {d i f f}} ^ {\text {r o i}}\right) \tag {4} +$$ + +$$ +\mathbf {Q} _ {\text {c a t}} = \mathcal {F} _ {\text {d i f f}} ^ {\text {c l s}} (\mathcal {M} _ {\text {c o m m}} ^ {\text {r o i}}), \quad \mathbf {Q} _ {\text {b b o x}} = \mathcal {F} _ {\text {d i f f}} ^ {\text {t e g}} (\mathcal {M} _ {\text {c o m m}} ^ {\text {r o i}}) +$$ + +where $\mathbf{P}_{\mathrm{cat}}, \mathbf{Q}_{\mathrm{cat}} \in \mathbb{R}^{N \times (C + 1)}$ denote the class logits for $C$ object categories plus background, and $\mathbf{P}_{\mathrm{bbox}}, \mathbf{Q}_{\mathrm{bbox}} \in \mathbb{R}^{N \times 4}$ represent the predicted box coordinates. + +Classification Knowledge Transfer: For classification knowledge transfer, we use KL divergence with temperature scaling: + +$$ +\mathcal {L} _ {\mathrm {c l s}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \tau^ {2} D _ {K L} \left(\mathbf {Q} _ {\text {c a t}} ^ {i} \| \mathbf {P} _ {\text {c a t}} ^ {i}\right) \tag {5} +$$ + +where $\mathbf{Q}_{\mathrm{cat}}^i$ $\mathbf{P}_{\mathrm{cat}}^i$ are temperature-scaled softmax outputs for the $i$ -th proposal, and $\tau$ is the temperature parameter. + +Regression Knowledge Transfer: For box regression, we use L1 loss: + +$$ +\mathcal {L} _ {\text {r e g}} = \frac {1}{N} \sum_ {i = 1} ^ {N} \left| \mathbf {Q} _ {\mathrm {b b o x}} ^ {i} - \mathbf {P} _ {\mathrm {b b o x}} ^ {i} \right| _ {1} \tag {6} +$$ + +Through this object-level knowledge transfer mechanism, $\mathcal{F}_{\mathrm{comm}}$ learns domain-invariant detection capabilities + +![](images/da278209d409b8ac0aedae915dec1b537e94043ada5c81a12d7badf06b6ef533.jpg) +Figure 3. Overview of the proposed methods. The framework consists of a frozen diffusion detector (top) and a trainable ResNet-based detector (bottom). Knowledge transfer is achieved through feature-level alignment $(\mathcal{L}_{\mathrm{align}},\mathcal{L}_{\mathrm{cross}})$ and object-level prediction alignment using shared RoIs $(\mathcal{L}_{\mathrm{cls}}$ and $\mathcal{L}_{\mathrm{reg}})$ . + +from $\mathcal{F}_{\mathrm{diff}}$ via ROI-level alignment. By sharing the same detection head while processing features from different sources, we encourage $\mathcal{F}_{\mathrm{comm}}$ to extract domain-agnostic object features that can generalize well across domains. + +# 3.6. Joint Optimization Objective + +The overall objective combines supervised detection learning with feature-level and object-level alignments: + +$$ +\mathcal {L} _ {\text {t o t a l}} = \underbrace {\mathcal {L} _ {\det } \left(\mathcal {F} _ {\operatorname {c o m m}} \left(\mathbf {x} _ {s}\right) , \mathbf {y} _ {s}\right)} _ {\text {s u p e r v i s e d l e a n i n g o n s o u r c e d o m a i n}} + +$$ + +$$ +\lambda_ {\text {f e a t u r e}} \underbrace {\left(\mathcal {L} _ {\text {a l i g n}} + \mathcal {L} _ {\text {c r o s s}}\right)} _ {\text {f e a t u r e - l e v e l a l i g n m e n t}} + \lambda_ {\text {o b j e c t}} \underbrace {\left(\mathcal {L} _ {\text {c l s}} + \mathcal {L} _ {\text {r e g}}\right)} _ {\text {o b j e c t - l e v e l a l i g n m e n t}} \tag {7} +$$ + +where $\mathcal{L}_{\mathrm{det}}$ is the detection loss on source domain data $(\mathbf{x}_s,\mathbf{y}_s)$ , with $\lambda_{\mathrm{feature}}$ and $\lambda_{\mathrm{object}}$ being the weights for feature-level and object-level alignment respectively. + +# 4. Experiments + +# 4.1. DG Detection Benchmarks + +Cross Camera. Train on Cityscapes [10] (2,975 training images from 50 cities) and test on BDD100K [74] day-clear split with 7 shared categories following SWDA [57], evaluating generalization across diverse urban scenes. + +Adverse Weather. Train on Cityscapes [10] and test on FoggyCityscapes [58] and RainyCityscapes [27] (synthesized by adding fog and rain effects), using the challenging + +0.02 split setting for FoggyCityscapes to evaluate robustness under degraded visibility conditions. + +Synthetic to Real. Train on Sim10K [31] (10K synthetic driving scenes rendered by GTA-V) and test on Cityscapes [10] and BDD100K [74] for the car category, examining synthetic-to-real transfer capability. + +Real to Artistic. Train on VOC [17] (16,551 real-world images from 2007 and 2012) and test on Clipart [29] (1K images, 20 categories), Comic [29] (2K images, 6 categories), and Watercolor [29] (2K images, 6 categories) following [40]. + +Diverse Weather benchmark. Train on Daytime-Sunny (26,518 images) and test on four challenging conditions: Night-Sunny (26,158 images), Night-Rainy (2,494 images), Dusk-Rainy (3,501 images), and Daytime-Foggy (3,775 images) following [66], evaluating robustness across diverse weather and lighting scenarios. We follow settings from OADG [33] for comparison. + +Corruption benchmark. A comprehensive test-only benchmark [47] with 15 different corruption types at 5 severity levels for Cityscapes [10], spanning noise, blur, weather, and digital perturbations to evaluate model robustness systematically. We follow settings from OADG [33] for comparison. + +# 4.2. Implementation Details + +Training settings: We adopt Faster R-CNN [52] with ResNet101 [20] backbone pretrained on ImageNet [55] as + +Table 1. Cross Camera DG and DA Results (%) on BDD100K. + +
MethodsBikeBusCarMotorPsn.RiderTruckmAP
DG methods (without target data)
CDSD [66] (CVPR'22)22.920.533.814.718.523.618.221.7
SHADE [76] (ECCV'22)25.119.036.818.424.124.919.824.0
SRCD [50] (TNNLS'24)24.821.538.719.025.728.423.125.9
MAD [70] (CVPR'23)-------28.0
DA methods (with unlabeled target data)
TDD [22] (CVPR'22)28.825.553.924.539.638.924.133.6
PT [8] (ICML'22)28.833.852.723.040.539.925.834.9
SIGMA [38] (CVPR'22)26.323.664.117.946.929.620.232.7
SIGMA++ [39] (TPAMI'23)27.126.365.617.847.530.421.133.7
NSA [80] (ICCV'23)-------35.5
HT [13] (CVPR'23)38.030.663.528.253.440.427.440.2
Ours (DG settings)
Diff. Detector (SD-1.5)38.931.071.537.661.547.038.546.6
Diff. Detector (SD-2.1)38.033.669.936.662.146.334.245.8
Diff. Guided (SD-1.5)38.433.472.038.360.347.035.046.3+20.9
Diff. Guided (SD-2.1)38.532.671.837.560.246.735.346.1+20.7
+ +baseline detector. Models are trained for 20K iterations with batch size 16, learning rate 0.02 and SGD optimizer. We use EMA updated model for stable training. Other settings follow MMDetection defaults [7]. + +Evaluation metrics: We report $\mathrm{AP}_{50}$ for individual categories and mAP across categories. For Corruption benchmark [47], we additionally report mPC (average $\mathrm{AP}_{50:95}$ across 15 corruptions with 5 levels) and rPC (ratio between mPC and clean performance). + +Domain augmentation: Following [19, 40], we employ Strong Augmentation including both color transformations (color jittering, contrast, equalization, sharpness) and spatial transformations (rotation, shear, translation). Additionally, we design domain-level augmentation strategies by applying FDA [72], Histogram Matching, and Pixel Distribution Matching between source domain images to generate diverse training samples. + +Hyper-parameters: We set diffusion steps $T = 5$ and max-timestep as 500 for artistic benchmarks and 100 for other benchmarks as described in Sec. 3.3. The loss weights are set as $\lambda_{\mathrm{feature}} = 0.5$ and $\lambda_{\mathrm{object}} = 1$ in Eq. 7. + +# 4.3. Results and Comparisons + +We compare our approach against existing DG methods (target domain unseen) and DA methods (target domain unlabeled). Our results include Diff. Detector trained solely on source domain (Sec. 3.3), SD-1.5 and SD-2.1 using different StableDiffusion [53] versions, and Diff. Guided which applies our alignment approach to Faster R-CNN [52] baseline through Diff. Detector as described in Sec. 3.4 and 3.5. + +In all tables, bold and underline denote the best and second-best results. Yellow background highlights the best average performance. And $+x$ indicates $\mathrm{mAP}(\%)$ gains over baseline. + +We conduct extensive experiments across six challenging benchmarks to evaluate our method in Tab. 1, 2, 3, + +Table 2. Adverse Weather DG and DA Results (%) on FoggyCityscapes. + +
MethodsBusBikeCarMotorPsn.RiderTrainTruckmAP
DG methods
FACT [71] (CVPR'21)27.731.335.923.326.241.23.013.625.3
FSDR [28] (CVPR'22)36.634.143.327.131.244.411.919.331.0
MAD [70] (CVPR'23)44.040.145.030.334.247.442.425.638.6
DA methods
MGA [79] (CVPR'22)53.236.961.527.943.147.350.330.243.8
MTTrans [75] (CVPR'22)45.946.565.232.647.749.933.825.843.4
OADA [73] (CVPR'22)48.539.862.934.347.846.550.932.145.4
MIC [25] (CVPR'23)52.447.567.040.650.955.333.733.947.6
SIGMA++ [39] (TPAMI'23)52.239.961.034.846.445.144.632.144.5
CIGAR [42] (CVPR'23)56.641.362.133.746.147.344.327.844.9
CMT [3] (CVPR'23)66.051.263.741.445.955.738.839.650.3
HT [13] (CVPR'23)55.950.367.540.152.155.849.132.750.4
Ours (DG settings)
Diff. Detector (SD-1.5)56.250.466.739.950.259.539.938.050.1
Diff. Detector (SD-2.1)55.549.667.040.450.458.229.236.448.3
Diff. Guided (SD-1.5)53.854.267.545.652.160.853.932.452.5+21.8
Diff. Guided (SD-2.1)55.153.967.043.451.959.542.234.851.0+20.3
+ +Table 3. Adverse Weather DG and DA Results $(\%)$ on RainyCityscapes. + +
MethodsmAP
DG methods
FACT [71] (CVPR'21)39.9
FSDR [28] (CVPR'22)42.8
SCG [70] (CVPR'23)39.1
MAD [70] (CVPR'23)42.3
DA methods
MGA [79] (CVPR'22)43.0
TDD [22] (CVPR'23)50.3
CMT [3] (CVPR'23)52.1
SIGMA++ [39] (TPAMI'23)46.9
Ours (DG settings)
Diff. Detector (SD-1.5)58.2
Diff. Detector (SD-2.1)56.1
Diff. Guided (SD-1.5)57.9+21.5
Diff. Guided (SD-2.1)58.3+21.9
+ +Table 4. Synthetic to Real DG and DA Results $(\%)$ of category car on Cityscapes and BDD100K. + +
MethodsCityscapesBDD100K
DG methods
CDSD [66] (CVPR'22)35.227.4
SHADE [76] (CVPR'22)40.930.3
SRCD [50] (TNNLS'24)43.031.6
DA methods
SWDA [57] (CVPR'19)40.742.9
MTTrans [75] (CVPR'22)57.9-
SIGMA [38] (CVPR'22)53.7-
TDD [22] (CVPR'22)53.4-
MGA [79] (CVPR'22)54.1-
SIGMA++ [39] (TPAMI'23)53.7-
CIGAR [42] (CVPR'23)58.5-
NSA [80] (ICCV'23)56.3-
Ours (DG settings)
Diff. Detector (SD-1.5)62.864.4
Diff. Detector (SD-2.1)64.564.1
Diff. Guided (SD-1.5)59.7+22.358.2+30.0
Diff. Guided (SD-2.1)57.3+19.954.5+26.3
+ +Table 5. Generalization detection Results (\%) on Diverse Weather benchmark. DF: Daytime-Foggy, DR: Dusk-Rainy, NR: Night-Rainy, NS: Night-Sunny, as described in Sec. 4.1. + +
MethodsDFDRNRNSAverage
CDSD [66] (CVPR'22)33.528.216.636.628.7
SHADE [76] (CVPR'22)33.429.516.833.928.4
CLIPGap [63] (CVPR'23)32.026.012.434.426.2
SRCD [50] (TNNLS'24)35.928.817.036.729.6
G-NAS [67] (AAAI'24)36.435.117.445.033.5
OA-DG [33] (AAAI'24)38.333.916.838.031.8
DivAlign [12] (CVPR'24)37.238.124.142.535.5
UFR [43] (CVPR'24)39.633.219.240.833.2
Diff. Detector (SD-1.5)43.342.527.847.040.2
Diff. Detector (SD-2.1)44.641.623.246.439.0
Diff. Guided (SD-1.5)44.737.421.748.738.1+13.9
Diff. Guided (SD-2.1)44.737.120.049.337.8+13.6
+ +4, 6, 5 and 7. Our comprehensive evaluations demonstrate that the diffusion detector consistently achieves SOTA + +Table 6. Real to Artistic DG and DA Results (%) on Clipart, Comic, Watercolor. + +
MethodsClipartComicWatercolor
DG methods
Div. (CVPR'24)33.725.552.5
DivAlign (CVPR'24)38.933.257.4
DA methods
SWDA (CVPR'19)-29.453.3
MCRA (ECCV'20)-33.556.0
I3Net (CVPR'21)-30.151.5
DBGL (ICCV'21)-29.753.8
AT (CVPR'22)49.3-59.9
D-ADAPT (ICLR'22)49.040.5-
TIA (CVPR'22)46.3--
LODS (CVPR'22)45.2-58.2
CIGAR (CVPR'23)46.2--
CMT (CVPR'23)47.0--
Ours (DG settings)
Diff. Detector (SD-1.5)58.351.968.4
Diff. Detector (SD-2.1)51.746.662.1
Diff. Guided (SD-1.5)40.8+13.629.7+11.654.2+12.7
Diff. Guided (SD-2.1)32.7+5.524.9+6.850.6+9.1
+ +performance in DG settings and even surpasses most domain adaptation methods that require target domain data. Through effective feature and object alignment, our diffusion guidance mechanism successfully enhances detector generalization under moderate domain gaps. However, its improvement becomes more limited when facing extreme domain shifts, particularly in Real to Artistic benchmarks (in Tab. 6). + +# 5. Ablation Studies + +Table 10. Model calibration performance with D-ECE [32] metric. + +
DetectorD-ECE(%) ↓
BDD100KCityscapes (car)Clipart
FR-R101 Baseline10.920.210.8
Diff. Detector8.58.75.5
BDD100KCityscapes (car)Cliaprt
FR-101 BaselineAccuracy1.0/Perfect CalibrationOutputGao1.0/Perfect CalibrationOutput1.0/Perfect CalibrationOutput
0.8/Perfect CalibrationOutputGao0.6/Perfect CalibrationOutput0.8/Perfect CalibrationOutput
0.6/Perfect CalibrationOutputGao0.4/Perfect CalibrationOutput0.6/Perfect CalibrationOutput
0.4/Perfect CalibrationOutputGao0.2/Perfect CalibrationOutput0.2/Perfect CalibrationOutput
0.0/Perfect CalibrationOutputGao0.0/0.1/0.2/0.3/0.4/0.5/0.6/0.7/0.8/0.9/1.0Confidence0.0/0.1/0.2/0.3/0.4/0.5/0.6/0.7/0.8/0.9/1.0Confidence
Diff DetectorAccuracy1.0/Perfect CalibrationOutputGao1.0/Perfect CalibrationOutputGao1.0/Perfect CalibrationOutputGao
0.8/Perfect CalibrationOutputGao0.6/Perfect CalibrationOutputGao0.8/Perfect CalibrationOutputGao
0.6/Perfect CalibrationOutputGao0.4/Perfect CalibrationOutputGao0.6/Perfect CalibrationOutputGao
0.4/Perfect CalibrationOutputGao0.2/Perfect CalibrationOutputGao0.4/Perfect CalibrationOutputGao
0.0/Perfect CalibrationOutputGao0.0/0.1/0.2/0.3/0.4/0.5/0.6/0.7/0.8/0.9/1.0Confidence0.0/0.1/0.2/0.3/0.4/0.5/0.6/0.7/0.8/0.9 1.0Confidence
+ +Figure 5. Reliability Diagram on different target domains. Curves closer to the diagonal indicate better performance. + +# 5.1. Studies on Diffusion Detector + +Comparison with stronger backbones: We evaluate against recent advanced models [14, 21, 37, 44, 45] under same settings. Results in Tab. 9 demonstrate our diffusion backbone's superior generalization through effective domain-invariant feature extraction. + +We investigate two key parameters for extracting features from diffusion models: the number of diffusion steps $T$ and max timesteps (Sec. 3.3). + +Analysis of diffusion steps $T$ : Tab. 8 shows that larger $T$ values improve performance but increase inference time. We set $T = 5$ as default for balancing accuracy and efficiency. + +Analysis of max timesteps: Fig. 4 demonstrates that larger timesteps (e.g., 500) benefit benchmarks with severe domain shifts like Real-to-Artistic, while others perform well at timestep 100. + +Insights on generalization: Our empirical results reveal two key findings: (1) Without noise diffusion (max timestep 0), the model inherits strong transfer capability from largescale pre-training, similar to GLIP [37]; (2) The noiseadding and denoising process enhances generalization, with higher noise levels particularly benefiting larger domain shifts through learning domain-invariant features. + +# 5.2. Studies on Diffusion Guided Detector + +Analysis of proposed modules: Tab. 11 validates our components' effectiveness for domain generalization. Domain augmentation yields limited gains (2.7%) for the diffusion detector but significant improvement (11.0%) for baseline, indicating diffusion detector relies more on inherent generalization while trainable-backbone detectors benefit more from diverse training samples. + +Feature-level and object-level alignment improve performance by $3.5\%$ and $6.4\%$ respectively, showing effective representation learning under diffusion guidance. The consistent gains $(6.1\%)$ with data augmentation further demonstrate our alignment approach's compatibility with conventional techniques. + +Analysis of $\lambda_{\mathrm{feature}}$ and $\lambda_{\mathrm{object}}$ : As shown in Fig. 6, we investigate the impact of different weighting factors $\lambda_{\mathrm{feature}}$ and $\lambda_{\mathrm{object}}$ . We observe that larger weights lead to improved performance on the target domain while slightly degrading the source domain performance. This trade-off suggests an inherent conflict between the model's ability to fit training data and generalize to unseen target domain data. + +# 5.3. Model Calibration Performance for DG + +Our diffusion detector demonstrates superior confidence calibration compared to FR-R101 baseline (Fig. 5, Tab. 10). The Diff. Detector reduces D-ECE [32] to $8.5\%$ , $8.7\%$ , and $5.5\%$ on BDD100K, Cityscapes, and Clipart datasets respectively. As shown in Fig. 5, our calibration curves more + +Table 7. Generalization detection Results (%) on Cityscapes Corruption benchmark. (mPC and rPC are defined in Sec. 4.2). + +
MethodsNoiseDefocusGlassMotionZoomWeatherDigital
CleanGauss.ShotImpulseSnowFrostFogBrightContrastElasticJPEGPixelmPC ↑rPC ↑
FSCE [60] (CVPR'21)43.17.410.28.223.320.321.54.85.623.637.138.031.940.020.423.221.048.7
OA-Mix [33] (AAAI'24)42.77.29.67.722.818.821.95.45.223.637.338.731.940.220.222.220.848.7
OA-DG [33] (AAAI'24)43.48.210.68.424.620.522.34.86.125.038.439.732.840.222.023.821.850.2
Diff. Detector (SD-1.5)34.720.323.217.226.821.723.73.416.624.232.534.430.633.729.124.424.169.5
Diff. Detector (SD-2.1)34.718.420.915.726.220.521.94.014.322.631.433.829.332.527.921.522.765.5
Diff. Guided (SD-1.5)42.111.013.610.825.014.221.43.45.424.039.640.336.339.218.916.021.3+5.750.5+12.3
Diff. Guided (SD-2.1)42.28.210.58.221.612.420.13.03.124.539.239.535.838.723.119.620.5+4.948.6+10.4
+ +Table 8. Testing results and inference costs of different diffusion steps $T$ + +
TBDD 100KCityscapes (car)ClipartInference Time (ms)
128.649.837.4270
234.954.148.6404
546.662.858.3789
1047.162.658.91,424
2045.661.457.72,820
+ +![](images/604521f00b1fc001b64b3247e8c3bfe4cc29645cf50274d55d353109cff29f33.jpg) +Figure 4. Testing results of different max timesteps. + +Table 9. Comparison of Diffusion backbone and stronger models + +
ModelsClipartComicWatercolorDFDRNRNS
ConvNeXt-base [45]43.626.655.139.739.223.445.9
VIT-base [14]29.515.543.024.825.811.423.0
Swin-base [44]30.218.042.637.238.922.642.2
MAE (VIT-base) [21]28.116.744.432.532.617.034.3
Glip (Swin-tiny) [37]39.218.750.438.536.320.345.5
Diffusion backbone58.351.968.443.442.527.847.0
+ +Table 11. Ablation studies of our framework components. Settings: domain augmentation (Aug.), feature-level alignment (Fea.), and object-level alignment (Obj.). Foggy Cityscapes (F-C), Rainy Cityscapes (R-C) + +
SettingsAug. Fea. Obj.BDDF-CR-CDFDRNRNS
Diff. Detector✓44.548.054.441.340.424.343.7
46.6+2.150.1+2.158.2+3.843.3+2.042.5+2.127.8+3.547.0+3.3
FR-R101 baseline✓25.430.736.428.824.112.431.4
36.2+10.847.9+17.250.1+13.739.9+11.134.8+10.716.4+4.041.2+9.8
Diff. Guided✓29.8+4.434.2+3.541.2+4.834.2+5.424.9+0.814.4+2.035.2+3.8
✓34.9+9.538.3+7.643.1+6.737.2+8.426.3+2.216.4+4.038.1+6.7
✓38.1+12.740.4+9.745.9+9.538.6+9.828.4+4.316.8+4.439.5+8.1
✓46.3+20.952.5+21.857.9+21.544.7+15.937.4+13.321.7+9.348.7+17.3
+ +closely follow the diagonal line, indicating better alignment between predicted confidence scores and empirical accuracies across domains. + +![](images/ccc8b04ddff725ee851c20f8665495e3ee64b97bb69db49b5ac8e096bb394259.jpg) +Figure 6. Testing results of $\lambda_{\mathrm{feature}}$ and $\lambda_{\mathrm{object}}$ on source domain and target domain. + +![](images/a96b4dfcf02aa57c7a38a8168053a95e2dd15d33d66c6d00fd29989e132d87ec.jpg) + +# 5.4. Limitations + +Despite achieving strong results across various benchmarks, our diffusion detector faces efficiency challenges. The large parameter count and multi-step denoising process incur substantial computational costs (Tab. 8), limiting its applicability to larger-scale scenarios. + +Moreover, while leveraging diffusion models' generalization capability, performance gains remain limited under severe domain shifts (Tab. 6). Future work could explore more efficient architectures and effective learning strategies to better handle extreme domain gaps. + +# 6. Conclusion + +This paper addresses DG detection through two key contributions. First, we propose a diffusion detector that extracts domain-invariant representations by fusing multi-step features during diffusion. Second, to enable other detectors to benefit from such generalization capability, we develop a diffusion-guided detector framework that transfers knowledge to conventional detectors through feature and object level alignment. Extensive evaluations on six domain generalization benchmarks demonstrate substantial improvements across different domains and corruption types. Our work not only provides an effective solution for domain-generalized detection but also opens up new possibilities for leveraging diffusion models to enhance visual recognition robustness. + +# References + +[1] Yogesh Balaji, Swami Sankaranarayanan, and Rama Chellappa. 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Existing GFS-PCS methods enhance prototypes via interacting with support or query features but remain limited by sparse knowledge from few-shot samples. Meanwhile, 3D vision-language models (3D VLMs), generalizing across open-world novel classes, contain rich but noisy novel class knowledge. In this work, we introduce a GFS-PCS framework that synergizes dense but noisy pseudo-labels from 3D VLMs with precise yet sparse few-shot samples to maximize the strengths of both, named GFS-VL. Specifically, we present a prototype-guided pseudo-label selection to filter low-quality regions, followed by an adaptive infilling strategy that combines knowledge from pseudo-label contexts and few-shot samples to adaptively label the filtered, unlabeled areas. Additionally, we design a novel-base mix strategy to embed few-shot samples into training scenes, preserving essential context for improved novel class learning. Moreover, recognizing the limited diversity in current GFS-PCS benchmarks, we introduce two challenging benchmarks with diverse novel classes for comprehensive generalization evaluation. Experiments validate the effectiveness of our framework across models and datasets. Our approach and benchmarks provide a solid foundation for advancing GFS-PCS in the real world. The code is at here. + +# 1. Introduction + +Understanding dense 3D semantics is essential for many vision applications [20, 35, 42, 52, 53, 61, 73], and few-shot point cloud semantic segmentation (FS-PCS) has emerged + +![](images/f14e9e4c25a7fb39b4ef3788cf4f055d6e94d13203970150e55c8c6fd9476b3a.jpg) + +![](images/700d9eac044c575dd7bcce33f62fa6004be3671d7043f2f707b311486cb07cda.jpg) +Figure 1. Comparison of our framework with previous work. Top: Prior work [56, 66] primarily enhances prototypes through interaction modules that integrate support/query features, making predictions based on refined prototypes. However, they are limited by the sparse knowledge from few-shot samples. Bottom: Our framework addresses this limitation by leveraging the extensive open-world knowledge from 3D VLMs through pseudo-labels. We mitigate the noise inherent in 3D VLMs by calibrating their raw pseudo-labels with precise few-shot samples, thereby effectively expanding novel class knowledge while ensuring reliability. + +as a valuable task [2, 77], enabling models to extend from base to novel classes with minimal annotations for novel classes. However, typical few-shot models require additional support samples for each novel class at inference and only predict novel classes, ignoring base classes. To address this, generalized few-shot point cloud semantic segmentation (GFS-PCS) [66] was introduced, allowing models to directly segment both base and novel classes after few-shot adaptation, making it more practical for real-world use. + +Current GFS-PCS models [17, 33, 34, 66] primarily utilize prototype learning [51], representing each class as a prototype and predicting based on the relationship between query points and these prototypes. As shown in Fig. 1, these methods mainly focus on refining prototypes through interactions with support/query samples for enhanced segmentation. For instance, CAPL [56] adapts base prototypes to novel classes using co-occurrence knowledge from support samples and contextual information from queries. GW [66] encodes shared geometric structures into geometry prototypes to enhance semantic prototypes. However, these approaches remain limited in novel class generalization due to the sparse knowledge available from few-shot samples. + +In parallel, 3D vision-language models (3D VLMs) have been developed to enable open-vocabulary recognition by aligning 3D and language features. Leveraging language models trained on vast open-text data, 3D VLMs exhibit strong generalization abilities, allowing recognition of open-set classes in 3D. Since paired 3D-text data is scarce, some approaches [5, 18, 44, 54, 75] distill 2D features from 2D VLMs [12, 27] into their 3D encoders, while others [9, 10, 21, 67] use captioning models [47, 60] to generate scene- or region-level descriptions, enabling point-language alignment for direct 3D learning. Recognizing the open-world potential of 3D VLMs, we propose utilizing their rich knowledge to enhance GFS-PCS. A straightforward method to integrate 3D VLMs [44, 67] is to generate dense pseudolabels of novel classes as additional supervision. However, predictions from 3D VLMs are often noisy, compounding errors in GFS-PCS models. Meanwhile, sparse support samples offer accurate annotations for novel classes. Therefore, given the dense but noisy pseudo-labels from 3D VLMs and the accurate yet limited support samples, we propose a new GFS-PCS framework, named GFS-VL, to combine the strengths of both, as in Fig. 1. + +Specifically, GFS-VL incorporates three novel techniques. First, we introduce a pseudo-label selection technique that uses accurate few-shot data to filter pseudolabels, retaining only high-quality regions while excluding noisy predictions. Second, as filtered wrong predictions will leave some regions unlabeled, potentially corresponding to novel objects, we present an adaptive infilling approach to enrich these regions. It combines knowledge from pseudo-label contexts and few-shot samples to construct an adaptive prototype set to label unlabeled regions, effectively considering both the completion of incomplete masks and the discovery of missing classes. Third, to further utilize few-shot samples, we propose a novel-base mix strategy, embedding support samples into training scenes. Unlike traditional 3D data augmentation [39, 49, 64, 65, 71, 82], which mainly aims at fully-supervised segmentation and mixes object contexts, our approach emphasizes preserving contextual cues, which is crucial for novel class learn + +ing [56] by helping identify challenging novel classes. + +Furthermore, we identify limitations in current evaluation benchmarks. Existing benchmarks based on ScanNet [7] and S3DIS [3] datasets include only six novel classes, limiting diversity and failing to represent the complexity of real-world scenarios where novel classes are constantly varying. To address this, we introduce two challenging benchmarks: one with 40 novel classes from ScanNet200 [48] and another with 18 novel classes from ScanNet++ [70]. As detailed in Sec. 3.2, these benchmarks provide broader and more representative coverage of novel classes, enabling a more comprehensive evaluation of models' generalization capabilities. + +By fully integrating the benefits of 3D VLMs and few-shot data, our approach achieves state-of-the-art GFS-PCS performance on both existing and newly established benchmarks. Experiments demonstrate the effectiveness and generalizability of our framework across various models and datasets. Additionally, previous baselines exhibit limited performance when evaluated on our new benchmarks, underscoring the necessity of our benchmarks for assessing real-world generalization. Together, our methods and benchmarks would offer critical insights and tools to advance future research on GFS-PCS. + +# 2. Related Work + +# 2.1. Few-shot 3D Point Cloud Segmentation + +3D point cloud segmentation is fundamental in understanding scene semantics, with many fully-supervised methods advancing this field [8, 15, 23, 24, 28, 40, 43, 58, 63, 76, 78]. However, these methods need expensive large-scale point-level annotations and have fixed output spaces. To address these limitations, FS-PCS was introduced in attMPTI [77], aiming to generalize to novel classes with limited support samples. FS-PCS research can be divided into two categories based on how relationships between query points and support classes are modeled: i) Feature optimization [16, 31, 37, 41, 59, 62, 72, 80, 81] – These methods refine support prototypes or query features to enhance class separation. Final predictions are made using non-parametric, distance-based metrics, which implicitly model support-query relationships. ii) Correlation optimization [1, 2] – These approaches directly optimize correlations between support and query samples, explicitly modeling their relationships. COSeg [2] pioneered this approach recently and corrected two issues of foreground leakage and sparse point distribution in the previous FS-PCS setting. + +# 2.2. Generalized Few-shot 3D Point Cloud Segmentation + +While standard few-shot models adapt effectively to novel classes with limited data, they are constrained to predict + +only novel classes and require support samples to specify target classes during inference. A more practical task, generalized few-shot segmentation, occurs to require predicting both base and novel classes at inference without support samples, as first introduced in 2D segmentation [4, 14, 17, 25, 33, 34, 36, 38, 56]. The pioneer work PIFS [4], using the prototype learning paradigm [51], fine-tunes base and novel prototypes with a distillation loss, while CAPL [56] refines base prototypes using co-occurrence priors from support samples and dynamic contextual information from queries. For 3D, GW [66] introduces this setting to point cloud segmentation. GW models shared local geometric structures across base and novel classes as “geometry words” and then builds geometric prototypes to enhance the semantic prototypes, which are learned similarly to CAPL [56] by leveraging contextual information. To mine background semantics, Tsai et al. [57] clustered background points to generate pseudo-class prototypes distinct from base classes, leveraging multiple 2D views and 2D foundation models to link these points with class prompts. + +# 2.3. 3D Vision-Language Models + +3D VLMs align 3D point cloud features with language features, enabling open-world 3D understanding. However, developing these models poses unique challenges compared to 2D, mainly due to the scarcity of paired 3D-text data. To address this, recent work leverages multi-view 2D images, commonly associated with 3D point clouds, as intermediaries [30]. Some methods [5, 18, 19, 44, 54, 60, 75, 79] distill 2D features from 2D VLMs [12, 27, 46, 68] into their 3D encoders. For instance, OpenScene [44] aligns 3D and text representations by optimizing 3D-2D alignment using 2D VLMs [12, 27]. However, extracting these 2D features is computationally expensive, and the learned 3D features may inherit 2D prediction errors. Other approaches [9, 10, 21] generate point-language paired data by using captioning models [47, 60] to produce text descriptions of images. While effective, these captions are often at the scene level, limiting their ability to capture fine-grained 3D features. RegionPLC [67] recently introduced high-quality region-level 3D-language associations, supporting robust 3D learning by dense regional language supervision. + +# 2.4. Point Cloud Data Augmentation + +To address data limitations in the 3D domain, numerous methods have been developed to expand point cloud distributions. One category augments individual point clouds by altering geometric properties [22, 29, 32, 45, 50], using techniques such as shape transformations and patch shuffling. Another approach uses mixing techniques for 3D objects [6, 26, 74] and 3D scenes [11, 49, 64, 65, 71, 82]. For instance, Mix3D [39] mixes points from two scenes as an out-of-context augmentation for semantic segmenta + +
DatasetBaseNovelMax (F)Min (F)Max (P)Min (P)
S3DIS761852959,92930,013
ScanNet1364111334,4791,148
ScanNet200124573310212,641279
ScanNet++12181438284,375604
+ +Table 1. Statistics for GFS-PCS benchmarks across four datasets. Base/Novel indicates the number of base and novel classes. Max/Min (F) is the maximum and minimum occurrences of each novel class across the entire dataset, while Max/Min (P) is the maximum and minimum average number of points per novel class. + +tion, while methods like [49] select domain-specific points with semantic information to mix across domains. Other methods, such as [64], relocate objects to less frequent locations to vary spatial distributions. Notably, most augmentation methods in semantic segmentation [39, 64] and detection [82] modify the original context of target classes, pushing models to learn object patterns independently of surroundings. However, we argue that preserving contextual dependencies is crucial for GFS-PCS, where novel classes often involve challenging, hard-to-detect objects. Isolated object patterns alone are insufficient for effective novel class generalization [56]. In contrast, our proposed novel-base mix augmentation retains key contextual information when incorporating support samples into training scenes, enhancing models' ability to recognize novel classes. + +# 3. GFS-PCS Overview + +# 3.1. Problem Definition + +GFS-PCS requires the model to identify both base and novel classes present in test scenes. Let $C^{\mathrm{b}}$ denote the set of base class names with size $N_{b}$ and $C^{\mathrm{n}}$ the set of novel class names with size $N_{n}$ . The total number of classes is $N_{c} = N_{b} + N_{n}$ . The base and novel class sets are mutually exclusive, i.e., $C^{\mathrm{b}} \cap C^{\mathrm{n}} = \emptyset$ . Evaluation is conducted on the test dataset $\mathbf{D}_{\mathrm{test}}$ to assess segmentation across all classes $C^{\mathrm{b}} \cup C^{\mathrm{n}}$ . For training, the model is first trained on base classes and then registered with novel classes. The base dataset $\mathbf{D}_{\mathrm{base}}$ is defined as $\mathbf{D}_{\mathrm{base}} = \{\mathbf{X}_{\mathrm{b}}^{\mathrm{i}}, \mathbf{Y}_{\mathrm{b}}^{\mathrm{i}}\}_{i}$ , where $\mathbf{X}_{\mathrm{b}}^{\mathrm{i}}$ represents the $i$ -th point cloud and $\mathbf{Y}_{\mathrm{b}}^{\mathrm{i}}$ contains the corresponding base class labels. For the novel class dataset, we define $\mathbf{D}_{\mathrm{novel}}$ as the collection of $K$ -shot support samples: $\left\{\left\{\mathbf{X}_{\mathrm{k}}^{\mathrm{c}}, \mathbf{Y}_{\mathrm{k}}^{\mathrm{c}}\right\}_{k=1}^{K}\right\}_{c=N_{b}}^{N_{c}}$ . Each novel class $c$ has $K$ support samples $\left\{\mathbf{X}_{\mathrm{k}}^{\mathrm{c}}, \mathbf{Y}_{\mathrm{k}}^{\mathrm{c}}\right\}_{k=1}^{K}$ with exclusive labels $\left\{\mathbf{Y}_{\mathrm{k}}^{\mathrm{c}}\right\}_{k=1}^{K}$ . The base classes occupy class indices in the range $[0, N_{b})$ , while novel classes are indexed in the range $[N_{b}, N_{c})$ , with background regions labeled as $-1$ . For simplicity, we denote a data sample from $\mathbf{D}_{\mathrm{base}}$ as $\mathbf{X}_{\mathrm{b}}$ and $\mathbf{Y}_{\mathrm{b}}$ , while $\mathbf{X}_{\mathrm{n}}^{\mathrm{c}}$ and $\mathbf{Y}_{\mathrm{n}}^{\mathrm{c}}$ refer to a support sample of class $c$ in $\mathbf{D}_{\mathrm{novel}}$ . + +# 3.2. New Evaluation Benchmarks + +Current evaluation benchmarks for GFS-PCS utilize the ScanNet [7] and S3DIS [3] datasets. However, weiden + +![](images/f5bb79464d175a1899e8d59daf6b07285dcea192dc311073f40c472ffc01f189.jpg) +Figure 2. Overview of the proposed GFS-VL. (a), (b) Given an input point cloud $\mathbf{X}_{\mathrm{b}}$ , we apply a novel-base mix to embed support samples into the training scene while preserving essential context. The scene is then processed by a 3D VLM, using all class names as prompts to generate raw predictions $\hat{\mathbf{Y}}$ . Leveraging support prototypes $\{\mathbf{p}^c\}$ , the raw predictions undergo pseudo-label selection to filter out noisy regions, followed by adaptive infilling to label the filtered, unlabeled areas, yielding refined supervision $\mathbf{Y}_{\mathrm{b}}''$ for training the 3D segmentor. (c), (d) illustrate the details of the pseudo-label selection and adaptive infilling processes. + +tify limitations in the number and diversity of novel classes in these benchmarks. As shown in Tab. 1, while ScanNet includes 13 base classes and S3DIS has 7, both datasets include only 6 novel classes. Our analysis of the frequency and the average number of points per novel class further highlights the lack of diversity among these limited novel classes in these two benchmarks. This indicates that current evaluations are not sufficiently representative of the complexity of real-world novel categories, failing to robustly assess models' generalization abilities. To address this, we propose two new and more challenging evaluation benchmarks based on ScanNet200 [48] and ScanNet++ [70] datasets. These new benchmarks, as detailed in Tab. 1, feature a larger number and greater diversity of novel classes, providing a more realistic and comprehensive testbed for evaluating model generalization to novel categories. + +# 4. Method + +# 4.1. Overview + +In our proposed framework GFS-VL, we adopt a canonical segmentor architecture consisting of a backbone and a linear classification head. This minimalistic structure retains flexibility and simplicity, facilitating reproducibility. + +Following the standard GFS-PCS procedure [66], the segmentor is initially trained on base classes. The backbone, denoted as $\Phi$ , and the linear classifier for base classes, $\mathcal{H}_b$ , are employed to make base class predictions $\mathbf{P}_{\mathrm{b}}$ : + +$$ +\mathbf {F} = \Phi (\mathbf {X} _ {\mathrm {b}}) \in \mathbb {R} ^ {N _ {p} \times D}, \mathbf {P} _ {\mathrm {b}} = \mathcal {H} _ {b} (\mathbf {F}) \in \mathbb {R} ^ {N _ {p} \times N _ {b}}, \tag {1} +$$ + +where $N_{p}$ is the number of points in the point cloud input $\mathbf{X}_{\mathrm{b}}$ , and $\mathbf{F}$ represents backbone features with a channel dimension of $D$ . Then, when registering novel classes, a new linear classifier $\mathcal{H}_n$ is introduced to handle the novel classes. The concatenated predictions from both classifiers form the complete output $\mathbf{P}$ for all base and novel classes: + +$$ +\mathbf {P} = \left[ \mathcal {H} _ {b} (\mathbf {F}), \mathcal {H} _ {n} (\mathbf {F}) \right] \in \mathbb {R} ^ {N _ {p} \times N _ {c}}, \tag {2} +$$ + +where $[\cdot, \cdot]$ denotes concatenation. Subsequently, the model is fine-tuned on the base and few-shot samples, enabling it to simultaneously segment both base and novel classes. To fully exploit the rich knowledge from 3D VLMs while minimizing potential noise interference, we propose GFS-VL, as shown in Fig. 2, to maximize the utility of limited but accurate novel samples to guide the learning process. We detail each designed module in the following sections, presented under the 1-shot setting for clarity. + +# 4.2. Pseudo-label Selection + +A direct method for utilizing 3D VLMs in GFS-PCS is to use their predictions as pseudo-labels for novel classes. However, these raw predictions are noisy, hindering few-shot models from learning good novel class representations. Moreover, such noisy pseudo-labels could introduce error accumulation from the 3D VLMs into the few-shot models. + +Therefore, we introduce an effective pseudo-label selection method by utilizing the valuable few-shot support samples to guide the selection of reliable novel class predictions. Specifically, for each novel class, we first com + +pute support prototypes using the few-shot samples. This is achieved by applying the vision encoder $\Theta_v$ of the 3D VLM $\Theta$ to compute masked average features for each novel class: + +$$ +\mathbf {F} _ {\mathrm {n}} ^ {\mathrm {c}} = \Theta_ {v} (\mathbf {X} _ {\mathrm {n}} ^ {\mathrm {c}}) \in \mathbb {R} ^ {N _ {p} \times D _ {v}}, +$$ + +$$ +\mathbf {p} ^ {\mathrm {c}} = \frac {\sum_ {i = 1} ^ {N _ {p}} \mathbf {F} _ {\mathrm {n} , \mathrm {i}} ^ {\mathrm {c}} \mathbf {Y} _ {\mathrm {n} , \mathrm {i}} ^ {\mathrm {c}}}{\sum_ {i = 1} ^ {N _ {p}} \mathbf {Y} _ {\mathrm {n} , \mathrm {i}} ^ {\mathrm {c}}}, \quad c = N _ {b}, \dots , N _ {c} - 1, \tag {3} +$$ + +where $D_v$ is the feature dimension of the 3D VLM, and $\mathbf{p}^c \in \mathbb{R}^{D_v}$ represents the support prototype for novel class $c$ . For clarity, we define this prototype extraction process as $\mathcal{F}_{\mathrm{pool}}$ . Thus, Eq. (3) becomes: $\mathbf{p}^c = \mathcal{F}_{\mathrm{pool}}(\mathbf{X}_n^c, \mathbf{Y}_n^c)$ . + +Next, given the current base training input $\mathbf{X}_{\mathrm{b}}$ with base labels $\mathbf{Y}_{\mathrm{b}}$ , we prompt the 3D VLM $\Theta$ using all base and novel class names to obtain predictions $\hat{\mathbf{Y}} \in \mathbb{R}^{N_p}$ . Let $\hat{C}_{\mathrm{n}}$ be the novel class indices existing in $\hat{\mathbf{Y}}$ . We then compute the predicted prototype $\mathbf{u}^{\mathrm{c}}$ for each novel class in $\hat{C}_{\mathrm{n}}$ : + +$$ +\mathbf {u} ^ {\mathrm {c}} = \mathcal {F} _ {\text {p o o l}} \left(\mathbf {X} _ {\mathrm {b}}, \mathbf {1} _ {[ \hat {\mathbf {Y}} = c ]}\right), \quad c \in \hat {\boldsymbol {C}} _ {\mathrm {n}}. \tag {4} +$$ + +Here, $\mathbf{1}_{[\hat{\mathbf{Y}} = c]}$ is a binary mask, set to 1 where $\hat{\mathbf{Y}}$ equals the class index $c$ and to 0 otherwise. Then, we can filter the raw predictions to select high-quality novel class pseudo-labels: + +$$ +\hat {\mathbf {Y}} _ {\mathrm {i}} = \left\{ \begin{array}{l l} - 1, & \text {i f} \hat {\mathbf {Y}} _ {\mathrm {i}} \in [ 0, N _ {b}) \text {o r} \\ & \left(\hat {\mathbf {Y}} _ {\mathrm {i}} \in \left[ N _ {b}, N _ {c}\right) \text {a n d} \right. \\ & \quad \operatorname {s i m} \left(\mathbf {u} ^ {\hat {\mathbf {Y}} _ {\mathrm {i}}}, \mathbf {p} ^ {\hat {\mathbf {Y}} _ {\mathrm {i}}}\right) < \tau), \\ \hat {\mathbf {Y}} _ {\mathrm {i}}, & \text {o t h e r w i s e .} \end{array} \right. \tag {5} +$$ + +Here, if the predicted label $\hat{\mathbf{Y}}_{\mathrm{i}}$ for the $i$ -th point is a base class, or a novel class with cosine similarity below a threshold $\tau$ between the predicted class prototype $\mathbf{u}^{\hat{\mathbf{Y}}_{\mathrm{i}}}$ and the support prototype $\mathbf{p}^{\hat{\mathbf{Y}}_{\mathrm{i}}}$ , we filter this pseudo-label by setting it to $-1$ . Otherwise, we retain the original pseudo-label. Note this filtering process can be efficiently implemented using mask-based indexing without iterating each point. + +Now the updated $\hat{\mathbf{Y}}$ contains only reliable pseudo-labels for novel classes. Given the original base class labels $\mathbf{Y}_{\mathrm{b}}$ , its background region (labeled as $-1$ ) serves as a potential area for novel classes. Therefore, we merge the updated $\hat{\mathbf{Y}}$ into the background region in $\mathbf{Y}_{\mathrm{b}}$ to generate augmented labels $\mathbf{Y}_{\mathrm{b}}^{\prime}$ with additional reliable novel class pseudo-labels: + +$$ +\mathbf {Y} _ {\mathrm {b}} ^ {\prime} = \mathbf {Y} _ {\mathrm {b}}, \tag {6} +$$ + +$$ +\mathbf {Y} _ {\mathrm {b}} ^ {\prime} [ \mathbf {Y} _ {\mathrm {b}} ^ {\prime} = - 1 ] = \hat {\mathbf {Y}} [ \mathbf {Y} _ {\mathrm {b}} ^ {\prime} = - 1 ]. +$$ + +# 4.3. Adaptive Infilling + +After selection, $\mathbf{Y}_{\mathrm{b}}^{\prime}$ includes reliable supervision for novel classes, while some regions remain unlabeled due to filtered low-quality predictions. These filtered predictions from the 3D VLM usually assign wrong labels, either by entirely missing true novel areas or partially mislabeling them [55]. + +Consequently, $\mathbf{Y}_{\mathrm{b}}^{\prime}$ contains unlabeled regions that potentially correspond to missing or incomplete novel labels. + +To address these gaps, we propose an adaptive infilling approach that utilizes both the few-shot samples and the current labels $\mathbf{Y}_{\mathrm{b}}^{\prime}$ to build an adaptive prototype set for novel classes. This set allows us to assign novel labels adaptively to unlabeled regions, ensuring more comprehensive coverage of novel classes. We begin by extracting novel class prototypes from $\mathbf{Y}_{\mathrm{b}}^{\prime}$ : + +$$ +\mathbf {v} ^ {\mathrm {c}} = \mathcal {F} _ {\text {p o o l}} \left(\mathbf {X} _ {\mathrm {b}}, \mathbf {1} _ {\left[ \mathbf {Y} _ {\mathrm {b}} ^ {\prime} = c \right]}\right), \quad c \in C _ {\mathrm {n}} ^ {\mathrm {y}}, \tag {7} +$$ + +where $C_{\mathrm{n}}^{\mathrm{y}}$ represents the novel class indices present in $\mathbf{Y}_{\mathrm{b}}^{\prime}$ . Using both these extracted prototypes and pre-computed support prototypes from the few-shot samples, we construct an adaptive prototype set, defined as $\{\mathbf{m}^{\mathrm{c}}\}$ , where: + +$$ +\mathbf {m} ^ {\mathrm {c}} = \left\{ \begin{array}{l l} \mathbf {v} ^ {\mathrm {c}}, & \text {i f} c \in C _ {\mathrm {n}} ^ {\mathrm {y}}, \\ \mathbf {p} ^ {\mathrm {c}}, & \text {o t h e r w i s e}, \end{array} \right. \quad \text {f o r} c = N _ {b}, \dots , N _ {c} - 1. \tag {8} +$$ + +This set $\{\mathbf{m}^{\mathrm{c}}\}$ incorporates novel class prototypes $\mathbf{v}^{\mathrm{c}}$ from $\mathbf{Y}_{\mathrm{b}}^{\prime}$ if they exist; otherwise, it defaults to the few-shot support prototypes $\mathbf{p}^{\mathrm{c}}$ . By adapting to the current pseudolabels, this set facilitates the completion of incomplete novel class pseudo-labels while allowing for the discovery of missed novel classes based on support prototypes. + +Next, we initialize $\mathbf{Y}_{\mathrm{b}}^{\prime \prime} = \mathbf{Y}_{\mathrm{b}}^{\prime}$ . For each unlabeled point $\mathbf{Y}_{\mathrm{b,i}}^{\prime \prime}$ with feature $\mathbf{F}_{\mathrm{b,i}}$ from $\Theta_v$ , we calculate its cosine similarity with each prototype $\mathbf{m}^{\mathrm{c}}$ as $S_{\mathrm{b,i}}^{\mathrm{c}} = \sin (\mathbf{F}_{\mathrm{b,i}},\mathbf{m}^{\mathrm{c}})$ and assign the corresponding novel class label if the maximum similarity exceeds a threshold $\delta$ : + +$$ +\mathbf {Y} _ {\mathrm {b}, \mathrm {i}} ^ {\prime \prime} = \left\{ \begin{array}{l l} \underset {c} {\arg \max } S _ {\mathrm {b}, \mathrm {i}} ^ {\mathrm {c}}, & \text {i f} \underset {c} {\max } S _ {\mathrm {b}, \mathrm {i}} ^ {\mathrm {c}} \geq \delta , \\ - 1, & \text {o t h e r w i s e .} \end{array} \right. \tag {9} +$$ + +This adaptive infilling mechanism effectively integrates knowledge from few-shot support samples with the current pseudo-label context, creating adaptive prototypes that help discover missed novel objects and complete partial pseudolabels, thereby enhancing the quality of novel region labels. + +# 4.4. Novel-Base Mix + +To more sufficiently utilize support samples, we introduce a novel-base mix approach that effectively integrates these valuable samples with the training data. Specifically, we start by randomly sampling a novel sample $\mathbf{X}_{\mathrm{n}}^{\mathrm{c}}$ from $\mathbf{D}_{\mathrm{novel}}$ . To enhance the model's focus on novel class, we crop the local bounding region based on the novel class mask $\mathbf{Y}_{\mathrm{n}}^{\mathrm{c}}$ : + +$$ +\mathbf {X} _ {\mathrm {n}} ^ {\text {l o c a l}}, \mathbf {Y} _ {\mathrm {n}} ^ {\text {l o c a l}} = \mathcal {F} _ {\text {c r o p}} \left(\mathbf {X} _ {\mathrm {n}} ^ {\mathrm {c}}, \mathbf {Y} _ {\mathrm {n}} ^ {\mathrm {c}}\right), \tag {10} +$$ + +where $\mathcal{F}_{\mathrm{crop}}$ represents the local cropping operation. + +We then construct a new training input by mixing the cropped novel sample $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ with the current base input + +$\mathbf{X}_{\mathrm{b}}$ . Unlike previous mixup methods [39, 64], which discard scene context, we argue that context information is essential for models to better recognize challenging novel objects and propose to preserve it. To achieve this, we extract the four corners in the XY plane for both $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ and $\mathbf{X}_{\mathrm{b}}$ , and then select a pair of opposite corners between them: + +$$ +\mathbf {L} _ {\mathrm {b}}, \mathbf {L} _ {\mathrm {n}} ^ {\mathrm {l o c a l}} = \mathcal {F} _ {\mathrm {p a i r}} (\mathcal {F} _ {\mathrm {c o r n e r}} (\mathbf {X} _ {\mathrm {b}}), \mathcal {F} _ {\mathrm {c o r n e r}} (\mathbf {X} _ {\mathrm {n}} ^ {\mathrm {l o c a l}})), \tag {11} +$$ + +where $\mathcal{F}_{\mathrm{corner}}$ extracts the four corner points in the XY projections, and $\mathcal{F}_{\mathrm{pair}}$ randomly selects an opposing corner pair. Possible pairs include, for example, the leftmost corner of $\mathbf{X}_{\mathrm{b}}$ with the rightmost corner of $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ , or the uppermost corner of $\mathbf{X}_{\mathrm{b}}$ with the lowermost corner of $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ . Here, $\mathbf{L}_{\mathrm{b}}$ and $\mathbf{L}_{\mathrm{n}}^{\mathrm{local}}$ are the coordinates of the selected corners. To align $\mathbf{X}_{\mathrm{b}}$ with $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ at the chosen corners, we compute a translation vector $\mathbf{T} = \mathbf{L}_{\mathrm{b}} - \mathbf{L}_{\mathrm{n}}^{\mathrm{local}}$ and apply it to translate $\mathbf{X}_{\mathrm{n}}^{\mathrm{local}}$ , yielding the final mixed result. This ensures a close connection between the samples without losing context, which is crucial for effective novel class learning. Visualizations of the output can be found in Sec. 5.3, with further details in the supplementary material. + +# 5. Experiments + +# 5.1. Experimental Setup + +Datasets. Our new evaluation benchmark builds on two datasets: 1) ScanNet200 [48] - This dataset extends the labeling scope of ScanNet [7] from 20 to 200 classes, adding finer-grained subclasses of existing categories and numerous new classes. 2) ScanNet++ [70] - Comprising 460 scenes with annotations for over 1000 unique classes, ScanNet++ is designed to capture a wide range of object types. To establish a comprehensive GFS-PCS benchmark, we selected the most frequent classes from each dataset, ensuring adequate representation across scenes. Our final benchmark includes 57 classes for ScanNet200 (with 40 novel classes) and 30 classes for ScanNet++ (with 18 novel classes). Full class lists are in the supplementary material. We follow the standard training/testing splits for each dataset, adhering to the preprocessing and augmentation settings from [63], where raw input points are voxelized at a $0.02\mathrm{m}$ grid size. Notably, unlike prior GFS-PCS evaluations [66, 77], which test models on small blocks, we test on whole scenes to better simulate real-world scenarios. + +Implementation Details. Our framework uses a straightforward segmentor with a backbone and a linear classification head, optimized for efficiency and simplicity. By default, we use Point Transformer V3 (PTv3) [63] as the backbone and 3D VLM RegionPLC [67]. The segmentor is first pre-trained on base classes of each dataset, after which we add a separate linear classification head for novel classes, enabling lightweight and efficient adaptation to novel classes in 20 fine-tuning epochs. The pre-training + +![](images/bfd2d2a340ec8fda9f1b4ed152099c246f181513429290b619bcfbab71a27231.jpg) +Figure 3. Qualitative comparison between GW [66] and our GFS-VL on ScanNet200. Class colors are shown at the top. + +setting follows [63] with 800 epochs, and we use Adam optimizer for fine-tuning with learning rates: 0.001 for ScanNet200 and ScanNet, and 0.007 for ScanNet++. More details are in the supplementary material. For evaluation, we adopt metrics outlined in [66]: mean Intersection-over-Union (mIoU) for base classes (mIoU-B), novel classes (mIoU-N), all classes (mIoU-A), and the harmonic mean of mIoU-B and mIoU-N (HM) which captures overall performance while mitigating bias towards base classes [69]. + +# 5.2. Experimental Results + +In our evaluation, we benchmark our method against baseline models attMPTI [77] and PIFS [4] following [66], along with the state-of-the-art GFS-PCS model GW [66] and FS-PCS model COSeg [2]. For fairness, all baseline models are retrained using the same backbone as our model. We also include a Fully Supervised model as an upper bound, obtained by fine-tuning an identical model to ours on ground-truth labels for both base and novel classes. + +Following [56, 66], we evaluate two support scenarios, 5-shot and 1-shot, averaging performance across five randomly-seeded support set versions. As shown in Tab. 2, on ScanNet200, our model achieves substantial improvements across all metrics and support scenarios, including a $28.57\%$ increase in HM and a $23.37\%$ boost in mIoU-N over the closest baseline, GW, in the 5-shot setting. Qualitative comparisons in Fig. 3 further illustrate the superior segmentation accuracy of our model compared to GW. Similar trends are seen on ScanNet++ (see Tab. 3), where our model improves HM by $17.88\%$ and mIoU-N by $12.79\%$ compared to GW (1-shot). For the traditional ScanNet benchmark with only six novel classes, we report results in Tab. 4 using baseline performance from [66], where our model significantly surpasses all baselines with an impressive $34.94\%$ gain in mIoU-N and $39.33\%$ in HM for the 1-shot task. + +The substantial and consistent gains across diverse datasets and metrics highlight our method's strong adaptability to diverse and complex novel classes by effectively integrating valuable few-shot samples with the semantic insights of 3D VLMs [9, 44]. In contrast, baseline models rely + +
Method5-shot1-shot
mIoU-BmIoU-NmIoU-AHMmIoU-BmIoU-NmIoU-AHM
Fully Supervised68.7039.3245.5150.0268.7039.3245.5150.02
PIFS [4]28.783.829.076.7117.842.876.024.88
attMPTI [77]37.134.9911.768.7954.843.2814.146.17
COSeg [2]57.675.2116.259.5447.034.0313.097.42
GW [66]59.288.3019.0314.5555.236.4716.7411.56
GFS-VL (ours)67.5731.6739.2343.1268.4829.1837.4540.92
+ +Table 2. Comparisons of our method with baselines on the new ScanNet200 benchmark. The best results are highlighted in bold. + +
Method5-shot1-shot
mIoU-BmIoU-NmIoU-AHMmIoU-BmIoU-NmIoU-AHM
Fully Supervised65.4537.2448.5347.4765.4537.2448.5347.47
PIFS [4]39.985.7419.4410.0336.664.9517.638.71
attMPTI [77]55.894.1924.877.7853.163.5523.406.66
COSeg [2]59.346.9627.9112.4558.496.2427.1411.26
GW [66]51.3511.0327.1618.1546.716.6322.6611.59
GFS-VL (ours)60.0521.6637.0231.8261.3919.4236.2129.47
+ +Table 3. Comparisons of our method with baselines on the new ScanNet++ benchmark. The best results are highlighted in bold. + +
Method5-shot1-shot
mIoU-BmIoU-NmIoU-AHMmIoU-BmIoU-NmIoU-AHM
Fully Supervised78.7160.3772.9168.3378.7160.3772.9168.33
attMPTI [77]16.313.1212.355.2112.971.629.572.88
PIFS [4]35.143.2125.565.8835.802.5425.824.75
CAPL [56]38.2214.3931.0720.8838.7010.5930.2716.53
GW [66]40.1818.5833.7025.3940.0614.7832.4721.55
GFS-VL (ours)78.3051.2269.7561.9178.5649.7269.4560.88
+ +Table 4. Comparisons of our method with baselines on the old ScanNet benchmark. The best results are highlighted in bold. + +solely on limited few-shot samples, constraining their capacity for novel class generalization and resulting in lower scores on the benchmarks. Moreover, the reduced performance on our new benchmarks emphasizes their value as a rigorous and comprehensive evaluation setting. These benchmarks challenge models to demonstrate robust generalization across diverse classes, fostering a deeper understanding of GFS-PCS for real-world applications. + +# 5.3. Ablation Studies + +We conducted ablation studies on the ScanNet200 [48] dataset using a single set of 5-shot support samples. + +Effect of Design Components. We assessed the effectiveness of each module in GFS-VL in Tab. 5a. The baseline (1 $^{\text{st}}$ row) shows performance using raw pseudo-labels directly from the 3D VLM. Adding Pseudo-label Selection (PS) in the $2^{\text{nd}}$ row significantly improves pseudo-label quality, resulting in a clear performance boost. Introducing Adaptive Infilling (AI) further enhances results by effectively assigning labels to unlabeled regions of novel classes ( $3^{\text{th}}$ row). Visualizations in Fig. 4 illustrate the quality improvements achieved with PS and AI, affirming their effectiveness. Lastly, Novel-Base Mix (NB-Mix), whether used with PS + +$(4^{\mathrm{rd}}$ row) or combined with PS and AI $(5^{\mathrm{th}}$ row), improves generalization by effectively integrating novel knowledge into the training samples. + +Results with Different 3D VLMs. We tested GFS-VLwith two prominent 3D VLMs, RegionPLC [67] and Openscene [44], as shown in the $2^{\mathrm{nd}}$ and $4^{\mathrm{th}}$ rows of Tab. 5b. Compared to their zero-shot results ( $1^{\mathrm{st}}$ and $3^{\mathrm{rd}}$ rows), our approach achieves substantial gains by effectively leveraging few-shot samples to refine and enhance the noisy knowledge in each 3D VLM. This demonstrates our framework's flexibility and effectiveness across diverse 3D VLMs. + +Impact of the Threshold in AI. Adaptive Infilling (AI) assigns novel class labels to unlabeled points based on similarity to adaptive prototypes, controlled by a threshold $\delta$ . In Tab. 5c, we explore different $\delta$ values and observe that $\delta = 0.9$ achieves the highest performance, which best balances enriching novel classes and maintaining label quality. + +Effect of the Threshold in PS. Pseudo-label Selection (PS) refines pseudo-labels by retaining only the most reliable regions predicted by the 3D VLM, based on a threshold $\tau$ . In Tab. 5d, we evaluate the effect of varying $\tau$ . The method performs robustly across different $\tau$ values, with the optimal + +
PSAINB-MixmIoU-BmIoU-NmIoU-AHM
65.5022.3031.4033.28
✓69.2626.5135.5138.35
✓✓66.2528.0336.0739.39
✓✓66.9428.2136.3639.69
✓✓✓67.4231.8139.3043.22
+ +(a) + +
3D VLMmIoU-BmIoU-NmIoU-AHM
RegionPLC [67]46.9723.7728.6531.56
Ours (RegionPLC)67.4231.8139.3043.22
Openscene [44]53.0715.1623.1423.58
Ours (Openscene)68.5620.0930.2931.07
+ +(b) + +
δmIoU-BmIoU-NmIoU-AHM
0.8066.6730.4138.0441.77
0.8566.2931.0038.4342.24
0.9067.4231.8139.3043.22
0.9566.2230.6838.1741.94
+ +(c) + +
τmIoU-BmIoU-NmIoU-AHMnmIoU-BmIoU-NmIoU-AHM
0.567.1931.3338.8842.73167.4027.1335.6138.68
0.667.4231.8139.3043.22267.9527.7136.1839.36
0.766.6930.5638.1741.92366.9428.2136.3639.69
0.868.0630.6738.5442.28467.8427.8036.2339.44
+ +(d) + +
BackbonemIoU-BmIoU-NmIoU-AHM
PTv3 [63]67.4231.8139.3043.22
SCN [13]61.8531.9438.2442.13
+ +(f) + +
MixmIoU-BmIoU-NmIoU-AHM
Instance Mix68.2923.9333.2735.44
Mix3D [39]68.5024.8034.0036.42
NB-Mix67.9527.7136.1839.36
+ +(g) + +Table 5. Ablation study. (a) Effect of design components. (b) Results with different 3D VLMs. (c) Impact of the threshold in AI. (d) Effect of the threshold in PS. (e) Impact of different mix blocks. (f) Results with different backbones. (g) Comparison of mix strategies. + +![](images/6aa460f5cb84e34530022b77a8a823272938cab8f833278da6910489bc1e15ba.jpg) + +![](images/4c4b6d2163943a3d746e0212de53bb29f5e1d8ac6fead159354295f8d85381dd.jpg) +Query + +![](images/0a6069c24f9419d593c554c0ad32cac3a69474e9dd327cc0932205cd97deb537.jpg) + +![](images/0cc9461e0e0fc855246832b80b9700e6c5630a331ee0f59921c1f1e93d972540.jpg) +Base Class Labels + +![](images/c27e64b474292d886eea018dedbb47da88d63106ae66e427b4c96667f1626660.jpg) + +![](images/39609683652e9be6cfea7479922ef120f10b84efbcc53e33d94cf0f93fd422b2.jpg) +Full Class labels + +![](images/0c0b2a7d54ef6e629f21e490e59d62879032a4093a0b11ff483bec363acb72c6.jpg) + +![](images/93291e2e9c93c3fe6898637434c2e4a72947cb0fab89394381b4571f5ae44cbe.jpg) +Raw Pseudo-Label + +![](images/70319958d0997757d57dfa9db0ff4ddb56e54611a447fe3e3730610bdba532bd.jpg) + +![](images/a78e1e1aeec83978187920ed888830c0d13dd70aa10d26d9f6f289925526dc0a.jpg) +After PS + +![](images/64823e901af51dae383ff9228c05f97c7ad6f0521e3910b68e776b7079c194c9.jpg) + +![](images/f0164d5d49f6f044b16f33a6acf52e1e297da0076927b35b82f40cf59159cff1.jpg) +After AI + +![](images/b5aeda0325992ab944809fec00c97f4e75089fc9219218c309bf62e25ea2f96e.jpg) + +![](images/d4b672dd3aaf1cc416818f0bd4d287497b3c3e57a0f567303848096487bdb0b9.jpg) +Instance Mix + +![](images/40c69d37411f7efe3aa726ce73c397bed00f7ef37eefa2f6c82400cbe7f45175.jpg) +Figure 4. Visualization of the improvements in pseudo-label quality after applying Pseudo-label Selection (PS) and Adaptive Infilling (AI). Note that AI effectively discovers missed novel classes in the red circles and completes partial pseudo-labels in the green circles. +Mix3D +Figure 5. Visual illustration of mixing strategies. The red and green boxes represent the two novel samples mixed into the scene. + +![](images/7869576dae33a025ce3e93eeaff7a29dbab9f30f46098f83d3c03c3149d8aa3c.jpg) + +![](images/db8c052ff5bb306d5d8d36151fe33135b7d50813b75f2af515bfa4ee674f9198.jpg) +Novel-Base Mix (Ours) + +performance achieved at $\tau = 0.6$ . This robustness indicates that PS effectively selects relevant reliable regions without being overly sensitive to the threshold choice. + +Impact of Different Mix Blocks. In NB-Mix, we can adjust the number of novel blocks, denoted as $n$ , used to augment each training sample. Tab. 5e shows stable performance (with the AI module disabled) across different block counts, suggesting that NB-Mix effectively integrates novel class information. By default, we use three blocks. + +Results with Different Backbones. Besides varying 3D VLMs, we examined the effect of different backbones. We evaluated two backbones, PTv3 [63] and SparseConvNet (SCN) [13] in Tab. 5f. Our approach consistently performs well across both networks, confirming that GFS-VL is generalizable and not dependent on a specific backbone. + +Comparison of Mix Strategies. We investigated alterna- + +tive mix strategies for integrating novel support samples into training data in Tab. 5g. Specifically, we compared our NB-Mix with Instance Mix, which randomly inserts novel class objects from foreground masks into scenes, and Mix3D [39], which overlays two scenes for out-of-context augmentation. Fig. 5 shows the visual examples of these strategies. Our method outperforms these alternatives, highlighting the importance of preserving local context to effectively learn diverse and challenging novel classes. + +# 6. Conclusion + +This work introduces a GFS-PCS framework GFS-VL that synergizes dense but noisy pseudo-labels from 3D VLMs with accurate yet sparse few-shot samples, overcoming current GFS-PCS limitations in novel knowledge learning. GFS-VL utilizes prototype-guided pseudo-label selection to target high-quality regions and adaptive infilling to enrich pseudo-labels. Besides, the novel-base mix embeds few-shot samples into training scenes, preserving essential context for improved novel class learning. Identifying the limited diversity in current GFS-PCS evaluations, we introduce two benchmarks with broader, more diverse novel classes for more comprehensive generalization evaluation. GFS-VL achieves leading results and generalizes effectively across models and datasets, showing the potential of 3D VLMs in advancing GFS-PCS. 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However, we demonstrate through experiments that there is still unutilized information in entropy parameters estimated by neural networks in current methods, which can be used for more accurate probability estimation. Thus we introduce generalized Gaussian entropy model, which controls the tail shape through shape parameter to more accurately estimate the probability of latents. Meanwhile, to the best of our knowledge, existing methods use fixed likelihood intervals for each integer during arithmetic coding, which limits model performance. We propose Mean Error Discriminator (MED) to determine whether the entropy parameter estimation is accurate and then dynamically adjust likelihood intervals. Experiments show that our method significantly improves rate-distortion (RD) performance on three VAE-based models for point cloud attribute compression, and our method can be applied to other compression tasks, such as image and video compression. + +# 1. Introduction + +In recent years, point clouds have become an important type of 3D visual data, with widespread applications in virtual reality [29], autonomous driving [30], and various other fields. With the massive generation of point cloud, there is an urgent need for efficient compression methods. Point clouds consist of two main aspects: geometry information and attribute information. Geometry information refers to the 3D coordinates of the points, while attribute information includes various details such as color and reflectance. Current geometry compression methods, such as the traditional coding algorithms used in G-PCC [14] and V-PCC [15], as well as deep learning-based methods like SparsePCGC [26], OctAttention [7] and EHEM [25], have achieved efficient compression of point cloud geometry. However, + +![](images/15e63a99ab0b9ecc13996e442279bd1f67250b2d5bfdbefe5486ea9418cd6799.jpg) +Figure 1. Rate-speed comparison on 8iVFBv2 [1] and MVUB [18]. Left-top is better. + +![](images/42620f78f0b53893055cc2cfbd5d902e5841c28b7981660b19a75066e27d734e.jpg) +Figure 2. Dynamic likelihood intervals. When the prediction of mean is inaccurate, squeeze the likelihood interval of $\lfloor \mu \rceil$ so that the remaining integer likelihood intervals can shift towards the center of the entropy model, thereby increasing the likelihood. On the contrary, when the prediction is accurate, the likelihood interval of $\lfloor \mu \rfloor$ is stretched. + +for attribute compression, the achievable compression ratios with current methods are still far below those for geometry compression. Therefore, our focus is on point cloud attribute compression based on lossless geometry. + +Variational autoencoders (VAEs) [13] have played an important role in deep learning-based compression frameworks. Based on VAE, Balle et al. [2] propose using hyperpriors to generate multivariate Gaussian distributions + +for arithmetic coding of latents. Later, in point cloud attribute compression, Gaussian or Laplacian distributions determined by the mean and scale, have been used as entropy models for latents [9, 19, 20]. In fact, we demonstrate through experiments that these entropy model parameters can be utilized to further improve the performance of the model. + +On the other hand, we need to transform continuous entropy models into discrete probability tables for arithmetic coding [22], where each integer corresponds to a probability. Previous work [2] directly uses the half neighborhood of integers as likelihood intervals to calculate discrete probability tables. Our experiment shows that this fixed likelihood interval limits the performance of the model. + +Based on the above discussion, we propose: + +- Using generalized Gaussian distribution which is more expressive as the entropy model to provide more accurate probability estimation of the latents. +- Determining the accuracy of the current entropy model based on mean, scale and decoded latents, then dynamically adjusting the likelihood intervals for more efficient arithmetic coding. +- Developing a two-step training strategy, as our method does not make significant changes to the original structure of the model except adding a few modules, allowing it to be well applied to current VAE-based models. + +# 2. Related Work + +# 2.1. Learned Image Compression + +Learned image compression is a highly developed field, and its methods are of significant reference value for the compression of point cloud attributes. Balle et al. [2] are the first to propose an image compression method based on hyperpriors, which has become the foundational framework for subsequent image compression techniques. Building on the hyperprior model, Minnen et al. [20] introduce a context module that allows for more accurate estimation of entropy parameters. However, the serial computation required by the context module substantially increases encoding and decoding times. He et al. [9] propose a checkerboard model that utilizes context from anchor regions to assist in the encoding of non-anchor regions, reducing the encoding and decoding time with almost no performance loss. Cheng et al. [5] suggest replacing Gaussian distributions with mixture Gaussian distributions as the entropy model. Minnen et al. [19] propose leveraging context between channels to assist in the encoding process. Recent work [10-12] has focused on maximizing the use of contextual information while maintaining the parallelism of the context modules. + +![](images/b87ec03dd18c7fccc11a40cd84f4b6435a09de3d348b2f65ecaa5c1d928ef098.jpg) +Figure 3. Operational diagrams: Variational compression model with hyperprior and onext. + +# 2.2. Point Cloud Attribute Compression + +In traditional point cloud attribute compression methods, the main research focus is on how to optimize prediction and transformation. Song et al. [24] propose using different prediction methods for point clouds with different features, Shao et al. [23] propose using graph transform instead of discrete cosine transform (DCT), and Peng et al. [21] propose learning an optimal Laplacian matrix through convex optimization to achieve better graph transform. + +In recent years, the performance of deep learning-based methods has gradually surpassed traditional methods. Wang et al. [26] propose the first learned point cloud attribute compression framework based on context and hyperpriors. Recent work [27] aims at how to more efficiently utilize context. Guo et al. [8] propose using context between channels to increase the parallelism of context modules and combining sparse convolution and transformer to better capture local and global information. Mao et al. [17] propose layering point clouds to more fully utilize context achieves SOTA RD performance. Zhang et al. [6, 31] also propose using neural networks to enhance traditional methods, which compensates for the shortcomings of traditional methods' insufficient predictive ability. + +# 3. Preliminary + +# 3.1. Variational Compression Model with Hyperprior and Context + +The framework of the variational compression model with hyperprior and context is shown in Figure 3. $\pmb{y}$ is the latent representation after encoding, while $\pmb{z}$ is the hyper latent for estimating the entropy model of $\pmb{y}$ . During training, quantization is replaced by adding uniform noise from $\mathcal{U}(-\frac{1}{2},\frac{1}{2})$ to $\pmb{y}$ or $\pmb{z}$ . The entropy model for the decoding part of $\hat{\pmb{y}}$ is jointly estimated by $\hat{\pmb{z}}$ and the context obtained from the decoded part, while $\hat{\pmb{z}}$ is compressed by a factorized entropy model. The model uses rate-distortion cost as the loss function for end-to-end training: + +$$ +\begin{array}{l} R + \lambda \cdot D = E _ {\boldsymbol {x} \sim p _ {\boldsymbol {x}}} \left[ - \log_ {2} p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) - \log_ {2} p _ {\hat {\boldsymbol {z}}} (\hat {\boldsymbol {z}}) \right] \\ + \lambda \cdot E _ {\boldsymbol {x} \sim p _ {\boldsymbol {x}}} [ d (\boldsymbol {x}, \hat {\boldsymbol {x}}) ] \tag {1} \\ \end{array} +$$ + +where entropy is used to estimate the bitrate of $\hat{\pmb{y}}$ and $\hat{z}$ , and $d(\pmb{x},\hat{\pmb{x}})$ is the distortion of the reconstructed point cloud, usually represented by MSE or MS-SSIM [28]. + +In fact, $\hat{\pmb{y}}$ occupies the vast majority of the total bitrate (usually more than $95\%$ ), of which the probability is modeled by Gaussian likelihoods: + +$$ +p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) = \prod_ {i} \left[ \mathcal {N} (\mu_ {i}, \sigma_ {i} ^ {2}) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i}). (2) +$$ + +The Gaussian distribution in Equation 2 could be replaced with mixture Gaussian distribution or Laplacian distribution. + +# 3.2. Generalized Gaussian Distribution + +If the random variable $X\sim \mathcal{G}(\mu ,\sigma ,\beta)$ ,then + +$$ +P (X = x) = \frac {\beta}{2 \sigma \Gamma \left(\frac {1}{\beta}\right)} e ^ {- \frac {| x - \mu | ^ {\beta}}{\sigma^ {\beta}}} \tag {3} +$$ + +where + +$$ +\Gamma (z) = \int_ {0} ^ {\infty} t ^ {z - 1} e ^ {- t} d t. \tag {4} +$$ + +Compared to the Gaussian distribution, generalized Gaussian distribution [3] has an additional shape parameter $\beta$ to control whether the distribution has a heavy tail or a light tail, as shown in Figure 4a. + +It is worth noting that the generalized Gaussian distribution degenerates into a Laplacian distribution when $\beta = 1$ , or a Gaussian distribution when $\beta = 2$ . + +# 4. Explore a More Accurate Likelihood + +# 4.1. The Relationship Between Latent and Entropy Parameters + +Obviously, the closer $\mu$ is to $\hat{y}$ in Equation 2, the greater the likelihood and the lower the bitrate, which can be written as: + +$$ +\underset {\boldsymbol {\mu}} {\arg \max } p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) = \hat {\boldsymbol {y}}, \tag {5} +$$ + +thus we can consider $\mu$ as the predicted value of $\hat{y}$ . Next, we analyze the optimal value of the scale parameter $\sigma$ by fixing $\mu$ and $\hat{y}$ : + +$$ +\arg \max _ {\boldsymbol {\sigma}} p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}). \tag {6} +$$ + +We can conclude that the $i$ -th element of $\sigma$ satisfies: + +$$ +\sigma_ {i} = \arg \max _ {\sigma} \left[ \mathcal {N} \left(\mu_ {i}, \sigma^ {2}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i}). \tag {7} +$$ + +Since + +$$ +\mathcal {N} \left(\mu_ {i}, \sigma^ {2}\right) \left(\hat {y} _ {i}\right) = \frac {1}{\sqrt {2 \pi \sigma^ {2}}} e ^ {- \frac {\left(\hat {y} _ {i} - \mu_ {i}\right) ^ {2}}{2 \sigma^ {2}}}, \tag {8} +$$ + +![](images/87f6d56be69f14fc606aaac91d2245f8e436b84ae5b38d2e8b51a6d42d1c2f25.jpg) +(a) + +![](images/1d0967ee68a9e8593c068e701756afd2626fec9abc68bcc64260416c116ab829.jpg) + +![](images/450a7343bdda5d4120e725cb85e5fe89aa94f0c65768708d772d5eeb7d361c9f.jpg) +(b) +(c) +Figure 4. Function diagram: (a) Generalized Gaussian distribution with different shape parameter $\beta$ while $\mu = 0$ . (b) The relationship between likelihood interval radius $\delta$ of $\lfloor \mu \rceil$ and $\pi = P(\hat{y} = \lfloor \mu \rceil)$ , which is detailed discussed in Section 5.2. (c) Optimal scale $\sigma$ for $y - \mu$ using Gaussian distribution and Laplacian distribution as the entropy model respectively. + +for situations with accurate predictions ( $\mu_{i}$ and $\hat{y}_i$ are close), the bitrate is relatively low. Therefore, we consider the case of inaccurate predictions where $\mu_{i}$ and $\hat{y}_i$ have a noticeable difference. To simplify the calculations in this situation, we make the following approximations: + +$$ +\begin{array}{l} f \left(\hat {y} _ {i}, \mu_ {i}, \sigma\right): = \frac {1}{\sqrt {2 \pi} \sigma} e ^ {- \frac {\left(\hat {y} _ {i} - \mu_ {i}\right) ^ {2}}{2 \sigma^ {2}}} \\ \approx \frac {1}{\sqrt {2 \pi} \sigma} \int_ {\hat {y} _ {i} - \mu_ {i} - \frac {1}{2}} ^ {\hat {y} _ {i} - \mu_ {i} + \frac {1}{2}} e ^ {- \frac {t ^ {2}}{2 \sigma^ {2}}} d t \\ = \int_ {\hat {y} _ {i} - \frac {1}{2}} ^ {\hat {y} _ {i} + \frac {1}{2}} \frac {1}{\sqrt {2 \pi \sigma^ {2}}} e ^ {- \frac {(t - \mu_ {i}) ^ {2}}{2 \sigma^ {2}}} d t \\ = \left[ \mathcal {N} \left(\mu_ {i}, \sigma^ {2}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i}). \\ \end{array} +$$ + +Then find $\sigma^{opt}$ by the partial derivative: + +$$ +\begin{array}{l} \frac {\partial f}{\partial \sigma^ {o p t}} = \frac {1}{\sqrt {2 \pi}} e ^ {- \frac {\left(\hat {y} _ {i} - \mu_ {i}\right) ^ {2}}{2 \left(\sigma^ {o p t}\right) ^ {2}}} \left[ \frac {\left(\hat {y} _ {i} - \mu_ {i}\right) ^ {2}}{\left(\sigma^ {o p t}\right) ^ {4}} - \frac {1}{\left(\sigma^ {o p t}\right) ^ {2}} \right] \tag {10} \\ = 0, \\ \end{array} +$$ + +so the optimal $\sigma_{i}$ for $(\hat{y}_i,\mu_i)$ can be approximated by $\sigma^{opt} = |\hat{y}_i - \mu_i|$ . Moreover, we can get the same result if the Gaussian distribution in Equation 2 is replaced with + +a mixture Gaussian distribution (fix the mixture weights $\pmb{w}$ ) or Laplacian distribution. To visually show the relationship between $\sigma^{opt}(y, \mu)$ and $|y - \mu|$ , we numerically compute $\sigma^{opt}(y, \mu)$ and present the results in Figure 4c. + +In general, the optimal $\sigma$ can be approximated as: + +$$ +\arg \max _ {\boldsymbol {\sigma}} p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) \approx | \hat {\boldsymbol {y}} - \boldsymbol {\mu} | \tag {11} +$$ + +From the above deduction, the scales $\sigma$ could be considered as the prediction of the absolute residual between the latent and means. + +# 4.2. Preliminary Improvements for Failed Predictions + +As discussed above, we can determine whether the predicted mean $\mu_{i}$ for $\hat{y}_i$ is accurate by $\sigma_{i}$ : $\mu_{i}$ and $\hat{y}_i$ are more likely to have a noticeable difference if $\sigma_{i}$ is relatively large, which usually needs more bits for arithmetic encoding. The integration intervals for calculating likelihoods are typically at the "tail" of the entropy model for these "failed predictions", thus we can improve the entropy model: + +- Adopting a more "heavy-tailed" entropy model, such as generalized Gaussian distribution with shape parameter $\beta < 1$ . +- Sacrificing the likelihood interval of integers at the central for the likelihood interval of integers at the tail. + +Based on the above discussion, we make preliminary improvements to SparsePCAC, which is a classical variational compression model for point cloud attribute compression with hyperprior and autoregressive context. As SparseP-CAC uses Laplacian distribution as its entropy model, we first roughly assume that for $i$ with $\sigma_{i} > 2$ , the predicted mean $\mu_{i}$ for $\hat{y}_i$ is inaccurate, then use more heavy-tailed distributions and likelihood intervals closer to the center for these $i$ without retraining. + +Specifically, we directly use the trained model to obtain the latent and parameters of entropy models, but modify the likelihood calculation during encoding and decoding: for $0 < \sigma_{i} \leq 2$ , let + +$$ +p _ {\hat {y} _ {i} | \hat {z}} (\hat {y} _ {i} | \hat {z}) = \left[ \mathcal {L} \left(\mu_ {i}, \sigma_ {i}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i}). \tag {12} +$$ + +For $2 < \sigma_{i}$ and $|\hat{y}_i - \mu_i| \leq \frac{1}{2}$ , let + +$$ +p _ {\hat {y} _ {i} | \hat {z}} (\hat {y} _ {i} | \hat {z}) = \left[ \mathcal {G} \left(\mu_ {i}, \sigma_ {i}, 0. 5\right) * \mathcal {U} \left(- \frac {1}{4}, \frac {1}{4}\right) \right] (\hat {y} _ {i}). \tag {13} +$$ + +For $2 < \sigma_{i}$ and $|\hat{y}_i - \mu_i| > \frac{1}{2}$ , let + +$$ +p _ {\hat {y} _ {i} | \hat {z}} (\hat {y} _ {i} | \hat {z}) = \left[ \mathcal {G} \left(\mu_ {i}, \sigma_ {i}, 0. 5\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i} + \Delta) \tag {14} +$$ + +where the offset $\Delta$ is: + +$$ +\Delta = \frac {1}{4} \operatorname {s g n} \left(\mu_ {i} - \hat {y} _ {i}\right). \tag {15} +$$ + +We use generalized Gaussian distribution with $\beta = 0.5$ for $i$ satisfying $\sigma_{i} > 2$ in Equation 13 and 14, and narrow the likelihood interval of $\lfloor \mu_i\rfloor$ , making the likelihood intervals of the remaining integers closer to the center. + +![](images/81404aa7463c2b6d5f1f992195ed8b5ab1c25fd4d53a54e833ce0155cf0428e0.jpg) +Figure 5. Results of preliminary experiment. To highlight the differences between different methods, the horizontal axis is calculated by subtracting improved bpp from the bpp of SparsePCAC. + +Figure 5 shows the results of the above improvements made to the SparsePCAC. From Figure 5, it can be seen that although the model structure has not been modified or retrained, there is still a noticeable improvement in encoding performance. + +# 5. Proposed Method + +The overall framework of the proposed method is illustrated in Figure 6 based on the above deduction and experimental results. We utilize the generalized Gaussian entropy model and dynamic likelihood interval to encode latents more efficiently, which will be detailed discussed next. + +# 5.1. Generalized Gaussian Entropy Model + +For the input point cloud $\pmb{x}$ , we can first obtain quantized latent $\hat{\pmb{y}}$ and hyper latent $\hat{\pmb{z}}$ through autoencoders $(g_{a}, g_{s})$ and $(h_{a}, h_{s})$ : + +$$ +\hat {\boldsymbol {y}} = Q (\boldsymbol {y}) = Q \left(g _ {a} (\boldsymbol {x})\right) \tag {16} +$$ + +$$ +\hat {z} = Q (z) = Q \left(h _ {a} (\boldsymbol {y})\right), +$$ + +then use the generalized Gaussian distribution as the entropy model for $\hat{\pmb{y}}$ : + +$$ +p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) \sim \mathcal {G} (\boldsymbol {\mu}, \boldsymbol {\sigma}, \beta). \tag {17} +$$ + +We estimate the mean and scale of the generalized Gaussian entropy model by combining hyperprior and context, + +![](images/7bc51167c7cd3144eec2454eb7e44b5466d1977c9ae966180b3b5e01da085be0.jpg) +Figure 6. Overall framework. We propose using the generalized Gaussian distribution as the entropy model to better estimate the probability of latents, and dynamically adjust likelihood intervals based on predicted entropy parameters. The entire network is trained by proposed two-step training strategy. Q represents quantization and C represents concatenation. Blue and red lines represent the encoding and decoding steps respectively, while yellow lines represent the steps that need to be performed in both encoding and decoding. + +which is similar to SparsePCAC: + +$$ +\left(\mu_ {i}, \sigma_ {i}\right) = g _ {e p} \left(g _ {c m} \left(\hat {\boldsymbol {y}} _ {< i}\right), h _ {s} (\hat {\boldsymbol {z}})\right). \tag {18} +$$ + +As the likelihood is determined by the probability density function in Equation 3 which depends on $\pmb{x} - \pmb{\mu}$ (i.e., $\hat{\pmb{y}} - \pmb{\mu}$ ), $\pmb{\sigma}$ and $\pmb{\beta}$ , the optimal $\pmb{\beta}$ can be determined given $\hat{\pmb{y}} - \pmb{\mu}$ and $\pmb{\sigma}$ in order to maximize the likelihood. Different from $\mu_{i}$ and $\sigma_{i}$ , $\hat{y}_i$ is unknown when determining $\beta_{i}$ , so we propose another context model $h_{cm}$ to extract context from the absolute difference between predicted $\pmb{\mu}$ and decoded $\hat{\pmb{y}}$ : + +$$ +\mathcal {C} = h _ {c m} \left(\left| \hat {\boldsymbol {y}} - \boldsymbol {\mu} \right| < i\right). \tag {19} +$$ + +Therefore, we combine $(\mu, \sigma)$ and context $\mathcal{C}$ to estimate $\beta$ : + +$$ +\begin{array}{l} \beta_ {i} = h _ {e p} \left(\mathcal {C}, \boldsymbol {\mu} _ {\leq i}, \boldsymbol {\sigma} _ {\leq i}\right) \tag {20} \\ = h _ {e p} \left(h _ {c m} \left(\left| \hat {\boldsymbol {y}} - \boldsymbol {\mu} \right| _ {< i}\right), \boldsymbol {\mu} _ {\leq i}, \sigma_ {\leq i}\right). \\ \end{array} +$$ + +# 5.2. Dynamic Likelihood Interval + +In current methods, when performing arithmetic encoding on $\hat{y}_i$ using a continuous entropy model $\mathcal{G}(\mu_i,\sigma_i,\beta_i)$ , the probability of integer $n$ is determined based on fix likelihood intervals: + +$$ +\begin{array}{l} P \left(\hat {y} _ {i} = n\right) = \left[ \mathcal {G} \left(\mu_ {i}, \sigma_ {i}, \beta_ {i}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (n) \tag {21} \\ = \int_ {n - \frac {1}{2}} ^ {n + \frac {1}{2}} \mathcal {G} (y | \mu_ {i}, \sigma_ {i}, \beta_ {i}) d y. \\ \end{array} +$$ + +Results of preliminary experiment indicate that a fixed likelihood interval does not fully utilize the effective information contained in the parameters of the entropy model. In fact, we can determine whether the prediction for $\hat{y}_i$ is accurate based on the entropy model parameters and decoded latent. If the prediction is inaccurate, indicated by a large $|\hat{y}_i - \mu_i|$ , we can obtain a more precise discrete probability distribution for arithmetic encoding by shortening the likelihood interval for the central region integers, which causes bigger likelihoods of the integers in the marginal regions as the likelihood intervals of these integers converge toward the center. Conversely, if the prediction is accurate, we can extend the likelihood interval for the central region integers by sacrificing the likelihood interval of the marginal region integers. + +However, it is challenging to accurately determine whether the likelihood interval of each integer should be extended or shortened. Therefore, we consider scaling the likelihood interval of $\lfloor \mu_i\rfloor$ while translating the likelihood intervals of the remaining integers to obtain a more accurate discrete probability distribution for the sake of model simplicity and effectiveness, which is illustrated in Figure 2. + +As discussed above, we should first determine the accuracy of the prediction $\mu_{i}$ for $\hat{y}_i$ . Therefore, we estimate the probability of $\hat{y}_i = \lfloor \mu_i\rfloor$ using Mean Error Discriminator + +
Encoder ga*Decoder gs*Hyper Encoder ha*Hyper Decoder hs*Context Prediction gcm*, hcmEntropy Parameters gcp*Entropy Parameters hcpMean Error Discriminator dme
SConv 3c64TSCov 3c128 s2↑SCov 3c128TSCov 3c128 s2↑Masked 5c256SCov 1c384SCov 1c384SCov 1c384
SCov 3c128 s2↓SCov 3c128Leaky ReLUSCov 3c128Leaky ReLULeaky ReLULeaky ReLULeaky ReLU
Leaky ReLULeaky ReLUSCov 3c128SCov 3c128 s2↓Leaky ReLUSCov 1c256SCov 1c256SCov 1c256
SCov 3c128TSCov 3c128SConv 3c128SCov 3c128 s2↓SConv 3c256Leaky ReLULeaky ReLULeaky ReLU
SConv 3c128SConv 3c128Leaky ReLUSCov 3c128Leaky ReLUSCov 1c256SCov 1c256SCov 1c256
SConv 3c128TSCov 3c64 s2↑SCov 3c128 s2↓SCov 3c128 s2↓Sigmoid
SCov 3c128 s2↓SCov 3c3
+ +Table 1. Network Architecture. The modules marked with * refer to SparsePCAC and will be replaced with corresponding modules in subsequent experiments while $h_{cm}$ we propose is consistent with $g_{cm}$ . "SConv" is sparse convolution and "TSCov" is transposed sparse convolution. + +$d_{me}$ based on $(\pmb {\mu},\pmb {\sigma})$ and context $\mathcal{C}$ + +$$ +\begin{array}{l} \pi_ {i}: = P (\hat {y} _ {i} = \lfloor \mu_ {i} \rceil) \\ = d _ {m e} \left(\mathcal {C}, \boldsymbol {\mu} _ {\leq i}, \boldsymbol {\sigma} _ {\leq i}\right) \tag {22} \\ = d _ {m e} \left(h _ {c m} \left(\left| \hat {\boldsymbol {y}} - \boldsymbol {\mu} \right| _ {< i}\right), \boldsymbol {\mu} _ {\leq i}, \boldsymbol {\sigma} _ {\leq i}\right). \\ \end{array} +$$ + +Next, We determine the likelihood intervals of $\lfloor \mu_i\rfloor$ and the remaining integers separately. In order to determine the likelihood interval of $\lfloor \mu_i\rfloor$ : + +$$ +L I \left(\left\lfloor \mu_ {i} \right\rceil \mid \mu_ {i}, \sigma_ {i}, \pi_ {i}\right) = \mathcal {U} \left(- \frac {\delta_ {i}}{2}, \frac {\delta_ {i}}{2}\right) (\left\lfloor \mu_ {i} \right\rceil), \tag {23} +$$ + +we set the range for $\delta_{i}$ as follow: + +$$ +\frac {1}{1 + \sigma_ {i}} \leq \delta_ {i} \leq \frac {1}{1 - e ^ {- \sigma_ {i}}}. \tag {24} +$$ + +Equation 24 uses $\sigma$ to determine the upper bound of stretching $(\frac{1}{1 - e^{-\sigma_i}}$ , with a range of $(1, + \infty))$ and the lower bound of squeezing $(\frac{1}{1 + \sigma_i}$ , with a range of $(0,1))$ of the scaling ratio $\delta_{i}$ . Since larger $\sigma_{i}$ means inaccurate $\mu_{i}$ , it is better to reduce the likelihood interval of $\mu_{i}$ at this time, so Equation 24 ensures that both upper bound and lower bound will decrease when $\sigma_{i}$ increases. By combining the bounds of $\delta_{i}$ and the probability $\pi_{i}$ , the final $\delta_{i}$ is: + +$$ +\delta_ {i} = \left\{ \begin{array}{l l} 1 + (2 \pi_ {i} - 1) \left(\frac {1}{1 - e ^ {- \sigma_ {i}}} - 1\right) & \text {i f} \pi_ {i} \geq \frac {1}{2} \\ 1 - (1 - 2 \pi_ {i}) \left(1 - \frac {1}{1 + \sigma_ {i}}\right) & \text {i f} \pi_ {i} < \frac {1}{2} \end{array} . \right. \tag {25} +$$ + +Equation 25 uses the relationship between $\pi_{i}$ and 0.5 to determine whether to stretch or squeeze, and uses $|2\pi_{i} - 1|$ (to make the whole function continuous) and $\sigma_{i}$ to determine the final $\delta_{i}$ . As shown in Figure 4b, for $\pi_{i} \geq \frac{1}{2}$ , we consider that $\hat{y}_{i}$ is more likely to be in the tail of the entropy model, which leads us to shorten the likelihood interval of $\lfloor \mu_{i} \rfloor$ . Conversely, we expand the likelihood interval of $\lfloor \mu_{i} \rfloor$ for $\pi_{i} < \frac{1}{2}$ . + +Naturally, for integer $n \neq \lfloor \mu_i \rfloor$ , we set its likelihood interval as: + +$$ +L I \left(n \mid \mu_ {i}, \sigma_ {i}, \pi_ {i}\right) = \left\{ \begin{array}{l l} \mathcal {U} \left(\frac {\delta_ {i}}{2} - 1, \frac {\delta_ {i}}{2}\right) (n) & \text {i f} n > \lfloor \mu_ {i} \rceil \\ \mathcal {U} \left(- \frac {\delta_ {i}}{2}, - \frac {\delta_ {i}}{2} + 1\right) (n) & \text {i f} n < \lfloor \mu_ {i} \rceil \end{array} . \right. \tag {26} +$$ + +# 5.3. Network Architecture + +The structures of different neural network modules in our method are outlined in Table 1. Please note that the modules marked with * are the same as SparsePCAC for example. In subsequent experiments, we will replace the structures of these modules with those of corresponding modules in different existing methods. + +# 5.4. Loss Function + +We still use the rate-distortion cost with MSE distortion as the loss function for training: + +$$ +\begin{array}{l} \mathcal {L} = R + \lambda \cdot D \\ = E _ {\boldsymbol {x} \sim p _ {\boldsymbol {x}}} \left[ - \log_ {2} p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) - \log_ {2} p _ {\hat {\boldsymbol {z}}} (\hat {\boldsymbol {z}}) \right] \tag {27} \\ + \lambda \cdot E _ {\boldsymbol {x} \sim p _ {\boldsymbol {x}}} [ d (\boldsymbol {x}, \hat {\boldsymbol {x}}) ], \\ \end{array} +$$ + +but the likelihoods of latent $\hat{\pmb{y}}$ need to be calculated according to generalized gaussian entropy model and dynamic likelihood intervals: + +$$ +p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) = \prod_ {i} \left[ \mathcal {G} \left(\mu_ {i}, \sigma_ {i}, \beta_ {i}\right) * L I \left(\mu_ {i}, \sigma_ {i}, \pi_ {i}\right) \right] (\hat {y} _ {i}). \tag {28} +$$ + +# 6. Experimental Results + +# 6.1. Datasets + +To show the model's transferability, we construct the training and testing datasets as follow: + +Training Dataset. We use ShapeNet [4] and COCO [16] to construct the training dataset as in [26]. We randomly sample points from the meshes in ShapeNet, apply random rotation to them, and then quantize the coordinates into 8-bit integers to represent the geometry of point clouds. The number of points in each point cloud ranges from 50,000 to 100,000. Next, we randomly select images from COCO and project them onto the point clouds obtained through the aforementioned steps as the attributes of these point clouds. We generate 12,000 samples for training by this approach. + +Testing Dataset. We selected nine point cloud sequences from 8iVFBv2 [1] and MVUB [18] as the testing dataset. Each point cloud sequence contains between 200 and 300 frames, with each frame consisting of 500,000 to 2,000,000 points, which contains rich texture information. + +![](images/070867a54fea186a8b7a7edd1a5177ff080f18ebfea3a0c1116438d36fb88ff1.jpg) + +![](images/ab6ab4741084fcc684c5846c0ec0183113c5b2a7153b7c9f0e210cf5387ae6fc.jpg) + +![](images/c36335cec65abc4299e9b03d60fa59ad4229738379da733a2a00016df93782c1.jpg) + +![](images/1c736dc2587edc698f36bc3caf7c22c3dcf0b21b3e7cf96ef55af136d367331c.jpg) + +![](images/097710e4535758a279ec61dfc4e7eac79d611aed94bef29e93e164a057406e85.jpg) + +![](images/2819d42f9b6e0dd1e01ddee0d4a4aaea7f8d7f608abc20137a2316df6adf18b4.jpg) + +![](images/ef9491bfc7f744279d0cb6549df5fbf86195e44e5de87e51c1e659b384b6d794.jpg) +Figure 7. Demonstration of rate-distortion curves for the proposed method applied to three baseline models on nine point cloud sequences. + +![](images/60ad3a2d6f16074562acc5dfe342b6dce4083cf3036de8a2d57b989f3a2ad401.jpg) + +![](images/67e57d2fd069d5fa8a22d75da1efeec420c9ccf02f7c81852125f22c7471c87e.jpg) + +# 6.2. Baseline Models + +We apply the proposed method to the following VAE-based models to demonstrate the effectiveness of our method. + +SparsePCAC: The first variational model with hyperprior and context for point cloud attribute compression, which generates autoregressive context serially using masked sparse convolutions [26]. + +TSC-PCAC: The TSCM module is introduced based on SparsePCAC, which combines transformer and sparse convolution to better capture both local and global information. Additionally, a channel-based context module is proposed to reduce encoding and decoding time [8]. + +SPAC: One of the current state-of-the-art frameworks based on VAE. SPAC proposes using Fast Fourier Transform to hierarchically process the point clouds and then compress them by SparsePCAC, where the high-frequency layers could leverage the context from the low-frequency layers while coding [17]. + +# 6.3. Two-Step Training + +We apply the generalized Gaussian entropy model and dynamic likelihood intervals proposed in Section 5 to each baseline model in Section 6.2. Then train these improved models and compare the coding results with those of the baseline models. Specifically, we replace the structures of + +the modules marked with * in Table 1 (i.e., the modules in the classic variational compression model with hyperprior and context) with the corresponding module structures from baseline models. For the sake of simplicity and effectiveness in training, we perform following two-step training to prevent the model from being difficult to converge due to too many parameters: + +- First train the modules in the baseline models, including the autoencoder $(g_{a}, g_{s})$ , hyper autoencoder $(h_{a}, h_{s})$ , context model $g_{cm}$ and the estimating module $g_{ep}$ for mean and scale. Meanwhile, disable $h_{cm}, h_{ep}$ and $d_{me}$ we propose, and set $\beta = 1, \pi = \frac{1}{2}$ , thus the generalized Gaussian distribution degenerates into Laplacian distribution and dynamic likelihood intervals degenerates into $\mathcal{U}(-\frac{1}{2}, \frac{1}{2})$ : + +$$ +\begin{array}{l} p _ {\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}} (\hat {\boldsymbol {y}} | \hat {\boldsymbol {z}}) = \prod_ {i} \left[ \mathcal {G} (\mu_ {i}, \sigma_ {i}, 1) * L I \left(\mu_ {i}, \sigma_ {i}, \frac {1}{2}\right) \right] (\hat {y} _ {i}) \\ = \prod_ {i} \left[ \mathcal {L} \left(\mu_ {i}, \sigma_ {i}\right) * \mathcal {U} \left(- \frac {1}{2}, \frac {1}{2}\right) \right] (\hat {y} _ {i}). \tag {29} \\ \end{array} +$$ + +- Train $h_{cm}, h_{ep}$ and $d_{me}$ while freezing the modules trained in the first step. + +We set $\lambda = 400, 1000, 4000, 8000$ and $16000$ in order to get different bitrate points. + +
Point CloudsOurs vs SparsePCACOurs vs TSC-PCACOurs vs SPAC
BD-BR(%)BD-PSNR(dB)BD-BR(%)BD-PSNR(dB)BD-BR(%)BD-PSNR(dB)
YYUVYYUVYYUVYYUVYYUVYYUV
Andrew-10.46-11.970.350.38-8.82-9.990.210.24-6.07-6.380.130.14
David-9.92-11.930.410.46-9.37-10.090.310.32-5.18-5.350.170.17
Longdress-10.39-10.650.340.36-8.87-9.310.240.25-5.29-5.700.150.16
Loot-10.83-11.150.520.54-8.43-9.670.360.39-4.29-5.760.180.22
Phil-9.35-10.970.390.42-7.95-9.400.250.29-5.03-5.920.130.15
Redandblack-10.06-10.500.350.36-8.02-8.830.240.25-5.24-5.870.200.20
Ricardo-9.74-11.070.470.49-8.76-9.240.330.36-5.20-5.930.210.22
Sarah-10.85-11.000.390.42-8.34-10.110.270.28-6.38-8.130.210.24
Soldier-11.96-13.930.590.61-7.99-8.910.290.32-4.77-5.960.180.21
Average-10.40-11.460.420.45-8.51-9.510.280.30-5.27-6.110.170.19
+ +Table 2. BD-BR and BD-PSNR comparisons between three baseline models improved by proposed method and original results. + +
Point CloudsSparsePCAC with GGEMSparsePCAC with DLI
BD-BR(%)BD-PSNR(dB)BD-BR(%)BD-PSNR(dB)
Andrew-5.940.18-6.510.30
David-5.030.22-6.600.28
Longdress-5.790.16-6.470.29
Loot-5.190.21-7.700.30
Phil-6.080.17-5.490.25
Redandblack-5.480.20-6.460.28
Ricardo-5.820.16-6.160.28
Sarah-5.110.18-7.940.27
Soldier-5.900.19-8.130.31
Average-5.590.19-6.830.28
+ +# 6.4. Rate-Distortion Performance + +Figure 7 illustrates the rate-distortion performance of different methods in nine point cloud sequences. Table 2 shows the BD-BR and BD-PSNR gains achieved by applying generalized Gaussian entropy model and dynamic likelihood interval to baseline models. + +As shown in Figure 7 and Table 2, our method improves performance across all baseline models. The largest improvement is observed for SparsePCAC, which achieves an average bitrate reduction of $11.46\%$ , followed by TSC-PCAC with an average bitrate reduction of $9.51\%$ . The smallest improvement is observed for SPAC, which still results in an average bitrate saving of $6.11\%$ . We be believe this outcome can be attributed to the fact that SparsePCAC has the weakest performance among the baseline models, with less accurate entropy parameter estimation. Therefore, adjustments to the entropy model and likelihood intervals are more effective in this case. In contrast, SPAC already has relatively accurate estimation for mean and scale parameters, so even optimal adjustments lead to a smaller improvement in performance. + +# 6.5. Computational Complexity + +Table 4 illustrates the encoding and decoding time for compressing point cloud sequences using different methods. + +Our method does not significantly affect the parallelism of baseline models' encoding and decoding, as we set the + +Table 3. Ablation study for GGEM (generalized Gaussian entropy model) and DLI (dynamic likelihood interval) based on SparseP-CAC. + +
MethodsOurs vs SparsePCACOurs vs TSC-PCACOurs vs SPAC
OriginOursOriginOursOriginOurs
Enc.(s)74.05163.743.928.24132.60287.59
Dec.(s)427.63904.177.6017.80108.58231.14
+ +Table 4. Comparison of complexity. Take the average time of encoding and decoding all point clouds as results. + +second context module $h_{cm}$ to be the same as $g_{cm}$ . For TSC-PCAC with the highest parallelism, our method incurs the least additional encoding and decoding time. In contrast, for SparsePCAC, which uses a fully serial context module, our method incurs the most additional time. + +# 6.6. Ablation Study + +In order to separately demonstrate the effectiveness of generalized Gaussian entropy model and dynamic likelihood interval, we add only one of these two modules to SparseP-CAC then perform two-step training, and the results are shown in Table 3. We can learn from Table 3 that both generalized Gaussian entropy model and dynamic likelihood interval have a positive effect on improving coding performance, which is consistent with the results from the preliminary experiment. + +# 7. Conclusion and Future Work + +We conduct simple experiments to demonstrate the limitations of current Gaussian and Laplace entropy models. Then we propose using generalized Gaussian distribution for more accurate probability estimation of latents and leverage MED to dynamically adjust the likelihood intervals of integers. Our method significantly improves the RD performance of three tested VAE-based models. Since our method only adds a few modules to original models without fundamentally changing their architecture, and can be trained by proposed two-step training, it is easily portable to other SOTA VAE-based models. + +In future work, we will focus on enhancing the parallelism of proposed modules and testing our method on other compression tasks, such as image and video compression. + +# References + +[1] 8i Labs. 8i voxelized full bodies version 2 - a voxelized point cloud dataset. 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However, its effectiveness with non-Gaussian noise remains unexplored. In this paper, we propose Generalized R2R (GR2R), extending the R2R framework to handle a broader class of noise distribution as additive noise like log-Rayleigh and address the natural exponential family including Poisson, Gamma and Binomial noise distributions, which play a key role in many applications including low-photon imaging and synthetic aperture radar. We show that the GR2R loss is an unbiased estimator of the supervised loss and that the popular Stein's unbiased risk estimator can be seen as a special case. A series of experiments with Gaussian, Poisson, and Gamma noise validate GR2R's performance, showing its effectiveness compared to other self-supervised methods. + +# 1. Introduction + +Image restoration is essential in many scientific and engineering applications, from medical imaging to computational photography. State-of-the-art image restoration approaches train a deep network to predict clean images from noisy measurements. However, most approaches are based on supervised learning, which requires clean image datasets for effective deep network training [11]. This reliance introduces significant challenges, such as the scarcity of clean image data in many important medical and scientific imaging applications [2], and the risk of models overfitting or memorizing specific examples [12, 26]. As a result, there is growing interest in developing robust self-supervised learning strategies that can operate exclusively on noisy data [7, 18, 22], representing a promising direction for the future of image processing and computer vision. + +Self-supervised image denoising has attracted significant attention for its potential to perform denoising without relying on clean, paired data, making it a baseline for many image restoration techniques. Methods in this domain are often classified based on the level of prior knowledge they require about the noise distribution [29]. + +The first class of methods relies on two independent noisy realizations per image to construct a loss that uses these pairs as inputs and targets. Noise2Noise [18] can obtain performance close to supervised learning, but obtaining independent noisy pairs is impossible in many applications. The second class only assumes that the noise distribution is independent across pixels. Blind Spot Networks, for example, rely on a masking strategy applied to the input or within the network itself [1, 15, 30]. This approach forces the network to predict denoised values based solely on neighboring pixels, leveraging the assumption of local spatial correlations within the image. As the central pixel is not used, these methods generally have suboptimal performance. + +The third family of methods assumes that the noise distribution is fully known, and can obtain performances that are on par with supervised learning. Stein's Unbiased Risk Estimator (SURE) [27] loss matches the supervised loss in expectation, and is available for Gaussian, Poisson [17] and Poisson-Gaussian noise distributions [17]. However, SURE requires approximating the divergence of the restoration function [24], which can lead to suboptimal results. The computation of the divergence is avoided by Noise2Score [14], which approximates the score of the noisy distribution during training and leverages Tweedie's formula to denoise at the test time. Finally, Recorrupted-to-Recorrupted [20, 22] synthetically recorrupts a noisy image into noisy pairs, removing the need to approximate the divergence term, while remaining an unbiased estimator of the supervised loss. However, this method has been mostly demonstrated with Gaussian noise. + +This work extends the R2R framework to address noise types beyond the traditional additive Gaussian model by introducing Generalized R2R (GR2R). Our formulation covers two noise modalities: additive noise and noise distri + +![](images/d08b139124e742ecf1cbe5d13091b9c587fa35c10c3bce24d435a1daee55fbd0.jpg) +Figure 1. Overview of GR2R framework. Given a noisy image $\pmb{y} \sim p(\pmb{y}|\pmb{x})$ , which belongs to a NEF, GR2R generates pairs of independent noisy images $\pmb{y}_1$ and $\pmb{y}_2$ through additional recorruption to enable self-supervised denoising learning $\hat{f}(\pmb{y}_1) \approx \mathbb{E}\{\pmb{x}|\pmb{y}_1\}$ . + +butions within the natural exponential family. By generating independent noisy image pairs from a single noisy image following a specified noise distribution, we establish equivalence to supervised learning through traditional mean-square-error (MSE) loss. Additionally, we demonstrate that the GR2R approach can be seen as a generalization of the well-known SURE loss, which does not require the computation of divergences. We further propose using the negative log-likelihood loss that takes into account the noise distribution of the recorrupted measurements and show how the method can be adapted to tackle general inverse problems. The GR2R framework enables training any deep network for NEF noise distributions without requiring modifications to the network structure. We conduct simulations for Gaussian, Poisson, and Gamma noise distributions on image datasets where these distributions are particularly relevant, including magnetic resonance imaging (MRI), natural image denoising, and synthetic aperture radar (SAR). Results demonstrate that GR2R effectively handles diverse noise distributions, achieving a performance on par with fully supervised learning. + +# 2. Related Work + +Supervised and Self-Supervised Learning. The goal of supervised learning is to learn a deep denoiser operator $\hat{\pmb{x}} = \hat{f}(\pmb{y})$ given noisy/clean paired data $(\pmb{y}, \pmb{x})$ . This process can be mathematically described by the minimization of the supervised loss function as follows + +$$ +\hat {f} = \underset {f} {\arg \min } \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \mathcal {L} _ {\operatorname {S U P}} (\boldsymbol {x}, \boldsymbol {y}; f), \tag {1} +$$ + +where $\mathcal{L}_{\mathrm{SUP}}(\pmb {x},\pmb {y};f) = \| f(\pmb {y}) - \pmb {x}\| _2^2$ , which is the MSE between the estimation and clean images'. The optimal estimator is the Minimum MSE $\hat{f} (\pmb {y})\approx \mathbb{E}\{\pmb {x}|\pmb {y}\}$ . In practice, + +the expectation is approximated with a finite dataset with $N$ samples, i.e., $\frac{1}{N}\sum_{i=1}^{N}\mathcal{L}_{\mathrm{SUP}}(\boldsymbol{x}^{(i)},\boldsymbol{y}^{(i)};f)$ . By simple algebra manipulation $\mathcal{L}_{\mathrm{SUP}}$ can be split between unsupervised and supervised terms as follows + +$$ +\mathcal {L} _ {\mathrm {S U P}} (\boldsymbol {x}, \boldsymbol {y}; f) = \| f (\boldsymbol {y}) - \boldsymbol {y} \| _ {2} ^ {2} + 2 f (\boldsymbol {y}) ^ {\top} (\boldsymbol {y} - \boldsymbol {x}) + \mathrm {c o n s t}. +$$ + +When there is no access to the set of clean images $\pmb{x}$ , self-supervised methods aim to approximate/eliminate the term that contains access to $\pmb{x}$ , $f(\pmb{y})^\top (\pmb{y} - \pmb{x})$ by building a self-supervised loss $\mathcal{L}_{\mathrm{SELF}}$ such that + +$$ +\mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \mathcal {L} _ {\text {S E L F}} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \mathcal {L} _ {\text {S U P}} (\boldsymbol {x}, \boldsymbol {y}; f) + \text {c o n s t .} \tag {2} +$$ + +Stein's Unbiased Risk Estimator. Assuming that the measurements are corrupted by Gaussian noise, $\pmb{y}|\pmb{x} \sim \mathcal{N}(\pmb{x},\pmb{I}\sigma^2)$ and $f$ be weakly differentiable, SURE proposes the following self-supervised loss + +$$ +\mathcal {L} _ {\text {S U R E}} (\boldsymbol {y}; f) = \| f (\boldsymbol {y}) - \boldsymbol {y} \| _ {2} ^ {2} + 2 \sigma^ {2} \sum_ {i = 1} ^ {n} \frac {\partial f _ {i}}{\partial y _ {i}} (\boldsymbol {y}), \tag {3} +$$ + +where the last term is the divergence of $f$ at $\pmb{y}$ . Consequently, SURE guarantees that + +$$ +\mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \left\{f (\boldsymbol {y}) ^ {\top} (\boldsymbol {y} - \boldsymbol {x}) \right\} = \mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \left\{\sigma^ {2} \sum_ {i = 1} ^ {n} \frac {\partial f _ {i}}{\partial y _ {i}} (\boldsymbol {y}) \right\}, +$$ + +therefore, the SURE expectation loss serves as an unbiased risk estimator of its supervised counterpart, with $\hat{f}(\boldsymbol{y}) \approx \mathbb{E}\{\boldsymbol{x}|\boldsymbol{y}\}$ . Noteworthy advancements beyond Gaussian noise include the Hudson lemma [10], which extends SURE to the exponential family, and GSURE [8], which further extends it to non-i.i.d exponential families. + +Noise2Void and Blind Spot Networks. Noise2Void methods and blind spot networks build constrained denoisers $f$ that do not look at the central pixel for denoising, ie $\frac{\partial f_i}{\partial y_i}(\pmb{y}) = 0$ for all $\pmb{y} \in \mathbb{R}^n$ and $i = 1, \dots, n$ . Then, a constrained network $f$ can be trained on simple measurement consistency + +$$ +\mathcal {L} _ {\mathrm {M C}} (\boldsymbol {y}; f) = \| f (\boldsymbol {y}) - \boldsymbol {y} \| _ {2} ^ {2}, \tag {4} +$$ + +where, if the noise distribution is independent across pixels, i.e., $p(\boldsymbol{y}|\boldsymbol{x}) = \prod_{i=1}^{n} p(y_i|x_i)$ , then we have that + +$$ +\mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \left\{f (\boldsymbol {y}) ^ {\top} (\boldsymbol {y} - \boldsymbol {x}) \right\} = 0. +$$ + +Alternatively, approaches such as Neigh2Neigh [9, 31] design a custom loss function that removes the central pixel instead of using a blind spot denoiser. However, note that the learned network is not optimal for MMSE because $\hat{f} (\pmb {y})\neq \mathbb{E}\{\pmb {x}|\pmb {y}\}$ , due to the zero derivative constraint. + +Noise2Noise. Assume a training set of paired noisy/noisy images is available. Specifically, the authors in [18] described the pairs of noisy images as + +$$ +\boldsymbol {y} _ {1} \sim p (\boldsymbol {y} _ {1} | \boldsymbol {x}), \quad \boldsymbol {y} _ {2} \sim p (\boldsymbol {y} _ {2} | \boldsymbol {x}), \tag {5} +$$ + +then, a denoiser operator $f$ is adjusted to minimize the squared $\ell_2$ loss + +$$ +\mathcal {L} _ {\mathrm {N 2 N}} \left(\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2}; f\right) = \| f \left(\boldsymbol {y} _ {1}\right) - \boldsymbol {y} _ {2} \| _ {2} ^ {2}, \tag {6} +$$ + +since the noisy pairs are independent with $\pmb{y}_1, \pmb{y}_2$ independent conditioned on $\pmb{x}$ and $\mathbb{E}\{\pmb{y}_1|\pmb{x}\} = \mathbb{E}\{\pmb{y}_2|\pmb{x}\} = \pmb{x}$ , then the supervised term is reduced such that + +$$ +\begin{array}{l} \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {x}} \left\{f (\boldsymbol {y} _ {1}) ^ {\top} (\boldsymbol {y} _ {2} - \boldsymbol {x}) \right\} \\ = \mathbb {E} _ {\boldsymbol {y} _ {1} | \boldsymbol {x}} f (\boldsymbol {y} _ {1}) ^ {\top} \mathbb {E} _ {\boldsymbol {y} _ {2} | \boldsymbol {x}} (\boldsymbol {y} _ {2} - \boldsymbol {x}) = 0, \\ \end{array} +$$ + +hence, the Noise2Noise expectation loss closely matches its supervised counterpart $\mathbb{E}_{\boldsymbol{y}_1,\boldsymbol{y}_2|\boldsymbol{x}}\mathcal{L}_{\mathrm{N2N}}(\boldsymbol{y}_1,\boldsymbol{y}_2;f) = \mathbb{E}_{\boldsymbol{y}_1|\boldsymbol{x}}\mathcal{L}_{\mathrm{SUP}}(\boldsymbol{x},\boldsymbol{y}_1;f) + \mathrm{const}$ , where $\hat{f}(\boldsymbol{y}_1) \approx \mathbb{E}\{\boldsymbol{x}|\boldsymbol{y}_1\}$ . However, while the minimization of $\mathcal{L}_{\mathrm{N2N}}$ does not require access to clean data, sampling independent pairs of noisy images $(\boldsymbol{y}_1,\boldsymbol{y}_2)$ is impractical in many real applications. + +Recorrupted2Recorrupted. A more realistic scenario is the unsupervised case, with only access to unpaired noisy measurements. Assuming that the noise distribution is Gaussian $\boldsymbol{y} \sim \mathcal{N}(0, I\sigma^2)$ , R2R [22] proposed the recorruption of noisy measurements as follows + +$$ +\boldsymbol {y} _ {1} = \boldsymbol {y} + \tau \boldsymbol {\omega}, \quad \boldsymbol {y} _ {2} = \boldsymbol {y} - \boldsymbol {\omega} / \tau , \tag {7} +$$ + +where $\omega \sim \mathcal{N}(\mathbf{0},\sigma^2\mathbf{I})$ . Then, the unsupervised denoising loss is defined as + +$$ +\mathcal {L} _ {\mathrm {R 2 R}} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {y}} \| f (\boldsymbol {y} _ {1}) - \boldsymbol {y} _ {2} \| _ {2} ^ {2}. \tag {8} +$$ + +The new measurements $\mathbf{y}_1$ and $\mathbf{y}_2$ are generated given an single $\mathbf{y}$ . While the loss is defined with an expectation, in practice, only a single pair of $(\mathbf{y}_1, \mathbf{y}_2)$ is generated per batch of $\mathbf{y}$ . R2R is equivalent to the supervised cost function defined in Equation (1) on the re-corrupted pair $\mathbf{y}_1$ since $\mathbb{E}_{\mathbf{y}|\mathbf{x}}\mathcal{L}_{\mathrm{R2R}}(\mathbf{y};f) = \mathbb{E}_{\mathbf{y}_1|\mathbf{x}}\mathcal{L}_{\mathrm{SUP}}(\mathbf{x},\mathbf{y}_1;f) + \mathrm{const}$ , where $\hat{f} (\pmb {y}_1)\approx \mathbb{E}\{\pmb {x}|\pmb {y}_1\}$ . Two recent works have proposed an extension of R2R to Poisson noise [16, 21] which is similar to the one presented here, while we extend these results to a much larger family of noise distributions, and show its close links with SURE. + +# 3. Generalized R2R + +We extend the R2R loss to different noise distributions. In particular, we present extensions to i) additive noise distributions beyond Gaussian noise and ii) noise distributions belonging to the natural exponential family. + +# 3.1. Non-Gaussian Additive Noise + +Assuming that $\pmb{y} = \pmb{x} + \pmb{\epsilon}$ where the only condition is that $p(\epsilon)$ is independent of $\pmb{x}$ we have the following proposition. + +Proposition 1. Let $\mathbf{y} = \mathbf{x} + \epsilon$ with noise distribution $p(\epsilon)$ independent of $\mathbf{x}$ and let the estimator $f$ be analytic. If $\mathbf{y}_1$ and $\mathbf{y}_2$ are sampled according to (7), then + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {R 2 R}} (\boldsymbol {y}; f) \propto \mathbb {E} _ {\epsilon , \omega} \| f (\boldsymbol {y} + \tau \omega) - \boldsymbol {x} \| _ {2} ^ {2} \\ + \sum_ {i = 1} ^ {n} \sum_ {k = 0} ^ {\infty} \frac {1}{k !} \frac {\partial^ {k} f _ {i}}{\partial \pmb {x} _ {i} ^ {k}} (\pmb {x}) \mathbb {E} _ {\epsilon_ {i}, \omega_ {i}} \left(\epsilon_ {i} - \frac {\omega_ {i}}{\tau}\right) \left(\epsilon_ {i} + \tau \omega_ {i}\right) ^ {k}, \\ \end{array} +$$ + +where $\omega$ is drawn independently of $\epsilon$ , and the proportionality ignores any term not including $f$ . + +The proof is included in Supplementary Materials (SM). In the original R2R case, $\epsilon$ and $\omega$ are assumed to follow the same Gaussian distribution, then $(\epsilon - \frac{\omega}{\tau})$ and $(\epsilon + \tau \omega)$ are independent random variables, meaning that the error term is zero. Proposition 1 shows that the R2R loss can still be accurate beyond this assumption, showing that low-order functions, e.g., linear reconstruction $f$ , only require that $\omega$ matches the second-order moment ( $k = 1$ ) of $\epsilon$ , as + +$$ +\mathbb {E} \omega_ {i} ^ {2} = \mathbb {E} \epsilon_ {i} ^ {2}, \tag {9} +$$ + +for $i = 1, \ldots, n$ , whereas for quadratic functions, the case $k = 2$ imposes the constraint + +$$ +\mathbb {E} \omega_ {i} ^ {3} = \frac {1}{\tau} \mathbb {E} \epsilon_ {i} ^ {3}, \tag {10} +$$ + +higher-order functions will require matching higher-order moments $k > 2$ . + +
ModelGaussian y ~ N(x, Iσ2)Poisson z ~ P(x/γ), y = γzGamma y ~ G(ℓ, ℓ/x)Binomial z ~ Bin(ℓ, x), y = z/ℓ
y1y1 = y + √(α/1-α)ω, ω ~ N(0, Iσ2)y1 = y - γω/1-α, ω ~ Bin(z, α)y1 = y o (1 - ω) / (1 - α), ω ~ Beta(ℓα, ℓ(1 - α))y1 = y - ω/ℓ, 1-α, ω ~ HypGeo(ℓ, ℓα, z)
y2y2 = 1/α y - (1-α)/α y1
LαGR2R-NLL||f(y1) - y2||22-γy2T log f(y1) + 1T f(y1)log f(y1) + y2/f(y1)- y2T log f(y1) + (y2 - ℓ)T log(1 - f(y1))
LαGR2R-MSE||f(y1) - y2||22
SURE = lim LαGR2R-MSE||f(y) - y||22 + 2σ2∑i=1n ∂fi/∂yi(y)||f(y) - y||22 + 2 ∑i=1n yi(fi(y) - fi(y - γei))||f(y) - y||22 + 2 ∑i=1n ∑k≥1 b(ℓ,k)(-yi)k+1 Γ(ℓ) ∂kfi/∂yi k(y)not available2
+ +Table 1. Summary of GR2R losses. Popular noise distributions belonging to the natural exponential family and the associated splitting functions with $\alpha \in (0,1)$ , negative-log likelihood losses. As $\alpha \to 0$ , the proposed GR2R loss is equivalent to a SURE-based loss, consisting of the quadratic measurement consistency and a divergence-like term. For Gamma noise $b(\ell, k) = (\ell(k - 1)) / (k(\ell + k - 1))$ . + +# 3.2. Beyond Additive Noise: Exponential family + +In many applications, the noise affecting the measurements is not additive. For example, Poisson noise arises in photon-counting devices [19], and the Gamma distribution is used to model speckle noise [23]. Our main theorem extends the R2R framework to a much larger family of noise distributions, the NEF. Specifically, we assume that we obtain a measurement $\mathbf{y} \sim p(\mathbf{y}|\mathbf{x})$ where the observation model belongs to the NEF whose density is described as + +$$ +p (\boldsymbol {y} | \boldsymbol {x}) = h (\boldsymbol {y}) \exp \left(\boldsymbol {y} ^ {\top} \eta (\boldsymbol {x}) - \phi (\boldsymbol {x})\right), \tag {11} +$$ + +where $h$ , $\eta$ and $\phi$ are known function according to the specific distribution (see SM for examples). Among the NEF are the popular Gaussian, Poisson, Gamma, Binomial, and Beta noise distributions. For this family of measurements distribution, we generalize the corruption strategy as + +$$ +\boldsymbol {y} _ {1} \sim p \left(\boldsymbol {y} _ {1} \mid \boldsymbol {y}, \alpha\right), \tag {12} +$$ + +$$ +\boldsymbol {y} _ {2} = \frac {1}{\alpha} \boldsymbol {y} - \frac {(1 - \alpha)}{\alpha} \boldsymbol {y} _ {1}, \tag {13} +$$ + +where $p(\boldsymbol{y}_1|\boldsymbol{y},\alpha)$ is the conditional distribution of $\boldsymbol{y}_1$ given $\boldsymbol{y}$ , then, we generalize the MSE loss as + +$$ +\mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {y}, \alpha} \| f (\boldsymbol {y} _ {1}) - \boldsymbol {y} _ {2} \| _ {2} ^ {2}. \tag {14} +$$ + +According to the noise distribution of $\pmb{y}$ , we propose obtaining $\pmb{y}_1$ and $\pmb{y}_2$ in different ways, as seen in Table 1. + +If the noise is Gaussian, we have that $p(\pmb{y}_1|\pmb{y},\alpha) = \mathcal{N}(\pmb{y},\frac{\alpha\pmb{I}}{1 - \alpha})$ , and the proposed loss boils down to the standard R2R loss in Eq. (7) under the change of variables $\tau = \sqrt{\frac{\alpha}{1 - \alpha}}$ . The following theorem demonstrated that if the pair images are generated according to Table 1, the proposed GR2R strategy is equivalent to the supervised loss. + +Theorem 1. Let $p(\pmb{y}|\pmb{x})$ density function of $\pmb{y}$ that belong to the NEF (up to a transformation of $\pmb{x}$ ); with $\mathbb{E}\{\pmb{y}|\pmb{x}\} = \pmb{x}$ . The measurements admit the decomposition $\pmb{y} = (1 - \alpha)\pmb{y}_1 + \alpha\pmb{y}_2$ with $\alpha \in [0,1]$ where $\pmb{y}_1$ and $\pmb{y}_2$ are independent random variables, generated according to Table 1, whose distribution $p_1(\pmb{y}_1|\pmb{x})$ and $p_2(\pmb{y}_2|\pmb{x})$ also belong to the NEF, with means $\mathbb{E}\{\pmb{y}_1|\pmb{x}\} = \mathbb{E}\{\pmb{y}_2|\pmb{x}\} = \pmb{x}$ , and variances $\mathbb{V}\{\pmb{y}_1|\pmb{x}\} = \frac{\mathbb{V}\{\pmb{y}|\pmb{x}\}}{1 - \alpha}$ and $\mathbb{V}\{\pmb{y}_2|\pmb{x}\} = \frac{\mathbb{V}\{\pmb{y}|\pmb{x}\}}{\alpha}$ . Moreover, the conditional distributions $p(\pmb{y}_1|\pmb{y})$ and $p(\pmb{y}_2|\pmb{y})$ do not depend on $\pmb{x}$ , we have that + +$$ +\mathbb {E} _ {\pmb {y} | \pmb {x}} \mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\pmb {y}; f) = \mathbb {E} _ {\pmb {y} _ {1} | \pmb {x}} \| f (\pmb {y} _ {1}) - \pmb {x} \| _ {2} ^ {2}. +$$ + +The proof is included in the SM. One important aspect is the parameter $\alpha$ , consequently, by defining the signal-to-noise ratio (SNR) of a random variable $z$ as $\mathrm{SNR}(z) := \frac{\|\mathbb{E}z\|_2^2}{\mathbb{E}\|\pmb{z} - \mathbb{E}\pmb{z}\|_2^2}$ we have that the SNR of the new variables is + +$$ +\operatorname {S N R} \left(\boldsymbol {y} _ {1}\right) = (1 - \alpha) \operatorname {S N R} (\boldsymbol {y}), +$$ + +$$ +\operatorname {S N R} \left(\boldsymbol {y} _ {2}\right) = \alpha \operatorname {S N R} (\boldsymbol {y}), +$$ + +and thus have a strictly lower SNR than the original measurement $\pmb{y}$ . A good choice of $\alpha$ should strike the right balance between having inputs $\pmb{y}_1$ with SNR close to that of $\pmb{y}$ , without having too noisy outputs $\pmb{y}_2$ . In the SM, we evaluate different values of $\alpha$ in different noise settings, finding in most cases that the best $\alpha$ lies in the interval [0.1, 0.2]. + +Equivalence with SURE Loss. Interestingly, our GR2R using MSE unsupervised loos is a generalization of the SURE loss when $\alpha \rightarrow 0$ without the need to calculate the divergence term. To show that, let us introduce the following proposition. + +Proposition 2. Assume that $f$ is analytic, $p(\pmb{y}|\pmb{x})$ belongs to the NEF, and that $a_{k}:\mathbb{R}\mapsto \mathbb{R}$ as + +$$ +a _ {k} (y _ {i}) = \lim _ {\alpha \rightarrow 0} \mathbb {E} _ {y _ {2, i} | y _ {i}, \alpha} (y _ {2, i} - y _ {i}) (\alpha y _ {2, i}) ^ {k}, +$$ + +for all $i = 1, \dots, n$ verifies $|a_k(y_i)| < \infty$ for all positive integers $k \geq 1$ . Then, + +$$ +\begin{array}{l} \lim _ {\alpha \rightarrow 0} \mathcal {L} _ {\mathrm {G R} 2 \mathrm {R} - \mathrm {M S E}} ^ {\alpha} (\boldsymbol {y}; f) = \\ \| f (\boldsymbol {y}) - \boldsymbol {y} \| _ {2} ^ {2} + 2 \sum_ {i = 1} ^ {n} \sum_ {k \geq 1} (- 1) ^ {k + 1} a _ {k} (y _ {i}) \frac {1}{k !} \frac {\partial^ {k} f _ {i}}{\partial y _ {i} ^ {k}} (\boldsymbol {y}) + \mathrm {c o n s t .} \\ \end{array} +$$ + +The proof is included in the SM. With these results, Table 1 shows the equivalence for various popular noise distributions belonging to the natural exponential family. Interesting, the standard Gaussian case, we have $a_1(y_i) = \sigma^2$ and $a_k(y_i) = 0$ for $k \geq 2$ , recovering the standard SURE formula. In general, if the estimator verifies $\frac{\partial^k f_i}{\partial y_i^k}(\pmb{y}) \approx 0$ for higher order derivatives $k \geq 2$ , we have + +$$ +\begin{array}{l} \lim _ {\alpha \rightarrow 0} \mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\boldsymbol {y}; f) \approx \\ \| f (\boldsymbol {y}) - \boldsymbol {y} \| _ {2} ^ {2} + 2 \sum_ {i = 1} ^ {n} a _ {1} (y _ {i}) \frac {\partial f _ {i}}{\partial y _ {i}} (\boldsymbol {y}) + \mathrm {c o n s t}, \\ \end{array} +$$ + +where $a_1(y_i) = \lim_{\alpha \to 0} \mathbb{V}\{y_{2,i}|y_i,\alpha\}$ . + +Connection with GSURE. The popular GSURE loss introduced by Eldar [8] is defined as + +$$ +\mathcal {L} _ {\mathrm {G S U R E}} (\boldsymbol {y}; f) = \| f (\boldsymbol {y}) + \nabla \log h (\boldsymbol {y}) \| _ {2} ^ {2} + 2 \sum_ {i = 1} ^ {n} \frac {\partial f _ {i}}{\partial y _ {i}} (\boldsymbol {y}), +$$ + +and is an unbiased estimator of + +$$ +\mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \mathcal {L} _ {\text {G S U R E}} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \| f (\boldsymbol {y}) - \eta (\boldsymbol {x}) \| _ {2} ^ {2}, \tag {15} +$$ + +where $\eta$ and $h$ are the functions associated with the exponential family decomposition in Eq. (11). The equivalence of our method compared with GSURE only occurs for the Gaussian noise case (up to scaling of $f(\pmb{y})$ by $\sigma^2$ ), where $h(\pmb{y}) = -\sigma^2\pmb{y}$ and $\eta(\pmb{x}) = \sigma^2\pmb{x}$ . The GSURE loss targets the estimator $\hat{f}(\pmb{y}) \approx \mathbb{E}\{\eta(\pmb{x})|\pmb{y}\}$ , whereas in this work we focus on the conditional mean $^3$ $\hat{f}(\pmb{y}) \approx \mathbb{E}\{\pmb{x}|\pmb{y}\}$ . + +# 3.3. Negative-Log Likelihood Loss + +If $\pmb{y}_1$ and $\pmb{y}_2$ are independent, we could use the MSE unsupervised loss, as is detailed in the previous section, as an unbiased estimator of the supervised loss $\mathcal{L}_{\mathrm{SUP}}(\pmb{x}, \pmb{y}_1; f)$ . Although the choice of $\pmb{y}_1$ and $\pmb{y}_2$ are based on the noise distribution $\pmb{y}$ , the MSE loss is suboptimal since it does not try to maximize the probability likelihood of the $\pmb{y}$ noise distribution. We propose instead to minimize the negative log-likelihood (NLL) as the loss function + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {G R 2 R - N L L}} ^ {\alpha} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {y}} \left\{\phi (f (\boldsymbol {y} _ {1})) - \boldsymbol {y} _ {2} ^ {\top} \eta (f (\boldsymbol {y} _ {1})) \right\} \\ = \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {y}} \left\{- \log p _ {2} \left(\boldsymbol {y} _ {2} | \hat {\boldsymbol {x}} = f (\boldsymbol {y} _ {1})\right) \right\} + \text {c o n s t}, \\ \end{array} +$$ + +where $p_2$ corresponds to the distribution of $\mathbf{y}_2$ given $\mathbf{x}$ , which belongs to the exponential family, as shown in Theorem 1. For the additive Gaussian noise case, the negative log-likelihood function reduces to the standard MSE, i.e, $-\log p_2(\mathbf{y}_2|f(\mathbf{y}_1)) \propto \| f(\mathbf{y}_1) - \mathbf{y}_2\|_2^2$ . Table 1 shows the losses for popular noise distributions belonging to the NEF. This loss is unbiased estimator of a supervised negative-log-likelihood loss, whose optimal solution is also the condition mean (the proof is included in the SM). + +Proposition 3. Under the assumptions of Theorem 1, we have that + +$$ +\begin{array}{l} \mathbb {E} _ {\boldsymbol {y} | \boldsymbol {x}} \mathcal {L} _ {\mathrm {G R 2 R - N L L}} ^ {\alpha} (\boldsymbol {y}; f) = \\ \mathbb {E} _ {\boldsymbol {y} _ {1} \mid \boldsymbol {x}} \left\{- \log p _ {2} \left(\boldsymbol {x} \mid f (\boldsymbol {y} _ {1})\right) \right\} + \text {c o n s t}, \\ \end{array} +$$ + +whose minimizer is the minimum mean squared error estimator $f(\pmb{y}_1) = \mathbb{E}\{\pmb{x}|\pmb{y}_1\}$ . + +# 3.4. Test Time Inference + +Once the deep denoiser $\hat{f}$ is trained in a self-supervised way, the following Monte Carlo approximation is used to mitigate the effect of re-corruption + +$$ +\hat {\boldsymbol {x}} \approx \frac {1}{J} \sum_ {j = 1} ^ {J} \hat {f} \left(\boldsymbol {y} _ {1} ^ {(j)}\right). \tag {16} +$$ + +where $\pmb{y}_1^{(j)}\sim p(\pmb {y}_1|\pmb {y},\alpha)$ are i.i.d. samples. + +# 4. Simulations and Results + +In this section, we extend the experimental validation of the GR2R framework to denoising tasks beyond the additive Gaussian noise model, specifically addressing log-Rayleigh, Poisson and Gamma noise. We conduct a comparative analysis with state-of-the-art unsupervised denoising methods, including SURE [24], PURE [17], Neigh2Neigh [9], and Noise2Score [13], to benchmark the performance of GR2R against unbiased estimators, as well as Noise2X paradigms. To further strengthen our analysis, we replicate the original R2R framework's reported performance on Gaussian noise. GR2R is agnostic to the choice of architecture; therefore, the DRUnet [33] architecture was utilized for Poisson denoising, while DnCNN [32] was used for denoising under the Gamma and Gaussian noise model. + +Table 2. Mean and Variance of the PSNR/SSIM scores with the additive log-Rayleigh noise. + +
R2R [22]GR2R (ours)Supervised Learning
2nd Moment3rd Moment
25.32 ± 0.7929.47 ± 1.5129.93 ± 1.50
0.576 ± 0.080.813 ± 0.040.831 ± 0.04
+ +Table 3. PSNR/SSIM results on Poisson noise. GR2R-NLL stands for the proposed GR2R with Negative Log-Likelihood Loss. + +
Poisson NoiseMethods
Noise Level (γ)PURE [17]Neigh2Neigh [9]GR2R-NLL (ours)GR2R-MSE (ours)SUP-MSE
0.0132.69/0.91933.37/0.92933.90/0.93533.92/0.93533.96/0.933
0.124.37/0.63128.27/0.82728.30/0.82728.35/0.82728.39/0.827
0.522.98/0.62324.90/0.65125.07/0.71624.69/0.69825.32/0.727
1.017.94/0.46923.56/0.65323.69/0.65823.49/0.64623.85/0.668
Noisy ImagePURENeigh2NeighGR2R-NLLSUPReference
+ +![](images/2399ca0d346933464e3915707e9382118599da4ed2d7e0be42ec94dd7fae0b88.jpg) + +![](images/359e27e11ec98429b9a616270023af01db1aad7c53ec5eff5f179978a21d46ae.jpg) + +![](images/96b9d762420514c5843a97a3cde2a8e7efab53834ba82cb84160d3956a865cb8.jpg) + +![](images/66b79a1fcd029edb969bf0beccb302a327eb5615871bf4de33ea83121349d21a.jpg) + +![](images/201e0a5ce9e24f43a3648b283a1a0204de735942ad8f6adab050e7b376488ee4.jpg) + +![](images/d8b23292f82e8895fcb1b8c61f2a459ca0213d054a11a5ff258fef0825f4826f.jpg) + +![](images/a95bad9d248badbca560a5132d49d852fb45e46bb63866c3d134ea7479b6c7d4.jpg) +Figure 2. Denoising results for Poisson noise with $\lambda = 0.5$ . The first column shows noisy input images, and the last column shows the ground truth reference. Intermediate columns present results from PURE, Neigh2Neigh, GR2R-NLL (proposed), and a supervised MSE-based method (SUP). PSNR values, shown in yellow in the top-right corner of each image, quantify the performance of each method. + +![](images/d1bce8d7b3021166cd53f097d2b05f139e08a9613a230be5dd5c576d296372a9.jpg) + +![](images/bc8b3371814aedd647d7ac2078c7a4fd08772f6578c5b5946d127f3c164509db.jpg) + +![](images/efdd5a238d0679721f6e80aa98388ef09180a3fbcc6a58ace400045eafda22c2.jpg) + +![](images/720fa3203b99d051729527723f2f02f66d7e4ae4c80cbe4a6052ffebc0fb1b51.jpg) + +![](images/f8152ffa63d9e8650eeb177d4bf9c257995684474f2848df98eb357b20fce052.jpg) + +# 4.1. Non-Gaussian Additive Noise + +We first evaluate the robustness of the GR2R for non-Gaussian additive noise using the DIV2K dataset with crops of $512 \times 512$ pixel resolution, with the train split (900 images) for training and the validation split (100 images) for testing. The dataset was corrupted with log-Rayleigh noise [25], which is non-symmetric, normalized to have a standard deviation $\sigma = 0.1$ and zero mean. We compare with the standard R2R [22] approach, which recorrupts the noisy data using Gaussian additive noise until matching the second order moment, the noise variance, i.e., $\omega \sim \mathcal{N}(\mathbf{0},\mathbf{I}\sigma^2)$ . We train for 100 epochs with a batch size of 16 and an initial learning rate of 5e-4. In our GR2R approach, we generate additional noise $\omega$ following Theorem 1 by sampling using a maximum entropy approach such that the second and third order moments conditions in Eq. (9) and Eq. (10) hold. Precisely, $\boldsymbol{w}$ is adjusted to match until the third order moment using a gradient descent algorithm, as presented by the authors in [3]. We computed $J = 15$ Monte Carlo Samples for the inference according to Eq. (16) for both scenarios. + +The results are shown in Section 3.4. Adding the third-order correction significantly improves more than $3\mathrm{dB}$ compared with the baseline R2R, being only $0.5\mathrm{dB}$ below the supervised learning setting, with a similar variance of $\pm 1.51$ among estimations. The reader is referred to the SM for additional information on the sampling algorithm. + +# 4.2. Poisson Noise + +We evaluate our method on the Poisson denoising problem with gain $\gamma$ (as defined in Table 1) using the DIV2K dataset. The dataset, comprising high-resolution images of $512 \times 512$ resolution, was corrupted by Poisson-distributed noise. The denoising models were trained with three unsupervised approaches, including PURE and Neigh2Neigh. The training consists of 300 epochs with a batch size of 50 and an initial learning rate of 1e-3, decreasing by a factor of 0.1 during the final 60 epochs. In our GR2R approach, training pairs were generated with a setting of $\alpha = 0.15$ , as detailed in the first column of Table 1. We computed $J = 5$ Monte Carlo samples for the test according to Eq. (16). + +Quantitative results for Poisson noise denoising are summarized in Table 3, with visual results presented in Figure 2. As shown, our proposed GR2R closely match the metrics of the supervised MSE-based model. GR2R-MSE performs well at higher counts (where the noise distribution is closer to Gaussian), while GR2R-NLL loss demonstrates robustness in the low-count regime. Neigh2Neigh is the second-best unsupervised technique but has drawbacks compared to GR2R. It downsamples noisy images, losing high-frequency details, and requires two model evaluations per step, increasing computational costs. GR2R, however, uses a single-term loss and one forward pass per step, making it more efficient and scalable for high-resolution image noise removal. + +Table 4. PSNR/SSIM results on Gamma noise. GR2R-NLL stands for the proposed GR2R with Negative Log-Likelihood Loss. + +
Gaussian NoiseMethods
Number of looks (l)Neigh2Neigh [9]GR2R-NLL (ours)GR2R-MSE (ours)Supervised-MSE
3030.34/0.84830.43/0.86231.58/0.90131.86/0.906
1528.56/0.80228.71/0.82429.55/0.86229.76/0.865
525.71/0.70325.79/0.72526.35/0.76726.72/0.784
122.19/0.56022.19/0.54522.38/0.59922.56/0.611
sy ImageNeigh2NeighGR2R-NLLGR2R-MSESUPRefere
+ +![](images/43f92322cd5e1f696050f947b83ab44cad4ac2634815dc645e9052ae9131d1f5.jpg) + +![](images/458fd16a1b2cae9e880e82664a7d790f616a3df191dc3fd312a0821c91e01bc1.jpg) +Figure 3. Denoising results for Gamma Noise with $\ell = 5$ . The first column shows noisy images, and the last column shows the ground truth reference. Intermediate columns present results from Neigh2Neigh, GR2R-NLL (proposed), GR2R-MSE (proposed) and a supervised MSE-based (SUP). PSNR values, shown in yellow in the top-right corner of each image, quantify the performance of each method. + +![](images/e9554c3f5b8bd4ddcfefc9ad8eae93d9ebf2cafac27d0e4283cf6dfdd5a55772.jpg) + +![](images/8391194af9c7febcfb5459304a0cd71d0bcf24a42bc178fc92e76744e17a3fbf.jpg) + +![](images/f992e4104db3d2664f696be0bb780bdafe274a80ef8d9a3dc0901106d30da290.jpg) + +![](images/4de0abf43cffa15654b57100c56754268b7617506f9ee4e691ef306c480bb8bd.jpg) + +![](images/cdcf666d129ef971f157a7467df882449028b46616011a7ceb986744583ee9c7.jpg) + +![](images/12412199a20163f7665a8652d47eec8a6110957f45ea7db43c767b37610bc6fe.jpg) + +![](images/973ab96c13fab5705aa4b6b4d8afcc841a5d99392a497faa3177ea92ee85817f.jpg) + +![](images/5fc76f7b1c6fdd25cd61b91b42d5d786156e41c589e34447d5272acc5df3d936.jpg) + +![](images/ec928a4e5af3bac37e662c17bcb51ca0c147bd412d7cbb0268df5e2d6470dc65.jpg) + +![](images/7680982704f3a9a81b24735bdd366fe4fa61c436c611c8da1b7587fe662ebdd2.jpg) + +# 4.3. Gamma Noise + +To examine performance under Gamma noise, we tested on the SAR Image Despeckling dataset with the number of looks $\ell \in \{1,5,15,30\}$ [6]. This dataset includes 127 images with a resolution of $512\times 512$ , each corrupted via Gamma-based sampling to simulate Gamma noise effects. Training under unsupervised methods, including Neigh2Neigh trained for 400 epochs at a batch size of 20. Starting from a learning rate of 1e-3, the rate was decreased by a factor of 0.1 over the last 80 epochs. For the GR2R method, we generate image pairs using the parameters of the first column in Table 1, with $\alpha = 0.2$ . The prediction was performed using Equation (16), where $J$ was set to 10. + +Quantitative results for Gamma noise reduction, shown in Table 4, highlight the superior performance of the GR2R framework and its GR2R-MSE variant compared to Neigh2Neigh across all tested noise levels. The supervised MSE-based method achieves the highest PSNR and SSIM, with GR2R-MSE closely matching its performance, particularly at higher SNR $(\ell = 30)$ . The performance between methods converges at lower SNR $(\ell = 1)$ ; however, GR2R remains competitive with a PSNR of 22.38 dB, matching Neigh2Neigh and achieving a slightly higher SSIM. Visual comparisons in Figure 3 for Gamma noise at $\ell = 5.0$ demonstrate that GR2R and GR2R-MSE deliver enhanced image quality and reduce noise artifacts more effectively than Neigh2Neigh. + +# 4.4. Gaussian Noise + +To evaluate the performance of denoising under Gaussian noise, we tested our model on the fastMRI dataset, applying noise levels of $\sigma \in \{0.05, 0.1, 0.2, 0.5\}$ . The dataset, comprising 900 images at a resolution of $256 \times 256$ , was corrupted with additive Gaussian white noise of zero mean (AGWN) at each level. Training was carried out using four unsupervised techniques: Noise2Score, SURE, Neigh2Neigh, and our proposed GR2R framework, for 600 epochs with a batch size of 32. The learning rate was initialized at 1e-3 and reduced by a factor of 0.1 over the final 48 epochs. GR2R generated training pairs in line with the configuration in the first column of Table 1, with $\alpha$ set to 0.5. Inference was performed using Equation (16) with $J = 5$ . + +Quantitative results, summarized in Table 5, show that GR2R achieves a denoising performance comparable to the supervised MSE baseline at all noise levels. This outcome is expected, given the equivalence between GR2R training and supervised training, where independent noisy image pairs are generated. Specifically, at $\sigma = 0.05$ , GR2R achieves PSNR and SSIM values nearly identical to the highest performing supervised method (35.38 dB vs. 35.41 dB). At elevated noise levels, specifically $\sigma = 0.2$ and $\sigma = 0.5$ , GR2R demonstrates robust denoising capabilities (30.24 dB and 25.81 dB), closely aligned with the supervised results (30.38 dB and 25.93 dB) and surpassing other self-supervised approaches. + +Table 5. PSNR/SSIM results for Gaussian noise. In the case of Gaussian noise for GR2R, the MSE and NLL variants are the same. + +
Gaussian noiseMethods
Noise Level (σ)Noise2Score [13]SURE [24]Neigh2Neigh [9]GR2R (ours)Supervised-MSE
0.0534.42/0.91635.31/0.93435.07/0.93335.38/0.93335.41/0.935
0.131.02/0.76632.76/0.91032.57/0.90833.03/0.91133.14/0.913
0.229.34/0.76729.77/0.87429.73/0.87030.24/0.88030.38/0.883
0.522.94/0.43325.52/0.71425.61/0.71725.81/0.81025.93/0.813
+ +# 5. Extension to General Inverse Problems + +The proposed method can be extended to general inverse problems $\pmb{y} \approx \pmb{A}\pmb{x}$ with $\pmb{A} \in \mathbb{R}^{m \times n}$ where the observation model $p(\pmb{y}|\pmb{A}\pmb{x})$ belongs to the NEF with mean $\mathbb{E}\{\pmb{y}|\pmb{x}\} = \pmb{A}\pmb{x}$ , by considering the main loss function as + +$$ +\mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {y} _ {1}, \boldsymbol {y} _ {2} | \boldsymbol {y}} \| \boldsymbol {A} f (\boldsymbol {y} _ {1}) - \boldsymbol {y} _ {2} \| _ {2} ^ {2}, \tag {17} +$$ + +which is an unbiased estimator of the clean measurement consistency loss + +$$ +\mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y}} \mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\boldsymbol {y}; f) = \mathbb {E} _ {\boldsymbol {x}, \boldsymbol {y} _ {1}} \| \boldsymbol {A} (f (\boldsymbol {y} _ {1}) - \boldsymbol {x}) \| _ {2} ^ {2}. +$$ + +This adaptation is straightforward from denoising to the general inverse problem in contrast to other methods, such as Neigh2Neigh, requiring that $\pmb{y}$ is in the image domain. If $\mathrm{rank}(\pmb {A}) = n$ , then the GR2R minimizer is the optimal MMSE estimator, that is $\hat{f} (\pmb {y}_1)\approx \mathbb{E}\{\pmb {x}|\pmb {y}_1\}$ . However if $\mathrm{rank}(\pmb {A}) < n$ , then $\pmb{A}$ has a non-trivial nullspace and $\hat{f} (\pmb {y}_1)\neq \mathbb{E}\{\pmb {x}|\pmb {y}_1\}$ . In this case, it is still possible to learn in the nullspace of $\pmb{A}$ if we can access a family of different $\{A_g\}_{g = 1}^G$ operators [7, 28] or if we can assume that the image distribution $p(\pmb {x})$ is approximately invariant to a set of transformations $\{\pmb{T}_g\in \mathbb{R}^{n\times n}\}_{g = 1}^G$ , such as translations or rotations [4, 5]. See [28] for a detailed discussion of self-supervised learning when $\pmb{A}$ is incomplete. These additional assumptions can be incorporated via a second loss term: in the case of a single operator $\pmb{A}$ and invariance, we propose to minimize + +$$ +\mathcal {L} _ {\mathrm {G R 2 R - M S E}} ^ {\alpha} (\boldsymbol {y}; f) + \mathcal {L} _ {\mathrm {E I}} (\boldsymbol {y}; f) \tag {18} +$$ + +where the Equivariant Imaging (EI) loss [4] is defined as + +$$ +\mathcal {L} _ {\mathrm {E I}} (\boldsymbol {y}; f) = \mathbb {E} _ {g} \mathbb {E} _ {\boldsymbol {y} _ {1} | \boldsymbol {y}} \| f \left(\boldsymbol {A} \boldsymbol {T} _ {g} \hat {\boldsymbol {x}}\right) - \boldsymbol {T} _ {g} \hat {\boldsymbol {x}} \| _ {2} ^ {2} \tag {19} +$$ + +with $\hat{x} = f(y_1)$ . Figure 4 presents the results of comparing the EI framework using the $\mathcal{L}_{\mathrm{MC}}$ loss against EI with our GR2R strategy. We tested GR2R on the DIV2K dataset, using a binary mask $A$ with entries following a Bernoulli distribution with $p = 0.9$ (fixed throughout the dataset to maintain a fixed null-sapce), and corrupting measurements with Poisson noise at $\gamma = 0.05$ . The results show that while EI effectively addresses the inpainting problem but still preserves the noise artifacts, in contrast, GR2R successfully tackles both denoising and inpainting simultaneously, delivering results that are comparable to its supervised counterpart. More details and experiments using other distributions are shown in the SM. + +![](images/02b05613dc1f1b93c1e55290cc0a4485de00f8e8bb20985f8069d4ba7bc92651.jpg) +Noisy Measurement +GR2R-MSE + EI + +![](images/e1d2e3a05e1283785fc63b46762ce03b371513b8588336ce4c60c72653b7e4e7.jpg) +EI +Supervised + +![](images/4b96905bce1effff74bf8a472d92b9248aca14b66bba68219ae1f235af5cf397.jpg) +Figure 4. GR2R on Inpainting with Poisson Noise. We compared GR2R with the equivariant imaging framework, consisting of $\mathcal{L}_{\mathrm{MC}} + \mathcal{L}_{\mathrm{EI}}$ , and supervised training. The the GR2R framework consists of $\mathcal{L}_{\mathrm{GR2R - MSE}} + \mathcal{L}_{\mathrm{EI}}$ . Our findings confirm the effectiveness of GR2R for application in general inverse problems. + +![](images/526251f7e6253508181876d37c9992d363c84f5117ce5e31bd5e28988b04dcda.jpg) + +# 6. Conclusions + +We present the Generalized Recorrupted-to-Recorrupted (GR2R), which extends the original R2R framework to additive noise and natural exponential family (NEF). We specifically evaluate its performance on Poisson, Gamma, and log-Rayleigh noise in addition to Gaussian noise. The key advantages are simplicity and efficiency: GR2R requires only a simple single-term loss and a single forward pass per training step, and it does not rely on continuous approximations to handle discrete noise distributions (e.g., Poisson or Binomial) used in previous methods (e.g., PURE, Noise2Score). Moreover, GR2R shows that our method recovers SURE-type loss when $\alpha \rightarrow 0$ . Furthermore, our re-corruption strategy generates independent noisy pairs directly within the measurement space; naturally extends its applicability beyond image denoising to a wide range of self-supervised inverse problems as inpainting. + +Acknowledgments. Julián Tachella is supported by the ANR grant UNLIP (ANR-23-CE23-0013), and VIE-UIS supports the UIS contribution under grant 3968. + +# References + +[1] Joshua Batson and Loic Royer. Noise2self: Blind denoising by self-supervision. In International Conference on Machine Learning, pages 524-533. 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However, in image based disease classification, such as glioma sub-typing, distinguishing between classes using image semantic attributes can be challenging. To address this challenge, we introduce a novel GZSL method that eliminates the dependency on semantic information. Specifically, we propose that the primary of most classification in clinic is risk stratification, and classes are inherently ordered rather than purely categorical. Based on this insight, we present an inter-class feature augmentation (IFA) module, where distributions of different classes are ordered by their risk levels in a learned feature space using pre-defined joint conditional Gaussian distribution model. This ordering enables the generation of unseen class features through feature mixing of adjacent seen classes, effectively transforming the zero-shot learning problem into a supervised learning task. Our method eliminates the need for explicit semantic information, avoiding the cross-modal alignment between visual and semantic features. Moreover, the IFA module for GZSL requires no structural modifications to the existing classification models. In the experiment, both in-house and public datasets are used to evaluate our method across different tasks, including glioma subtyping, Alzheimer's disease (AD) classification and diabetic retinopathy classification. Experimental results demonstrate that our method outperforms the state-of-the-art GZSL methods with statistical significance. + +# 1. Introduction + +Deep learning (DL) based classification has achieved significant success in various domains, such as computer vi + +sion, natural language processing, and medical diagnostics. To build powerful DL-based classification models, a large number of labeled data is required in training phase. It is known that data annotation is usually a labor-intensive and time-consuming task, especially for the tasks involving medical images. Moreover, because of low incidence rates, rare diseases or fine-grained subtypes often have very few samples, hindering the performance of DL-based classification [24]. For classes not presented in training dataset, i.e., unseen classes, traditional DL-based models fail to provide reliable classification results [20]. Therefore, there is a pressing need for DL-based methods capable of handling the classification of unseen classes. + +Over the past decade, zero-shot learning (ZSL) has emerged as a promising solution for recognizing unseen classes [18]. It enables models to generalize from seen classes to unseen classes by leveraging auxiliary information. Conventional ZSL methods focus solely on classifying unseen classes with the assumption that testing data does not contain any samples of seen classes. However, such assumption does not align with real-world conditions, making it challenging to be applied in most of practical scenarios. + +Recently, generalized zero-shot learning (GZSL) has been proposed to classify unseen classes in the presence of seen classes [1]. Due to its close alignment with real-world scenarios, GZSL has been widely studied [6, 11, 14, 19]. Existing GZSL methods can be categorized into two types: embedding-based methods and generative-based methods [24]. Specifically, the embedding-based methods map visual and semantic features into a common space. In this way, visual information of unseen classes can be inferred by semantic features. The generative-based methods adopt generative models to synthesize features or images of unseen classes, transforming the zero-shot problem into a supervised learning task. To enhance the performance of generative models, semantic information is usually used as + +condition in the generation process. Clearly, GZSL methods typically rely on semantic information to bridge the gap between seen and unseen classes. In existing GZSL methods, semantic information can take various forms, such as attributes [17] and word vectors [8]. However, defining appropriate semantic information could be a greater challenge. For example, in clinic, due to the heterogeneity of tumors, there is no clear criterion for the characteristics of tumor subtypes in medical images. As a result, distinguishing between tumor subtypes using semantic information is difficult. Moreover, semantic information-based GZSL methods often face cross-modal alignment challenges, primarily arising from the fundamental differences between visual features and semantic representations. As a result, learning complexity increases, and classification performance is negatively impacted. + +In this paper, we propose a novel GZSL method that does not rely on explicit semantic information. Our method is specifically designed for image-based classification in clinical settings. It is known that the primary of most classification in clinic is risk stratification. For instance, brain gliomas are classified into three main subtypes, which are oligodendroglioma, astrocytoma, and glioblastoma [30]. The median survival times (in months) of these three subtypes are 119, 36, and 8, respectively [23]. In Alzheimer's disease (AD), according to the severity of cognitive impairment, patients are classified into normal, mild cognitive impairment (MCI), and AD, respectively. Therefore, classes in clinic is inherently ordered rather than purely categorical. Based on this insight, our method introduces an inter-class feature augmentation (IFA) module, where image features of different classes are encouraged to distribute in the order of their corresponding risks through a pre-defined joint conditional Gaussian distribution model. In this way, features of unseen classes can be generated through feature mixing of neighboring seen classes. With both seen and unseen class features, supervised training can be performed. + +Our method avoids the using of explicit semantic information by leveraging the inherently ordered property of clinical classes. Therefore it can effectively tackle the challenge of appropriate definition of semantic information and eliminates potential visual-semantic alignment problems. Fig. 1 illustrates the difference between existing GZSL methods and our methods. In the experiment, our method is evaluated across different tasks, including brain glioma subtyping, AD classification and diabetic retinopathy classification using in-house and public datasets (ADNI [12] and APTOS [13]). Evaluation results demonstrate that our method outperforms the state-of-the-art (SOTA) methods with statistical significance, and the proposed IFA is an effective way for GZSL. + +The main contributions of our study are listed as follows: We propose a novel GZSL method that eliminates the + +![](images/fe209e1cd209245bc600260231f059c5125dd3d6cc123ed97ac8650bd49b6f6b.jpg) + +![](images/30f50433399c5618c3c8947ba9c62827a2556c0a3579760387aac9af7dbc95b9.jpg) +Figure 1. Existing generalized zero-shot learning (GZSL) methods leverage explicit semantic information to bridge the gap between seen and unseen classes (top), while no semantic information is required in our method (bottom). + +need for explicit semantic information and substantially alleviates the cross-modal alignment problem. + +- Based on the insight that clinical classes are ordered, we present a new IFA module that imposes ordinal constraint on the feature distribution of different classes, allowing the generation of unseen class features from neighboring seen classes. +- Extensive experiments are conducted to validate our method, and evaluation results demonstrate the superiority of our method over SOTA methods. + +# 2. Related Work + +GZSL methods can be categorized into two main types: embedding-based methods and generative-based methods: + +**Embedding based methods:** the basic idea is to learn a mapping function to project visual features of seen classes into a semantic space or vice versa, facilitating the recognition of unseen classes through similarity measures. Methods such as semantic embedding, visual embedding, and latent space embedding have been proposed. For example, Kim et al. proposed a semantic feature extraction-based GZSL framework. It used a modified autoencoder and similarity-based loss functions to remove attribute-irrelevant information, significantly improving classification accuracy on benchmark datasets [14]. Liu et al. proposed a PSVMA framework to achieve GZSL. It incorporated dual semantic-visual transformers for instance-centric semantic feature adaptation, by which semantic + +![](images/74dbe00943ef72daa027843fd26b02c8a45b79564b89d7938a89624be656f4c6.jpg) +Figure 2. Structure of our method, and for simplicity, three classes are illustrated. Our method is composed of a classification backbone and an inter-class feature augmentation (IFA) module. The classification backbone is formed by an encoder, a global average pooling (GAP), and a classification head, and it is responsible for deriving features from input images and predicting the corresponding classes. The IFA module is used to impose ordinal constraint on the features of all classes through a pre-defined joint conditional Gaussian distribution model, based on which features of unseen classes can be generated and used to train the classification head. + +disambiguation and knowledge transferability can be enhanced [19]. In addition, out-of-distribution (OOD) [5] and graph-based GZSL methods [31] have also been explored. These methods are particularly effective in the scenarios where semantic space is well-defined and can be leveraged to infer the characteristics of unseen classes. However, due to the gap between visual and semantic information, embedding-based methods often suffer from cross-modal alignment difficulties and high bias. + +Generative based methods: in these methods, generative models, such as generative adversarial networks (GANs) [10] and variational autoencoder (VAE) [15], are adopted to synthesize samples of unseen classes conditioned by semantic information. In this way, GZSL can be transformed into a fully supervised learning method. For example, Han et al. proposed a hybrid GZSL framework, where feature generation and contrastive embedding were combined to achieve integrated class-wise and instance-wise supervision [11]. Chen et al. proposed a SD-GZSL framework. It used a conditional VAE to disentangle visual features into semantic-consistent and semantic-unrelated representations [6]. Gao et al. proposed a Zero-VAE-GAN framework for GZSL, where VAE and GAN were combined to generate high-quality features of unseen classes [9]. + +Clearly, semantic information plays an important role in both embedding and generative based GZSL methods. As aforementioned, defining appropriate semantic information to distinguish between classes could be a greater challenge, especially in clinical settings. Moreover, using semantic information could possibly cause the issue of cross-modal alignment problems between visual and semantic features, + +degrading classification performance. Our method shows a new way of GZSL without the need of semantic information, effectively addressing these issues. + +# 3. Methodology + +The structure of our method is shown in Fig. 2. It is composed of two main components: the classification backbone and the inter-class feature augmentation (IFA) module. Assuming that $D = \{I_1, I_2, \dots, I_N\}$ includes images of all classes and is divided into subgroups $D_1, D_2, \dots, D_C$ , each contains images of one class, i.e., $D_c = \{I_{c,1}, I_{c,2}, \dots, I_{c,N_c}\}$ , $c = 1, \dots, C$ , where $C$ is the number of classes and $N_c$ is the number of images belonging to class $c$ . If $c$ is an unseen class, then $N_c = 0$ , i.e., $D_c = \emptyset$ . For the input images in $D$ , features $F = \{f_1, f_2, \dots, f_N\}$ are first derived by the encoder $\Phi_\theta$ and the global average pooling (GAP) of the classification backbone, based on which a Gaussian distribution can be modeled for the features of each seen class $\{\mu_c, \sigma_c^2\}$ . To make features of all classes distribute in the order of their corresponding risks, in the IFA module, an ordinal constraint using a pre-defined joint conditional Gaussian distribution model is imposed. In this way, for unseen classes, their features can be generated from neighboring seen classes. Based on the features of both seen and unseen classes, the final classification head at the end of the classification backbone can be trained in a fully supervised manner. Details of our method are discussed in the following sections. + +# 3.1. The Classification Backbone + +The classification backbone is composed of an encoder $\Phi_{\theta}$ ( $\theta$ is parameter set), a global average pooling (GAP), and a classification head. A pre-trained 3D-ResNet18 [2] is adopted as the encoder $\Phi_{\theta}$ . For each input image $I_i \in \mathbb{R}^{H \times W \times L \times M}$ of seen classes, where $H$ , $W$ , and $L$ , are the height, width, and slice number of the input image, and $M$ is the number of modalities in the input image, $\Phi_{\theta}(I_i) \in \mathbb{R}^{\frac{H}{8} \times \frac{W}{8} \times \frac{L}{8} \times 32}$ is derived by the encoder, which is further fed to the GAP to get the image feature $f_i \in \mathbb{R}^{32}$ . Based on $f_i$ , the classification head can produce the corresponding class. Cross-entropy is adopted as the loss function of the classification backbone, which is defined as: + +$$ +\mathcal {L} _ {\mathrm {C E}} = - \sum_ {i = 1} ^ {N} \sum_ {c = 1} ^ {C} y _ {i} (c) \log \left(p _ {i} (c)\right), \tag {1} +$$ + +where $y_{i}(c)$ and $p_i(c)$ are the ground truth and the predicted probability of $I_{i}$ belonging to class $c$ , respectively. + +Since there is no images of unseen classes, image features of unseen classes are unavailable for the classification head in training phase. To tackle this issue and achieve GZSL, the IFA module is presented to impose an ordinal constraint on the encoder, by which features of different classes are distributed in the order of their corresponding risks, and unseen classes can then be generated using neighboring seen classes. + +# 3.2. The Inter-Class Feature Augmentation Module + +By default, in DL-based classification methods, feature distribution of each class is regarded as independent Gaussian distribution, and the joint feature distribution of all classes can be defined as: + +$$ +\mathcal {P} \left(F _ {1}, F _ {2}, \dots , F _ {C}\right) = \prod_ {c = 1} ^ {C} \mathcal {N} \left(\mu_ {c}, \sigma_ {c} ^ {2}\right), \tag {2} +$$ + +where $F_{c} = \{f_{c,1}, f_{c,2}, \dots, f_{c,N_{c}}\}$ , $c = 1, \dots, C$ contains features of images in $D_{c}$ , $\mathcal{N}(\mu_{c}, \sigma_{c}^{2})$ represents Gaussian distribution of features in $F_{c}$ , $\mu_{c}$ and $\sigma_{c}^{2}$ are mean and deviation defined as: + +$$ +\mu_ {c} = \frac {1}{N _ {c}} \sum_ {f _ {c, i} \in F _ {c}} f _ {c, i}, \tag {3} +$$ + +$$ +\sigma_ {c} ^ {2} = \frac {1}{N _ {c} - 1} \sum_ {f _ {c, i} \in F _ {c}} \left(f _ {c, i} - \mu_ {c}\right) ^ {2}. \tag {4} +$$ + +To make the feature distributions of all classes in a desired order, a pre-defind joint conditional Gaussian distribution model [21] is defined in the IFA module to impose ordinal constraint on the features derived by the encoder, which is formulated as: + +$$ +\mathcal {Q} \left(\hat {F} _ {1}, \hat {F} _ {2}, \dots , \hat {F} _ {c}\right) = \mathcal {P} \left(\hat {F} _ {1}\right) \mathcal {P} \left(\hat {F} _ {2} \mid \hat {F} _ {1}\right) \dots \mathcal {P} \left(\hat {F} _ {\mathrm {C}} \mid \hat {F} _ {\mathrm {C} - 1}\right), \tag {5} +$$ + +where $\hat{F}_c, c = 1, \dots, C$ represents the features of different classes distributed in a desired order. (5) can be also presented as: + +$$ +\mathcal {N} \left(\left[ \begin{array}{c} \hat {\mu} _ {1} \\ \hat {\mu} _ {1} + \Delta_ {2} \\ \vdots \\ \hat {\mu} _ {1} + \sum_ {i = 2} ^ {C} \Delta_ {i} \end{array} \right], \left[ \begin{array}{c c c c} \hat {\sigma} _ {1} ^ {2} & \dots & \dots & \hat {\sigma} _ {1} ^ {2} \\ \hat {\sigma} _ {1} ^ {2} & \hat {\sigma} _ {1} ^ {2} + \hat {\sigma} _ {2} ^ {2} & \dots & \vdots \\ \vdots & \vdots & \ddots & \vdots \\ \hat {\sigma} _ {1} ^ {2} & \dots & \dots & \sum_ {c = 1} ^ {C} \hat {\sigma} _ {c} ^ {2} \end{array} \right]\right). \tag {6} +$$ + +where $\hat{\mu}_{1}$ stands for the mean feature of $\hat{F}_1$ and can be regarded as the starting center point of the ordinal distribution of all classes, $\hat{\sigma}_c^2$ is the deviation of $\hat{F}_c$ , and $\Delta_c$ is a shifting vector and is used to ensure desired ordering of classes. $\hat{\mu}_{1}$ , $\hat{\sigma}_c^2$ and $\Delta_c$ are learnable variables in our method. + +To impose the ordinal constraint, the KL divergence [16] based ordinal loss is applied to make the real feature distribution (i.e., $\mathcal{P}$ ) aligned with the pre-defined one (i.e., $\mathcal{Q}$ ), which is defined as: + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {O D}} = \operatorname {K L} \left(\mathcal {Q} \left(\hat {F} _ {1}, \hat {F} _ {2}, \dots , \hat {F} _ {C}\right) \| \mathcal {P} \left(F _ {1}, F _ {2}, \dots , F _ {C}\right)\right) \\ = \sum_ {c = 1} ^ {C} \left[ \ln \left(\frac {\sigma_ {c}}{\hat {\sigma} _ {c}}\right) + \frac {\hat {\sigma} _ {c} ^ {2} + \left(\hat {\mu} _ {c} - \mu_ {c}\right) ^ {2}}{2 \sigma_ {c} ^ {2}} - \frac {1}{2} \right]. \tag {7} \\ \end{array} +$$ + +Besides the ordinal loss $\mathcal{L}_{\mathrm{OD}}$ , which encourages the alignment of feature distribution of $F_{c}$ and $\hat{F}_c$ , $c = 1,\dots,C$ , a contrastive learning based distinctiveness loss $\mathcal{L}_{\mathrm{DIS}}$ is introduced. It is used to enhance the distinctiveness of feature distribution between different classes, which is defined as: + +$$ +\mathcal {L} _ {\mathrm {D I S}} = - \sum_ {i = c _ {1}} ^ {C} \sum_ {c _ {j} = 1 \atop c _ {j} \neq c _ {i}} ^ {C} | c _ {j} - c _ {i} | \cdot K L \left(\mathcal {N} \left(\mu_ {c _ {i}}, \sigma_ {c _ {i}} ^ {2}\right) \| \mathcal {N} \left(\hat {\mu} _ {c _ {j}}, \hat {\sigma} _ {c _ {j}} ^ {2}\right)\right), \tag {8} +$$ + +where $|c_{j} - c_{i}|$ is the class distance between $c_{i}$ and $c_{j}$ . It serves as a weighting factor and strongly suppresses the alignment of $c_{i}$ and $c_{j}$ with large class distance. Since the ordinal constraint imposed by the IFA module, feature distribution of all classes are ordered. In this way, for the unseen class $c_{u}$ , its corresponding features can be generated from $c_{u}$ 's neighboring seen classes, which is defined as: + +$$ +f _ {c _ {u}, n} ^ {\prime} = \frac {1}{2} \left(f _ {c _ {p}, i} + f _ {c _ {q}, j}\right) + \epsilon , \tag {9} +$$ + +where $f_{c_u,n}^{\prime}, n = 1, \dots, N_{c_u}$ are the generated features of the unseen class $c_u$ , $f_{c_p,i}, i = 1, \dots, N_{c_p}$ and $f_{c_q,j}, j = 1, \dots, N_{c_q}$ are features randomly selected from $c_p$ and $c_q$ which are neighboring seen classes of $c_u$ , $\epsilon$ is Gaussian noise, which is introduced to enhance diversity of generated features and avoid overfitting. + +Based on the features of seen classes as well as the generated features of unseen classes, the classification head in the backbone can be trained in a supervised manner. + +# 3.3. The Training Strategy + +Our method employs a two-stage training approach. In the first stage, we use only images from seen classes to train our model, which enables it to learn patterns of ordinal-related features that capture the progressive nature of clinical conditions. During this phase, the model develops an understanding of how features change across the severity spectrum represented by the seen classes. + +In the second stage, we generate features for unseen classes by leveraging the learned ordinal relationships and the features of neighboring seen classes. These generated features are then used to further train the classification backbone, allowing it to recognize both seen and unseen classes effectively. The loss function of our method is defined as: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {C E}} + \lambda_ {1} \mathcal {L} _ {\mathrm {O D}} + \lambda_ {2} \mathcal {L} _ {\mathrm {D I S}}, \tag {10} +$$ + +where $\lambda_{1}$ and $\lambda_{2}$ are weights for the ordinal loss and distinctiveness loss, and they are set to 1 and 0.1, respectively. + +# 4. Experiments + +Both in-house(Glioma) and public datasets(ADNI, APTOS) are used to evaluate our method. The in-house dataset is collected in our cooperation hospitals, and it consists of multimodal MR images (T1, T1 contrast-enhanced, T2, and FLAIR) of 726 patients with confirmed glioma. The glioma subtypes of each patient are available. Specifically, 137, 18, and 571 patients are diagnosed as oligodendroglioma (O), astrocytoma (A), and glioblastoma (GBM), respectively. In our experiment, astrocytoma is set to the unseen class. The public datasets include ADNI [12] and APTOS [13]. The ADNI dataset contains MR images of 653 patients diagnosed as normal (N, 403 patients), mild cognitive impairment (MCI, 28 patients), and Alzheimer's disease (AD, 222 patients). The unseen class is set to MCI. The APTOS dataset includes 2D retinal images used for diabetic retinopathy (DR) classification. Based on the severity, images in the APTOS dataset is categorized to No DR (level 0), Mild NPDR (level 1), Moderate NPDR (level 2), Severe NPDR (level 3), or Proliferative DR (level 4), respectively. The APTOS dataset is officially split into training set (1434, 300, 808, 154, and 234 images for level 0 to 4), validation set (172, 40, 104, 22, and 28 images), and testing set (199, 30, 87, 17, and 33 images), respectively. For the in-house and ADNI datasets, five-fold cross-validation is applied, while for the APTOS dataset, our method is trained according to its official data splitting. Moreover, level 1, 2, and 3 are regarded as the unseen classes in the APTOS + +dataset, respectively. For the APTOS dataset, Swin Transformer [22] instead of the 3D-ResNet18 is adopted by the encoder of our method to handle 2D images. + +Besides our method, five SOTA GZSL methods, including DFZSL [28], HSVA [4], CE-GZSL [11], FREE [3], and SD-GZSL [6], are also evaluated in our experiment, and all of them require semantic information. Specifically, DFZSL uses a CLIP-based method [26] to recover virtual data and aligns visual-text features, enabling zero-shot classification. HSVA employs hierarchical semantic-visual adaptation to improve the alignment between semantic and visual domains. CE-GZSL adopts a deep calibration network to reduce the domain shift between seen and unseen classes. FREE refines generated features using a self-adaptive margin center loss and a semantic cycle-consistency loss to enhance discriminability for unseen classes. SDGZSL uses a conditional VAE to disentangle visual features into semantic-consistent and semantic-unrelated representations, by which only semantic-relevant features are transferred and generalization ability of unseen classes can be enhanced. Additionally, a fully supervised method is included, which is trained with original data in these three datasets (i.e., no unseen classes). All methods under evaluation are implemented using PyTorch 2.1.0 with CUDA 12.1, and trained on the platform of Intel i7-9700, 32G, RTX 3090 GPU 24G, and Ubuntu 22.04.1. + +# 4.1. Evaluation of Classification Results + +Since explicit semantic information is required in the five SOTA methods, the word-embedding method proposed in [25] is used to get the semantic information. Specifically, several carefully designed domain-specific prompts are formulated to query a Large Language Model (LLM), aiming to derive key characteristics and distinguished semantic features for each class. For example, for the class of glioblastoma, the prompt "Describe the significant MRI features of glioblastoma" is used. The responses generated by the LLM are then encoded using a pre-trained text encoder from CLIP [26] to create the word-embedding for glioblastoma. This approach ensures high-quality semantic information for baseline methods. + +Classification performance is evaluated using metrics including seen Accuracy $(\mathrm{Acc_s})$ , unseen Accuracy $(\mathrm{Acc_u})$ , and Harmonic Mean (HM). Specifically, $\mathrm{Acc_s}$ and $\mathrm{Acc_u}$ measure the classification accuracy on the seen and unseen classes, respectively. The HM provides a balanced measure of performance across both seen and unseen classes, which is defined as: + +$$ +\mathrm {H M} = \frac {2 \times \mathrm {A c c} _ {\mathrm {s}} \times \mathrm {A c c} _ {\mathrm {u}}}{\mathrm {A c c} _ {\mathrm {s}} + \mathrm {A c c} _ {\mathrm {u}}}. \tag {11} +$$ + +Moreover, AUC is also calculated for each method under evaluation, and the Delong test [7] is adopted to measure the statistical significance. + +
DatasetMethodAccsAccuHMAUC
GliomaDFZSL70.055.661.90.810
HSVA63.061.162.00.727
CE-GZSL75.555.664.00.845
FREE73.461.166.70.764
SD-GZSL62.272.266.80.729
IFA (Ours)77.366.771.60.928
Supervision†88.283.385.70.950
ADNIDFZSL83.260.770.20.945
HSVA68.067.967.90.851
CE-GZSL82.464.372.20.930
FREE92.864.376.00.972
SD-GZSL87.260.771.60.933
IFA (Ours)93.673.682.40.973
Supervision†97.982.089.20.993
APTOS-1DFZSL63.853.358.10.900
HSVA39.273.351.10.690
CE-GZSL72.450.059.10.927
FREE71.456.763.20.933
SD-GZSL63.863.363.50.909
IFA (Ours)80.456.766.50.954
Supervision†83.363.372.00.972
APTOS-2DFZSL75.637.950.50.940
HSVA74.939.151.40.942
CE-GZSL75.642.554.40.946
FREE77.134.547.60.939
SD-GZSL76.339.151.70.940
IFA (Ours)81.743.356.60.950
Supervision†84.672.478.00.972
APTOS-3DFZSL69.735.346.80.942
HSVA72.029.441.80.940
CE-GZSL72.041.152.40.946
FREE79.435.348.90.950
SD-GZSL73.947.157.50.945
IFA (Ours)77.164.770.40.952
Supervision†83.741.155.20.972
+ +Table 1. Evaluation results of all methods on the in-house (glioma), and public (ADNI and APTOS) datasets. In the APTOS dataset, APTOS-x represents the dataset where class x is treated as the unseen class. Supervision† represents the fully supervised method, used as a reference for comparison with zero-shot methods. + +Evaluation results are shown in Table 1. Our method achieves high accuracy on seen classes and the highest scores of HM and AUC of all SOTA methods across both in-house and public datasets. Moreover, the corresponding $p$ values of the Delong test on AUC are all less than 0.05, i.e., statistical significance. + +# 4.2. Visualization of Ordinal-related Regions + +As aforementioned, our method proposes that classes in clinical setting stand for risk stratification, and they are ordered rather than categorical. Our method learns ordinal- or risk-related features, in this way, the feature distribution + +![](images/947cc987bbbf9684bb11ee61c862bf7032532bff9bfa41851c917638af99e8bb.jpg) +Figure 3. Heatmap using GradCAM in the tasks of classification of glioma (top), AD (middle), and DR (bottom), respectively. Each row shows the original image (left) and the GradCAM heatmaps (right). + +of unseen classes can be determined. In this section, Grad-CAM [27] is adopted to visualize the most important regions that focused by our method. + +Fig. 3 shows the heat maps derived from GradCAM in the tasks of classification of glioma, Alzheimer's disease (AD), and diabetic retinopathy (DR). For glioma, our method pays high attention to the necrosis which has strong correlation with the prognosis. For AD, hippocampus and temporal lobe are focused, which are recognized as the key factors related to AD. For DR, exudates—lipid deposits due to blood-retinal barrier breakdown—become more prominent as DR severity rises, and our method accurately locates these regions. + +# 4.3. Ordinal Feature Distribution + +To validate the relationships of feature distribution between different classes, we compute the KL divergence between feature distributions of all possible class pairs in the testing phase using real images of both seen and unseen classes. Fig. 4 presents the resulting matrices of KL divergence for glioma, AD, and DR classification tasks. + +The matrices reveal a clear pattern that neighboring classes have more similar feature distributions than those further apart. It confirms that feature distribution of all classes follows an ordinal relationship in the feature space that aligns with risk levels. Importantly, the distribution of unseen classes fits this ordinal pattern. + +![](images/c669e567f241e2afa571b559f5cd5a6bb6e2e9fc25acbd7c2dd0d372412427d1.jpg) +Figure 4. KL divergence matrices of different classes in the testing phase in the classification tasks of Glioma (left), ADNI (middle), and APTOS-1 (right) datasets. + +# 4.4. Ablation Study + +Effectiveness of the Ordinal Constraint. To demonstrate the effectiveness of the proposed IFA module, our method with or without the ordinal constraint is evaluated. Fig. 5 shows a visual comparison of feature distributions with and without the ordinal constraint imposed by the IFA module. Each point in Fig. 5 represents an image feature in the testing phase, which is projected into 2D space using t-SNE [29], and each class is marked in different color. + +It is clear that for our method with the IFA module (with ordinal constraint), the feature distribution of all classes shows a clear ordinal arrangement that matches their corresponding risks (Fig. 5 top). Notably, the generated features for unseen classes (green triangles) are consistent with the distribution, which are closely aligned with the real features of unseen classes. In contrast, for our method without the IFA module (Fig. 5 bottom) such ordinal distribution of classes cannot be observed, and the generated features of unseen classes have different distribution from the reals. + +Impact of the Discriminative Loss. We further investigate the effectiveness of distinctiveness loss $\mathcal{L}_{\mathrm{DIS}}$ adopted in our method. Table 2 shows the evaluation results of our method with or without the distinctiveness loss. Clearly, substantial improvements can be achieved with the distinctiveness loss, and it plays a crucial role in enhancing interclass separation, effectively reducing feature overlap between different classes. + +# 5. Conclusion + +In this paper, we proposed a novel semantic-free approach for generalized zero-shot learning. Specifically, an new inter-class feature augmentation (IFA) module was presented to leverage the ordered property of classes in clinical settings, where distribution of different classes is encouraged to be in the order of their risks in a learned feature space through a pre-defined joint conditional Gaussian distribution model. This enables the generation of features for unseen classes by interpolating between features from neighboring seen classes, effectively transforming the challenging GZSL problem into a supervised learning task. + +![](images/080470434737d133e89e4e7057b1a2cef8bdc726b49d14b2d411fafcfb000a8e.jpg) +Figure 5. Feature distribution of test images with (top) and without (bottom) ordinal constraints for the three datasets. The green triangles represent the generated features of unseen classes. + +
GliomaADNIAPTOS-1APTOS-2APTOS-3
\(L_{DIS}\)AccsAccuHMAccsAccuHMAccsAccuHMAccsAccuHMAccsAccuHM
✘67.961.164.492.867.978.484.226.740.578.929.943.383.431.846.1
✓77.366.771.693.673.682.480.456.765.381.743.356.677.164.770.4
+ +Table 2. Ablation study on the effect of the discriminative loss across different datasets. + +By leveraging the ordinal relationships among classes, our method avoids the requirements for semantic attributes of unseen classes, thus addressing key challenges in existing GZSL methods such as effective semantic descriptions and and visual-semantic cross-modal alignment problems. + +Our method was evaluated on multiple clinical datasets, including an in-house glioma subtyping dataset, the ADNI dataset for Alzheimer's disease classification, and the AP-TOS dataset for diabetic retinopathy grading. Experimental results demonstrated that our method outperformed state-of-the-art (SOTA) GZSL methods across all datasets with statistical significance. Visualization through GradCAM heat maps confirmed that our method can focus on disease-severity-related regions and learn features that capture the ordinal relationships between classes of different risk levels. Ablation studies further verified the effectiveness of each proposed component in our method. + +The primary limitation of our method is that it is workable for unseen classes which have neighboring seen classes, in this case, distribution of unseen classes can be well constrained by neighboring seen classes. Otherwise, the feature distribution of unseen classes has large or unlimited space (e.g., the unseen class ranks at two ends of all classes), which could cause a large discrepancy between + +features of generated unseen classes and the real one, hindering the classification accuracy for unseen classes. Future work could explore adaptive sampling strategies for boundary classes or incorporate partial supervision to better constrain these edge cases. + +# Acknowledgements + +This work is supported in part by National Key Research and Development Program of China (No. 2023YFC2411001, 2023YFC2411002), National Natural Science Foundation of China (No. 62073012), and Beijing Municipal Natural Science Foundation (No. 7222307). + +# References + +[1] Wei-Lun Chao, Soravit Changpinyo, Boqing Gong, and Fei Sha. An empirical study and analysis of generalized zero-shot learning for object recognition in the wild. In Computer Vision-ECCV 2016: 14th European Conference, Amsterdam, The Netherlands, October 11-14, 2016, Proceedings, Part II 14, pages 52-68. Springer, 2016. 1 +[2] Sihong Chen, Kai Ma, and Yefeng Zheng. 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(2) Spatiotemporal models are proven to lean heavily on one type of forgery artifact and ignore the other (e.g., learning spatial only): how can we ensure balanced learning from both? (3) Videos are naturally resource-intensive: how can we tackle efficiency without compromising accuracy? This paper attempts to tackle the three challenges jointly. First, inspired by the notable generality of using image-level blending data for image forgery detection, we investigate whether and how video-level blending can be effective in video. We then perform a thorough analysis and identify a previously underexplored temporal forgery artifact: Facial Feature Drift (FFD), which commonly exists across different deep-fakes. To reproduce FFD, we then propose a novel Video-level Blending data (VB), which is implemented by blending the original image and its warped version frame-by-frame, serving as a hard negative sample to mine more general artifacts. Second, we carefully design a lightweight Spatiotemporal Adapter (StA) to equip a pretrained image model with the ability to capture both spatial and temporal features jointly and efficiently. StA is designed with two-stream 3D-Conv with varying kernel sizes, allowing it to process spatial and temporal features separately. Extensive experiments validate the effectiveness of our methods. + +# 1. Introduction + +Current AI-generated Content (AIGC) technology enables effortless manipulation of facial identities in video content, bringing many impressive applications in fields such + +![](images/f6c5dabe90177391b2df2b9a098b9481c88379b5d0651897bdb0e51b3357aba4.jpg) +Figure 1. Illustration of Facial Feature Drift (FFD) phenomena in deepfake videos. We empirically select two relatively static consecutive frames to demonstrate the facial temporal inconsistency between fake frames (FFD), even when the two frames appear similar at the image level. + +as movie-making and entertainment [42, 61-63]. However, this technology can also be misused for malicious purposes, including violating personal privacy, spreading misinformation, and eroding trust in digital media [27, 29, 30]. Hence, there is a pressing need to establish a reliable system for detecting deepfake videos. + +Most prior deepfake detectors [25, 43, 46, 60, 69] perform well within the same dataset. However, they often fail to generalize well in cross-dataset scenarios where training and testing data distributions differ. Training with synthetic (blending) images appears to be one of the most effective solutions to this problem, as evidenced by [24, 44], which encourages detectors to learn generic representations (e.g., blending boundaries and inconsistencies between inner and outer faces) for detection. Given the notable success of image-level blending, an intriguing question arises: what about video-level blending? Can this method also be applied to learn general forgery artifacts in the video domain? + +To this end, we perform a comprehensive examination + +of current realistic forgery videos and discover an inconsistency in the facial organs between forgery frames (as illustrated in Fig. 1). We term this phenomenon as the Facial Feature Drift (FFD). As illustrated in Fig. 1, even when two consecutive frames appear relatively static (possibly without other unrelated effects), subtle unnatural drift and flickering can be observed within facial features (e.g., eyes, nose, etc.). This observation provides reasonable evidence that unnatural forgery artifacts are indeed present in the temporal domain of manipulated videos. + +To understand the underlying reasons, we argue that the primary factor is the randomness during the generation process of fake faces. Intuitively, the root cause of FFD can be attributed to the frame-by-frame face-swapping operation employed by existing deepfake algorithms. Deepfake algorithms typically create a fake frame by using DNNs to generate a counterfeit inner face. Given this context, it is important to note that the inner face between different frames within a single generated video may exhibit variations, as the DNN is not a deterministic function, thereby resulting in inconsistencies during the generation process of fake faces. Furthermore, as shown in Fig. 1, inconsistencies are observed mainly in high-frequency regions with complex and varying details (i.e., facial organs), which exhibit amplified sensitivity to generative randomness. For these reasons, we pay special attention to the facial organs, which clearly differ from previous works (Tab. 1). Also, features of facial organs are typically more robust than the non-facial areas such as skin, sensitive to random perturbations (e.g., compression). + +To encourage the detection model to capture FFD in the given deepfake, we introduce a novel Video-level Blending data called VB to simulate and reproduce FFD. The overall creation pipeline of VB is illustrated in Fig. 2. Specifically, we generate VB by first applying warping operations separately to facial organs and then performing image-level blending to generate one synthesis image. The process is repeatedly conducted for all frames within one clip to create a set of synthesis images (video-level pseudo-fakes). VB can serve as the hard negative samples for mining more general discriminative features for detection. + +Additionally, to capture the FFD artifact effectively while achieving the balance learning between spatial and temporal artifacts with lower computation resources, we propose a new spatiotemporal adapter-based architecture to "convert" a pretrained image model into a video model, enabling the model to learn additional temporal information, rather than designing a new video architecture from scratch. Specifically, we meticulously design a lightweight, plug-and-play Spatiotemporal Adapter (StA) that equips an image model (e.g., ViT or CNN) with spatiotemporal understanding capabilities. Throughout the whole training process, only the added adapters are updated, which signifi + +cantly reduces the training cost and allows us to leverage the powerful generalization capabilities of existing SoTA image models (e.g., CLIP) and future more advanced models. + +Overall, this work addresses three key challenges in detecting deepfake videos. Our main contributions are three-fold below. + +- We discover a previously underexplored forgery artifact in the temporal domain, where a subtle inconsistent artifact is observed in the location and shape of facial organs between frames. We term it Facial Feature Drift (FFD), which is general and commonly exists across different deepfake videos due to the generative randomness. +- To simulate FFD, we propose a Video-level Blending (VB) data, which serves as the hard negative samples to aid the model in learning the general temporal forgery features for improved generalization. +- To achieve the balance learning between spatial and temporal artifacts with lower computation resources, we propose a new Spatiotemporal Adapter called StA, which is plug-and-play and can be inserted into different (SoTA) image models (e.g., CLIP) to enhance their spatiotemporal understanding capabilities. + +# 2. Related Work + +# 2.1. Deepfake Image Detection + +Conventional image detectors [37, 43] typically focus on developing optimal CNN architectures (e.g., MesoNet, CapsuleNet). However, these methods often overlook the details present in the frequency domain of fake images, such as compression artifacts. To this end, several works [12, 39] utilize frequency information to improve the performance of detectors. Other notable directions are focusing on some specific representations, i.e., forgery region location [36], 3D decomposition [71], disentanglement [4, 11, 57], erasing technology [52], theoretic information [47], data quality [45], vulnerable points [35], and multimodal learning [20, 28, 50, 55, 65]. There are also several works [22, 41] based on face recognition [34, 68] for detection. These works typically utilize designed algorithms for detecting deepfakes from the view of representation learning. Another important direction of image forgery detection is data synthesis, which will be discussed in Sec. 2.3. + +# 2.2. Deepfake Video Detection + +There are parts of works [69] that focus on temporal artifacts. An early work [16] proposes to leverage the temporal inconsistency of the mouth movement. This work utilizes a pre-trained model to learn the natural lip movement as prior on a lip-reading dataset. FTCN [67] explores directly training a fully temporal 3D ConvNets with an attached temporal Transformer. However, detecting without spatial information may harm the generalization capability. STIL [13] con + +
MethodsBlending ModeIntroduced Artifacts
Image LevelVideo LevelFace LevelRegion Level
Face Xray [24], PCL [66], SBI [44], OST [3]✓✓
SLADD [2]✓✓
SeeABLE [23]✓✓
Ours✓✓
+ +Table 1. Comparison of our data synthesis method and other similar methods. Ours clearly differs from previous methods in terms of the level at which blending modes are focused (image-level vs. video-level) and the level at which artifacts are introduced (face-level vs. region-level). + +siders both spatial and temporal inconsistency and designs a spatiotemporal inconsistency Learning framework for deepfake video detection. RealForensics [17] introduces audio information and leverages self-supervised learning for representation learning. Wang et al. [53] propose a new learning method that alternatively trains and freezes the spatial and temporal convolutional layers in a 3D CNN (e.g., I3D R50). The result shows the importance of leveraging both spatial and temporal features for detecting deepfakes. Very recently, NACO [64] proposes to learn the natural consistency in a self-supervised manner for generalizable deepfake video detection. + +# 2.3. Deepfake Detectors Based on Data Synthesis + +Image-level Data Synthesis. One effective approach in deepfake detection is to use synthetic data (or blending data/images) for training. This strategy encourages models to learn generic representations for detecting deepfakes, such as blending boundaries and inconsistency between the inner and outer faces [44]. For instance, in the early stages, FWA [25] employs a self-blending strategy by applying image transformations (e.g., down-sampling) to the facial region and then warping it back into the original image. This process is designed to learn the wrapping artifacts during the deepfake generation process. Another noteworthy contribution is Face X-ray [24], which explicitly encourages detectors to learn the blending boundaries of fake images. Furthermore, SLADD [2] introduces an adversarial method to generate the most challenging blending choices for synthesizing data dynamically. Rather than swapping faces between two different identities, a recent art, SBI [44], proposes to swap with the same person's identity to reach a high-realistic face-swapping. ProDet [5] further explores the role of blending data and how to combine it with the original deepfake data. In additional to RGB-based augmentation, LSDA [56] proposes to augment the latent forgery space to achieve a more robust decision boundary. Given the notable generalization performance for detecting image forgery by using synthetic data, it remains an open question whether and how video-level synthetic data can be effective. + +Video-level Data Synthesis. Compared to image-level data synthesis (blending), very little work pays attention to de + +signing a suitable video-level blending method. We identify one notable work [53] that attempts to design video-level data synthesis by using techniques such as dropping/repeating one frame within a clip. However, it is possible that these simple operations might not explicitly represent the complex and general forgery pattern across different deepfake videos. Recall that in the image domain, we use blending technology to synthesize the forgery artifact, since the blending operation generally exists in the generation process of different deepfakes. So there are two main challenges: (1) What kinds of forgery features generally exist in the temporal domain? (2) How can blending be used to simulate it like image data synthesis? We will show our video-level blending method in the following section. + +# 3. Method + +# 3.1. Notation + +We first introduce some important notations as follows. Suppose we have a frame $\mathbf{I}$ from the original video. We define that the facial region $R$ contains several specific facial regions $r$ such as eyes, eyebrows, nose, and mouth. Let $\mathbf{L}_z$ be the landmark of region $z$ , where $z$ can be a specific facial region $r$ or the whole facial region $R$ . To transform landmarks, where transformation parameters are sampled from the uniform distribution, we set 3 hyperparameters $u_r, u_s, u_t$ to be the maximum rotation angle, scaling factor, and translation distance, respectively. After landmark perturbation, we will derive a new landmark $\mathbf{L}_R^*$ of the facial region $R$ and the corresponding warped image $\mathbf{I}_{\mathrm{warp}}$ . We consider the mask $\mathbf{M}_r(x,y)$ for region $r$ , indicating the blending weight at pixel $(x,y)$ . At last, we obtain the final blended frame $\mathbf{I}'$ which is composed of $\mathbf{I}_r'$ : blended frame about region $r$ , and $\alpha_r$ is used to control the blending weight for region $r$ . To better illustrate our method, we denote $\mathrm{dist}(x,y,\mathbf{L}_r)$ as a signed distance function calculating the shortest distance from a pixel $(x,y)$ to the closest landmark in $\mathbf{L}_r$ , $\mathrm{fdist}_r$ as a predefined fall-off distance for the mask of region $r$ and $\mathrm{clip}(x,\min ,\max)$ as a function that limits $x$ within the range [min,max]. + +![](images/b477d824d48ec1f83ebd88c2fbecd2d39e8c9b3bf31a6444386fb657a18d924a.jpg) + +![](images/202619653159e281c3e3e5078c2363b568b97d5fe22afa054128d9385e07cdcf.jpg) +Figure 2. The overall pipeline of the proposed video-level blending method (VB). The whole process involves repeatedly performing Frame-by-Frame Synthesis for a video clip. Two main steps in the frame-by-frame synthesis are Landmark Perturbation and Region Mask Extraction, where the former is designed to add random perturbation to the given facial landmarks and the latter is to extract the mask of each facial organ. The detailed algorithms can be seen in the text. + +# 3.2. Video-level Data Synthesis + +Our video-level blending data (VB) is to simulate the Facial Feature Drift (FFD) phenomenon through landmark perturbation and region mask extraction on facial organs between frames. The image blending process involves several steps, including warped image generation, region mask extraction, dynamic blending, and composite image formation, each contributing to the final blended video frame. Note that perturbation parameters $u_{r}, u_{s}$ , and $u_{t}$ introduce variability in the appearance of facial regions across frames, contributing to the realism of the video by mimicking natural movements and expressions. + +Landmark perturbation. Our goal is to manifest FFD, that is perturbation of landmarks region. Assuming that the perturbation parameter follows the uniform distribution $U_{[0,u_i]}, i \in \{\mathrm{r},\mathrm{s},\mathrm{t}\}$ , we sample parameters for current images perturbation. And we can derive transformed landmarks $\mathbf{L}_R^* = \mathbf{A}\mathbf{L}_R$ , where $\mathbf{A}$ is the affine transformation matrix corresponding to sampled parameters. As a result, warp transformation can be written as: $\mathbf{I}_{\mathrm{warp}} = \mathbf{A}\mathbf{I}$ . + +Region Mask Extraction. Our method focuses on facial regions, and thus requires a mask to keep other regions the same while changing regions of interest. At the same time, we hope that the closer to the landmark, the more obvious the traces of perturbation will be. For each facial region $r$ with landmarks $\mathbf{L}_r$ , the generation of the mask $\mathbf{M}_r$ is formulated as: + +$$ +\mathbf {M} _ {r} (x, y) = 1 - \operatorname {c l i p} \left(\frac {\operatorname {d i s t} (x , y , \mathbf {L} _ {r})}{\operatorname {f d i s t} _ {r}}, 0, 1\right), r \in R. \tag {1} +$$ + +This equation ensures that the mask $\mathbf{M}_r$ smoothly transitions from 1 (fully included in blending) to 0 (excluded from blending) as the distance from the landmarks increases, up to a maximum defined by $\mathrm{fdist}_r$ . The hyperparameter $\mathrm{fdist}_r$ defines the farthest range that will be included in blending. + +Dynamic Blending. As we set various masks for different regions, we first create a blended image for each special region. Specifically, the dynamic blending process for a region $r$ is described by the equation: + +$$ +\mathbf {I} _ {r} ^ {\prime} = \left(\mathbf {M} _ {r} \cdot \mathbf {I} _ {\text {w a r p}}\right) + \left(\left(1 - \mathbf {M} _ {r}\right) \cdot \mathbf {I}\right), r \in R. \tag {2} +$$ + +Here, $\mathbf{I}_{\mathrm{warp}}$ is derived from $\mathbf{I}$ by applying an affine transformation that introduces perturbations in rotation, scale, and translation, simulating natural movements. $\mathbf{M}_r$ dictates how much of $\mathbf{I}_{\mathrm{warp}}$ versus $\mathbf{I}$ is used at each pixel, achieving a blended effect in the region $r$ . + +Composite Image Formation. Finally, VB image $\mathbf{I}'$ can be obtained through compositing blended images of different facial regions. The composite process is formulated as: + +$$ +\mathbf {I} ^ {\prime} = \sum_ {r \in R} \alpha_ {r} \cdot \mathbf {I} _ {r} ^ {\prime}, \quad \text {w h e r e} \sum_ {r \in R} \alpha_ {r} = 1. \tag {3} +$$ + +![](images/f10d54b507074b460b4f1351fb08195c8a7dc9b158bcbfa58e4122fc2e3d506a.jpg) +Figure 3. The overall pipeline of the proposed adapter-based strategy (StA). We propose a novel and efficient adapter-based method that can be plug-and-play inserted into any SoTA image detector. + +![](images/ba71183706aae37672f6501ffb0872473a655b55ecb9701cc34b19e98a4177ac.jpg) + +Each region $r$ contributes to $\mathbf{I}'$ based on its blending weight $\alpha_r$ , allowing for the balanced integration of all facial features into the cohesive final image. After generating a VB frame corresponding to each frame of the video, we synthesize VB frames into a new VB video. + +# 3.3. Spatiotemporal Adapters (StA) + +Here we propose a lightweight spatiotemporal adapter-based architecture (StA), enabling to capture spatiotemporal artifacts. The adapter contains two 3D-Conv layers for spatial and temporal modeling, followed by a cross-attention layer to extract the complex relationship between them. The 3D-Conv for spatial modeling is with the kernel size of $(1,N,N)$ , capturing the spatial-only information, while the 3D-Conv for temporal is $(N,1,1)$ , for temporal-only modeling. + +Formally, given a video clip $\mathbf{x}_k^{in} \in \mathbb{R}^{T \times H \times W \times C}$ (T frames within the same video), obtained from the $l$ -th stage of the pretrained image backbone. Where $C$ is the channels of feature maps, $H \times W$ for the spatial size, and $T$ represents the number of frames within the video clip. The spatial and temporal features can be computed as follows: + +$$ +\begin{array}{l} \mathbf {e} _ {k} ^ {s} = 3 \mathrm {D C o n v} _ {\mathrm {s}} \left(\mathbf {W} _ {\text {d o w n}} \cdot \mathbf {x} _ {k} ^ {i n}\right), \tag {4} \\ \mathbf {e} _ {k} ^ {t} = 3 \mathrm {D C o n v} _ {\mathrm {t}} \left(\mathbf {W} _ {\mathrm {d o w n}} \cdot \mathbf {x} _ {k} ^ {i n}\right), \\ \end{array} +$$ + +where $\mathbf{W}_{\mathrm{down}}\in \mathbb{R}^{C\times C^{\prime}}$ . 3DConv and 3DConv represent the 3D-Conv layers for spatial and temporal modeling. Specifically, we implement three DepthWise 3D-Conv layers with different scales (i.e., 3, 5, 7) to capture multi-scale features. After obtaining both the spatial $(\mathbf{e}_k^s)$ and temporal feature maps $(\mathbf{e}_k^t)$ , we apply a cross-attention layer to capture the high-level relationship between spatial and temporal features. First, we flatten the spatial and temporal dimensions and then permute the dimensions to prepare the tensors for multi-head attention: $\mathbf{e}_k^s\rightarrow \mathbf{p}_k^s\in \mathbb{R}^{(T\times H\times W)\times C}$ and $\mathbf{e}_k^t\to \mathbf{p}_k^t\in \mathbb{R}^{(T\times H\times W)\times C}$ . We then apply crossattention between permuted spatial and temporal features: + +$$ +\begin{array}{l} \mathbf {S 2 T} = \text {M u l t i H e a d A t t e n t i o n} \left(\mathbf {p} _ {k} ^ {t}, \mathbf {p} _ {k} ^ {s}, \mathbf {p} _ {k} ^ {s}\right), \\ \mathbf {T 2 S} = \text {M u l t i H e a d A t t e n t i o n} \left(\mathbf {p} _ {k} ^ {s}, \mathbf {p} _ {k} ^ {t}, \mathbf {p} _ {k} ^ {s}\right) \end{array} \tag {5} +$$ + +$$ +\mathbf {T 2 S} = \text {M u l t i H e a d A t t e n t i o n} \left(\mathbf {p} _ {k} ^ {s}, \mathbf {p} _ {k} ^ {t}, \mathbf {p} _ {k} ^ {t}\right), +$$ + +where S2T represents the result of integrating spatial information into the temporal dimension, while T2S represents the result of integrating temporal information into the spatial dimension. + +The attention outputs are reshaped back to their original dimensions: $\mathbf{S2T}^{\mathrm{perm}}\rightarrow \mathbf{S2T}^{\mathrm{orig}}\in \mathbb{R}^{B\times C\times T\times H\times W}$ and $\mathbf{T2S}^{\mathrm{perm}}\to \mathbf{T2S}^{\mathrm{orig}}\in \mathbb{R}^{B\times C\times T\times H\times W}$ . The final output is obtained by averaging the two attention results and adjusting the channels by an Upsampling layer $(up)$ : + +$$ +\mathbf {x} _ {k} ^ {\text {o u t}} = \frac {1}{2} \left(\mathbf {S 2 T} ^ {\text {o r i g}} + \mathbf {T 2 S} ^ {\text {o r i g}}\right) \cdot \mathbf {W} _ {\mathbf {u p}}. \tag {6} +$$ + +In the whole training process, only the added modules are updated (i.e., adapters and cross-attention layers, etc), significantly reducing the training cost. + +# 4. Results + +# 4.1. Setup + +Implementation Details. We use the CLIP ViT-L14 [40] as the default backbone. We also explore other architectures for experiments, as shown in Tab. 5. All preprocessing and training codebases are aligned to the deepfake benchmark [58]. Specifically, we uniformly sample 32 frames from each video during training and randomly select 8 consecutive frames as a clip for each iteration. We also employ several widely used data augmentations, such as CutOut, and ImageCompression, following [44, 56]. + +Evaluation Metrics. By default, we report the video-level Area Under the Curve (AUC) to compare our proposed method with prior works. Other evaluation metrics such as Accuracy (Acc.) and Equal Error Rate (EER) are also reported for a more comprehensive evaluation. + +Evaluation Protocols and Dataset. We adopt three standard protocols to evaluate our models: Protocol-1: cross + +Table 2. Protocol-1: Cross-dataset evaluations with image detectors. All detectors are trained on FF++_c23 [43] and evaluated on other datasets. The best results are highlighted in bold and the second is underlined. * indicates the results are directly cited from their original papers, otherwise the results are cited by [5, 32, 58]. †: we would like to highlight that the DFDC dataset is no longer downloadable. ‡: the LAA-Net is trained on high quality version of FF++ (raw) while our method uses the compressed c23 version. + +
DetectorVenuesCDF-v2DFDDFDC†DFDCPDFoWDFFFIWAvg.
F3Net [39]ECCV 20200.7890.8440.7180.7490.7300.7280.6490.743
SPSL [31]CVPR 20210.7990.8710.7240.7700.7230.7020.7940.769
SRM [33]CVPR 20210.8400.8850.6950.7280.7220.7020.7940.767
CORE [38]CVPRW 20220.8090.8820.7210.7200.7650.7240.7100.762
RECCE [1]CVPR 20220.8230.8910.6960.7340.7840.7560.7110.779
DCL [48]AAAI 20220.8820.9210.7500.7690.9750.7760.8630.851
SLADD* [2]CVPR 20220.797-0.772-----
SBI [44]CVPR 20220.8860.8270.7170.8480.8990.7030.8660.821
UIA-ViT* [72]ECCV 20220.889--0.795----
UCF [57]ICCV 20230.8370.8670.7420.7700.8080.7740.6970.785
SeeABLE* [57]ICCV 20230.873-0.7590.863----
IID* [19]CVPR 20230.8380.939-0.812----
CFM [32]TIFS 20230.8970.9520.7060.8020.9760.8230.8310.856
LSDA [56]CVPR 20240.8980.9560.7350.8120.8920.7560.8790.847
LAA-Net‡ [35]CVPR 20240.9540.984-0.869-0.800--
Ours-0.947(↓0.7%)0.965(↓1.9%)0.843(↑9.3%)0.909(↑6.1%)0.991(↑1.5%)0.848(↑2.5%)0.921(↑4.2%)0.911(↑5.5%)
+ +Table 3. Protocol-2: Cross-manipulation evaluations within FF++ domain. All models are trained on FF++ (c23) and tested on other forgeries. $\dagger$ indicates the results are obtained by using the official pre-trained model for evaluation, otherwise, the results are cited by [5, 58]. + +
DetectorUniFaceBlendFaceMobileSwape4sFaceDancerFSGANInswapSimSwapAvg.
RECCE [1]0.8980.8320.9250.6830.8480.9490.8480.7680.844
SBI [44]0.7240.8910.9520.7500.5940.8030.7120.7010.766
UCF [57]0.8310.8270.9500.7310.8620.9370.8090.6470.824
AltFreezing† [53]0.9470.9510.8510.6050.8360.9580.9270.7970.859
Ours0.9600.9060.9460.9800.9120.9640.9370.9310.942
+ +Table 4. Protocol-3: Cross-dataset evaluations with video detectors. The results of these detectors are directly cited from their original papers. + +
DetectorVenuesCDF-v2DFDCAvg.
LipForensics [16]CVPR 20210.8240.7350.780
FTCN [67]ICCV 20210.8690.7400.805
HCIL [14]ECCV 20220.7900.6920.741
RealForensics [17]CVPR 20220.8570.7590.808
LTTD [15]NeurIPS 20220.8930.8040.849
AltFreezing [53]CVPR 20230.895--
TALL-Swin [54]ICCV 20230.9080.7680.838
StyleDFD [6]CVPR 20240.890--
NACO [64]ECCV 20240.8950.7670.831
Ours-0.947(↑3.9%)0.843(↑3.9%)0.895(↑4.6%)
+ +dataset evaluation with image methods, Protocol-2: cross-manipulation evaluation on the FF++ data domain, and Protocol-3: cross-dataset evaluation with video methods. For Protocol-1 and Protocol-3, we evaluate the models by training them on FaceForensics++ (FF++) [43] and then + +Table 5. Ablation studies regarding the effectiveness of our proposed plug-and-play strategy (VB + StA). + +
Detector#ParamsTemporalCDF-v2DFDCAvg.
I3D-RGB [16]25M✓0.6250.6550.640
3D R50 [16]46M✓0.8240.7350.780
VTN [13]46M✓0.7340.6910.713
ViTrR [67]93M✓0.8690.7400.805
ViViT [53]310M✓0.895--
ISTVT [51]-✓0.6060.5510.579
ResNet-34 [18]21M×0.7420.6260.684
+ Ours21M✓0.8290.6660.748
ViT-b16-21k [10]84M×0.8340.7390.778
+ Ours22M✓0.8550.7720.814
CLIP-b16 [40]84M×0.8480.7410.795
+ Ours22M✓0.8660.7780.822
CLIP-114 [40]307M×0.9000.7980.854
+ Ours46M✓0.9470.8430.895
+ +testing them on seven other deepfake detection datasets. Note that $\mathrm{FF} + +$ has three different compression versions and we adopt the c23 version for training all methods in our experiments, following most existing works [56]. The evaluation datasets include Celeb-DF-v2 (CDF-v2) [26], DeepfakeDetection (DFD) [7], Deepfake Detection Challenge (DFDC) [9], the preview version of DFDC (DFDCP) [8], + +Table 6. Ablation studies regarding the effectiveness of StA and VB, separately. + +
StAVBCDF-v2WDF
AUCAcc.EERAUCAcc.EER
××0.9000.7390.1970.7940.5720.249
✓×0.9260.8120.1950.8420.6540.222
✓✓0.9470.8380.1760.8480.7020.212
+ +Table 7. Comparison of Fixed SBI and the proposed VB. + +
DetectorSpatialTemporalCDF-v2DFDCAvg.
Fixed SBI [16]✓×0.9020.8150.859
VB (proposed method)×✓0.9470.8430.895
Fixed SBI + VB✓✓0.9510.8460.899
+ +DeeperForensics (DFo) [21], WildDeepfake (WDF) [73], and FFIW [70]. For Protocol-2, we evaluate the models using the latest deepfake dataset DF40 [59], which contains diverse forgery data generated within the FF++ domain. By doing this, we can ensure that although the evaluation involves different forgeries, the data domain remains the same. + +# 4.2. Generalization Performance Evaluation + +Forgery methods in the real world can be highly diverse. Evaluating our model's performance in diverse scenarios is needed. We conduct both cross-dataset evaluations (Protocol-1 and Protocol-3) and cross-manipulation tasks, allowing us to determine whether the model can handle both previously unseen data domains and unseen fake methods. Results in Fig. 2, Fig. 3, and Fig. 4 show that our method generally outperforms other models on average, particularly on e4s, Inswap, and SimSwap methods (see Tab. 3). This demonstrates that our method learns more general features for detection, even for the latest techniques. + +# 4.3. Ablation Study + +Effectiveness of our plug-and-play strategy. To show the extensibility of our method, we apply it to various architectures, including ResNet-34 (CNN) and CLIP (ViT). Results in Tab. 5 indicate that our proposed method can imbue the original model with spatiotemporal modeling abilities. Our method also achieves better results with fewer training parameters, emphasizing the advantages of our design. + +Effectiveness of VB and StA. To evaluate the impact of the two proposed strategies (VB and StA) separately, we conduct ablation studies on CDF-v2 and WDF. The evaluated variants include the baseline CLIP-114 without any further modifications, the baseline with the proposed StA, and our overall framework $(\mathrm{StA} + \mathrm{VB})$ . The incremental + +Table 8. Ablation studies of the proposed cross-attention. + +
Fusion MethodCDF-v2DFDCWDFDFoAvg.
Linear combination (es^s + et^t)0.8860.7870.8050.9740.863
Cross-Attn (S2Torig + T2Sorig)0.9470.8430.8480.9910.905
+ +Table 9. Comparison with VideoMAE [51]. + +
MethodsBackbone.Train. Param.GFLOPsCDF-v2
VidMAEViT-B16871800.847
VidMAEViT-L143055970.830
OursViT-B16221040.866
OursViT-L14462780.947
+ +enhancement in the overall generalization performance with the addition of each strategy, as evidenced by the results in Tab. 6, underscores the effectiveness of these strategies. + +Image blending vs. video blending. Can image blending method, e.g., SBI, act as a "video augmentor"? We designed an ablation study to investigate the effectiveness of fixed SBI (without temporal inconsistency) and VB (without spatial artifacts) in video detection. Results in Table 7 show that SBI achieves lower results than VB, but the combination of both SBI and VB is more effective than VB alone. This suggests that SBI and VB could be complementary, with one focusing on spatial aspects and the other on temporal aspects. This finding may inspire future research on how to effectively utilize both techniques to improve generalization in video detection. + +Effectiveness of the proposed cross-attention module. By our experiments, we surprisingly found that the cross-attention module is significantly important in our StA architecture (see Tab. 8). This might indicate that the spatial and temporal information can be benefited to each other, potentially in a high-level manner (not linear). + +Evidence for the proposed spatiotemporal adapters can indeed learn spatial and temporal clues? To verify it with visualizations, we create a (boring) video by repeating a single image into a video sequence. We then pass the input to our spatial (S) and temporal (T) adapters (two pathways with different kernel sizes of 3D Convs). As expected, Fig. 4 shows that the outputs of S remain constant (same inputs), while the outputs of T are zero (no change in time). Plus, for a normal video as input, T_adapter can capture reasonable temporal-related motion, e.g., mouth movement. + +Comparison of different video-level blending solutions. To reproduce and simulate the FFD artifact, we propose a novel video-level blending data called VB. We also attempt to use other choices for implementation. In this subsection, we discuss the effectiveness of different video-level blending solutions for reproducing the FFD. Here, we discuss three potential solutions: (1) CBI (blend with other frames within one clip); (2) PFIG, the same method proposed in + +![](images/d33ccf41a5a14b41a38d789bfd48d38faa51e59854885d197e02f7822ec62804.jpg) +Boring video as input + +![](images/810d5e0db1a540f1752b545f0f5952258012a7a51f27138da99fb3eb8d074a89.jpg) +Normal video as input +Figure 4. GradCAM for demonstrating the attention regions of S- and T-Adapters. We create a "boring" video by repeating a single image into a video sequence. We show that the T-adapter can capture reasonable temporal-related motion like mouth movement, while the S-adapter's outputs remain constant due to the same input of the boring video. + +![](images/eed0038e6bf1f30323b083c2fd125003f02f13db315021050c7892900cd9fa98.jpg) +Figure 5. Comparison of different video-level blending strategies. We consider other two possible solutions to simulate the FFD: (1) CBI, which represents the face-hull blending of two frames with the same video clip; (2) PFIG [49], which represents the facial-region blending of the different videos. Our simulation method VB shows the most similar result to the original FFD in the fake data. Best viewed in color. + +[49] that performs the facial-region blending of two frames from different videos. First, we consider CBI, which performs the blending operation with another frame within the same clip. This method could introduce the inconsistent time shift of the facial region between frames. However, as we can see in Fig. 5, the inconsistency between frames is also too obvious, which does not align with the original fake (FFD). Second, we also consider PFIG [49], which performs blending between two frames (one real and one fake). PFIG randomly chooses one facial region of the fake and blends it into the real. Here, to simulate the FFD, we selectively choose a facial region from another frame within the same clip and blend it back into the real to generate the synthetic data. As we can see in Fig. 5, the blending region is mainly within a specific region (e.g., eyes), not aligned with the original fake. + +Comparison with video pre-trained models. We compare our architecture with other video pre-trained models like VideoMAE. However, their reliance on cross-frame attention across all frames can result in very high computational costs. Furthermore, previous work [53] demonstrates + +that naively training spatiotemporal models fails to achieve balanced learning of spatial and temporal artifacts. To address these, we propose a lightweight architecture using two parallel 3D Conv layers with adaptive kernels, one for spatial and the other for temporal. Tab. 9 empirically verifies our performance. + +# 5. Conclusion + +In this paper, we uncover a novel and previously underexplored temporal forgery artifact present across various manipulated videos, which we term Facial Feature Drift (FFD). To simulate this artifact, we propose a novel Video-level Blending data (VB), designed to aid the model in learning more general forgery artifacts within the temporal domain. We also propose an adapter-based strategy called (StA) for efficiently and effectively learning both the spatial and temporal forgery artifacts. Extensive experiments verify the effectiveness of the proposed methods. We hope that our work will inspire further research into (1) the development of video augmentations (also the approach to combine both image and video blending), and (2) efficient spatiotemporal adapter tuning in the deepfake video detection community. + +Acknowledgment. We thank all reviewers for their valuable and constructive comments. This work was supported in part by the Natural Science Foundation of China (No. 62202014, 62332002, 62425101). + +# References + +[1] Junyi Cao, Chao Ma, Taiping Yao, Shen Chen, Shouhong Ding, and Xiaokang Yang. End-to-end reconstruction-classification learning for face forgery detection. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4113-4122, 2022. +[2] Liang Chen, Yong Zhang, Yibing Song, Lingqiao Liu, and Jue Wang. Self-supervised learning of adversarial example: Towards good generalizations for deepfake detection. 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Given $n$ unposed input keyframes, the goal is to generate a video of the scene with a realistic camera trajectory and consistent geometry. From top to bottom: Ours, Luma Dream Machine [41] (a commercial video generation model), FILM [50] (a frame interpolation method). Luma hallucinates new buildings (left scene) and statues (right scene) without understanding the scene layout. FILM is unable to handle wide-baseline inputs and produces blurry transitions. See our supplement for video playback. + +![](images/c98ea4d9ce02f4f9dde0ff72ca93e96d3a7c05fa34836087fd88e00b847f0511.jpg) + +# Abstract + +We address the problem of generating videos from unposed internet photos. A handful of input images serve as keyframes, and our model interpolates between them to simulate a path moving between the cameras. Given random images, a model's ability to capture underlying geometry, recognize scene identity, and relate frames in terms of camera position and orientation reflects a fundamental understanding of 3D structure and scene layout. However, existing video models such as Luma Dream Machine fail at this task. We design a self-supervised method that takes advantage of the consistency of videos and variability of multiview internet photos to train a scalable, 3D-aware video model without any 3D annotations such as camera parameters. We validate that our method outperforms all baselines in terms of geometric and appearance consistency. We also show our + +model benefits applications that enable camera control, such as 3D Gaussian Splatting. Our results suggest that we can scale up scene-level 3D learning using only 2D data such as videos and multiview internet photos. + +# 1. Introduction + +Recent advances in video foundation models [6, 18, 24, 30, 82] learn rich spatio-temporal representations that capture the underlying structure and dynamics of the visual world. It is not surprising that these models contain strong 3D priors that can be used for a variety of downstream applications through finetuning, such as 3D object generation [10, 19] and novel view synthesis [17, 87]. + +In this paper, we further investigate the capabilities of video models to understand 3D structure of real-world scenes. To this end, we propose the task of generating videos from a + +handful (2-5) of unposed internet photos of the same scene. The generated frames should simulate a path moving between the locations of the cameras, from the first to the second, then from the second to the third, and so on. Given random images, a model's ability to capture underlying geometry, recognize scene identity, and relate frames in terms of camera position and orientation reflects a fundamental understanding of 3D structure and scene layout. + +Interestingly, we find that this task is challenging for existing video models. Even when scaled to a commercial level (e.g. Luma Dream Machine [41]), we find that these models often perform creative morphing effects rather than produce realistic camera motion. We show examples in Fig. 1. Frame interpolation methods such as FILM [12, 31, 50] are unable to handle wide baselines because they are generally trained on videos with very little camera motion, leading to blurry transitions. Luma Dream Machine generates high-resolution, sharp videos, but ignores the identity of the scene and creates new structures to fit the input keyframes. In the scene on the left (Sacre Coeur), for instance, Luma transforms the crowd and stairs into a new building. In the scene on the right (Lincoln Memorial Statue), it creates a second statue. + +Our main insight is that simply training for general video synthesis is not enough: we need to introduce scalable, 3D-aware objectives. Finetuning with camera poses is an option [39, 74], but collecting 3D annotations is costly [13, 65]. On the other hand, unstructured images and videos abound [1, 57]. + +Thus, we design two objectives. The first is multiview inpainting, which learns 3D priors without 3D annotations. The model takes a variable number of condition images, captured from random and wide-baseline viewpoints of a scene, and inpaints an $80\%$ masked target. Through this process, it learns to extract structural information and scene identity from the condition images, and the illumination and scene layout from the remaining $20\%$ of the target, in order to fill in the target image accurately. Multiview inpainting allows us to leverage the vast corpora of images, which, compared to existing video datasets, provides a greater variety of scenes, more diverse camera viewpoints, and is more accessible [65]. We train using internet photos to adapt to in-the-wild settings, but this objective can be trivially extended to other data sources, such as video, synthetic data, and self-driving datasets for further scaling. + +Our second objective is view interpolation, which takes the start and end frames of a video, and generates intermediate frames. It requires no annotations from the videos. + +We illustrate these two objectives in Fig. 2. These objectives are complementary in enabling our proposed task. Multiview inpainting addresses geometric understanding by training the model to extract 3D relationships from wide-baseline, unposed images. View interpolation addresses temporal coherence by training the model to generate smooth, + +consistent camera trajectories, which is our desired output. + +Finally, we unify these two objectives under the same diffusion denoising objective. We finetune from a video diffusion model, which adds noise to and denoises selected patches of images: the masked pixels in the multiview inpainting objective, and the intermediate frames in the view interpolation objective. This allows us to jointly train both objectives without additional strategies such as pretraining or distillation. As a result, our model can take noisy internet photos and produce consistent trajectories, even though it has never seen this input-output pairing during training. + +As shown in Fig. 1, our model produces a realistic camera path that captures the layout of the scene, even though the keyframes contain illumination variations and occlusions. For best viewing results, please visit our website, where we show side-by-side video playback for comparisons. Our approach and results suggest that multiview and video datasets can be complementary to each other even when disjoint. + +Following recent works that refer to input images that condition videos as "keyframes" [41, 70, 78, 83], and with the added challenge that our keyframes are internet photos, we refer to our approach as keyframe-conditioned video generation in-the-wild (KFC-W). In Sec. 4, we evaluate our method by 1) user studies that show it outperforms existing state-of-the-art video generation models; 2) downstream applications such as 3D reconstruction that validate its geometric and appearance consistency. + +To sum up, our contributions are as follows: + +1. We enable consistent video generation conditioned on wide-baseline, in-the-wild keyframes. +2. We propose a scalable self-supervised training scheme that takes advantage of both multiview and video datasets. The resulting model is 3D-aware without requiring 3D supervision such as camera poses. +3. We evaluate our method on multiple benchmarks and validate its geometric and appearance consistency. The generated videos can be converted into 3D models (e.g. 3DGS) for tasks requiring camera control. + +# 2. Related Work + +Reconstruction-based view synthesis. One way to synthesize videos is through 3D reconstruction and novel view synthesis, with NeRFs [44] and 3DGS [33] being popular methods from the past few years. However, even as follow-up work has improved rendering quality [3, 4, 67], speed [21, 45, 51], and has loosened the requirements on number of input views [14, 67, 72, 84] and poses [5, 11, 16, 27, 43], they are mostly confined to carefully curated captures. A smaller line of work extends these methods to in-the-wild setting [35, 37, 42, 62, 88] by optimizing from internet photos, but they require dense views, usually at least a few dozen, and preprocessing [56] to obtain camera parameters. Even then, the resulting methods lack the ability to fill in unseen + +![](images/583819b577fab10a2cd9c359ee216c2dec4c961d21aa13b9a2dbbf61cd81de08.jpg) +Figure 2. Training objectives. Left: Multiview inpainting. We provide $n$ condition images and one target image to a diffusion model. We add noise to $80\%$ of the target following the diffusion process. The condition images and remaining $20\%$ of the target are kept clean. Note how some regions in the target are not seen in the conditions. The model learns priors such as symmetry to generate a plausible image. Right: View interpolation. We take $k$ images from a video sequence and add noise to frame 2 to $k - 1$ following the diffusion process. The model generates a sequence following a plausible camera path connecting the first and last frames. + +![](images/9cecc61ee036d0a815689276977231a1f7f4468c03b786a3080f43f86b054073.jpg) + +viewpoints, leading to floaters and artifacts. + +More recently, starting from LRM [25], transformer-based [66] feed-forward methods [28, 68, 75, 80, 89] aim to perform view synthesis and even reconstruction through learned priors. However, these methods require accurate camera poses during training and testing, and are currently limited to the object-level [13] or high-quality video captures [92]. + +Generation-based view synthesis. Finetuning image foundation models [22, 53] to learn 3D geometry has also proven effective [39, 40, 73, 79, 93]. For example, 3DiM [73] and Zero-1-to-3 [39] fine-tune diffusion models to generate novel views conditioned on input views and poses, leveraging and enhancing geometric priors that come from large-scale pretraining. Follow-up work like ZeroNVS [8, 55, 58, 65, 85] generalizes to full scenes, but jittering, blurriness, and inconsistency across viewpoints are common in their outputs. A number of methods [17, 52, 64, 86, 87] generates image sets or videos to improve consistency, but 3D supervision is still required during training. This limits scalability since camera parameters for in-the-wild data are typically obtained through SfM [56, 60], which can be computationally expensive and unreliable for sparse views. + +Video generation and 3D learning. Video foundation models [2, 6, 7, 18, 23, 24, 30, 41, 59, 63, 82] have gained traction due to their potential for immersive storytelling. They also learn spatial and temporal priors useful for various downstream applications [9, 10, 17, 81, 87, 91]. For instance, VFusion3D [19] leverages the consistency in video models to generate 3D assets. 4DiM [74] jointly trains on video and 3D data for 4D reconstruction. In the same spirit, our work finetunes video foundation models with 3D-aware objectives and internet photos to scale up 3D learning in-the-wild. + +Relevant to our method is frame interpolation [12, 15, 26, 31, 41, 50, 70]. However, these models are trained on frames with little to no camera motion, but focus on moving objects. Later, we show these methods cannot handle wide-baseline views nor produce realistic camera motion. + +# 3. Method + +We first provide an overview of keyframe-conditioned video generation in-the-wild (KFC-W). The goal is to generate a sequence of consistent frames given a handful (2-5) of unposed internet photos. One core challenge is the absence of supervised training pairs, i.e., internet photos and clean videos from the same scene that we can use as ground truth to resemble our input-output during inference. Our approach is we instead take unpaired corpora of internet photos and videos, and jointly train two subtasks on each kind of data with the same model: multiview inpainting and view interpolation, shown in Fig. 2. + +For multiview inpainting, the only data annotation is that we take images from the same scene. Sources such as Wikipedia Commons provide millions of such multiview images with detailed indices and labels. Thus, we use MegaScenes [65], which contains 8M internet photos from 430k scenes labeled by Wikipedia Commons (we do not use any 3D supervision in the dataset). + +For view interpolation, we use RealEstate10k [92] and DL3DV [38]. Both datasets capture sequences of frames within a short time frame, without noticeable changes in illumination. They also do not contain dynamic objects, which are outside the scope of this paper. + +Both objectives are jointly trained on a latent Diffusion Transformer (DiT) [47, 53]. All images are passed through a pretrained VAE [34] encoder before further processing, including patchifying and adding noise based on diffusion processes. The image patches are then passed through the transformer. This process is shown in Fig. 3. + +Next, we explain our self-supervised approach (Sec. 3.1, 3.2) and inference and training details (Sec. 3.3, 3.4). + +# 3.1. Multiview Inpainting + +We develop a task that 1) learns 3D priors without 3D annotations, and 2) learns from unstructured image collections such as internet photos. + +The model takes a variable number of condition images, captured from random and wide-baseline viewpoints of a + +Figure 3. Multiview inpainting of internet photos and view interpolation of videos can be unified under the same denoising objective. Left: Training. We denoise the noisy patches (masked patches in multiview inpainting and intermediate frames in view interpolation), while extracting visual information from clean patches (blue patches) via self-attention. Then, we calculate a loss between the denoised (orange) and ground-truth patches. This process operates in latent space. +![](images/047237161fd0dde98bd42df3d9f4dc5b4b7486c01225d6507831cf8168aa2ced.jpg) +Right: Inference. Given unposed images of the same scene, we initialize and denoise a fixed number of frames via DDIM. + +![](images/641e9cbe038cc29d8570fe499d6a24ea6032c5a7860cd9874dc195f910a1dcee.jpg) + +scene, and inpaints an $80\%$ masked target. Through this process, it learns to extract structural information and scene identity from the condition images, and the illumination and scene layout from the remaining $20\%$ of the target, allowing the model to fill in the target image accurately. In the example in Fig. 2, the target image is taken from an angle rotated counter-clockwise, where some of the structure is not directly observed in the conditions. The model must understand priors such as symmetry to fill in the target. This is important for our final task, as input keyframes are sparse and the model must plausibly fill in content unseen in inputs. + +This approach is inspired by CroCo [76, 77], which observed that cross-view masked image modeling teaches strong 3D priors. Our implementation differs from CroCo in a few ways. CroCo only operates on two images (i.e. cross-view) because it creates a transformer decoder for each image, which becomes memory-heavy for multiple images. It obtains training pairs from in-the-wild images using camera poses and heuristics. It uses a deterministic MAE [20] objective which does not allow for probabilistic generation. In contrast, our method leverages self-attention for all images to take an arbitrary number of inputs, requires minimal annotations on data, and generates diverse outputs. + +We implement the patchify and masking operations in latent space [34, 53] since we use a latent DiT. To all patches of the same image, we add a frame index embedding (since transformers are order-agnostic). For three images, the frame index embeddings would be $(0,1,2)$ passed through a linear layer. The patches of the condition images and $20\%$ of the target are kept clean, while we apply the diffusion forward process to the remaining $80\%$ . We only calculate the loss between these $80\%$ of patches with ground truth. We also use + +a frozen semantic segmentation model on the RGB images to ignore transient objects such as people and vehicles; see our supplement for details. + +# 3.2. View Interpolation + +This task teaches the model to produce smooth, consistent frames given start and end condition images. + +From a video, we randomly sample $16 \times (n - 1) + 1$ sequential frames, where $n$ is the number of condition images and $2 \leq n \leq 5$ . Every 16th frame is a condition image; i.e. the first frame and 17th frame are condition images, and the 15 intermediate frames in between two conditions are targets that we add noise to using the forward diffusion process. To all patches of the same image, we add a frame index embedding. We simply pass the order of the images $(0, 1, 2, \dots, (n - 1) * 16)$ through a linear layer. We experimented with normalizing frame indices as well as learnable positional encodings, but found no difference. This simple objective alone teaches the model to interpolate between input images, though as we show in Sec. 4 as an ablation, it is not sufficient for wide-baseline and in-the-wild images. + +One important aspect of generating consistent in-the-wild videos is controlling illumination. During training, we condition every image on its own CLIP embedding [49]. We pass all images through a frozen CLIP encoder, and reshape the global feature map to the same shape as the image patches (recall these image patches come from encoding the RGB images through a VAE, then patchifying). Then, we simply perform addition before passing the patches into the transformer. We also experimented with modulation [48] but did not observe any differences. During inference, we condition all initialized noisy frames on a CLIP embedding of an + +image with a desired illumination. + +However, this alone does not force the model to use these embeddings, because the model can simply extract the illumination of the condition images, which, in videos, would be roughly the same as the targets'. Thus, we apply extreme color jittering to the condition images using PyTorch's ColorJitter transformation (details in supplement). The model must then extract illumination features from the CLIP embeddings to denoise the intermediate frames, since there is no other source that provides this information. Shown in Fig. 4, this mechanism allows us to specify a desired illumination during inference. In the top two rows, we randomly select one image (red-bordered), and condition all intermediate frames on its CLIP embedding. The output frames reflect the illumination of the red-bordered image, and remain consistent throughout the sequence. On the other hand, when we do not condition on CLIP embeddings (bottom row), generated frames do not maintain a consistent appearance. + +It is worth noting that CLIP embeddings likely only contain coarse information, since its training captions contain terms like "cloudy," "sunny," rather than physical properties such as sun angles. Thus, even though we show that this method is capable of controlling coarse illumination, such as the general color scale, there are many possibilities for future work for fine-grained control. + +Finally, we simulate segmentation by randomly masking regions of the condition images, since our input keyframes during inference will also be segmented for transient objects. See our supplement for details. + +# 3.3. Inference + +We show our inference pipeline on the right side of Fig. 3. It combines the two training objectives, with internet photos as input conditions (keyframes), and intermediate video frames as output. More formally, our input is a set of unposed images of the same scene $\mathbf{x} = \{x_1,\dots,x_n\}$ where $2\leq n\leq$ 5. Our model generates 15 frames in between each input pair $(x_{i},x_{i + 1})$ . We concatenate the frames into a video sequence $\mathbf{y} = \{y_1,y_2,\dots,y_k\}$ where $\{y_{1}\dots y_{15}\}$ represents a video path between $x_{1}$ and $x_{2}$ , and $k = 15\times (n - 1)$ . Thus, the order of the inputs affects the video sequence. To the inputs, we perform segmentation to ignore transient objects such as people and vehicles. To the intermediate frames, we condition them on a CLIP embedding. If not otherwise specified, we use the embedding of the first input. + +We run 50 DDIM [61] steps and decode only the intermediate frames. When showing generated videos, we do not include input keyframes as they may contain occlusions. + +# 3.4. Training Details + +We use a latent Diffusion Transformer (DiT) [47, 53]. When training on view interpolation we input sequences of 17, 33, 49, or 65 frames, corresponding to 2, 3, 4, and 5 keyframes, + +![](images/4e26b53b8143e4a009fa19abf352a9e33f54bed664d840a8b113f951748d6309.jpg) +Figure 4. Top two rows: We control illumination by conditioning on the CLIP embedding of the red-bordered image during inference. Bottom: Without this condition, illumination varies across frames. + +respectively. Our approach extends to longer videos or denser interpolated frames at the cost of compute (i.e., transformer sequence length). We chose 15 intermediate frames as a balance between compute and visual quality. + +An interesting observation is the model's ability to infer which task to perform based on the format of the input. We do not provide flags for context switching, but simply pass in a number of images corresponding to the objective. Intuitively, both objectives are sufficiently similar to the model, as condition images convey scene identity, and CLIP embeddings supply illumination information. The only difference is the output format and length which can be determined based on the frame indices. + +We finetune an internal pretrained text-to-video model, though our approach can be applied to any text-to-image or text-to-video model based on a transformer architecture. We inject our extra condition information - frame index embedding and CLIP embedding - by simply adding them to image patch tokens. Observations suggest that the specific model and checkpoint we use is comparable to state-of-the-art open-source video models such as CogVideoX-5B [82]. We train our model using MegaScenes, Re10k, and DL3DV on 32 NVIDIA A100 80G GPUs for 3 days. In the supplement, we provide details for reproducing our method. + +# 4. Experiments and Evaluation + +In the following experiments, we test on the Phototourism dataset [29] from the Image Matching Challenge, which contains images of 21 landmarks around the world collected from the internet, as well as the official test split of RealEstate10k (Re10k) [92]. + +From each scene in the Phototourism dataset, we randomly sample 3 sets each of 2, 3, 4, and 5 views, leading to 12 sets of sparse views per scene, and 252 sets in total. We call this our Phototourism test set. From the first 50 scenes from the Re10k test set, we randomly sample 3 sets each of 2, 3, 4, and 5 views, leading to 12 sets of sparse views per scene, and 600 sets in total. We call this our Re10k test set. + +We perform the following evaluations: + +1. We run video generation conditioned on the testing + +Table 1. User study results. For a given scene, users vote between ours and a baseline. Our method outperforms commercial models such as Luma on all three criteria. + +
vs.Win Rate of Ours (Full) on Phototourism
ConsistencyCamera MotionAesthetics
FLAVR [31]100.0%100.0%100.0%
LDMVFI [12]100.0%100.0%100.0%
FILM [50]100.0%100.0%100.0%
Ours (Video-Only)100%96.67%96.67%
Luma [41]60.21%73.63%60.21%
vs.Win Rate of Ours (Full) on Re10k
ConsistencyCamera MotionAesthetics
FLAVR [31]100.0%100.0%100.0%
LDMVFI [12]100.0%100.0%100.0%
FILM [50]99.50%81.00%99.50%
Ours (Video-Only)76.55%71.31%77.02%
Luma [41]83.65%84.86%68.27%
+ +images across multiple baselines, and conduct a user study that ask users to express a preference between pairs of results according to three separate criteria: "Consistency," "Camera path," and "Aesthetics." We show the user study interface and detailed descriptions of each criterion in Fig. 8. + +2. We validate the consistency of our generated frames in 3D geometry and appearance using two downstream applications. First, we run COLMAP [56] on the original sparse views, then include our generated frames. This experiment tests whether the generated frames are geometrically consistent with the original views and provide support for feature correspondences. Second, we optimize a 3D scene with 3D Gaussian Splatting (3DGS) [33] on the original sparse views, then on our generated frames. 3DGS minimizes a rendering-based reconstruction loss and requires input images be consistent in appearance. + +# 4.1. Video Interpolation and Generation + +Baselines. We compare to the following methods: FILM [50], FLAVR [31], LDMVFI [12], and Luma Dream Machine [41]. The first three are open-source frame interpolation methods, while Luma is a commercial video generation model and we use its paid Dream Machine API. We note that, to the best of our understanding, Luma is the only publicly accessible large-scale model that is capable of interpolating between wide-baseline views. Stable Video Diffusion [6], Pika Labs [36], Emu Video [18], and CogVideoX [82] do not support this feature. Runway's Gen-3 Alpha [54] supports "frame-interpolation," where input images must have little to no camera motion. We were not able to produce any reasonable results with it on our task. + +For methods that can only take two input images, we simply concatenate the videos from sequential keyframes. + +We also add an additional baseline: Ours (video-only). This is our method without the multiview inpainting training objective, trained solely on the view interpolation objective + +![](images/1481e4e0c171920f8c444bbcd8b8e1c427e84a844238a6004caa2c218ada4aae.jpg) +Figure 5. From top to bottom: Ours (Full), Luma, Ours (Video-only), FILM. Luma hallucinates new buildings (top scene) and produces jittering motions (bottom). Ours (Video-only) generates consistent videos on Re10k but not Phototourism. FILM is unable to handle wide-baseline inputs and produces blurry transitions. + +using DL3DV and Re10k, with all other training details kept identical. This ablation allows us to understand the effect of the multiview inpainting objective. It also serves as a comparison to a second large-scale video generation model (apart from Luma), though finetuning is necessary because our internal model was pretrained with text conditions only. We denote our full method Ours (Full). + +User study setup. For our study, we randomly sampled 25 scenes: 15 from the Phototourism dataset, and 10 from Re10k. Our method is compared to each baseline via pairwise comparisons. Users are shown two videos generated from the same input frames and are asked to select which method they prefer according to each evaluation criterion (or the user can select "Cannot Decide"). We show a visualization of the user study interface and detailed descriptions of each criterion in the supplement. When tallying the results, a direct vote counts as 1 point, and a "Cannot Decide" option counts as 0.5 votes each. For instance, two identical videos should both get 0.5 votes on each criterion, leading to a $50\%$ + +preference rate for that specific matchup. We calculate how often our method is preferred over each baseline, shown in Tab. 1, with results on the two datasets shown separately. + +Comparing to frame interpolation methods. For comparisons to frame interpolation baselines (FILM, FLAVR, LDMVFI), we collected responses from 10 users, with a total of 150 votes on the Phototourism test set, and 100 votes on the Re10k test set. + +As shown in Tab. 1, none of the baselines produce competitive video sequences on the Phototourism dataset. Their training data consists of small baselines or fixed cameras, and are trained to model dynamics rather than camera motion. On the Re10k dataset, only FILM can produce logical generated frames (and only when the camera motion is small), leading to a few "Cannot Decide" votes. See Fig. 5 (bottom scene is from Re10k) and our website for examples. + +Comparing to our ablated model and Luma. For comparisons to Ours (Video-only) and Luma, we collected responses from 42 users, with a total of 587 votes on the Phototourism test set, and 340 votes on the Re10k test set. + +Our video-only baseline (i.e., our model trained only with view interpolation) works well on the Re10k test set, as expected. Images from Re10k scenes are generally closer together, and the model has seen imagery from this domain during training. Many videos are nearly identical to Ours (Full), leading to a number of "Cannot Decide" ratings, although viewpoints with greater distances still led to flickering. On the other hand, this method cannot handle the wide-baselines and variability that appear in the Phototourism dataset, even though we used augmentation techniques such as color jittering and random masking during training. This demonstrates that introducing internet photos into training is crucial for dealing with in-the-wild scenes. + +For Luma, their Dream Machine API allows users to specify a prompt as well as a start and end keyframe. We set the prompt to "consistent illumination and smooth camera path" for all videos. Luma, as a commercial model, is sampled more densely and at a higher resolution, and trained on substantially more data on a larger model than ours. However, our method outperforms Luma on all metrics. Luma struggles in several ways on this task: there are noticeable illumination changes as Luma transitions from one source image to the next ("Consistency"). Luma also tends to hallucinate new buildings and structures ("Camera path"), shown in Fig. 1 and Fig. 5. This indicates that Luma does not understand the layout of the scene, and is instead generating morphing effects to match the condition images. We believe that Luma achieves a lower preference rate on "Aesthetics" due in part to these artifacts. In our own observations, Luma's frames can sometimes appear sharper, and dynamic objects such as people walking are modeled more realistically. This led Luma to be preferred for "Aesthetics" in many (but not most) comparisons. + +![](images/05f538072b0680bc85c5acb5d42e5517c16bf454f887ffbabf664029958c4c15.jpg) +Figure 6. We run an ablation "Long-Video" with only the view-interpolation objective, but trained on inputs with up to $5\mathrm{x}$ wider baselines. It fails to generalize to inputs with minimal overlap, while Ours (Full) still understands the scene layout. + +Table 2. Comparison of COLMAP reconstructions when run on original sets of sparse internet photos vs. adding in generated frames. Ours (Full) generates geometrically consistent images that provide feature correspondences. + +
COLMAP SfMSuccess RateRegistered Images
Only Internet Photos115/252378/882
+ Generated views (Full)235/252741/882
+ Generated views (Video-only)179/252589/882
+ +Surprisingly, Luma was rated as worse on Re10k scenes than on the Phototourism scenes, according to how often our method is preferred. Upon observation, we saw that its artifacts tend to be more noticeable in indoor scenes, marked by issues such as disappearing objects. Furthermore, Luma produces random jittering motions when the input viewpoints are very nearby, possibly to fill time. Please refer to our website for side-by-side comparisons of generated videos. + +These observations show our multiview inpainting objective teaches our model to be 3D-aware and understand depth and symmetry, leading to more realistic video sequences. + +Multiview inpainting improves general view interpolation. Since Ours (Video-only) works well on Re10k, we verify whether training only on videos, but with wide-baseline inputs, can replace multiview inpainting and internet photos. Thus, we run an ablation similar to Ours (Video-only), but with up to 5x wider baselines as conditions during training. Shown in Fig. 6, this model ("Long-Video") fails on inputs with minimal overlap, while Ours (Full) still understands the scene layout. This shows multiview inpainting combined with internet photos improves general view interpolation, not just on in-the-wild data. We argue that internet photos contain diverse viewpoints, such as extreme rotations and zooming, that cannot be easily learned from videos. + +Table 3. We run InstantSplat on sparse input images vs our generated frames and compare rendering metrics on 10 random images from each scene. Our method produces densely sampled frames while being consistent in illumination and geometry, leading to improved metrics. + +
MethodPhototourismRe10k
On Internet PhotosOn Generated FramesOn Original FramesOn Generated Frames
PSNR(↑)SSIM(↑)LPIPS(↓)PSNR(↑)SSIM(↑)LPIPS(↓)PSNR(↑)SSIM(↑)LPIPS(↓)PSNR(↑)SSIM(↑)LPIPS(↓)
InstantSplat11.7010.35100.570313.9600.41230.486419.8570.72690.266321.7980.79160.2190
+ +![](images/f47588da6e7edcac4620367cce792cf47d17b98f79426632d8e93e150ba36633.jpg) +Figure 7. We run InstantSplat [14] on original input views and on generated frames. The rendered results on generated frames exhibit fewer artifacts and sharper content. + +# 4.2. Application 1: SfM Reconstruction + +We validate whether our generated frames are consistent in geometry, and therefore suitable for downstream applications such as 3D reconstruction. We run COLMAP [56] on the original input views, then include our generated frames. COLMAP is unreliable on sparse views because when viewpoints are too far apart, COLMAP struggles to find sufficient matching features between pairs of images. As shown in Tab. 2, only $45\%$ of sets of sparse views are successfully reconstructed ("Only Internet Photos"). Of the 882 images total, $43\%$ were registered. On the other hand, COLMAP successfully reconstructed $93\%$ of sets of views when we included our video frames, which were generated from the same sets of sparse views ("+ Generated views (Full)"). Now, $84\%$ of the original frames could be registered, nearly doubling the amount. This shows our generated frames provide reliable feature correspondences that connect distant views. + +However, not all view interpolation methods achieve this effect. We also run this experiment by adding generated frames from the "Ours (Video-Only)" baseline, denoted "+" Generated views (Video-only). There was significantly less improvement: $71\%$ success rate and $67\%$ registered images. + +# 4.3. Application 2: 3D Gaussian Splatting + +We experiment with running 3D Gaussian Splitting (3DGS) on our generated frames. In contrast to COLMAP, which is + +robust to illumination changes, the input images for (vanilla) 3DGS must be consistent in appearance and illumination. To validate our method, we compare running 3DGS on original inputs vs. our generated frames (without the original inputs). We use InstantSplat [14], a 3DGS method that builds on COLMAP-Free-3DGS [16] and DUSt3R [69] to generate Gaussian Splats given sparse, unposed images. + +We show results in Tab. 3 and Fig. 7. "On Internet Photos" and "On Original Frames" refer to training each scene using the original sparse views in the test sets, while "On Generated Frames" refer to using our model's output when conditioned on those same sparse views. + +For each scene, we train with the default settings in the InstantSplat open-source code. Then, we sample 10 images not used for training from the scene, register their poses to the same coordinate frame, and render them using the trained model to report PSNR, SSIM [71], and LPIPS [90] metrics. We provide details in the supplement. + +Internet photos from the Phototourism dataset have wide baselines, significant occlusions, and varying illumination, which make it very difficult to train 3DGS methods based on a pixel-rendering loss. Our generated frames are denser and with more consistent illumination, leading to substantial improvements in reconstruction metrics. Even though the Re10K dataset has similar illumination conditions and smaller baselines across frames, we observe an improvement across all metrics as a result of training with denser frames. We provide rendered sequences on the website. + +Note that the metrics to the Phototourism dataset are much lower than those for Re10k because the testing ground-truth is also internet photos, which lead to high rendering losses (see the ground-truth column in Fig. 7). + +Through these applications, we show that video models trained with 3D-aware objectives can be useful as 3D priors for various downstream tasks. + +# 5. Future Work and Discussion + +Potential future work include scaling up data to model dynamic objects, enforcing a fine-grained constraint on illumination, and extrapolating to unseen views. We posit that brute-force scaling will not help video models understand the physical world. However, rather than incorporating conditions that can be difficult to estimate at scale, we jointly train a scalable 3D-aware objective. We suggest that this concept can be applied to other tasks as well, such as modeling motion that respects physical constraints [32]. + +# References + +[1] Sami Abu-El-Haija, Nisarg Kothari, Joonseok Lee, Apostol (Paul) Natsev, George Toderici, Balakrishnan Varadarajan, and Sudheendra Vijayanarasimhan. Youtube-8m: A large-scale video classification benchmark. 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This task aims to generate a sequence of 6DoF object poses from an action description and an initial state comprising the visual input and the object's initial pose. + +![](images/997a6e7d76861620834eb0fed5598a0cdc7029d74ce4b6eef7c672fd09c5e70c.jpg) + +![](images/14223d5eeed3ba88cbb28b0cbfe3316da598f7ac1611778db62e22969b9b6216.jpg) + +# Abstract + +Learning to use tools or objects in common scenes, particularly handling them in various ways as instructed, is a key challenge for developing interactive robots. Training models to generate such manipulation trajectories requires a large and diverse collection of detailed manipulation demonstrations for various objects, which is nearly unfeasible to gather at scale. In this paper, we propose a framework that leverages large-scale ego- and exo-centric video datasets — constructed globally with substantial effort — of Exo-Ego4D to extract diverse manipulation trajectories at scale. From these extracted trajectories with the associated textual action description, we develop trajectory generation models based on visual and point cloud-based language models. In the recently proposed egocentric vision-based in-a-quality trajectory dataset of HOT3D, we confirmed that our models successfully generate valid object trajectories, establishing a training dataset and baseline models for the novel task of generating 6DoF manipulation trajectories from action descriptions in egocentric vision. Our dataset and code: https://biscue5.github.io/egoscaler-project-page/. + +# 1. Introduction + +Use of tools and manipulation of objects at their will is an essential ability for developing robots that assist human activities. Especially having knowledge of manipulating numerous tools or objects in our work places and houses following the requests from humans is the next key technology for developing interactive robots that support us in daily scenes. One way to achieve this is to preliminarily learn various ways of manipulating objects from the human demonstration, as the recent robotic studies suggest that human demonstration acts as quite effective supervision for object manipulation trajectory generation [15, 24, 104]. However, this human demonstration-driven approach evokes the well-known limitation of data scarcity: the object manipulation trajectories from real human demonstrations are quite informative yet extremely limited and almost prohibitive for covering numerous objects we use in our daily lives. + +One promising solution for this is to make use of videos of daily working scenes for extracting human demonstrations of various object manipulations. Egocentric videos are becoming popular in virtual and augmented reality (VR/AR) [6] and even recording our daily life activities [21, 63] in both industry and research fields. For tracking human motions, HOT3D [3] provides quality 3D poses and models of hands and objects from precise lab recordings of human activity. Unfortunately, the precise record + +ing of human motion trajectories is still considerably costly, and hence such data is still limited for developing models that generate object manipulation trajectories whilst general purpose egocentric recordings are becoming available at scale as of the Ego4D [29] and Ego-Exo4D [30] datasets. Hereby, we assume extracting human motions for manipulating objects from egocentric vision datasets at scale is the key break-through for developing interactive robots. + +In this paper, we introduce a framework to extract an object manipulation trajectory, a sequence of 6DoF object positions and rotations, from egocentric videos. Our framework consists of the following: determination of temporal action span, extracting objects with the open-vocabulary segmentation model [74] and tracking them with the dense 3D point tracker [93], determining the camera coordinates, and obtaining the object rotation by the singular value decomposition from the translation between scenes. Applying this framework to egocentric videos from Ego-Exo4D [30], we construct EgoTraj with 28,497 object manipulation trajectories and corresponding action descriptions. Sec. 2.1 presents the dataset statistics from previous studies and ours. Our dataset emerges as the largest, containing 28,497 action descriptions and trajectories. While existing datasets such as H2O [46], EgoPAT3D [53], and HOT3D [3] rely on lab-recordings with multiple cameras or depth cameras, our dataset is extracted from ordinary egocentric videos with a single camera without pre-recorded camera coordinates or depth, and encompasses an entirely different order of magnitude in the variety of action verbs and objects from real-world scenarios. As our method does not rely on prerecorded camera coordinates, our method is applicable for most of egocentric video datasets, covering diverse object manipulations from egovision. + +With the extracted trajectories of EgoTraj, we develop a branch of models to generate object manipulations from the textual action description. The overview of the task, including extracted 6DoF object trajectory, is presented in Fig. 1. In experiments, we develop object manipulation trajectory generation models based on visual and point cloud-based language models with discretized trajectory tokens [9, 15, 44, 108]. Our experimental results on the HOT3D dataset demonstrate that our models successfully generate valid object manipulation trajectories. Furthermore, we conduct the experiments of generating action descriptions using our object trajectories, suggesting that utilizing trajectories enhances the generation performance, particularly for the similarity of verbs in the action descriptions. To the best of our knowledge, this is the first attempt to extract large-scale 6DoF object manipulation trajectories from egocentric videos without pre-recored camera coordinates and develop visual and point cloud-based language models for generating object manipulation trajectories from textual action descriptions. + +
Dataset#AD#Verb#Object#Trajectories
EgoPAT3D† [53]-261111,141
H2O† [46]-12813,653
HOT3D [3]9863033986
EgoTraj (Ours)28,4972284,15828,497
+ +Table 1. Dataset statistics from previous studies and ours. The "#AD" column denotes the number of action descriptions. "#Trajectories" of $\dagger$ is repored in [5]. Note that our dataset is constructed through a machine learning-based approach, while others are through precise annotations. + +# 2. Related Work + +# 2.1. Object Interaction Understanding + +Understanding object interaction involves two key factors of object affordance and manipulation motion. Koppula and Saxena [45] addressed human action anticipation by using object affordances to predict future motion trajectories. They demonstrated that understanding object affordance and predicting motion trajectories is beneficial for reactive robotic response. Subsequently, this field has been extensively explored in the contexts of object affordance learning [19] and object interaction prediction [29]. + +Object Affordance Learning. Object affordance learning aims to localize objects [14, 60, 77] or their specific parts [31, 48, 49, 61, 66] necessary for performing certain actions. This task has gained attention for applications in robotic manipulation [2, 40, 65]. However, most studies focus on grasping affordance, limiting various manipulation understandings. More recently, hand-object interaction generation [8, 11, 16, 98, 101] has been proposed, addressing both affordance learning and manipulation understanding in 3D space. This task builds upon richly annotated video datasets [46, 59] that include hand poses, object meshes, and scene point clouds. + +Object Interaction Prediction. Object interaction prediction includes various tasks such as interaction anticipation [25, 41, 57, 57, 64], next active object detection [7, 26, 45, 57, 71, 83, 96], and hand trajectory forecasting [58, 61, 62, 103]. These tasks have potential applications such as VR/AR [27], human-robot interaction [22, 81]. However, most studies addressed these tasks in 2D space, limiting their applications. To mitigate this limitation, recent work has extended these tasks into 3D space [5, 53]. For instance, Bao et al. [5] addressed 3D hand trajectory forecasting by proposing an uncertainty-aware state space transformer, extending conventional 2D trajectory forecasting task to 3D. Despite these advancements, addressing diverse manipulation motions remains challenging due to the high cost of annotations in 3D space. In contrast, our work proposes a framework to extract 6DoF object manipulation trajectories from egocentric videos, enabling the handling of diverse manipulation motions. From + +these extracted trajectories with the associated action descriptions, we address text-guided object manipulation trajectory generation. + +# 2.2. Egocentric Vision Dataset + +Egocentric videos encompass diverse object manipulation and hand activities, serving as potential resources for object interaction learning. A wide range of datasets and benchmarks have been proposed [17, 18, 29, 30, 51, 78]. For example, Ego-Exo4D [30] is a large-scale egocentric-exocentric dataset, providing rich multi-modal resources including gaze, point clouds, and texts. Based on these large-scale datasets, multiple detailed tasks have been developed [33, 58, 72, 75, 79, 85]. Additionally, several datasets have also been developed for specific purposes, including hand-object-interaction and VR tasks [3, 32, 46, 59, 90]. HOT3D [3] is an egocentric dataset for 3D hand and object tracking. Trajectories are captured using optical markers and OptiTrack cameras, resulting in precise hand poses and 6DoF object trajectories. While several other datasets [32, 46, 59] also provide similar hand and object poses, HOT3D covers a wider range of trajectories involving diverse objects and action scenarios. To this end, we utilize 6DoF object manipulation trajectories from HOT3D to validate model performance. + +# 2.3. Object Pose Estimation / Tracking + +Estimating object pose from visual sensors, termed object pose estimation, is a crucial topic for robotic perception [20]. Object pose tracking is an extended task of object pose estimation, aiming to efficiently track temporal object poses [52, 91]. Methods in both tasks often rely on objects' CAD models [35, 52, 69] or several reference images [34, 36, 80, 91]. Although pose estimation from visual input is similar to our task, we aim to understand and generate pose transformations during manipulation. Consequently, our task does not require any 3D object models or reference images of objects. + +# 2.4. Language Models for Visual / Robotic Tasks + +Recent advances in large auto-regressive models, such as large language models (LLMs) and vision-language models (VLMs), have established these models as powerful tools in computer vision [38, 50, 55, 56, 82, 95, 100, 107] and robotics [9, 44, 108]. For instance, PointLLM [94], a 3D-LLM for object point cloud understanding, has shown strong performance in 3D object captioning and has also demonstrated capability in scene-level point cloud understanding. Moreover, by embedding spatio-temporal information into language space, several studies have achieved comparable or superior performance to conventional approaches in image, video, and point cloud understanding benchmarks, such as object detection [12, 88], object track + +ing [87], temporal action localization [39], and 2D/3D visual grounding [88, 107]. Inspired by these studies, we develop trajectory generation models based on VLMs, formalizing our task as next token prediction task. + +# 3. Dataset Construction Framework + +We construct a large-scale training dataset containing 6DoF object manipulation trajectories along with images, depth maps, and action descriptions from an egocentric vision dataset of Ego-Exo4D [30]. Due to the cost and scalability, we propose an automated approach here. Note that our framework does not require any camera extrinsic parameters in advance. Additionally, we utilize precise 6DoF object manipulation trajectories extracted from HOT3D [3] dataset for the evaluation set. + +# 3.1. Training Data Creation + +As shown in Fig. 2, our pipeline consists of four stages. First, given an egocentric video, we determine the start and end timestamps of the action and identify the manipulated object within the scene. Second, we extract the position sequence of the manipulated object using an open-vocabulary segmentation model [74] and a dense 3D point tracker [93]. Third, we project the sequence into the camera coordinate system of the first frame using point cloud registration. Fourth, we extract a rotation sequence by computing the transformation between the two object point clouds using singular value decomposition. + +Temporal Action Localization. Based on the original annotated timestamps, we first split the raw egocentric video into multiple clips. Each clip spans a four-second interval centered on each timestamp. Next, we sample image frames within each clip and assign them sequential indices. We input these indexed frames along with the corresponding action description, originally annotated in Ego-Exo4D, into OpenAI GPT-4o [1] to determine the action's start and end timestamps: $t_{\mathrm{start}}$ and $t_{\mathrm{end}}$ . We denote the frames at $t_{\mathrm{start}}$ and $t_{\mathrm{end}}$ as $f_{\mathrm{start}}$ and $f_{\mathrm{end}}$ , respectively. Moreover, we use the model to extract the manipulated object name and determine whether the object is rigid or not. We filter out non-rigid objects as the transformation of the non-rigid objects is left for future work. We provide the system prompt in the Appendix. + +Position Sequence Extraction. We first use an open-vocabulary object segmentation model [74] to identify the manipulated object in the first frame $f_{\mathrm{start}}$ . This model takes $f_{\mathrm{start}}$ and the object name as inputs, and outputs a 2D segmentation map. Next, we employ an off-the-shelf monocular depth estimation model [97] and SpaTracker [93]. SpaTracker is a state-of-the-art dense point tracking model that tracks any 2D points in 3D space. Based on a sequence of frames between $t_{\mathrm{start}}$ and $t_{\mathrm{end}}$ , we obtain depth maps for + +![](images/4714baafe3d3ce5fb1399b44ce2d88b68809575981e2436813206308a4456090.jpg) +Figure 2. Trajectory extraction from egocentric videos. Four steps of (1) temporal action localization, (2) position sequence extraction, (3) trajectory projection, and (4) rotation sequence extraction. Our project page includes visualization of resulting trajectories with videos. + +each frame using a depth estimation model. For SpaTracker, we input the sequence of frames, the corresponding depth maps, and the segmentation map into the model. The model then outputs 3D tracking results of the segmented object. + +Trajectory Projection. Motions in egocentric videos can be separated into the object motions and the camera motions by the camera wearer. Due to the camera motions, tracking results are not aligned with the camera coordinate system of the start frame $f_{\mathrm{start}}$ . However, the camera motion between two consecutive frames can be assumed to be small and is represented by a projection matrix. To obtain the projection matrix between two consecutive frames, we use Depth Anything [97] to estimate depth, convert each RGB-D image frame into point clouds, and then apply point cloud registration to determine the projection matrix of the camera extrinsic parameters. We successfully obtain the sequence of the camera extrinsic parameters from each frame to $f_{\mathrm{start}}$ by multiplying these projection matrices. Recently, DUSt3R [89] can jointly perform camera pose estimation and point cloud construction, internally using point cloud registration of RoMa [10] and gradient-based optimization. However, we notice DUSt3R can squeeze detailed 3D motions of objects or hands in egocentric views, leaving this direction for future work. + +Each 2D image frame is first converted into a point cloud using an estimated depth map. Let $(i,j)$ denote the image pixel coordinates and $d_{ij}$ the corresponding depth, then + +$$ +\left[ \begin{array}{l} x \\ y \\ z \end{array} \right] = d _ {i j} K ^ {- 1} \left[ \begin{array}{l} i \\ j \\ 1 \end{array} \right], \tag {1} +$$ + +where $K$ is the camera's intrinsic parameters. Next, we compute the normals and Fast Point Feature Histograms (FPFH) [76] for each point cloud to perform registration. For initial alignment, we use RANSAC-based [23] feature matching between two point clouds using these FPFH features. We further refine the alignment using the colored it + +erative closest point algorithm [68]. With the above operations, we obtain camera extrinsic parameters for each frame. The 3D tracking results are then projected to the camera coordinate system of $f_{\mathrm{start}}$ by multiplying the coordinates at each timestep by the corresponding projection matrix. + +Rotation Sequence Extraction. As shown in Fig. 2, SpaTracker effectively handles self-occlusion, enabling the computation of temporal object pose transformations. Given the tracking result of the manipulated object, the object pose is computed using singular value decomposition (SVD). First, we set the initial pose of the manipulated object to an identity transformation: $[0,0,0]^T$ . We then compute the covariance matrix $H$ between the object point cloud at the initial timestamp and each subsequent timestamp. Applying singular value decomposition to $H$ gives $H = U\Sigma V^T$ . Finally, we compute the rotation matrix $R = VU^T$ , where $R \in \mathbb{R}^{3 \times 3}$ , and convert $R$ into a rotation vector $r \in \mathbb{R}^3$ . By concatenating the position and rotation sequences, we obtain the 6DoF object manipulation trajectory. Additionally, we calculate the minimum 3D bounding box from the object point cloud at the initial timestamp. + +# 3.2. Evaluation Data + +For evaluation, we utilize the existing 6DoF hand and object tracking dataset of HOT3D [3]. HOT3D is an egocentric view dataset for 3D hand and object tracking. The dataset is constructed using optical markers and multiple infrared OptiTrack cameras, yielding precise hand and object 6DoF information. The dataset is recorded with Project Aria glasses [21] and Quest 3 [63]. Unfortunately, the dataset does not include temporal action descriptions, resulting in a misalignment with our task setting. To mitigate this difference, we split the raw videos and determine the action start and end timestamps with action descriptions as described in Sec. 3.1. Additionally, we obtain depth maps using the depth estimation model and align the trajectories with the estimated depth maps for models that require depth or point + +![](images/5fb87aff03d491783116d05cd9ff46129b3d8c4eca4ee2cae51f71ac53bfd626.jpg) +Figure 3. Overview of model architecture. Our model architecture utilizes visual and point cloud-based language models as backbones and extends them by incorporating extended vocabularies for trajectory tokenization. + +clouds. Further details are provided in the Appendix. + +# 4. 6DoF Object Manipulation Generation + +Task Setting. Our task is to generate a sequence of 6DoF object poses for object manipulation, based on an action description and an initial state comprising a visual input and the initial pose of the object. Each pose in this sequence is defined by the position of the object's centroid and its rotation in 3D space. + +Model. Considering recent advancements in multi-modal language models [12, 39, 87, 88], we develop object manipulation trajectory generation models based on visual and point cloud-based language models (VLMs), formalizing our task as next token prediction task. This is achieved by incorporating an extended vocabulary for trajectory tokenization into the VLMs. An overview of the model architecture is depicted in Figure 3. + +Discretization of object poses. Inspired by robotic foundation models [9, 15, 44, 108], we discretize each continuous dimension into 256 bins. For each variable, we map the target variable to one of the 256 bins, where the bins are uniformly distributed within the bounds of each variable. Using this discretization, we obtain an $N \times 6$ array of discrete integers from a trajectory, where each point $(x,y,z,\mathrm{roll},\mathrm{pitch},\mathrm{yaw}) \in [0,255]^6$ . We reserve $N = 256$ special tokens as trajectory tokens. + +Backbones. As our framework is compatible with any vision-language models (VLMs), we employ several VLMs as the backbone architecture. + +- BLIP-2: BLIP-2 [50] is a VLM for image captioning and visual question answering. The model uses a pre-trained vision transformer from CLIP [73] and OPT + +(2.7B/6.7B) [102] as its language decoder. + +- VILA: VILA [54] is a state-of-the-art model for downstream vision-and-language tasks. It uses a similar architecture to BLIP-2 and is capable of reasoning over multiple images. +- PointLLM: PointLLM [94] is a 3D-LLM designed for 3D vision tasks, such as 3D question answering and 3D grounding. The model uses Point-BERT [99] from ULIP2 [95] as a colored point cloud encoder and LLaMA [84] with the Vicuna (7B/13B) [105] checkpoints as the language decoder. +- MiniGPT-3D: MiniGPT-3D [82] is a light-weight 3D-LLM for downstream 3D vision understanding tasks. This model uses a similar architecture to PointLLM and incorporates an extended Mixture of Experts [42, 43]. + +As existing VLMs do not utilize depth information, we extend BLIP-2 [50] and VILA [54] by incorporating an additional encoder for depth maps. To evaluate the effectiveness of depth information, we use a pre-trained image encoder as the depth encoder for each model. We concatenate the encoded depth features with image features and provide them as inputs to LLM. For the objective function, we employ cross-entropy loss across all backbone models. + +# 5. Experiments + +# 5.1. Experimental Setting + +Dataset. We apply our framework (Sec. 3.1) to EgoExo4D [30] dataset, resulting in collecting 28,497 samples. We split them into 27,788 training samples and 709 validation samples. Additionally, we use data extracted from HOT3D [3] as the test split, resulting in 986 test samples. We sample image frames at 20 fps from each video clip, resulting in the average extracted trajectory length of 33.17 frames. For model training and evaluation, trajectories longer than 20 frames are cropped to 20 frames in length due to the token sequence length limit, resulting in the average length being 15.39 frames. + +Baselines. We employ a traditional transformer architecture with a multi-layer perceptron head (Seq2Seq) that recursively predicts the next pose of trajectories [86, 106]. This architecture is often utilized for vehicle and pedestrian trajectory forecasting such as [28]. Further details are in the Appendix. We also apply a 3D hand trajectory forecasting model of USST [5]. USST is an uncertainty-aware state space Transformer model that utilizes the attention mechanism and aleatoric uncertainty. It generates future hand positions in 3D space from a past temporal sequence of the RGB frames and 3D hand positions. USST is different from our VLM-based models in several major points. First, our models use action descriptions while USST does not. Instead of action descriptions, USST depends on the past visual features. Second, USST can predict hand positions + +
ModelInput3DoF Training6DoF Training
3D pos.2D pos.3D pos.2D pos.3D rot.
ADEFDEADEFDEADEFDEADEFDEGD
Seq2Seq [86]Image0.2690.4750.2150.3720.3740.6250.3250.5280.559
BLIP-2 (2.7B) [50]Image0.2780.4640.2180.3460.2800.4650.2180.3440.545
BLIP-2 (6.7B) [50]Image0.2860.4870.2240.3650.2860.4750.2190.3490.543
VILA (3B) [54]Image0.5000.6620.4280.5460.4770.6190.3900.4890.826
VILA (8B) [54]Image0.3160.5120.2490.3880.2930.4780.2250.3470.545
Seq2Seq [86]Image + Depth0.3020.5410.2500.4380.3410.5580.2800.4520.590
BLIP-2 (2.7B) [50]Image + Depth0.2880.4810.2270.3630.2750.4580.2110.3320.543
BLIP-2 (6.7B) [50]Image + Depth0.2830.4770.2180.3510.2820.4690.2190.3450.542
VILA (3B) [54]Image + Depth0.3010.4920.2290.3550.2940.4800.2230.3440.541
VILA (8B) [54]Image + Depth0.2980.4940.2340.3680.3180.5130.2530.3910.563
MiniGPT-3D (2.7B) [82]Point cloud0.2990.4870.2360.3680.2810.4670.2180.3420.544
PointLLM (7B) [94]Point cloud0.2740.4590.2100.3280.2710.4580.2080.3270.541
+ +Table 2. Comparison of 3DoF and 6DoF object manipulation trajectory generation. The "Input" column indicates the visual modality input for each model. Lower values are preferable for all metrics. Best and secondary results are viewed in bold and underline. + +
Pre-trainedEgoTraj3D pos.2D pos.
ADEFDEADEFDE
USST [5]✓0.3190.4640.2250.315
USST [5]✓0.3030.4140.2430.310
USST [5]✓✓0.2540.4480.1860.307
+ +Table 3. Comparison with existing 3DoF trajectory forecasting methods. "Pre-trained" means the model is trained with densely recorded datasets of H2O [46] and EgoPAT3D [53]. + +considering the center of the hand but not rotations, while ours can predict both the positions and rotations of the objects. As USST is the hand position prediction model, we use object poses instead of hand poses for our task. + +Evaluation Metrics. We evaluate model performance using the following three metrics. + +- Average Displacement Error (ADE): ADE is the $l_{2}$ distance of points in each time step between the predicted and ground-truth trajectories. +- Final Displacement Error (FDE): FDE is the $l_{2}$ distance of the final points between the predicted and ground-truth trajectories. +- Geodesic Distance (GD): GD [92] is the angular difference between two rotation matrices as: + +$$ +d (R ^ {*}, R) = \arccos \left(\frac {t r (R ^ {*} {} ^ {T} R) - 1}{2}\right), +$$ + +where $R^{*}$ and $R$ denote the ground-truth and predicted 3D rotations, respectively. $tr$ denotes the trace of matrix. When generating trajectories, some VLM models can halt further generation when they predict a stop token. While this feature allows models to generate arbitrary lengths of trajectories that are not possible for the existing models as of USST [5], this causes a problem in the evaluation due to the varying trajectory length. Therefore, we apply padding or cutting up for the final pose of a generated trajectory to fit the length of the ground-truth for the evaluation. + +# 5.2. Results + +Tab. 2 presents the results of text-guided 3DoF and 6DoF object manipulation trajectory generation in HOT3D. VLM-based models outperform conventional Seq2Seq methods. Specifically, when comparing PointLLM to the Seq2Seq $(\pmb{v})$ model, PointLLM achieves a reduction of $0.103\mathrm{m}$ in ADE (3D). These results demonstrate the effectiveness of utilizing VLMs for object manipulation trajectory generation. + +Analysis of VLM-based models reveals two key insights. First, when comparing model performance across different visual modalities, the utilization of point clouds significantly contributes to performance improvement. Additionally, the use of depth maps in 2D-VLMs tends to result in better performance. These results suggest that incorporating spatial information such as depth and point clouds boosts model performance. Second, although general scaling laws suggest that larger LLMs achieve better performance, this trend does not consistently apply to trajectory prediction. For instance, BLIP-2 (2.7B) outperforms VILA (8B). These results suggest that improving model performance for our task requires not only increasing model size but also considering the specific characteristics of each LLM. + +Comparison with Existing Trajectory Set. Tab. 3 presents the performance of the USST models [5]. The USST model that is trained with our extracted trajectories from scratch performed on-par with the USST model that is pre-trained with densely recorded datasets [46, 53]. When we further fine-tuned the pre-trained USST model with our dataset, we observed the performance gain in many metrics, confirming the effectiveness of the automatically extracted trajectories. + +Probabilistic Sampling. There are possible multiple trajectories that match the given action description [13, 47]. It is difficult for existing models to generate multiple possible trajectories as USST does not rely on action descrip + +"Pick up the cellphone from the table with the right hand." + +![](images/667acfb42cf5c37a3775663b82f2e9843431c315edd94c8f7fe58ec64bfe6dad.jpg) + +![](images/e5cdac1d5ec5892ee2d0523795697158808bed7a639fdd3bd7ca672d49e055f0.jpg) + +![](images/a5ddbce9b62671aea0909c1a0e6c1da783e4309c4a5079154c2c8ee18832debc.jpg) + +![](images/4ead19c11812a6aa76bea86c8e6d405e7ba48d59c0f721c89e0e0d7bc1f40a77.jpg) + +"Stir the contents of the bowl with the wooden spoon using the right hand." + +![](images/9cb8c316813d82e1686c779e5e7f1945298a437a7937cd8d1e8870e3edca4ec1.jpg) + +![](images/4eb71dcaffb0b0d6671c74fd5edd9b3c35f7b737194d7a700dc325e98780a58f.jpg) + +![](images/7900af40342f4aaf79f3254bce6c51b4a1855e3c869c99586e773d6b968a9b43.jpg) + +![](images/6c290477caf78e97bf9903b4ea34e40a6320835abaca965e098e53f8170c1faa.jpg) + +"Pick up the bamboo plate from the table with both hands." + +![](images/959872eebf5f47d7b3a209a290ee012a68b45055c6d387a3a0b632d5b85736d7.jpg) +Initial state + +![](images/6a7334d33eec9b70f477b920e2a542d77aff3491db600c31b79114dddf6ca391.jpg) + +![](images/667cf5523d646788833d281a96ac25cf02348a9760ade7f2e8afd853e6b78da9.jpg) + +![](images/5a3e37f585a04762a75becd34c64c5f7c94ad0cea752e64f93a328f6a05b8a0e.jpg) + +
Sampling3D pos.2D pos.3D rot.
ADEFDEADEFDEGD
10.2710.4580.2080.3270.541
30.2360.4010.1780.2800.543
100.2120.3630.1580.2520.540
+ +Table 4. Performance comparison in probabilistic sampling for PointLLM [94]. "Sampling" column indicates the number of samples generated. + +tions. Fortunately, our model uses the language modeling approach that allows generating multiple different trajectories using nucleus sampling [37]. We employ PointLLM as it demonstrated the best performance among the baselines for this purpose. For each instance, we report the lowest ADE (3D) score from the sampled trajectories. Tab. 4 shows that increasing the number of samples improves model performance. These results imply that our model successfully generates multiple trajectory candidates to perform the given action descriptions. Meanwhile, the performance improvement for GD is smaller than other positional metrics, indicating the difficulty in generating accurate rotational movements. + +Data Scalability. As our framework automatically generates manipulation trajectories, we investigate the impact of dataset scale on model performance. We utilized training data at ratios of 1.0, 0.5, 0.1, 0.05, and 0.01 of the full dataset to assess performance across different dataset scales. Fig. 5 presents the performance comparison under varying dataset scales. We use PointLLM for this purpose + +![](images/af9e5c1dce20df1e81559d6705f2c807dc731cf7f6179c2b6495486fea85a1eb.jpg) +Figure 4. Qualitative results of PointLLM [94]. Generated trajectories are illustrated using 3D bounding boxes for visualization. + +![](images/a78d1291db4bc7577698065f17c1bcf131169680ad21b57910fb1f94fb51e16e.jpg) +Figure 5. Comparison of performance across different dataset scales for PointLLM [94]. + +as it achieved the highest performance in Tab. 2. The results, especially in ADE and FDE, indicate that model performance improves as the dataset size increases, demonstrating the effectiveness of our dataset creation framework. + +Qualitative Results. Fig. 4 illustrates the generated trajectories of PointLLM along with the changes of the 6DoF object pose from the initial pose. It is interesting that regardless of the difference of the objects in HOT3D from those in the Ego-Exo4D videos, our method successfully generates understandable object manipulation trajectories depending on action descriptions and their verbs. For example, the case in the middle row is with the verb "stir" and it yields a different trajectory from other examples. + +Action Description Change. We survey the impact of the action descriptions on the generation of trajectories, as it is highly expected that the generated trajectories are modified depending on the action descriptions. Fig. 6 presents two generated trajectories from the trained PointLLM, confirming two different movements depending on the action de + +![](images/b865bcad5654510611fd6fc506bb4a175d8c750c0460b690521b0e3a3b3c6530.jpg) +"Transfer the wooden spoon to the wooden plate with the right hand." + +![](images/40d9f2523730ab6cfdb761ebadebe55dd500f5844183880c1766036090239f5a.jpg) +"Stir the bowl with the wooden spoon in the right hand." +Figure 6. PointLLM [94] results with different action descriptions. The generations are visualized with 3D bounding boxes. + +
TrajectorySimvMETEORBLEU-4
BLIP-2 [50]✓58.5923.7611.93
67.5824.1912.48
PointLLM [94]✓43.0517.423.25
53.3317.564.44
+ +Table 5. Effect of trajectory information on image and 3D captioning performance The "Trajectory" column indicates whether trajectory information is utilized by the model $(\checkmark)$ . Higher values indicate better performance across all metrics. + +scriptions: the wooden spoon is pulled away from the plate in the top row while it stays on the bowl and is being shaken on the bottom row. Further visualizations including demonstration videos in our project page. + +# 5.3. Action Description Generation + +Finally, we conduct experiments of generating action descriptions with BLIP-2 and PointLLM. Indeed, current VLMs are so effective that they can learn to generate at firstlook plausible action descriptions from solely 2D image 3D scenery inputs. Therefore, we test two conditions of with and without trajectories. In addition to the standard metrics of METEOR [4] and BLEU-4 [67] for action description evaluation, we also report the similarity of the verbs between the generated and annotated trajectories, $\mathrm{Sim}_v$ , because they reflect the differences in the actions by camera wearers in egovision. $\mathrm{Sim}_v$ is computed as the cosine similarity of word embeddings [70]. Tab. 5 shows the results from BLIP-2 [50] and PointLLM [94]. The results indi + +![](images/ea1e611483f6a36942e1609646899182fa3cdabf358415e9210c9a9fa5793f4b.jpg) +Ground-Truth: +Pick up the dumbbell 5lb with the right hand. +BLIP-2 w/ trajectory: +Pick the cucumber from the table with her right hand. +BLIP-2 w/o trajectory: +Place the green apple container on the table with her right hand. + +![](images/0071acfe3d30b8fd601b3c7e31604ebc47630ca1cd42fcf3d6965240b084ae0e.jpg) +Ground-Truth: +Pick up the potato masher with the right hand. +PointLLM w/ trajectory: +Pick a measuring spoon from the countertop with his right hand +PointLLM w/o trajectory: +Turn the cucumber in her right hand with her right hand. +Figure 7. Qualitative results in image and 3D captioning task. The top and bottom figures depict generated captions of BLIP-2 [50] and PointLLM [94], respectively. "w/ and "w/o" indicate whether models utilize trajectory information. + +cate that utilizing trajectories boosts performance, particularly verb similarity, by nearly $10\%$ in both image and 3D captioning, confirming the effectiveness of our framework for extracting accurate manipulation trajectories that reflect human motion. Fig. 7 illustrates the qualitative results of image and 3D captioning, indicating that object motion trajectories enhance verb similarity in both models. + +# 6. Conclusion + +We developed a scalable framework to extract 6DoF object manipulation trajectories from egocentric videos. Using these trajectories, we created generation models for object manipulation trajectories based on visual and point cloud-based language models. Our experimental results on HOT3D dataset demonstrate that our models learn to generate object trajectories from action descriptions, providing fair baseline models for the new task. Moreover, utilizing trajectories for visual captioning tasks reveals that our dataset creation framework successfully extracts meaningful trajectories from egocentric videos. For future work, we construct a massive-scale dataset by adapting the proposed approach to other egocentric video datasets and investigate its effectiveness in robotic manipulation. + +Limitations. The current framework has two limitations. First, because our framework defines an object pose as a 6DoF bounding box, it cannot be applied to deformable objects such as clothes. Second, we observed failure cases in our dataset due to object segmentation and point-cloud registration. Segmentation can fail when similar objects are present, while registration can fail when camera pose changes abruptly. 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An overview of our proposed driving scene generation paradigm - UMGen. Starting from a random initialization (a) UMGen generates ego-centric, multimodal scenes frame-by-frame. Each scene encompasses four modalities: ego-vehicle action, map, traffic agent, and image; (b) UMGen offers multiple functions. It can autonomously generate multimodal scene sequences based solely on its own historical context, but also predict other modalities based on input ego-vehicle actions provided by users. Furthermore, UMGen can incorporate user-specified agent actions to create customized scene sequences. In three scene sequences, arranged from top to bottom, we demonstrate the ego vehicle autonomously driving straight through an intersection, executing a user-defined right turn, and encountering scenes where a user-specified white car cuts in front of it. For better visualization, a portion of the map in the last row is zoomed in. + +# Scene Imagination + +![](images/2088a81ef2bd8d274a219f42ce683a471ca2ca396aaec1c7a66269ada7e80b9c.jpg) + +![](images/c22a2385fac0d29d804a3800ea40a384139ff77a85a3f7fe3524633c981a8a19.jpg) +Interactive Ego-vehicle Control + +![](images/6b5adf718ba964981e75edd0264d3fdce10151a68ef15846f3cc44a6941d8dee.jpg) +User-Specified Scenes Generation +(b) Infer four modalities w/o or with conditions on user inputs + +![](images/d0abc198f1e84766aeeab2265b9135296e6c65ba3f9362b2ce5babd765c072e7.jpg) +Each modality is evolved by UMGen +Ego-vehicle is controlled to turn right + +![](images/bfc37aaf637239330bcb498b794ecf72fd20d4d8008f7b37e9f334979f0c4416.jpg) + +![](images/825bc662664fcf8e5d213509fce807de12d9fe7d69dffc687610303a6e50c256.jpg) +A white car is controlled to cut in + +![](images/0022e8d018126aea4590dead64203c302ebd16fb3e2e25e2f744ffe65420bd73.jpg) + +# Abstract + +Generative models in Autonomous Driving (AD) enable diverse scenario creation, yet existing methods fall short by only capturing a limited range of modalities, restricting the capability of generating controllable scenes for comprehensive evaluation of AD systems. In this paper, we in + +troduce a multimodal generation framework that incorporates four major data modalities, including a novel addition of the map modality. With tokenized modalities, our scene sequence generation framework autoregressively predicts each scene while managing computational demands through a two-stage approach. The Temporal AutoRegressive (TAR) component captures inter-frame dynamics for + +each modality, while the Ordered AutoRegressive (OAR) component aligns modalities within each scene by sequentially predicting tokens in a fixed order. To maintain coherence between map and ego-action modalities, we introduce the Action-aware Map Alignment (AMA) module, which applies a transformation based on the ego-action to maintain coherence between these two modalities. Our framework effectively generates complex, realistic driving scenes over extended sequences, ensuring multimodal consistency and offering fine-grained control over scene elements. Project page: https://yanhaowu.github.io/UMGen. + +# 1. Introduction + +Generative models are becoming increasingly essential across various domains [1, 12, 13, 21]. In Autonomous Driving (AD) systems, generative models are utilized for producing diverse driving scenes—particularly those that are rare or not well-represented in datasets [6, 28, 31] or real-life. More importantly, generative models can be used to build a closed-loop simulation system that generates realistic interactive scenes to test AD systems without causing potential accidents before deployment [29, 30]. Such capabilities enhance the safety, adaptability, and reliability of autonomous driving [8, 14, 24, 27] systems when dealing with the complexities of real-world driving conditions. + +To generate comprehensive driving scenes, as described in Tab. 1, most existing studies [7, 9] focus primarily on generating two modalities. For instance, GUMP [9] and TrafficGen [5] generate ego-action and agent motion within a given static map segment; DriveDreamer [28] and GAIA-1 [7] are capable of generating images given initial conditions. While these approaches offer valuable insights, they face some limitations. The lack of map progression in GUMP and TrafficGen limits their realism, as real-world driving scenes involve dynamically evolving maps from the ego-vehicle's viewpoint. DriveDreamer and GAIA-1 fail to forecast traffic agent motion, which limits control over agent behaviors and, consequently, constrains the generation of user-specific scenes. + +In this work, we propose a Unified Multimodal driving scene Generation framework (UMGen) for driving scenes, each containing four key modalities. Our framework integrates map prediction to enhance scene representation, enabling finer control over ego-action and agent behaviors. Generating these modalities scene-by-scene while ensuring consistency presents a significant challenge. To address the diverse domains of each modality, we frame scene generation as a sequence scene prediction task. However, directly applying an AutoRegressive (AR) model is impractical due to the high token count from the four modalities and the length of the video data. To address this, we decompose the + +
MethodsModalities
Ego-actionMapAgentImage
Drivendreamer [28]✓XX✓
TrafficGen [5]✓X✓X
GAIA-1 [7]✓XX✓
GUMP [9]✓X✓X
UMGen (Ours)✓✓✓✓
+ +Table 1. Comparison of different driving scene generation methods across four modalities. + +sequence prediction task into two stages: inter-frame prediction and intra-frame prediction. For inter-frame prediction, we propose the Temporal AutoRegressive (TAR) module, which models temporal evolution across frames using causal attention, allowing each token to be influenced only by its past states. For intra-scene prediction, we introduce the Ordered AutoRegressive (OAR) module, which captures relationships within each scene by enforcing a structured modality order, ensuring alignment and coherence across modalities. Together, TAR and OAR effectively capture cross-modal dependencies over time, enhancing alignment while reducing computational complexity. To further maintain consistency between ego-action and map data, we introduce an Action-aware Map Alignment (AMA) module. AMA applies an affine transformation, based on predicted ego-action, to prior map features, aligning them with the ego-vehicle's movement. This re-alignment preserves coherence between ego-action and map modalities. + +With these components, our model demonstrates strong capabilities in multimodal driving scene generation, as shown in Fig. 1, producing scene sequences that can span up to 60 seconds in duration. Additionally, thanks to the modality alignment capability provided by the AMA and OAR modules, our model can create specific multimodal-consistent scenes, like a cut-in situation, by controlling ego-vehicle and agents' actions. + +In summary, UMGen offers several key contributions: + +- We introduce a novel generative framework that integrates four distinct modalities—ego-action, road users, traffic maps, and images—with the flexibility to incorporate additional modalities, enhancing the scene representation and fidelity of driving scene generation. +- We design a computationally efficient AR approach, comprising TAR and OAR modules, to capture both interframe and intra-frame dependencies, enabling realistic scene generation with reduced computational costs. +- We introduce an AMA module to apply affine transformations to map features with the ego-vehicle's movement, ensuring consistency between ego-action and map. + +Our experimental results provide both quantitative and qualitative evidence of our method's effectiveness, showing that UMGen enables user-defined, ego-centric scenario generation adaptable to specific driving conditions. + +![](images/22fda16793fd544f7e9f9681a31f8e2ff612517fabaf30cc5f0978a1adb6ce33.jpg) +Figure 2. Pipeline of our UMGen. Given $T$ past frames of multimodal driving scenes, including ego-action, map, traffic agents, and image in each scene, each modality is tokenized into discrete tokens. The token embeddings are then processed through the Ego-action Prediction module, which forecasts the ego-action for $T + 1$ time step. Using this predicted ego-action, the AMA module adjusts the map features. Next, the TAR module aggregates temporal information across sequences, while the OAR module ensures sequential modality prediction within each frame by autoregressively generating each token conditioned on the aggregated history information. Finally, the predicted tokens are fed to the decoder to obtain the next scene. + +# 2. Related Work + +Autoregressive generative models. In recent years, AR generative models have achieved significant success in natural language processing and image generation, as evidenced by models such as GPT-2 [20] and VQGAN [3]. This architecture has since been adapted for autonomous driving scene generation, with methods like [19, 23, 32] leveraging it to predict agent behaviors, and GAIA-1 [7] applying it to generate high-quality driving videos sequentially. Our model, however, extends beyond generating limited-modality data by targeting the generation of multimodal data that collectively compose driving scenes. This extension results in a substantial increase in token count, especially as the number of scene frames grows, making the vanilla AR [7] approach—where tokens from different scene frames are concatenated into a single sequence—computationally prohibitive. Additionally, applying the AR mechanism solely along the temporal dimension—without incorporating an intra-frame AR mechanism—may lead to inconsistencies across modalities within the same frame [23, 32]. By contrast, our method consists of parallel inter-frame temporal prediction with intra-frame AR decoding which balances efficiency and consistency to enable multimodal driving scene generation. + +Driving scene sequence generation. Traditional methods rely on hand-crafted rules [2, 11, 14, 15] to generate driving scenes, limiting their ability to capture the diversity and realism of the real world. Recently, data-driven + +deep learning approaches have gained traction, but most focus on generating a limited set of modalities. For example, models like [10, 16, 26, 32] generate diverse agent trajectories based on map segments but fail to handle the emergence and disappearance of agents. GUMP [9] addresses this challenge through a GPT-like [20] generative framework. However, the lack of map generation confines trajectories to specific map segments with static perspectives, which differs from the real world, where vehicles are observed from the dynamic viewpoint of the ego-vehicle. While DriveDreamer2 [31] addresses this limitation by generating maps, it employs two separate networks for map and video generation, resulting in the loss of explicit per-frame control. Other models [6, 7, 17, 28], like Dreamforge, produce videos based on predefined traffic dynamics, which restricts interactivity and user-defined scene generation. In contrast, UMGen generates four essential modalities—ego-action, map, agent, and image—enriching scene representation within a unified framework and providing finer control over user-specific scene sequence generation. + +# 3. Method + +# 3.1. Problem Setup + +Our method generates multimodal driving scenes in an autoregressive scene-by-scene manner, starting from either a provided or self-generated initial scene sequence. To achieve this, we tokenize each scene element into sequential tokens, transforming the generation process into a scene token prediction task. These elements include the ego- + +vehicle's action, a traffic map, other scene agents, and the camera image. Specifically, the ego-vehicle action $\mathbf{a}_t^{AV}$ represents displacements along the $x$ and $y$ axes, as well as angular changes relative to the previous timestamp. The traffic map $\mathbf{m}_t$ depicts road layouts and situational details surrounding the ego vehicle, while the $N_{a}$ agents $\{\mathbf{a}_t^{(i)}\}_{i=1}^{N_a}$ represent each agent's coordinates, size, velocity, heading and category. This combination of data provides a comprehensive view of the scene's dynamic and static elements. Finally, the camera image $\mathbf{v}_t$ adds visual context. Thus, the multimodal scene at time $t$ is defined as $s_t = \{\mathbf{a}_t^{AV}, \mathbf{m}_t, \{\mathbf{a}_t^{(i)}\}_{i=1}^{N_a}, \mathbf{v}_t\}$ . Therefore, our task is to learn a neural network to generate the next scene $s_{t+1}$ , conditioned on $s_{1:t}$ . + +# 3.2. Framework + +Throughout the following formulation, we assume the availability of the past $T$ scenes as inputs to predict the scene at the $T + 1$ timestep. The pipeline of our model is demonstrated in Fig. 2, which comprises several core components: Tokenization, an Ego-action prediction module, an Action-aware Map Alignment (AMA) module, a Temporal AutoRegressive (TAR) module, and an Ordered Autoregressive (OAR) module. We discuss each component below. + +Tokenization. The ego-action and agent attributes are tokenized through discretization, whereas the raster map and image data are tokenized using pretrained VQ-GAN models [3]. Discrete tokens from modalities are arranged in a fixed sequence within each frame: ego-action, map, agent, and image. This sequence reflects the causal flow: the ego vehicle's actions modify the observable traffic map and influence the behavior of surrounding agents. These interactions are ultimately captured in the camera view. Using this order and the tokenizer functions, we obtain the ordered token at $t$ -th scene as follows: + +$$ +\mathbf {z} _ {t} = g \left(s _ {t}\right) = \left[ \mathbf {z} _ {t} ^ {\text {e g o}}, \mathbf {z} _ {t} ^ {\text {m a p}}, \mathbf {z} _ {t} ^ {\text {a g e n t}}, \mathbf {z} _ {t} ^ {\text {i m a g e}} \right], \tag {1} +$$ + +where $\mathbf{z}_t \in \mathbb{N}^N$ , $N$ denotes the total number of tokens obtained by concatenating tokens from all modalities and $g$ represents the tokenizer function. Unlike vanilla AR approaches [7] that concatenate tokens from multiple frames into a single sequence, we maintain tokens in a structured per-frame format. Consequently, the tokenized scene sequence across $T$ time steps is organized as: $\mathbf{Z} = [\mathbf{z}_1, \mathbf{z}_2, \dots, \mathbf{z}_T]$ , $\mathbf{Z} \in \mathbb{N}^{T \times N}$ , where tokens of each frame retain their intra-frame order. This structured token arrangement enables parallel aggregation of temporal information, forming the basis for subsequent modules. To ensure a fixed token count per frame, we apply padding or jointly sample agents across $T$ frames, preserving a consistent set of objects across all frames for temporal coherence. + +Token Embedding. Each token is embedded into latent features through learnable token embedding codebooks. All embeddings are then summed with a learnable positional + +embedding and projected to a unified dimension using a Multi-Layer Perceptron (MLP) head: + +$$ +\mathbf {e} _ {t} ^ {i} = \operatorname {M L P} \left(E m b e d \left(\mathbf {z} _ {t} ^ {i}\right) + P E (i)\right), \mathbf {e} _ {t} ^ {i} \in \mathbb {R} ^ {D} \tag {2} +$$ + +where $i$ is the position index in the token sequence of $\mathbf{z}_{\mathrm{t}}$ , $PE$ is the learnable position embedding and $Embed$ is the learnable token embedding. Thus, the token sequence representing an entire scene can be expressed as: + +$$ +\begin{array}{l} \mathbf {e} _ {t} = \underbrace {\left[ \mathbf {e} _ {t} ^ {1} , \dots , \mathbf {e} _ {t} ^ {n _ {e g o}} \right.} _ {\mathbf {e} _ {t} ^ {e g o}}, \underbrace {\left. \mathbf {e} _ {t} ^ {n _ {e g o} + 1} , \dots , \mathbf {e} _ {t} ^ {n _ {m}} \right.}, \tag {3} \\ \underbrace {\mathbf {e} _ {t} ^ {n _ {m} + 1} , \ldots , \mathbf {e} _ {t} ^ {n _ {a}}} _ {\{\mathbf {e} _ {t} ^ {a g e n t} \}}, \underbrace {\mathbf {e} _ {t} ^ {n _ {a} + 1} , \ldots , \mathbf {e} _ {t} ^ {n _ {v}}} _ {\mathbf {e} _ {t} ^ {i m g}} ], \\ \end{array} +$$ + +where $\mathbf{e}_t\in \mathbb{R}^{N\times D}$ , and the indices $n_{ego}$ , $n_m$ , $n_a$ , and $n_v$ correspond to the cumulative token counts for each modality. The terms $\mathbf{e}_t^{ego}$ , $\mathbf{e}_t^{map}$ , $\mathbf{e}_t^{agent}$ , and $\mathbf{e}_t^{img}$ represent the tokens derived from each modality at time step $t$ . More details about tokenization and token embedding can be found in the supplementary material section B. + +Ego-action Prediction. We first predict the next ego-action $\mathbf{e}_{T + 1}^{ego}$ , using it as a prior for generating the remaining modalities. Historical ego actions are aggregated via a cross-attention mechanism to capture the ego vehicle's intentions, which is then integrated with the current environment state $\mathbf{E}_T = \left[\mathbf{e}_T^{map},\mathbf{e}_T^{agent},\mathbf{e}_T^{img}\right]$ through another cross-attention mechanism: + +$$ +\begin{array}{l} \mathbf {u} _ {T} = C A _ {\text {h i s t}} \left(\mathbf {Q} = \mathbf {q}, \mathbf {K} = \left\{\mathbf {e} _ {1: T} ^ {e g o} \right\}, \mathbf {V} = \left\{\mathbf {e} _ {1: T} ^ {e g o} \right\}\right), \\ \mathbf {e} _ {T + 1} ^ {e g o} = C A _ {\text {e n v}} \left(\mathbf {Q} = \mathbf {u} _ {T}, \mathbf {K} = \left\{\mathbf {E} _ {T} \right\}, \mathbf {V} = \left\{\mathbf {E} _ {T} \right\}\right), \tag {4} \\ \end{array} +$$ + +where $\mathbf{q}$ represents the query tokens, and $CA_{\mathrm{hist}}$ and $CA_{\mathrm{env}}$ denote the two cross-attention blocks. This module serves as a basic planning component. + +Action-aware Map Alignment (AMA). The AMA module is motivated by the continuity of map features across adjacent frames: adjusting current map features based on the ego-vehicle's displacement offers a strong prior for the next timestep. As a result, we first rearrange the map feature vector $\mathbf{e}_T^{map}$ to obtain a spatial map representation, denoted as $\mathbf{F}_T = \Gamma (\mathbf{e}^{map})$ , where $\Gamma :\mathbb{R}^{N_m\times D}\to$ $\mathbb{R}^{H\times W\times D}$ . Here, $N_{m}$ refers to the number of tokens representing the map, and $H$ and $W$ denote the height and width of the resulting spatial map, respectively. An affine transformation, parameterized by $\theta$ , $dx$ , and $dy$ (derived from $\mathbf{e}_{T + 1}^{AV}$ ), generates a sampling grid $\mathbf{G}$ that maps coordinates from the original map representation $\mathbf{F}_T$ to the transformed locations. For each point $(x,y)$ in $\mathbf{F}_T$ , the transformed coordinates $(x^{\prime},y^{\prime})$ are given by: + +$$ +\left[ \begin{array}{l} x ^ {\prime} \\ y ^ {\prime} \end{array} \right] = \mathbf {G} (x, y) = \left[ \begin{array}{c c} \cos \theta & - \sin \theta \\ \sin \theta & \cos \theta \end{array} \right] \left[ \begin{array}{l} x \\ y \end{array} \right] + \left[ \begin{array}{l} d x \\ d y \end{array} \right]. \tag {5} +$$ + +Using the sampling grid $\mathbf{G}(x,y)$ , we interpolate $\mathbf{F}_T$ , producing the transformed map representation $\bar{\mathbf{F}}_T \in$ + +$\mathbb{R}^{H\times W\times D}$ that represents the transformed map features. Finally, we flatten the representation $\bar{\mathbf{F}}_T$ and add it with $\mathbf{e}_T^{map}$ to yield transformed map representation $\bar{\mathbf{e}}_T^{map}$ : + +$$ +\bar {\mathbf {e}} _ {T} ^ {m a p} = \operatorname {F l a t t e n} (\bar {\mathbf {F}} _ {T}) + \mathbf {e} _ {T} ^ {m a p}. \tag {6} +$$ + +Inter-frame Temporal Autoregression (TAR). With the predicted ego-action and transformed map features, the scene state is updated as $\bar{\mathbf{e}}_T = [\mathbf{e}_{T + 1}^{ego},\bar{\mathbf{e}}_T^{map},\mathbf{e}_T^{agent},\mathbf{e}_T^{img}]$ . For previous frames, we similarly obtain the ego-action and apply the AMA module to map features, resulting in $\bar{\mathbf{e}}_{1:T}\in \mathbb{R}^{T\times N\times D}$ . A causal self-attention (CSA) block is applied to $\bar{\mathbf{e}}_{1:T}$ , where each token attends only to tokens at the same position across previous scenes: + +$$ +\bar {\mathbf {e}} _ {T + 1} ^ {i} = \operatorname {C S A} \left(\bar {\mathbf {e}} _ {1} ^ {i}, \bar {\mathbf {e}} _ {2} ^ {i}, \dots , \bar {\mathbf {e}} _ {T} ^ {i}\right), \bar {\mathbf {e}} _ {T + 1} ^ {i} \in \mathbb {R} ^ {D}. \tag {7} +$$ + +Where $i$ denotes the token's position. This design captures temporal dependencies efficiently by processing tokens in parallel, thereby avoiding the computational costs associated with performing attention mechanism on the long sequence generated by token concatenation [7]. Subsequently, a bidirectional self-attention (SA) block facilitates information exchange between tokens within the same scene, yielding a coarse prediction $\mathbf{h}_{T + 1}$ for the next scene: + +$$ +\mathbf {h} _ {T + 1} = \mathrm {S A} \left(\bar {\mathbf {e}} _ {T + 1} ^ {1}, \dots , \bar {\mathbf {e}} _ {T + 1} ^ {N}\right), \mathbf {h} _ {T + 1} \in \mathbb {R} ^ {N \times D}. \tag {8} +$$ + +Intra-frame Ordered Autoregression (OAR). The OAR module leverages TAR predictions as temporal priors to enhance inter-frame continuity while maintaining intra-frame consistency through GPT-like autoregressive decoding. To predict the $i$ th token embedding $\mathbf{o}_{T + 1}^{i}$ , the OAR combines the previous token embedding $\mathbf{o}_{T + 1}^{1:i - 1}$ with the TAR-derived feature $\mathbf{h}_{T + 1}$ , incorporating temporal priors at each prediction step. The OAR then applies a causal self-attention block to sequentially predict each token embedding $\mathbf{o}_{T + 1}^{i}$ . Following this, a projection head is applied to $\mathbf{o}_{T + 1}^{i}$ , generating a probability vector $\mathbf{p}_{T + 1}^{(OAR,i)}\in \mathbb{R}^K$ , where $K$ represents the codebook size: + +$$ +\begin{array}{l} w _ {j} = \mathbf {o} _ {T + 1} ^ {j} + \mathbf {h} _ {T + 1} ^ {j + 1}, \quad j = 1, \dots , i - 1, (9) \\ \mathbf {o} _ {T + 1} ^ {i} = \operatorname {C S A} \left(w _ {1}, w _ {2}, \dots , w _ {i - 1}\right), (10) \\ \mathbf {p} _ {T + 1} ^ {(O A R, i)} = \operatorname {S o f t m a x} \left(\operatorname {M L P} \left(\mathbf {o} _ {T + 1} ^ {i}\right)\right). (11) \\ \end{array} +$$ + +A Top- $\mathbf{k}$ sampling strategy [20] is then used on $\mathbf{p}_{T+1}^{(OAR,i)}$ to select token $\mathbf{z}_{T+1}^i$ , which is transformed into embedding for the next prediction. This autoregressive structure aligns tokens contextually, preventing conflicts and enhancing modality coherence. + +Loss functions. Additional to the OAR predicted token probability $\mathbf{p}_{T + 1}^{OAR}$ , we also apply a projection head to $\mathbf{h}_{T + 1}$ to obtain $\mathbf{p}_{T + 1}^{TAR}$ . We then apply cross-entropy loss functions to calculate the total loss: + +$$ +\mathbf {p} _ {T + 1} ^ {(T A R)} = \operatorname {S o f t m a x} \left(\mathrm {M L P} \left(\mathbf {h} _ {T + 1}\right)\right), \tag {12} +$$ + +$$ +\mathcal {L} _ {\text {t o t a l}} = C E \left(\mathbf {p} _ {T + 1} ^ {O A R}, \mathbf {z} _ {T + 1}\right) + C E \left(\mathbf {p} _ {T + 1} ^ {T A R}, \mathbf {z} _ {T + 1}\right), \tag {13} +$$ + +where $CE$ represents the cross-entropy loss function. + +# 4. Experiments + +Our experiments evaluate the effectiveness of UMGen in both multimodal driving scene sequence generation and user-guided specific scene sequence generation. We also demonstrate that our model can generate realistic initial scenes, serving as the starting point for sequence generation. Finally, we conduct ablation studies to confirm the critical role of each module. + +# 4.1. Experimental Settings + +Training details. We randomly select a 21-frame sequence at each iteration, allowing the model to leverage up to 20 past frames. The training process is conducted over 300 epochs on 32 RTX4090 GPUs for two days. + +Evaluation details. Our experiments leverage two public datasets: nuPlan [2] and the Waymo Open Motion Dataset (WOMD) [4]. We assess the realism of the generated initial scenes using Maximum Mean Discrepancy (MMD) [5, 16, 26] scores, following the experimental setup in TrafficGen [5] on both nuPlan and WOMD datasets. The MMD metric quantifies the distributional divergence between the generated and ground-truth agent attributes. When generating initial scenes, we temporarily discard the TAR module since there is no temporal information needed. We present visualizations of the generated multimodal driving scene sequences based on the provided initial frames from nuPlan, verifying both the generation of diverse multimodal scenes and user-specified scene segments. For assessing the computational efficiency of the TAR module relative to the vanilla AR approach, we measure the per-token inference time and peak GPU memory usage during inference. To verify the efficacy of the OAR module in maintaining token consistency, we use both the MMD metric and the average collision rate (CR) among generated road users. Lower CR values indicate reduced conflicts between tokens, demonstrating better consistency. Further training and evaluation details are provided in the Appendix. + +# 4.2. Driving Scene Sequence Generation + +Unlike other methods that rely on supplementary conditions and generate limited modalities [6, 9, 28], our model is capable of generating diverse multimodal scene sequences from only given initial frames. To demonstrate the dynamic evolution of our multimodal scenes, as well as the temporal and multimodal consistency of the generated scenes, we present two video samples at different time intervals. + +As shown in the first row of Fig 3, we display the generated scenes at 15-second intervals, showing how all modalities evolve as the ego-vehicle moves. Specifically, the ego vehicle performs maneuvers such as lane changes, turns, and straight driving. The map modality generates a variety of road elements, including intersections, curves, and straight paths according to the ego vehicle's movement. The + +![](images/5c3f6d71c4e7d28e5c97a858e5b02a24d7cb1598401b98ba458cf638706c06f1.jpg) +Figure 3. Generated multimodal driving scenes by UMGen: The generated scenes evolve continuously from the ego vehicle's perspective. Red Box: ego-vehicle, Green Box: cars, Orange Box: pedestrians or cyclists, Arrow: agent velocities. + +number of agents decreases from numerous at the beginning to fewer on narrower roads. Furthermore, the image modality presents the corresponding visualization that reflects these dynamics. This capability of on-the-fly multimodal generation allows our approach to simulate a broader spectrum of driving worlds. The second row of Fig 3 shows 2-second intervals of the ego vehicle passing a hotel entrance. Dashed boxes are used to mark the same car across these frames, showing that its position and movement on the map remain consistent with those in the generated images. This multimodal consistency and temporal continuity provide a solid foundation for generating specified multimodal scenes in the subsequent sections. + +# 4.3. Initial Scene Generation + +The ability to generate realistic initial scenes is paramount for facilitating the generation of driving scene sequences. To evaluate the generated initial scenes, we follow the experimental setting of TrafficGen [5] and evaluate the MMD score on the WOMD [4] and nuPlan [2]. As shown in Table 2 and Table 3, our UMGen achieved lower MMD values compared to other approaches, indicating that it generates more realistic scenes. + +# 4.4. User-Guided Scene Sequence Generation + +The ability to generate interactive scene sequences that replicate real-world conditions, along with control over the ego vehicle's movements within these scenes, is essential + +
MethodPositionHeadingSizeVelocity
TrafficGen[5]0.14510.13250.09260.1733
LCTGen[26]0.13190.14180.10920.1938
SceneGen[25]0.13620.13070.11900.1772
UniGen[16]0.12080.11040.08150.1591
Ours0.07300.05500.05330.1502
+ +Table 2. MMD results on Waymo Open Motion Dataset + +
MethodPositionHeadingSizeVelocity
TrafficGen*0.09260.07990.08560.0988
Ours0.08280.06820.06740.0760
+ +Table 3. MMD results on nuPlan. $\star$ Results reproduced by us under the same experimental setting + +for validating AD systems. This section, therefore, focuses on user-guided scene generation, highlighting our model's flexibility in adapting to diverse ego-vehicle controls and simulating various traffic interactions. + +Interactive ego-vehicle control. To illustrate the model's ability to control ego-vehicle actions, we present visualization from two distinct generated scene sequences. As shown in the first row of Fig.4, we actively control the ego-vehicle to execute either a left turn or a right turn. The map undergoes corresponding rotations and transformations based on the ego vehicle's actions, while the image modality provides a visualization of these changes. Notably, although the scene observed after the right turn does not exist in the dataset, our model generates a corresponding multi + +![](images/2e03af44d92b344c5ebcd759ad7cbcf5d807a596f1d28eb79378cb8aa6613b3f.jpg) +Turn left +Gradual stop + +![](images/755f63a7f1e1279e3f21c1dee96bf43cb6e9447a550b10257568df09c0c698ec.jpg) +Figure 4. Generated scenes with input ego actions. The first row shows the interactive control of the ego vehicle to perform left and right turns. The second row shows the ego vehicle, initialized with a right-turn velocity or a gradual deceleration to a stop. Red box: ego-vehicle, green box: vehicle, orange box: pedestrians or cyclists, arrow: agent velocity. + +![](images/4081d83ac218e1ca6a9179223757764451f64361834bd02940b4c17dbf0db174.jpg) +Turn right + +![](images/f5c371da652743727ec72135375b352a2179548bafb9d80efd4ec83d45151c0e.jpg) +Lane change + +modal scene. In another scene (second row), instead of following the dataset's "gradual stop" action (left), we assign the ego vehicle a one-frame right-turn velocity. The model autonomously executes maneuvers of lane change and overtaking (right), showcasing its ability to interpret intention, predict maneuvers, and update modalities. Leveraging multimodal generation, we observe the ego vehicle avoids collision with the car ahead despite close proximity—an insight that would be challenging to achieve with models restricted to image-only predictions. + +User-specified agent control. UMGen also provides flexible control over other road users, enabling the generation of specific scenes. Moreover, it can simultaneously simulate how these controls impact the behavior of other road users. For example, in the scene shown in Fig.5, we simulate a sudden cut-in maneuver by assigning a forward-left velocity to the agent marked by yellow dashed boxes. In response, the ego-vehicle executes emergency braking (the velocity arrow quickly turns shorter), as shown in the second row, with a trailing agent (highlighted with white dashed boxes) also decelerating in reaction to the ego-vehicle's braking. Compared to the ego's spontaneous braking action, we can also simultaneously control the ego-vehicle to perform a lane change to avoid the collision, as shown in the third row. This shows the flexible controllability of our model. Notably, such agent control through speed settings and realistic interaction simulation are two key features that simplify the creation of specific scenes. Speed control offers a human-like way to adjust agent behavior, + +
MethodCR(%)MMD
PosiSizeHeadVel
UMGen-T5.60.0400.0430.0410.049
UMGen5.10.0380.0370.0400.036
+ +Table 4. MMD and collision rate results. UMGen-T represents UMGen without OAR module. CR: averaged agent collision rates. Vel: Velocity. + +while interaction simulation enables agents to respond dynamically to each other. Without these capabilities, generating such situations would require manual calculations of agent positions and interactions between road users. + +# 4.5. Ablation study + +In this section, we analyze each component of UMGen. + +Effectiveness of TAR. Our TAR module applies causal self-attention exclusively to tokens at the same position across historical frames, reducing the time complexity from $O((TN)^2)$ in the vanilla AR model to $O(T^2)$ for modeling temporal dependencies, where $T$ is the number of frames and $N$ is the number of tokens per frame. This design enhances computational efficiency and significantly reduces GPU memory usage. We conducted comparative experiments to validate these benefits using the vanilla AR model and UMGen, monitoring peak GPU memory usage and per-token inference time. As shown in Fig. 6, UMGen maintains stable performance, in contrast to the vanilla AR model, whose GPU memory consumption and inference time increase sharply with the addition of frames, highlighting the challenges of long-horizon scene generation. + +![](images/60e8cc0a814b378f524df0855bcbefd4a70f8894f947fba982a766a5a1327cd9.jpg) +Figure 5. Customized scenario generation by UMGen: The first row presents the original scene from the dataset. We assign a forward-left velocity to the vehicle highlighted by the yellow dashed line box and the ego-vehicle spontaneously takes a braking action (second row). Alternatively, we can actively control the ego-vehicle to perform a lane change (third row). Red box: ego-vehicle, green box: vehicle, arrow: agent velocity. + +![](images/9a48da37187137c1e7d670d618ba6ffa971844aba51a65172e9d1d6433e8205c.jpg) +Figure 6. Comparison of peak GPU memory usage and per-token inference time for the vanilla AR model and our UMGen. + +![](images/28346e362843a7e0c7983ff4de046230f1594fce8ae49766f3c56a37e33cc5ab.jpg) + +Decoding without OAR. Our OAR module autoregressively decodes tokens within a frame aiming to prevent inconsistency between tokens. To analyze the impact of this component, we created a variant of UMGen by removing the OAR module, directly decoding from the TAR output. This modified version, referred to as UMGen-T, was evaluated by generating scene sequences based on the initial frames provided by the nuPlan validation set. Performance was measured using the average collision rates between agents and MMD scores on generated scene sequences. As shown in Table 4, UMGen-T exhibits higher MMD values, indicating that its generated scenarios appear less realistic. More importantly, the elevated agent collision rates suggest that UMGen-T struggles to effectively capture intra-frame + +![](images/38a85da3c22a94002f28b0ff65a22c32b0466398700af4dac6f4c1608133cf81.jpg) +Figure 7. Map predictions with and without the AMA module. The bar below illustrates the ego vehicle's velocity over time. + +token relationships, resulting in more frequent conflicts. + +Improved coherence by AMA module. Given the role of the AMA module in maintaining map consistency relative to the ego vehicle's movement, we conducted experiments to assess its impact. We trained an alternative model without this module. As illustrated in Figure 7, we apply a forward-right velocity to the ego-vehicle while it was traveling along a straight road. With the AMA module enabled, the map adjusts accurately to reflect the ego-vehicle's actions. In contrast, without the AMA module, the map reveals a lack of responsiveness. This experiment underscores the importance of the AMA module in enhancing coherence between ego actions and map modalities. + +# 5. Conclusion and Discussion + +Conclusion. We have presented UMGen, a generative framework that enhances multimodal driving scene generation by integrating ego-action, road users, traffic maps, and images. Addressing existing limitations, UMGen formulates scene generation as a sequence prediction task, utilizing Temporal AutoRegressive (TAR) and Ordered AutoRegressive (OAR) modules to achieve temporal coherence and cross-modal alignment with reduced computational costs. Additionally, we introduce an Action-aware Map Alignment (AMA) module to ensure consistency between ego-action and map data by dynamically aligning map features with the ego-vehicle's movement. Experimental results have demonstrated the effectiveness of UMGen in generating diverse and realistic scenarios. In addition, it has been experimentally validated that UMGen can generate user-specified scenarios by controlling both the ego vehicle and other vehicles. This further highlights its potential as an interactive closed-loop simulator for AD systems. + +Discussion. Building on this, to further improve the quality of the generated images, one promising approach is to incorporate generated multimodal scenes as conditions for a diffusion model [18, 22]. Results demonstrating this approach are provided in the Appendix. + +# References + +[1] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. 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Behaviorgpt: Smart agent simulation for autonomous driving with next-patch prediction. arXiv preprint arXiv:2405.17372, 2024. 3 \ No newline at end of file diff --git a/CVPR/2025/Generating Multimodal Driving Scenes via Next-Scene Prediction/images.zip b/CVPR/2025/Generating Multimodal Driving Scenes via Next-Scene Prediction/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..feb2505c9d1c29029a4ecd8bb77cea3d009100f5 --- /dev/null +++ b/CVPR/2025/Generating Multimodal Driving Scenes via Next-Scene Prediction/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:3ac0a81a8bbff869c712075606eaffc804e7b93856fb1cca61931dac188a6b53 +size 791395 diff --git a/CVPR/2025/Generating Multimodal Driving Scenes via Next-Scene Prediction/layout.json b/CVPR/2025/Generating Multimodal Driving Scenes via Next-Scene Prediction/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..ef2694fc0e2fa51755c71e44ab7a3f42fd09ec46 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0000000000000000000000000000000000000000..b65c0e7aa245f4d208959569520f0034eddd0aca --- /dev/null +++ b/CVPR/2025/Generative Densification_ Learning to Densify Gaussians for High-Fidelity Generalizable 3D Reconstruction/full.md @@ -0,0 +1,340 @@ +# Generative Densification: Learning to Denseify Gaussians for High-Fidelity Generalizable 3D Reconstruction + +Seungtae Nam $^{1*}$ Xiangyu Sun $^{2*}$ Gyeongjin Kang $^{2}$ Younggeun Lee $^{2}$ Seungjun Oh $^{2}$ Eunbyung Park $^{1\dagger}$ $^{1}$ Yonsei University $^{2}$ Sungkyunkwan University + +https://stnamjef.github.io/GenerativeDensification/ + +![](images/122e65478ebb79a9e9c3c827c44311de1e9c3fbb15cd15fb3c608be47e7b862f.jpg) +(a) Coarse Gaussians + +![](images/287269827caab2ab19864ed0a01e76912f359d27d5be5467eccc47e412702ece.jpg) +(b) Remaining + +![](images/45b53628267017abd078c4f68ec959e10c7c5a00d23a1b0c59ebd9e418d7f110.jpg) +(c) Densified + +![](images/80a5e3409c1dd2897f6d2effb13bba63638a8a1ea69e3178fe0fa46748904cc2.jpg) +(d) Layer1 Output + +![](images/8ffab3e0215f0283ec8623f2b53127dd755cbd8a6d87f775ff66cfb35b966569.jpg) +(e) Layer2 Output + +![](images/8d2a59c0c7c64a6d79c54dd3b1173e618df48dddea28137e5592d353a6f19bb5.jpg) +(f) Union of Outputs + +![](images/e9006aa24cd4953c96592ac1b45280979288c8a4392d41c8d36ffb3ae3224ec5.jpg) +(g) Fine Gaussians + +![](images/7b150dbfee56e4effbbce8daf42f508e206e066c5eb314afa0d74749f136fcf4.jpg) +Figure 1. Our method selectively densifies (a) coarse Gaussians from generalized feed-forward models. (c) The top $K$ Gaussians with large view-space positional gradients are selected, and (d-e) their fine Gaussians are generated in each densification layer. (g) The final Gaussians are obtained by combining (b) the remaining (non-selected) Gaussians with (f) the union of each layer's output Gaussians. + +![](images/3b026985bc932afaf8378b613fc335dc1b0c548f7e47e2b8bb6bacb31aae8022.jpg) + +![](images/fadbc8707d809288a3b3b3a5f093605c118577d6d739eacc6c5e5078efbcdd32.jpg) + +![](images/2714742066eec2cbd6fccf2c6b3a9413e6c8c0879a2ed3e903172fc5f8762c55.jpg) + +![](images/5c2d0a97f6b03bccd2b6eb17ffdf9eb6f1c6a5add60966a8da891f0bb88178ec.jpg) + +![](images/ac2ecbf9f6ee4cba83799a55a4ba9b45fd748591d8f687950f6f3f84f65c7ea4.jpg) + +![](images/9b134bb01a21506664d1c867225790520ce409484b1d92fab5c8c754f5048666.jpg) + +# Abstract + +Generalized feed-forward Gaussian models have made significant strides in sparse-view 3D reconstruction by leveraging prior knowledge from large multi-view datasets. However, these models often struggle to represent high-frequency details primarily due to the limited number of Gaussians. While the densification strategy from per-scene 3D Gaussian splatting can be adapted for feed-forward models, it typically requires tens of thousands of optimization steps to reconstruct fine details and can easily lead to overfitting in sparse-view scenarios. In this paper, we propose Generative Densification, an efficient and generalizable densification strategy specifically tailored for feedforward models. Instead of iteratively splitting and cloning raw Gaussian parameters, our method up-samples feature representations produced by feed-forward models and generates their corresponding fine Gaussians in a single forward pass, leveraging learned prior knowledge for en + +hanced generalization. Experimental results on both object-level and scene-level reconstruction tasks demonstrate that our method outperforms state-of-the-art approaches with comparable or smaller model sizes, achieving notable improvements in representing fine details. + +# 1. Introduction + +3D Gaussian splatting (3D-GS) [18] has been a massive success in high-quality 3D scene reconstruction and real-time novel view synthesis, representing a 3D scene with a set of learnable Gaussian primitives and exploiting a fast differentiable rasterization pipeline. Since its introduction, numerous studies have explored 3D-GS as a versatile 3D representation with various applications extending beyond the per-scene optimization. One notable example is generalized feed-forward Gaussian models [3, 7, 49], which generate Gaussian primitives to reconstruct 3D scenes or objects in a single forward pass. By leveraging prior knowledge learned from large multi-view datasets (e.g., Objverse [9, 10], RE10k [50]), these models can reconstruct 3D scenes or objects from just a single or a few images. + +![](images/ccb3d0b5a67fde9084da8223d06dafd534e74161e21c0dadf11520a3e0dcbab8.jpg) +Figure 2. Generative Densification overview. Our method selectively densifies Gaussians with large view-space positional gradients. + +While effective and promising, the feed-forward Gaussian models often face challenges in capturing high-frequency details primarily due to the limited number of Gaussians and the lack of a densification strategy tailored for these approaches. One possible solution is to generate more Gaussians, but this does not fully address the problem. For example, in the pixel-aligned Gaussian model [3], a widely adopted architecture in the feed-forward models (see Sec. 2 for details), we can predict multiple Gaussians per pixel. However, this strategy uniformly increases the number of Gaussians across the entire 3D space, resulting in an excess of unnecessary small Gaussians that may degrade rendering quality and speed. Ideally, the scene details should be represented by numerous small Gaussians, while smoother regions can be covered by a few large Gaussians. + +In per-scene 3D-GS optimization, adaptive densification strategy selectively increases the number of Gaussians to better reconstruct complex 3D geometry and fine details. Specifically, every few optimization steps, it densifies only the Gaussians with large view-space positional gradients, replicating the existing Gaussians or splitting them into smaller ones when more Gaussians are required. Through repeated optimization and densification processes, the Gaussians gradually become non-uniformly distributed, with numerous small Gaussians concentrated in detailed areas and a few large Gaussians scattered across smooth regions. This simple heuristic algorithm has demonstrated its effectiveness across various real-world scenes and objects. + +A straightforward approach to extend the densification strategy to the feed-forward Gaussian models is to fine-tune the output Gaussians from the feed-forward models using the original 3D-GS optimization and densification procedure. However, directly applying the densification strategy used in per-scene optimization scenarios presents several challenges. For example, it demands tens and thousands of optimization steps to converge and reconstruct the fine details, which significantly reduces generation speed. Additionally, the per-scene 3D-GS optimization usually assumes many input images from various viewpoints, whereas the + +feed-forward models typically take just a few views or even a single view image. Thus, the densification and extensive optimization to a few view images can easily lead to overfitting, compromising the feed-forward models' ability to generalize and synthesize novel views effectively. + +In this paper, we propose Generative Densification (GD), an efficient generative densification strategy for generalized feed-forward Gaussian models, which is designed in accordance with the following principles: 1) adaptability, allowing the model to distinguish Gaussians that requires densification and those that do not; and 2) generalizability, enabling the model to learn and leverage prior knowledge from large multi-view datasets. Inspired by the 3D-GS densification strategy, our approach leverages view-space positional gradients to identify where additional Gaussians are needed. We selectively densify the top $K$ Gaussians with large gradients, and the remaining (non-selected) Gaussians are used together with the densified ones to render high-fidelity images (Fig. 2). Unlike the 3D-GS densification strategy, the proposed $GD$ densifies the selected Gaussians based on the learned prior knowledge for the purpose of generalizable 3D reconstruction. More specifically, $GD$ densifies feature representations from feed-forward models instead of raw Gaussian parameters, embedding prior knowledge in these features for improved generalization. + +We further propose to utilize an efficient point-level transformer [37] to implement $GD$ . Due to the quadratic increase in memory and the unstructured nature of point-level 3D data, it is infeasible to apply naive self-attention on hundreds of thousands of input Gaussians. While local attention can be applied within groups of neighboring Gaussians, finding the neighbors by calculating and comparing distances between the Gaussians is computationally expensive. Instead, we sort the Gaussians in traversing order of space-filling curves [28] to rearrange them into non-overlapping groups and apply group-wise attention, enabling efficient operations directly in 3D space. Additionally, while we selectively densify the Gaussians with large view-space positional gradients, multiple rounds of densification are unnec + +essary for all of them. To optimize this process, we predict a confidence mask for each densification layer to filter out the Gaussians that do not require further densification. + +We integrated $GD$ into two recent feed-forward Gaussian models: LaRa [5] for object-level reconstruction and MVSplat [7] for scene-level reconstruction. On the largescale Gobjaverse [38] and RE10k [50] datasets, two models incorporating our method achieved the best performance, significantly improving reconstruction quality compared to their respective baselines. Qualitative analysis further highlights that the fine Gaussians generated by $GD$ effectively capture thin structures and intricate details, which are often challenging for the coarse Gaussians to represent accurately (Fig. 1). Additionally, cross-dataset evaluations confirm that $GD$ consistently improves image quality, demonstrating its robust generalizability across different datasets. + +# 2. Related Work + +Feed-forward Gaussian Models. Feed-forward Gaussian models learn a mapping from a single or a set of few input images to a set Gaussian representations that can be rendered into any viewpoint. One common approach combines a pre-trained image encoder [2, 14, 27] with a learnable embedding decoder, where the decoder generates 3D features via a series of cross-attention between 3D embeddings and image features. These 3D features are commonly represented as voxels [5, 45], point-cloud [24], or a hybrid of point-cloud and triplane [52], and Gaussians are typically obtained by decoding the features using an MLP. + +Another approach involves pixel-aligned Gaussian representations [3, 33], where each Gaussian is assumed to be on a ray of each pixel and distanced from the ray origin by a depth. The depth is either directly regressed from pixelwise image features [33] or determined by the probability that a Gaussian exists at a depth along a ray [3]. Since its introduction, substantial efforts have been made to estimate the depth more accurately [7, 23, 32, 40, 46], scale up models for better generalizability [34, 41, 47], and generate 3D scenes leveraging learned prior [15, 21, 36]. Recent works further leverage these representations to cover wide-ranging views [6, 8, 35, 51] or reconstruct 4D scenes [20, 30]. + +While effective, both approaches often struggle to reconstruct fine details, mainly due to the limited number of Gaussians and the lack of a densification strategy specifically designed for feed-forward models. We aim to develop a unified densification framework that can be seamlessly applied to both of these representative approaches. + +Adaptive Density Control of Gaussians. Adaptive densification [18] plays a crucial role in capturing fine details and controlling the number of Gaussians. However, it relies heavily on well-initialized Gaussians, and its core operations (splitting, cloning, and pruning) are not sufficiently effective, often leading to blurry reconstructions, overfitting, + +and slow training. A line of studies [17, 19] tackles the reliance on accurate initialization, achieving comparable or superior rendering quality even with random initialization. Another line of studies [1, 13, 26, 42, 48] explores alternative densification criteria beyond view-space positional gradients to better capture Gaussians in blurry regions. Recently, overfitted Gaussian pruning [11] and aggressive densification [25] have been introduced, with the former enhancing generalization and the latter accelerating training. + +These methods typically require more than thousands of optimization and densification steps, and the discussions are limited to per-scene scenarios. Instead of directly applying them to generalized settings, we learn from large multi-view datasets to generate fine Gaussians in a single forward pass. + +# 3. Method + +# 3.1. Generative Densification + +A feed-forward Gaussian model is a function $\Phi$ that maps a set of images $\mathcal{I} = \{I_v\}_{v=1}^V$ and camera poses $\mathcal{C} = \{C_v\}_{v=1}^V$ to a set of Gaussians $\mathcal{G} = \{(\mu_i, \alpha_i, \Sigma_i, c_i)\}_{i=1}^N$ and their associated features $\mathcal{F} = \{f_i\}_{i=1}^N$ : + +$$ +\mathcal {G}, \mathcal {F} = \Phi (\mathcal {I}, \mathcal {C}), \tag {1} +$$ + +where $V$ is the number of input views, and $N$ is the number of Gaussians. Each feature $f_{i}$ is the penultimate feature extracted from the feed-forward model (see Sec. 3.3), which can be decoded into Gaussian parameters, including center position $\mu_{i}$ , opacity $\alpha_{i}$ , covariance $\Sigma_{i}$ , and spherical harmonics (SH) coefficient $c_{i}$ . + +Our goal is to learn a model $\Psi$ that adaptively densifies Gaussians generated by a variety of feed-forward models: + +$$ +\tilde {\mathcal {G}} = \Psi (\mathcal {G}, \mathcal {F}, \mathcal {I}, \mathcal {C}). \tag {2} +$$ + +First, we calculate gradient scores to split the Gaussians into two groups, $\mathcal{G}_{\mathrm{den}}$ and $\mathcal{G}_{\mathrm{rem}}$ , the Gaussians requires densification and the remaining Gaussians, respectively. More specifically, we compute the scores as the norms of the gradients with respect to view-space coordinates of Gaussian positions and average the norms across the $V$ input views: + +$$ +s _ {i} = \frac {1}{V} \sum_ {v = 1} ^ {V} \| \nabla_ {p \left(\mu_ {i}, v\right)} \mathcal {L} _ {\mathrm {M S E}} \left(I _ {v}, \hat {I} _ {v}\right) \| _ {2}, \tag {3} +$$ + +where $\mathcal{L}_{\mathrm{MSE}}(I_v,\hat{I}_v)$ is a mean squared error loss between ground truth images $(I_{v})$ and rendered images $(\hat{I}_v)$ , and $p(\mu_i,v)\in \mathbb{R}^2$ denotes the projected coordinate of $i$ -th Gaussian position onto input view $v$ . Then, we select the top $K$ scoring Gaussians $(\mathcal{G}_{\mathrm{den}})$ , and their positions and features $(\mathcal{X}_{\mathrm{den}}\in \mathbb{R}^{K\times 3},\mathcal{F}_{\mathrm{den}}\in \mathbb{R}^{K\times D})$ are passed to the densification module, which consists of $L$ layers of serialized attention (SA), up-sampling (UP), splitting via learnable masking + +(SPLIT), and Gaussian head (HEAD) blocks (Fig. 3-(a)): + +$$ +\left(\tilde {\mathcal {X}} ^ {(l)}, \tilde {\mathcal {F}} ^ {(l)}\right) = \mathrm {S A} \left(\mathcal {X} _ {\text {d e n}} ^ {(l - 1)}, \mathcal {F} _ {\text {d e n}} ^ {(l - 1)}\right), \tag {4} +$$ + +$$ +\left(\mathcal {X} ^ {(l)}, \mathcal {F} ^ {(l)}\right) = \mathrm {U P} \left(\tilde {\mathcal {X}} ^ {(l)}, \tilde {\mathcal {F}} ^ {(l)}\right), \tag {5} +$$ + +$$ +\left(\mathcal {X} _ {\text {d e n}} ^ {(l)}, \mathcal {F} _ {\text {d e n}} ^ {(l)}, \mathcal {X} _ {\text {r e m}} ^ {(l)}, \mathcal {F} _ {\text {r e m}} ^ {(l)}\right) = \text {S P L I T} \left(\mathcal {X} ^ {(l)}, \mathcal {F} ^ {(l)}\right), \tag {6} +$$ + +$$ +\mathcal {G} ^ {(l)} = \operatorname {H E A D} \left(\mathcal {X} _ {\text {r e m}} ^ {(l)}, \mathcal {F} _ {\text {r e m}} ^ {(l)}\right), \tag {7} +$$ + +for $l\in \{1,\dots,L - 1\}$ , where $\mathcal{X}_{\mathrm{den}}^{(0)} = \mathcal{X}_{\mathrm{den}}$ and $\mathcal{F}_{\mathrm{den}}^{(0)} = \mathcal{F}_{\mathrm{den}}$ . Here, we initialize the input positions as the Gaussian center positions. SA( $\cdot, \cdot$ ): $\mathbb{R}^{K\times 3} \times \mathbb{R}^{K\times D} \to \mathbb{R}^{K\times 3} \times \mathbb{R}^{K\times D}$ , efficiently aggregates scene information through serialized attention. UP( $\cdot, \cdot$ ): $\mathbb{R}^{K\times 3} \times \mathbb{R}^{K\times D} \to \mathbb{R}^{\tilde{K}\times 3} \times \mathbb{R}^{\tilde{K}\times D}$ ( $\tilde{K} >> K$ ), up-samples the Gaussian positions and features. SPLIT( $\cdot, \cdot$ ): $\mathbb{R}^{\tilde{K}\times 3} \times \mathbb{R}^{\tilde{K}\times D} \to \mathbb{R}^{\tilde{K}_{\mathrm{den}}\times 3} \times \mathbb{R}^{\tilde{K}_{\mathrm{den}}\times D} \times \mathbb{R}^{\tilde{K}_{\mathrm{rem}}\times 3} \times \mathbb{R}^{\tilde{K}_{\mathrm{rem}}\times D}$ ( $\tilde{K} = \tilde{K}_{\mathrm{den}} + \tilde{K}_{\mathrm{rem}}$ ), divides the up-sampled positions and features into those requiring further densification in the next layer and the remaining ones (see Appendix C for further details). By using the remaining ones, we generate each layer's Gaussians $\mathcal{G}^{(l)}$ using HEAD( $\cdot, \cdot$ ) block. For the $L$ -th layer, we generate the Gaussians by $\mathcal{G}^{(L)} = \mathrm{HEAD}(\mathrm{UP}(\mathrm{SA}(\mathcal{X}_{\mathrm{den}}^{(L - 1)}, \mathcal{F}_{\mathrm{den}}^{(L - 1)}))),$ and the final set of fine Gaussians is obtained as follows: + +$$ +\tilde {\mathcal {G}} = \mathcal {G} _ {\text {r e m}} \cup \left\{\bigcup_ {l = 1} ^ {L} \mathcal {G} ^ {(l)} \right\}. \tag {8} +$$ + +# 3.2. Architecture Details + +**Serialized Attention.** Due to the quadratic increase in memory requirements and the unstructured nature of the Gaussian representations, it is infeasible to apply self-attention directly to all input Gaussians. One alternative is to group the Gaussians by searching for their neighbors and apply group-wise attention. While this approach allows the model to consider the relative positions of the neighbors, searching for neighbors across hundreds of thousands of Gaussians is memory and computationally expensive. + +Serialized attention [37] enables efficient operations on unstructured point clouds by sorting them in traversing order of given space-filling curves [28]. Following its design principles, we first encode each Gaussian position into a serialized code, an integer value that reflects its order in the space-filling curves [37]. Then, the Gaussian features are structured by sorting the serialized codes and divided into non-overlapping groups, where self-attention is applied within the same group. By adapting serialized attention, our method efficiently embeds prior knowledge and local scene context into the features, allowing the output features to be used as sources for generating fine Gaussians. + +Up-sampling. In the UP block, we predict residuals for each Gaussian position and feature (Fig. 3-(b)). We generate $R$ offsets for each Gaussian position by passing the input + +![](images/0d34589f1c03365bbd446d9ae32e60d08ea882541d8ccd8e4fa12041e80a229d.jpg) +A Affine H Head G Gradient masking L Learnable masking +a) Architecture Details +Figure 3. (a) Given Gaussians and features, out method selects $K$ Gaussians and densifies their positions and features through densification module. (b) Predicted positional and feature residuals are added to their respective inputs after a broadcasting operation. + +![](images/6caccaab8ae9de526f1248db77d23f473e7c280e1de34655f2f6639bbd13e3dc.jpg) +b) Up-sampling Details + +features through an MLP parameterized by $\theta_x^{(l)}$ . These predicted offsets are then positionally encoded, concatenated with the input features, and transformed to residual features using another MLP parameterized by $\theta_f^{(l)}$ . More formally, + +$$ +\Delta x _ {i} ^ {(l)} = \mathrm {M L P} \left(\tilde {f} _ {i} ^ {(l)}; \theta_ {x} ^ {(l)}\right), \tag {9} +$$ + +$$ +\Delta f _ {i, j} ^ {(l)} = \mathrm {M L P} (\gamma (\Delta x _ {i, j} ^ {(l)}) \oplus \tilde {f} _ {i} ^ {(l)}; \theta_ {f} ^ {(l)}), \tag {10} +$$ + +where $\tilde{f}_i^{(l)}\in \mathbb{R}^D$ is the feature of $i$ -th Gaussian after the $l$ -th serialized attention block. $\Delta x_{i}^{(l)}\in \mathbb{R}^{R\times 3}$ is the predicted $R$ offsets per Gaussian, and $\Delta x_{i,j}^{(l)}\in \mathbb{R}^3$ denotes each predicted offset. Similarly, $\Delta f_i^{(l)}\in \mathbb{R}^{R\times D}$ is the predicted $R$ residuals per Gaussian feature, and $\Delta f_{i,j}^{(l)}\in \mathbb{R}^D$ denotes each predicted residual. $\gamma (\cdot)$ is a positional encoding function, and $\oplus$ represents a concatenation operator. The output positions and features are obtained by adding the residuals to their respective inputs, following the broadcasting of the input positions and features to align the dimensions. + +Splitting via Learnable Masking. In the SPLIT block, we use learnable masking to filter out Gaussians not requiring further densification in the next layer. While gradient masking initially selects Gaussians $(\mathcal{G}_{\mathrm{den}})$ for densification, computing gradients in every layer introduces considerable computational overhead. Instead, we predict a confidence score $s_i^{(l)} \in [0,1]$ for each Gaussian using an MLP parame + +![](images/64e0363d9f29fa62a28b54e8e456c3d818cadc291c584f7ff2812bd497e47a5c.jpg) +Figure 4. Overview of the Generative Densification pipelines for object-level (top) and scene-level (bottom) reconstruction tasks. + +terized by $\theta_s^{(l)}$ and a sigmoid function $\sigma (\cdot)$ . More formally, + +$$ +s _ {i} ^ {(l)} = \sigma \left(\mathrm {M L P} \left(f _ {i} ^ {(l)}; \theta_ {s} ^ {(l)}\right)\right), \tag {11} +$$ + +where $f_{i}^{(l)} \in \mathbb{R}^{D}$ is the feature for the $i$ -th Gaussian. Based on these predicted scores, the top $\tilde{K}_{\mathrm{den}}$ scoring Gaussians are selected for further densification, while the remaining $\tilde{K}_{\mathrm{rem}}$ Gaussians are decoded into Gaussian parameters. + +Since the top-k operation is non-differentiable, we attach the computational graph of the score $s_i^{(l)}$ to the input features $f_i^{(l)}$ while keeping the feature values intact: + +$$ +f _ {i} ^ {(l)} = \operatorname {S G} \left(f _ {i} ^ {(l)} - f _ {i} ^ {(l)} s _ {i} ^ {(l)}\right) + f _ {i} ^ {(l)} s _ {i} ^ {(l)}, \tag {12} +$$ + +where $\mathsf{SG}(\cdot)$ is a stop-gradient operator. Analogous to the straight-through estimator [43], the gradients with respect to the output features $\partial \mathcal{L} / \partial f_i^{(l)}$ propagate back to the second term of the Eq. (12), hence, which enables us to learn the confidence scoring function and do end-to-end training. + +Gaussian Head. In the Gaussian HEAD block, the positions and features of the remaining Gaussians $(\mathcal{X}_{\mathrm{rem}}^{(l)},\mathcal{F}_{\mathrm{rem}}^{(l)})$ filtered out by the learnable masking block, are decoded into a set of Gaussian parameters $(\mathcal{G}^{(l)})$ . Their positions are set to match the input positions $(\mathcal{X}_{\mathrm{rem}}^{(l)})$ , while the remaining attributes (opacities, covariances, SH coefficients) are generated from the input features $(\mathcal{F}_{\mathrm{rem}}^{(l)})$ using an MLP. + +# 3.3. Applying Generative Densification + +We present two models incorporating generative densification, based on LaRa [5] and MVSplat [7]. For object-level reconstruction, we use the Gaussians and the volume features generated by the LaRa as input, from which we generate fine Gaussians (top row of Fig. 4). For scene-level reconstruction, fine Gaussians are generated per view by + +utilizing the pixel-aligned Gaussians and image features extracted from the MVSplat (bottom row of Fig. 4). Additionally, residual learning is incorporated into the scene-level model to better reconstruct complex real-world scenes. Further details on the residual learning and the pipelines are provided in Appendix B and Appendix C, respectively. + +# 4. Experiment + +# 4.1. Experimental Setup + +Implementation Details. We jointly trained the generative densification module with the LaRa backbone for 30 epochs, and then fine-tuned for 20 epochs to achieve further improvements in rendering quality. The training was conducted on four A6000-48G GPUs over 3.5 days, with a batch size of 4 per GPU. Similarly, the MVSplat backbone was trained jointly with our densification module for 300,000 iterations, followed by fine-tuning for 150,000 iterations. The scene-level training was conducted on four H100-80G GPUs over 6.5 days, also with a batch size of 4 per GPU. For a detailed description of the network and training hyperparameters, please refer to Appendix D. + +Datasets. We train and evaluate our object-level model on Gobjaverse [38] dataset, a large-scale multi-view dataset with an image resolution of $512 \times 512$ . To further demonstrate the cross-domain capability, we evaluate our method on Google Scanned Objects [12] dataset and a subset of Co3D [29] test set, following LaRa [5]. Similarly, we train and evaluate our scene-level model on RE10k [50] with an image resolution of $256 \times 256$ , and further evaluate it on two cross-domain datasets, ACID [22] and DTU [16], following MVSplat [7]. For both models, we use training and testing splits provided in each dataset without any modifications. + +Baselines. We compare our object-level model against the original LaRa [5], as well as LGM [34] and GS-LRM [47]. + +Table 1. Quantitative comparisons of our object-level models against their baselines. 'Our-fast' is trained on the Gobjverse [38] training set for 30 epochs, and 'Ours' is further fine-tuned for 20 epochs. 'Ours (w/ residual)' is trained on the same set for 50 epochs with residual learning (Appendix B). LaRa is re-evaluated using the publicly available checkpoint and our view-sampling method (Appendix D). + +
Method#Param. (M)Gobjaverse [38]GSO [12]Co3D [29]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
MVSNeRF [4]0.5214.480.8960.18515.210.9120.15412.940.8410.241
MuRF [39]15.714.050.8770.30112.890.8850.27911.600.8150.393
LGM [34]41519.670.8670.15723.670.9170.06313.810.7390.414
GS-LRM [47]300---30.520.9520.050---
LaRa [5]12527.490.9380.09329.700.9590.06021.180.8620.216
Ours-fast13428.230.9430.08430.620.9640.06221.670.8640.209
Ours13428.580.9450.08031.060.9660.05821.720.8650.209
Ours (w/ residual)13428.750.9460.07831.230.9670.05822.080.8670.206
+ +![](images/70cdd27878f3fb39c44476269fbc7b04efa1a3cb37757450f775c9be037a3e6a.jpg) +Figure 5. Qualitative comparisons of our object-level model trained for 50 epochs against the original LaRa. The zoomed-in parts within the red boxes are shown on the right side of the second and third columns, focusing on the comparison of fine detail reconstruction. The two images in the rightmost column present the Gaussians input to and output from our generative densification module, respectively. + +Additionally, we include two feed-forward NeRF models, MVSNeRF [4] and MuRF [39], for reference. For comparing our scene-level model, we include feed-forward NeRF models (pixelNeRF [48], GNPR [31], and MuRF [39]) and pixel-aligned Gaussian models (pixelSplat [3], Depth-Splat [40], and the original MVSplat [7]) as baselines. + +# 4.2. Results + +Object-level Reconstruction. Fig. 5 compares the rendered images from the baseline LaRa against those from our object-level model. Our model clearly outperforms LaRa in reconstructing fine details, such as the white dots on the red ribbon (first row of Fig. 5) and the intricate floral patterns on the socks (second row of Fig. 5). It is also evident that our densification strategy effectively captures detailed areas and generate fine Gaussians, as shown in the rightmost column of Fig. 5. While LaRa quickly learns the object's general shape by leveraging explicit volume representations, it struggles to accurately represent edges or contours. + +The quantitative comparison provided in Tab. 1 further demonstrates the ability of our model to capture and recon + +struct fine details. Our model achieves the highest PSNR in both in-domain reconstruction and cross-dataset generalization tasks. It even outperforms GS-LRM, the current state-of-the-art model for object-level reconstruction, using significantly fewer number of parameters (300M vs. 134M). This highlights that selectively generating Gaussians in the detailed areas can be more effective than uniformly generating numerous Gaussians across the entire object. + +Scene-level Reconstruction. Fig. 6 and Fig. 7 compare the rendered images from the baseline MVSplat against those from our scene-level model. Our model better reconstructs thin structures and fine details, such as the guardrail (first row of Fig. 6) and the wave (second row, first column of Fig. 7). Moreover, we empirically found that our method reduces the opacity of Gaussians in empty space, making them less visible in the rendered images. For example, it makes the floaters more transparent near the water pipe (second row of Fig. 6) and the iron fence (first row, first column of Fig. 7), removing artifacts in the images. + +In the quantitative comparisons, our model not only outperforms the baselines including DepthSplat [40] on the in + +![](images/4a801e8bbe1636e0d25a0147fd5d9d66528fe3dbfc7e88e45d660de44e2d73cf.jpg) +Figure 6. Qualitative comparisons of our scene-level model against the original MVSplat on the RE10k [50] dataset. + +![](images/d1d7b2bce937b4debb5b313edac762b238686e7f5ecc8ff35a77a48ffc46fdb7.jpg) +Figure 7. Qualitative comparisons of our scene-level model against the original MVSplat on the ACID [22] and DTU [16] datasets. + +![](images/6b326b55f5babdb962c813e8d75e53e4b9abfb95e956c7a9188e3bf9e5acf1f4.jpg) + +domain reconstruction task (Tab. 2), but also consistently achieves the best performance on the cross-dataset generalization task (Tab. 3). While DepthSplat is concurrent work, we include it as a baseline for the reader's reference. Our model outperforms DepthSplat with fewer parameters (37M vs. 28M) and a smaller batch size (32 vs. 16). Additionally, unlike DepthSplat, which relies on a pretrained depth predictor, our model is solely trained with multi-view images. + +# 4.3. Analysis and Ablations + +We begin by providing an intuitive example comparing coarse and fine Gaussians, with an analysis of their positions, opacities, and scales. Here, coarse Gaussians refer to the selected input Gaussians for densification, while fine Gaussians represent the union of each layer's output. Next, we present ablation results to demonstrate: 1) the superiority of our method over naive densification, 2) the adaptiveness of gradient masking and its role in improving rendering quality, 3) the effectiveness of learnable masking in reducing redundant Gaussians and accelerating model inference, and 4) the necessity of combining both masking strategies to balance rendering quality and inference speed. + +Table 2. Quantitative comparisons of our scene-level model against its baselines on the RE10k [50] dataset. The MVSplat-finetune model is fine-tuned for 150,000 iterations from the MVSplat checkpoint at 300,000 iterations. * indicates concurrent work. + +
Method#Param. (M)PSNR ↑SSIM ↑LPIPS ↓
pixelNeRF [44]25020.430.5890.550
GPNR [31]2724.110.7930.255
MuRF [39]15.726.100.8580.143
pixelSplat [3]125.125.890.8580.142
MVSplat [7]1226.390.8690.128
MVSplat-finetune1226.460.8700.127
DepthSplat* [40]3726.760.8770.123
Ours27.827.080.8790.120
+ +Table 3. Cross-dataset generalization results on the ACID [22] and DTU [16] datasets. All models are trained on the RE10k [50] training set and evaluated on each dataset without fine-tuning. + +
MethodACID [22]DTU [16]
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
pixelSplat [3]27.640.8300.16012.890.3820.560
MVSplat [7]28.150.8410.14713.940.4730.385
Ours28.610.8470.14114.050.4770.380
+ +Comparison of Coarse and Fine Gaussians. The left side of Fig. 8 illustrates that reconstructing contours is chal + +![](images/e1087706660e52fd5cc041b52ab8648ec3a566acb00a1adf1297077a706e9439.jpg) +Figure 8. 2D histograms of Gaussian attributes. Each pixel represents a histogram bin, with brighter colors for higher counts. + +lenging with insufficient number of Gaussians. Although these areas are covered by large Gaussians with no visible holes in the rendered image, it still appears blurry, with the object not clearly separated from the background (Fig. 5). As shown on the right side of Fig. 8, fine Gaussians have smaller scales and lower opacities compared to coarse Gaussians, indicating that our method reconstructs details by accumulating partially overlapping small Gaussians. + +Effectiveness of Generative Densification. Increasing the per-voxel Gaussian count in LaRa raises the total number of Gaussians by $68\%$ , but only results in a slight PSNR improvement (second row of Tab.4). In contrast, our method achieves a significantly higher PSNR with a comparable Gaussian count (third row of Tab.4). Moreover, although LaRa cannot be trained with more than 80k Gaussians due to memory overhead, our approach handles over 110k Gaussians on the same GPU. The scene-level model shows similar results, further illustrating the efficiency and effectiveness of our adaptive strategy (last row of Tab. 4). + +Gradient Masking. The first row of Tab. 5 presents the re-evaluation of the 'Ours-fast' model from Tab. 1, where all masking blocks are removed. In comparison to the model with a single gradient masking block (second row of Tab. 5), there is a notable increase in the number of Gaussians, and the average inference time for reconstructing a single scene rises by $32\%$ . Additionally, the PSNR decreases by 0.52 dB, highlighting that the adaptive densification enabled by gradient masking improves rendering quality compared to densely producing an excess of Gaussians across the scene. + +Learnable Masking. Learnable masking plays a pivotal role in reducing computational and memory demands by controlling the number of Gaussians generated in each densification layer. Ideally, it should filter out Gaussians not requiring further densification without compromising image quality. As shown in the second and third rows of Tab. 5, although masking leads to a minor decrease in PSNR, it re + +Table 4. Comparison against naïve densification. Object and scene models are evaluated on the GSO [12] and RE10k [50] datasets. + +
Method#Gauss. ↓PSNR ↑SSIM ↑LPIPS ↓
LaRa (2 Gaussians per voxel)46,87829.700.9590.060
LaRa (3 Gaussians per voxel)79,11129.770.9610.068
Ours (K=6,000)78,08430.950.9650.060
MVSplat (1 Gaussian per pixel) [7]65,00026.390.8690.280
MVSplat (3 Gaussians per pixel) [7]195,00026.540.8720.127
Ours (K=30,000)173,00027.080.8790.120
+ +Table 5. Ablation results on two masking strategies with varying configurations, evaluated on the GSO [12] dataset. 'Grad.' and 'Learn.' refer to gradient and learnable masking (Sec. 3), respectively, while 'None' indicates no masking is applied. Inference time ('Time') is measured in milliseconds on a single A6000 GPU. + +
Masking Configuration#Gauss.↓Time↓PSNR↑
1stMasking2ndMasking
NoneNone413,06625530.21
Grad.(K=12k)None151,96819330.73
Grad.(K=12k)Learn.(Kden=19k)114,35118730.62
Grad.(K=15k)Learn.(Kden=24k)130,05619830.68
Grad.(K=30k)Learn.(Kden=48k)189,32220830.63
Grad.(K=12k)Grad.(Kden=19k)114,37119930.12
Learn.(K=12k)Learn.(Kden=19k)114,56518829.31
+ +sults in a substantial $25\%$ reduction in the number of Gaussians and notably accelerates model inference. This indicates that the efficiency gains from reducing the number of Gaussians outweigh the slight drop in image quality, emphasizing the significance of learnable masking. + +Combining Gradient and Learnable Masking. Both masking strategies can be used interchangeably to reduce the number of Gaussians and accelerate inference. However, gradient masking is primarily designed to select detailed regions for adaptive densification, in addition to reducing overhead. The last row of Tab. 5 shows a significant PSNR drop when replacing gradient masking with learnable masking, highlighting that the former is better suited for selecting to-be-densified Gaussians. Conversely, learnable masking can be replaced with gradient masking, but rendering quality still lags behind that of the combined model (second last row of Tab. 5), which demonstrates the necessity of using a combination of both masking strategies. + +# 5. Conclusion + +We proposed generative densification, an efficient densification strategy tailored for generalized feed-forward Gaussian models. We integrated the proposed method into LaRa and MVSplat, providing practical guidance for real-world applications. Extensive experiments demonstrate that our method effectively reconstruct high-frequency details by generating fine Gaussians, establishing new benchmarks in both object-level and scene-level reconstruction tasks. We believe our work paves the way for future research on feedforward adaptive densification leveraging learned prior. + +# Acknowledgements + +This research was supported by the Ministry of Science and ICT (MSIT) of Korea, under the National Research Foundation (NRF) grant (RS-2024-00337548), the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by the Korea Government (MSIT) (RS-2020-II201361, Artificial Intelligence Graduate School Program (Yonsei University)), and Samsung Research Funding & Incubation Center of Samsung Electronics under Project Number SRFC-IT2401-01, and the Korea-US Collaborative Research Fund (KUCRF), funded by the Ministry of Science and ICT and Ministry of Health & Welfare, Republic of Korea (grant number: RS-2024-00468417). + +# References + +[1] Samuel Rota Bulò, Lorenzo Porzi, and Peter Kontschieder. 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(a) Benefiting from the compact BEV-Point representation, GaussianCity can generate unbounded 3D cities using 3D Gaussian splatting (3D-GS). (b) As the number of points increases, VRAM usage during 3D-GS training rises significantly, whereas BEV-Point, acting as a compact representation, maintains a constant VRAM usage. (c) As the number of points increases, BEV-Point exhibits significantly lower growth in file storage compared to 3D-GS. (d) The proposed GaussianCity achieves not only superior generation quality but also the best efficiency in 3D city generation. + +![](images/78466dbe90f6f706ac1e4affbfbdd3e09cd85e3369170e2c981e1c5c0c66af5e.jpg) +CityDreamer (0.18 FPS) +(d) Comparisons of Visuals and Runtimes on the GoogleEarth Dataset + +![](images/2fbe0f2d53f55b970cb6945b75b85de799792790105103807e739abcab10b98b.jpg) +GaussianCity (10.72 FPS) + +# Abstract + +3D city generation with NeRF-based methods shows promising generation results but is computationally inefficient. Recently 3D Gaussian splatting (3D-GS) has emerged as a highly efficient alternative for object-level 3D generation. However, adapting 3D-GS from finite-scale 3D objects and humans to infinite-scale 3D cities is non-trivial. Unbounded 3D city generation entails significant storage overhead (out-of-memory issues), arising from the need to expand points to billions, often demanding hundreds of Gigabytes of VRAM for a city scene spanning $10\mathrm{km}^2$ . In this paper, we propose GaussianCity, a generative Gaussian splatting framework dedicated to efficiently synthesizing unbounded 3D cities with a single feed-forward pass. Our key insights are two-fold: 1) Compact 3D Scene Representation: We introduce BEV-Point as a highly compact intermediate representation, ensuring that the growth in VRAM usage for unbounded scenes remains constant, thus enabling unbounded city generation. 2) Spatial-aware Gaus + +sian Attribute Decoder: We present spatial-aware BEV-Point decoder to produce 3D Gaussian attributes, which leverages Point Serializer to integrate the structural and contextual characteristics of BEV points. Extensive experiments demonstrate that GaussianCity achieves state-of-the-art results in both drone-view and street-view 3D city generation. Notably, compared to CityDreamer, GaussianCity exhibits superior performance with a speedup of 60 times (10.72 FPS vs. 0.18 FPS). + +# 1. Introduction + +The generation of 3D assets has attracted considerable attention from both academia and industry due to its significant potential applications. With the rapid advancements in generative modeling, there have been notable achievements in 3D content generation, encompassing the production of objects [12, 51, 53], avatars [10, 19, 23], and scenes [35, 54, 55]. City generation, recognized as one of the most demanding tasks in 3D content creation, holds + +wide-ranging applications across domains such as gaming, animation, film, and virtual reality. + +In recent years, significant progress has been made in the field of 3D city generation. Both InfiniCity [30] and CityDreamer [54] employ NeRF [37] to generate unbounded photorealistic 3D cities, achieving promising results. However, these methods sample points at the same density and aggregate color values for all points along rays, resulting in inefficiencies during inference and loss of details. Over the past year, 3D Gaussian splatting (3D-GS) [22] has gained widespread use in 3D generation, offering a significantly faster rendering technique by leveraging GPU-based rasterization. Moreover, 3D-GS provides a more flexible way to represent details, leveraging more 3D Gaussians to capture finer intricacies. However, existing 3D-GS-based generators [13, 33, 51] only produce finite-scale objects or scenes containing a limited number of 3D Gaussians. As illustrated in Figure 1(b-c), when the scene scales up, the demands for GPU memory (VRAM) and file storage grow dramatically, making it infeasible for unbounded scene generation. + +To address these issues, we propose GaussianCity, the first generative Gaussian splatting for unbounded 3D city generation. As shown in Figure 1(a), GaussianCity leverages a highly compact scene representation, namely BEV-Point, to decouple Gaussian attributes into two major parts: position-related attributes and style-related attributes. The position-related attributes can be further condensed into bird's-eye-view (BEV) maps, while the style-related attributes can be compressed into a style lookup table. Only visible BEV points are considered during the rendering and optimization process, ensuring that VRAM usage is kept at a constant level. To generate 3D Gaussian attributes from BEV points, we present BEV-Point Decoder, which leverages Point Serializer to capture structural and contextual characteristics of unstructured BEV points. Notably, the contextual characteristics of points are inherently preserved during point sampling within a local 3D patch in NeRF, whereas these are disrupted due to the unstructured nature of BEV points. The Gaussian Rasterizer is finally employed to render the image from the generated Gaussian attributes. + +The contributions are summarized as follows: + +- To the best of our knowledge, we propose the first 3D-GS generative model for unbounded 3D city generation with both high realism and efficiency. +- We introduce BEV-Point as a highly compact representation, which ensures that the VRAM usage remains constant as the scene size scales up. +- We present BEV-Point Decoder, which leverages Point Serializer to capture both structural and contextual characteristics of unstructured BEV points. +- Extensive experiments showcase the superiority of GaussianCity over state-of-the-art methods for 3D city generation in terms of both generation quality and efficiency. + +# 2. Related Work + +3D Gaussian Splatting. 3D Gaussian splatting (3D GS) [22] has gained considerable attention in recent months, demonstrating promising rendering results and faster performance compared to NeRF [37]. Numerous methods have been proposed to integrate 3D GS into the 3D reconstruction of objects [49, 56, 62], avatars [42, 46, 61], and scenes [31, 34, 36]. Furthermore, several approaches [24, 38] have aimed to optimize the high memory consumption of 3D GS during reconstruction. 3D GS is also extensively used in the generation of 3D objects [50, 51], 3D avatars [1, 33, 60], and 3D scenes [13]. However, these methods only generate small-scale 3D assets and are not memory-efficient for representing large-scale 3D assets. Benefiting from 3D-GS, efficiently applying it to 4D object [15, 44] and human [25, 27, 57] generation with deformation becomes feasible. + +Scene Generation. Unlike impressive models for generating objects and avatars, generating scenes presents greater challenges due to their extremely high diversity. Earlier approaches [26, 32] generate scenes by synthesizing videos, which lack 3D awareness and cannot ensure 3D consistency. Semantic image synthesis methods [16, 40, 48] exhibit promising results in generating scene-level content by conditioning on pixel-wise dense correspondence, such as semantic segmentation maps or depth maps. Several methods [7, 13, 59] generate natural 3D scenes by performing inpainting and outpainting on RGB images or feature maps. However, most methods can only interpolate or extrapolate a limited distance from the input views and lack generative capabilities. Recent approaches [4, 11, 30, 54] have achieved 3D consistent scenes at an infinite scale through unbounded layout extrapolation. Another set of works focuses on indoor scene synthesis using costly 3D datasets [3, 14] or CAD object retrieval [41]. + +# 3. Our Approach + +# 3.1. Background: 3D Gaussian Splatting + +As introduced in [22], 3D Gaussian splattering (3D-GS) is an explicit point-based 3D scene representation, using a set of 3D Gaussians with various attributes to model the scene. Each Gaussian is characterized by a center $\mathbf{x} \in \mathbb{R}^3$ , a scaling factor of $\mathbf{s} \in \mathbb{R}^3$ , and a rotation quaternion $\mathbf{q} \in \mathbb{R}^4$ . Additionally, it maintains opacity value $\alpha \in \mathbb{R}$ and a color feature $\mathbf{c} \in \mathbb{R}^C$ for rendering, where spherical harmonics can model view-dependent effects. These parameters can collectively be denoted by $\mathbf{A} = \{\mathbf{x}_i, \mathbf{s}_i, \mathbf{q}_i, \alpha_i, \mathbf{c}_i\}_{i=1}^N\}$ , where $N$ is the number of 3D Gaussians. Rendering 3D Gaussians involves projecting them onto the image plane as 2D Gaussians and performing alpha composition for each pixel in front-to-back depth order, thus determining the final color and alpha. + +![](images/0dfcb4b8e78f77a4794fbbb1b500851774c1574fea9db72f1981d8c54d669493.jpg) +Figure 2. The framework of GaussianCity. To create an unbounded 3D city, the BEV points are firstly generated from a local patch of the BEV maps, which includes the height field $\mathbf{H}$ , semantic map $\mathbf{S}$ , and binary density map $\mathbf{D}$ . Then, the BEV-Point attributes $\{\mathbf{I},\mathbf{C}_A,\mathbf{C}_R,\mathbf{F}_S\}$ are generated for each point and the Style Lookup Table: $\mathcal{T}(\mathbf{L})\to \mathbf{Z}_T$ is generated for each instance. Next, BEV-Point Decoder generates the Gaussian attributes $\mathbf{A}$ from BEV-Point attributes. Finally, Gaussian Rasterizer $\mathcal{R}$ produces the rendered image $\mathbf{R}$ . + +# 3.2. BEV-Point Initialization + +Within 3D-GS, all 3D Gaussians undergo initialization with a predefined set of parameters during optimization. However, as the scene scales up, the VRAM usage increases dramatically, making it impractical to generate large-scale scenes. Addressing this issue, we propose a highly compact representation namely BEV-Point. In the BEV-Point representation, only visible BEV points are retained since only they impact the appearance of the current frame. It ensures that VRAM usage remains constant because the number of visible BEV points does not increase with the scene scale, given fixed camera parameters. + +In a local patch of a bird's-eye-view (BEV) map comprising a semantic map $\mathbf{S}$ and a height field $\mathbf{H}$ , a collection of BEV points within this patch can be produced by extruding the pixels in the semantic map $\mathbf{S}$ according to the corresponding values in the height field $\mathbf{H}$ . We further introduce the binary density map $\mathbf{D}$ to adjust the sampling density for different semantic categories. This is driven by the observation that certain categories exhibit simpler textures (e.g., roads, water areas), allowing for reduced density to manage computational costs, while other categories (e.g., building facades) possess intricate textures, necessitating a greater number of points for representation. The coordinates of the generated BEV points, denoted as $\mathbf{C}_F \in \mathbb{R}^{N_{\mathrm{pt}} \times 3}$ , can be generated as + +$$ +\mathbf {C} _ {F} = \left\{\left(x, y, z\right) \mid \mathbf {H} _ {(x, y)} \leq z \text {a n d} \mathbf {D} _ {(x, y)} = 1 \right\} \tag {1} +$$ + +where $N_{\mathrm{pt}}$ is the number of BEV points. + +Benefiting from the binary density map $\mathbf{D}$ , a significant number of redundant BEV points have been omitted. However, the remaining number, typically 20 million BEV points, is still too large for optimization. To address this issue, we additionally conduct ray intersection to obtain the binary visibility map $\mathcal{V}:(x,y,z)\to v$ , where $v\in \{0,1\}$ for filtering out the visible BEV points. Therefore, the coordinates of the visible BEV points $\mathbf{C}_A\in \mathbb{R}^{N_{\mathrm{pt}}\times 3}$ can be generated as + +$$ +\mathbf {C} _ {A} = \{(x, y, z) \mid (x, y, z) \in \mathbf {C} _ {F} \text {a n d} \mathcal {V} (x, y, z) = 1 \} \tag {2} +$$ + +# 3.3. BEV-Point Feature Generation + +The features in the BEV-Point representation can be divided into three categories: instance attributes, BEV-Point attributes, and style look-up table. The instance attributes encompass fundamental details such as Instance label, size, and center coordinates for each instance. The BEV-Point attributes determine the appearance within the instance, while the style look-up table controls the style variation across instances. + +Instance Attributes. The semantic map S provides semantic labels for BEV points. Following CityDreamer [54], the instance map $\mathbf{Q}$ is introduced to handle the diversity of buildings and cars in urban environments. Specifically, + +$$ +\mathbf {Q} = \operatorname {I n s t} (\mathbf {S}) \tag {3} +$$ + +where $\operatorname{Inst}(\cdot)$ denotes instantiation on semantic maps by detecting connected components. Therefore, the instance label $\mathbf{I} \in \mathbb{R}^{N_{\mathrm{pt}} \times 1}$ for BEV points can be computed as + +$$ +\mathbf {I} = \left\{\mathbf {Q} _ {(x, y)} \mid (x, y, z) \in \mathbf {C} _ {A} \right\} \tag {4} +$$ + +Obviously, $\mathbf{Q}_{(x,y)}\in \mathbf{L}$ , where $\mathbf{L} = \{1,2,\dots ,N_{\mathrm{ins}}\}$ and $N_{\mathrm{ins}}$ is the number of instances. The size $S(l)\in \mathbb{R}^3$ represents the size of the 3D bounding box of the instance $l$ , where $l\in \mathbf{L}$ . The center $\mathcal{C}(l)\in \mathbb{R}^3$ denotes the coordinates of the center of the bounding box of the instance $l$ . + +BEV-Point Attributes. In BEV-Point initialization, the absolute coordinate $\mathbf{C}_A$ is generated, with the origin set at the center of the world coordinate system. Besides the absolute coordinate, the relative coordinate $\mathbf{C}_R \in \mathbb{R}^{N_{\mathrm{pt}} \times 3}$ is introduced, with its origin set at the center of each instance, to specify the normalized point coordinates relative to the instance. Specifically, + +$$ +\mathbf {C} _ {R} = \left\{\mathbf {C} _ {R} ^ {i} \mid \mathbf {C} _ {R} ^ {i} \in \mathbb {R} ^ {3} \right\} _ {i = 1} ^ {N _ {\mathrm {p t}}} \tag {5} +$$ + +where $\mathbf{C}_R^i$ can be derived as + +$$ +\mathbf {C} _ {R} ^ {i} = \frac {2 \left(\mathbf {C} _ {A} ^ {i} - \mathcal {C} (\mathbf {I} ^ {i})\right)}{\mathcal {S} (\mathbf {I} ^ {i})} \tag {6} +$$ + +where $\mathbf{C}_A^i$ and $\mathbf{I}^i$ denote the $i$ -th values in $\mathbf{C}_A$ and $\mathbf{I}$ , respectively. + +During generation, integrating contextual information for BEV points becomes essential. It is achieved by introducing scene features $\mathbf{F}_S\in \mathbb{R}^{N_{\mathrm{pt}}\times C_{FS}}$ derived from BEV maps and indexed using absolute coordinates $\mathbf{C}_A$ . Specifically, + +$$ +\mathbf {G} = \mathcal {E} (\mathbf {H}, \mathbf {S}) \tag {7} +$$ + +$$ +\mathbf {F} _ {S} = \left\{\mathbf {G} _ {(x, y)} \mid (x, y, z) \in \mathbf {C} _ {A} \right\} \tag {8} +$$ + +where $\mathcal{E}$ denotes the Scene Encoder. $\mathbf{G}$ is with the same size of $\mathbf{H}$ and $\mathbf{S}$ . + +Style Look-up Table. In 3D-GS, the appearance of 3D Gaussians is defined by the attributes of each Gaussian. As the number of 3D Gaussians increases, the demands on VRAM and file storage grow significantly, making unbounded scene generation infeasible. To further reduce computational costs, the appearances of instances are encoded into a set of latent vectors $\mathbf{Z}_T \in \mathbb{R}^{N_{\mathrm{ins}} \times C_Z}$ , i.e., + +$$ +\mathbf {Z} _ {T} = \left\{\mathbf {z} _ {T} ^ {i} \mid \mathbf {z} _ {T} ^ {i} \in \mathbb {R} ^ {C Z} \right\} _ {i = 1} ^ {N _ {\text {i n s}}} \tag {9} +$$ + +The style look-up table $\mathcal{T}$ queries the style code $\mathbf{z}_T^i\sim$ $\mathcal{N}(0,1)$ for the instance $l$ . Specifically, + +$$ +\mathbf {z} _ {T} ^ {i} = \mathcal {T} (l) \tag {10} +$$ + +# 3.4. BEV-Point Decoding + +The BEV-Point decoder is designed to generate the Gaussian Attributes $\mathbf{A}$ using the BEV-Point features. It comprises five key modules: positional encoder, point sanitizer, point transformer, modulated MLP, and Gaussian rasterizer. + +Positional Encoder. Rather than feed coordinates directly into the subsequent networks, the positional encoder transforms each point coordinate and corresponding features into a higher-dimensional positional embedding $\mathbf{F}_P \in \mathbb{R}^{N_{\mathrm{pt}} \times C_{F_P}}$ as follows + +$$ +\mathbf {F} _ {P} = \mathcal {P} (\operatorname {C o n c a t} \left(\mathbf {C} _ {R}, \mathbf {F} _ {S}\right)) \tag {11} +$$ + +where $\mathcal{P}(\cdot)$ is the positional encoding function that is applied individually to each value in the given feature $x$ . + +$$ +\mathcal {P} (x) = \left\{\sin \left(2 ^ {i} \pi x\right), \cos \left(2 ^ {i} \pi x\right) \right\} _ {i = 0} ^ {N _ {\mathrm {P E}} - 1} \tag {12} +$$ + +Point Serializer. Unlike NeRF [37], which maintains spatial correlation among sampled points along rays, BEV points and 3D Gaussians are unstructured and unordered due to their irregular nature of point clouds. Therefore, directly applying Multi-layer Perceptrons (MLPs) to generate Gaussian attributes from $\mathbf{F}_P$ may not yield optimal results, as MLPs do not fully consider the structural and contextual characteristics of point clouds. + +To transform unstructured BEV points into a structured format, we present the point serializer $\mathcal{L}:(x,y,z)\to o$ where $o\in \mathbb{Z}$ , to convert the point coordinates into an integer reflecting its order within the given BEV points. + +$$ +\mathcal {L} (x, y, z, g) = \left\lfloor \frac {x}{g ^ {2}} + \frac {y}{g} + z \right\rfloor \tag {13} +$$ + +where $g$ is the grid size that controls the scale of the discrete space for serialization. This ordering ensures that points are rearranged based on the spatial structure defined by the point serializer, resulting in neighboring points in the data structure being close together in space. Thus, the serialized feature $\mathbf{F}_P^S \in \mathbb{R}^{N_{\mathrm{pt}} \times C_{F_P}}$ can be derived as + +$$ +\mathbf {F} _ {P} ^ {S} = \left\{\mathbf {F} _ {P} ^ {O _ {i}} \right\} _ {i = 1} ^ {N _ {\mathrm {p t}}} \tag {14} +$$ + +where $\mathbf{F}_P^{O_i}$ denotes the features of the $O_{i}$ -th BEV point in $\mathbf{F}_P$ . $O_{i}$ denotes the order generated by the point sanitizer. + +Point Transformer. After serialization, the features of BEV points can be processed by a modern Transformer $\mathcal{F}$ [52], producing the feature $\mathbf{F}_T\in \mathbb{R}^{N_{\mathrm{pt}}\times C_{F_T}}$ + +$$ +\mathbf {F} _ {T} = \mathcal {F} \left(\mathbf {F} _ {P} ^ {S}\right) \tag {15} +$$ + +Modulated MLPs. The attributes of 3D Gaussians $\mathbf{A} \in \mathbb{R}^{N_{\mathrm{pt}} \times C_A}$ are generated by applying MLPs $\mathcal{M}$ [21], which + +modulate the style code $\mathbf{Z}_P$ and instance labels $\mathbf{I}$ with the features of BEV points. + +$$ +\mathbf {A} = \mathcal {M} (\operatorname {C o n c a t} \left(\mathbf {F} _ {P}, \mathbf {F} _ {T}\right), \mathbf {Z} _ {P}, \mathbf {I}) \tag {16} +$$ + +where $\mathbf{Z}_P = \{\mathcal{T}(\mathbf{I}^i)\}_{i = 1}^{N_{\mathrm{pt}}}$ + +Gaussian Rasterizer. Given the camera intrinsic and extrinsic parameters $\mathbf{K} \in \mathbb{R}^{3 \times 3}$ and $\mathbf{T} \in \mathbb{R}^{4 \times 4}$ , the image can be rendered with the Gaussian rasterizer $\mathcal{R}$ . + +$$ +\hat {\mathbf {R}} = \mathcal {R} \left(\mathbf {C} _ {A}, \mathbf {A}, \mathbf {K}, \mathbf {T}\right) \tag {17} +$$ + +During rasterization, default values are employed if the required attributes are not generated in $\mathbf{A}$ . These defaults include scale factor $\mathbf{s} = \mathbf{1}$ , rotation quaternion $\mathbf{q} = [1,0,0,0]$ , and opacity $\alpha = 1$ . + +# 3.5. Loss Functions + +The generator is trained using a hybrid objective that combines reconstruction loss with adversarial learning loss. Specifically, we leverage the L1 loss, VGG loss [20], and GAN loss [29] in this combination. + +$$ +\ell = \lambda_ {\mathrm {L} 1} | | \hat {\mathbf {R}} - \mathbf {R} | | + \lambda_ {\mathrm {V G G}} \operatorname {V G G} (\hat {\mathbf {R}}, \mathbf {R}) + \lambda_ {\mathrm {G A N}} \operatorname {G A N} (\hat {\mathbf {R}}, \mathbf {S} _ {G}) \tag {18} +$$ + +where $\mathbf{R}$ denotes the ground truth image. $\mathbf{S}_G$ is the semantic map in perspective view. + +# 4. Experiments + +# 4.1. Datasets + +GoogleEarth [54]. The GoogleEarth dataset, sourced from Google Earth Studio, comprises 400 orbit trajectories captured over Manhattan and Brooklyn. Each trajectory comprises 60 images, with orbit radiuses spanning from 125 to 813 meters and altitudes ranging from 112 to 884 meters. In addition to the images, GoogleEarth provides camera intrinsic and extrinsic parameters, along with 3D semantic and building instance segmentation. + +KITTI-360 [28]. KITTI-360 is an extensive outdoor suburban dataset known for its intricate scene geometry. Within this dataset, scenes are rich in highlights and shadows, resulting in significant variations in the appearance of objects across different scenes. Captured in urban scenarios spanning approximately $73.7\mathrm{km}$ of driving distance, KITTI-360 provides comprehensive 3D bounding box annotations for various classes such as buildings, cars, roads, vegetation, and more. + +# 4.2. Evaluation Protocols + +FID and KID. Fréchet Inception Distance (FID) [17] and Kernel Inception Distance (KID) [5] are metrics for the quality of generated images. Following CityDreamer [54], FID and KID are calculated based on 15K generated frames + +on the GoogleEarth dataset. As for the KITTI-360 dataset, FID and KID are computed using 5K generated frames, consistent with the settings of UrbanGIRAFFE [58]. + +Depth Error. We employ depth error (DE) to assess the 3D geometry following EG3D [8]. The pseudo ground truth depth maps for the generated frames are obtained from a pretrained model [43]. For NeRF-based methods, the depth maps are generated by the accumulation of density $\sigma$ . Conversely, GaussianCity allows for the direct acquisition of depth maps by rasterization. DE is calculated as the L2 distance between the two normalized depth maps. We evaluate DE using 100 frames for each assessed method following CityDreamer [54]. + +Camera Error. Following CityDreamer [54], the camera error (CE) is introduced to evaluate the multi-view consistency. CE quantifies the disparity between the inference camera trajectory and the estimated camera trajectory from COLMAP [45], computed as the scale-invariant normalized L2 distance between the reconstructed and generated camera poses. + +Runtime. Runtime is used to gauge efficiency. It measures the time taken to generate a 960x540 image on the GoogleEarth dataset. All timings are conducted on an NVIDIA Tesla A100, excluding IO time, and averaged over 100 iterations. + +# 4.3. Implementation Details + +Hyperparameters. The grid size $g$ is set to 0.01 and $N_{\mathrm{PE}}$ is set to 64. The feature channels $C_Z, C_{F_S}, C_{F_P}$ , and $C_{F_T}$ are set to 256, 61, 1280, and 256, respectively. The Gaussian attributes $\mathbf{A}$ consist of RGB values only (i.e., $C_A = 3$ ). Initially, the loss weights $\lambda_{\mathrm{L1}}$ , $\lambda_{\mathrm{VGG}}$ , and $\lambda_{\mathrm{GAN}}$ are set to 10, 10, and 0.5, respectively. Afterward, $\lambda_{\mathrm{L1}}$ and $\lambda_{\mathrm{VGG}}$ are reduced by half every 20,000 epochs. + +Training Details. The generator is trained using an Adam optimizer with $\beta = (0, 0.999)$ and a learning rate of $10^{-4}$ . The discriminator is optimized using an Adam optimizer with $\beta = (0, 0.999)$ and a learning rate of $5 \times 10^{-7}$ . Training continues for 200,000 iterations with a batch size of 8 on eight NVIDIA Tesla V100 GPUs. The images are randomly cropped to sizes of $448 \times 448$ for GoogleEarth and $448 \times 224$ for KITTI-360. + +# 4.4. Main Results + +Comparison Methods. On the GoogleEarth dataset, we compare the proposed method to SGAM [47], Persistent-Nature [7], SceneDreamer [11], InfiniCity [30], and CityDreamer [54], following the protocol established by CityDreamer. Except for InfiniCity, whose code is not accessible, we retrain the remaining methods using the released code on the GoogleEarth dataset to ensure fair comparisons. On the KITTI-360 dataset, we compare our method to StyleGAN2 [21], GSN [14], GIRAFFE [39], and Urban + +Table 1. Quantitative comparison on GoogleEarth and KITTI-360. The best results are highlighted in bold. Note that "RT:" denotes "Runtime", measured in milliseconds on an NVIDIA Tesla A100. + +
GoogleEarthKITTI-360
MethodFID ↓KID ↓DE ↓CE ↓RT. ↓MethodFID ↓KID ↓
SGAM [47]277.640.3580.575239.291193StyleGAN [21]31.90.021
Pers.Nature [7]123.830.1090.32686.371167GSN [14]160.00.114
SceneDreamer [11]213.560.2160.1520.186620GIRAFFE [39]112.10.117
CityDreamer [54]97.380.0960.1470.0605580UrbanGIR. [58]39.60.036
GaussianCity86.940.0900.1360.05793GaussianCity29.50.017
+ +![](images/ce34cf6867a50259f7d3516e3dd31169308b169fc0f11ec4594ecb01c81444e1.jpg) +Figure 3. Qualitative comparison on GoogleEarth. Note that "Pers.Nature" is short for PersistentNature [7]. The visual results of InfiniCity [30] are provided by the authors since the source code is not accessible. + +GIRAFFE [58], following the protocol outlined by UrbanGIRAFFE. As the training code and pretrained model for UrbanGIRAFFE are unavailable, the results of UrbanGIRAFFE are directly obtained from [58]. + +Comparison on GoogleEarth. Figure 3 shows qualitative comparisons against baselines on the GoogleEarth dataset. PersistentNature utilizes a tri-plane representation, which faces difficulties in generating realistic renderings. Both SceneDreamer and InfiniCity employ voxel grids as their + +representation, yet they still encounter significant structural distortions in buildings due to all buildings being assigned the same semantic label. CityDreamer and GaussianCity both introduce instance labels, achieving improved generation results. However, CityDreamer composites two neural fields, resulting in artifacts at the seams of images. In contrast, GaussianCity achieves better visual results and significantly lower runtime, as indicated in Table 1. + +Comparison on KITTI-360. Figure 4 illustrates qualita + +![](images/2d71338cc619fe31c1b909feebdbc003c3449ae4b9137af5e9d2b5ac9d111d63.jpg) +Figure 4. Qualitative comparison on KITTI-360. The visual results of UrbanGIRAFFE [58] are provided by the authors since the training code and pretrained model are unavailable. + +![](images/7c5e338053f191977e6ca1bd81b6b3f137e8e1d45e3e86ba47acc4ef722371ce.jpg) +Figure 5. User study on GoogleEarth and KITTI-360. All scores are in the range of 5, with 5 indicating the best. Note that "Pers.Nature" and "UrbanGIR." denotes PersistentNature [7] and UrbanGIRAFFE [58], respectively. + +tive comparisons against baseline methods on the KITTI-360 dataset. GSN uses an implicit representation named latent grid, which can easily introduce structural distortion in street-view generation. UrbanGIRAFFE employs a voxel grid as its 3D representation, but due to the resolution limitations of the voxel grid, the generated scenes may exhibit jagged artifacts. In contrast, GaussianCity adopts a more flexible point cloud as its representation, thus yielding superior visual results. The lower FID and KID scores in Table 1 also attest to the effectiveness of the proposed method. + +User Study. To more accurately evaluate the 3D consistency and quality of the unbounded 3D city generation, we conduct an output evaluation [6], following the user study conducted in CityDreamer. In this study, we requested feed + +back from 20 volunteers to assess each generated camera trajectory based on three criteria: 1) the perceptual quality of the imagery, 2) the level of 3D realism, and 3) the 3D view consistency. Ratings are provided on a scale of 1 to 5, with 5 indicating the highest rating. The results are shown in Figure 5, demonstrating that the proposed method significantly surpasses the baselines by a considerable margin. + +# 4.5. Ablation Studies + +Effectiveness of BEV-Point Representation. The proposed BEV-Points, a compact scene representation, are essential for enabling 3D-GS to generate unbounded scenes by 1) considering point visibility during generation and 2) adjusting sampling density for different semantic cate + +Table 2. Effectiveness of BEV-Point Representation. Note that "RayInt." denotes "Ray Intersection", respectively. The VRAM usage and inference time are measured on an NVIDIA Tesla A100. + +
VisibilityDensity#PointsVRAM (G)Time (s)
XX31MOut of Memory
X✓20MOut of Memory
Region✓1.4MOut of Memory
Instance✓680K10.340.16
RayInt.X38.0K1.410.10
RayInt.✓31.7K1.390.09
+ +Table 3. Effectiveness of BEV-Point Decoder. Note that "Ser." and "Pt.Trans." denote "Point Validator" and "Point Transformer", respectively. + +
Ser.Pt.Trans.FID ↓KID ↓DE ↓CE ↓
XX151.270.1790.1850.135
X✓119.400.1380.1590.118
✓✓86.940.0900.1360.057
+ +Table 4. Comparison of different serialization methods. Note that "Eq. 13" denote the serialization used in Point Allocator. + +
Eq. 13HilbertFID ↓KID ↓DE ↓CE ↓
✓✗86.940.0900.1360.057
✗✓86.720.0880.1360.056
✓✓86.280.0830.1350.055
+ +gories using a binary density map. Table 2 compares different methods for considering point visibility, including no consideration, region-based, instance-based, and ray-intersection-based strategies for point selection. All methods keep the number of points constant: "region-based" selects points within the camera coverage, "Instance-based" selects visible instances, and "ray-intersection-based" identifies visible points through ray intersection [2]. The "ray-intersection-based" method is the most efficient compared to "region-based" and "instance-based" approaches, eliminating the most invisible points and reducing the total number of points by $97.7\%$ and $96\%$ , respectively. The density map is crucial in the BEV-Point representation because it reduces the number of points for semantic categories that have less texture and need fewer points. As shown in Table 2, removing the density map increases the point count by $20\% -50\%$ . As shown in Figure 1(b-c), the proposed BEV-Point representation maintains constant VRAM usage during training, unlike the original 3D-GS [22], which is impractical for unbounded scene generation due to excessive VRAM consumption. Additionally, it significantly reduces file storage as the number of points increases. + +Effectiveness of BEV-Point Decoder. BEV-Point Decoder + +consists of two key components: Point Validator and Point Transformer. As shown in Table 3 and Figure I, removing both components leads to a significant degeneration due to the absence of spatial correlations. Introducing only the Point Validator partially establishes spatial correlation, but it does not achieve the same effectiveness as using both components together. + +Effectiveness of Compilation Methods. To investigate the impact of different serialization methods in point serializer, we compare the effects of using Equation 13, Hilbert curve [18] adopted in [9, 52], and both simultaneously on the generation results. As shown in Table 4, different serialization methods have minimal impact on the final generation results. We employ Equation 13 in Point Serializer because of its reduced computational complexity. Kindly refer to Figure II for more qualitative comparisons. + +# 4.6. Limitations + +While our method demonstrates promising results for unconditional 3D city generation, it still has several limitations. Firstly, the BEV-Point Initialization elevates points to a height based on the corresponding value in the height field, which assumes buildings adhere to the Manhattan assumption and cannot represent hollow structures. Secondly, the BEV-Point decoder does not fully exploit the expressive capacity of 3D-GS, as it only predicts RGB in the Gaussian attributes. However, predicting an excessive number of attributes simultaneously may destabilize the training process. Kindly refer to the discussion in Section A.2. + +# 5. Conclusion + +In this paper, we introduce GaussianCity for generating unbounded 3D cities. It is the first method to employ 3D-GS for unbounded scene generation. We introduce BEV-Point, a highly compact scene representation to mitigate the substantial increase in VRAM usage associated with representing large-scale scenes using 3D-GS. Additionally, we present BEV-Point Decoder, which leverages Point Serializer to capture the structural and contextual characteristics of unordered BEV points. Compared to previous methods, GaussianCity achieves better visual results and a 60-fold increase in runtime speed compared to CityDreamer. Extensive experimental results demonstrate the effectiveness of the proposed GaussianCity in generating both drone-view and street-view in city scenes. + +Acknowledgements. This study is supported by the Ministry of Education, Singapore, under its MOE AcRF Tier 2 (MOET2EP20221- 0012, MOE-T2EP20223-0002), NTU NAP, and under the RIE2020 Industry Alignment Fund - Industry Collaboration Projects (IAF-ICP) Funding Initiative, as well as cash and in-kind contribution from the industry partner(s). + +# References + +[1] Rameen Abdal, Wang Yifan, Zifan Shi, Yinghao Xu, Ryan Po, Zhengfei Kuang, Qifeng Chen, Dit-Yan Yeung, and Gordon Wetzstein. Gaussian shell maps for efficient 3D human generation. In CVPR, 2024. 2 +[2] John Amanatides and Andrew Woo. A fast voxel traversal algorithm for ray tracing. In Eurographics, 1987. 8 +[3] Miguel Ángel Bautista, Pengsheng Guo, Samira Abnar, Walter Talbott, Alexander Toshev, Zhuoyuan Chen, Laurent Dinh, Shuangfei Zhai, Hanlin Goh, Daniel Ulbricht, Afshin Dehghan, and Joshua M. Susskind. GAUDI: A neural architect for immersive 3D scene generation. 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However, how to collect substantial point-wise annotations of the point clouds at affordable cost for the end-to-end network training still needs to be solved. In this paper, we propose Generative Hard Example Augmentation (GHEA) to achieve novel examples of point clouds, which enrich the data for training the segmentation network. Firstly, GHEA employs the generative network to embed the discrepancy between the point clouds into the latent space. From the latent space, we sample multiple discrepancies for reshaping a point cloud to various examples, contributing to the richness of the training data. Secondly, GHEA mixes the reshaped point clouds by respecting their segmentation errors. This mixup allows the reshaped point clouds, which are difficult to segment, to join as the challenging example for network training. We evaluate the effectiveness of GHEA, which helps the popular segmentation networks to improve the performances. + +# 1. Introduction + +Semantic point cloud segmentation requires understanding the surrounding contexts of the 3D points to be segmented. These point-based contexts capture the points' spatial configuration and their categories' co-existence. Because the point cloud is a flexible structure, it leads to a high degree of freedom to determine the neighbors of each point, thus yielding diverse point-based contexts. + +Deep networks [1-8] have been widely used to learn point-based contexts. They learn from sufficient, challenging data to adapt to diverse contexts. Point clouds are usually collected at an expensive cost, limiting the amount of training data. To augment training data, some methods [9-14] rely on the pre-scribed manipulation of the entire semantic point cloud (e.g., rotate, crop, and scale) or the indi + +vidual points (e.g., create, remove, and shift). But they produce less challenging examples, where some point-wise category labels could be problematic after manipulation. Another family of methods [15-21] use the generative network to produce novel point clouds with diverse shapes, allowing challenging examples to emerge. Unlike the deformation of semantic point clouds, the newly generated point clouds have unavailable point-wise labels to align. They are inapplicable to the end-to-end training of segmentation network. + +In this paper, we propose the Generative Hard Example Augmentation (GHEA) to augment the semantic point cloud data for training the general segmentation networks. We illustrate the training of the segmentation network with GHEA in Figure 1, where the whole pipeline consists of the Generative Point Cloud Reshape, Generative Example Mixup, and Network Update. + +In the Generative Point Cloud Reshape (see Figure 1(a)), we employ the generative network to reshape the semantic point cloud as new training examples. Given a pair of semantic point clouds, the generative network learns their discrepancy in terms of the spatial distribution of points in different categories. It embeds this discrepancy into a latent space. The generative network regards a semantic point cloud as a source example to sample multiple discrepancy representations from the latent space. Each representation reconfigures each point of the source example to a new location. It also renews the reconfigured point's category label, yielding a more reasonable label than the trivial manipulation of available points. We reshape each source example, generating novel examples with point-wise category labels. + +In the Generative Example Mixup (see Figure 1(b)), we pass the generated examples of point cloud into the segmentation network, which predicts the segmentation scores for points. Each point of the generated examples has a renewed label compared to the predicted score for measuring the segmentation error. We respect the segmentation errors for mixing up multiple generated examples. This is done by using the segmentation errors to weigh the discrepancy representations, which correspond to the generated examples individually. We regard the weighted representations + +![](images/3e52c29a2665387c526b1581b44f060bca313e73d9825d9d269d7151e2b00de0.jpg) +Figure 1. The pipeline of GHEA. (a) In the generative point cloud reshape, the generative network learns from the discrepancy between the source and target examples. It generates new examples with point-wise labels. (b) In the generative example mixup, the segmentation network evaluates the segmentation errors for each generated example, weighted and aggregated as the hard example. We aggregate the hard example with the source examples, adding it to the target examples to update the segmentation and generative network. + +as a mixup discrepancy in the latent space. The generated examples with many segmentation errors contribute heavily to the mixup discrepancy, which reshapes the source example to a hard example. + +In the Network Update (see the blue arrow in the top of Figure 1), we aggregate the source and hard examples to update the segmentation network. We add the hard examples to the target example (see the dash arrow in the bottom of Figure 1) for updating the generative network, thus adjusting the latent space of discrepancy. It allows the Generative Point Cloud Reshape to produce more diverse and challenging examples, further augmenting the training data. + +We equip the general segmentation networks with GHEA, effectively improving the performances on the ShapeNetPart [22], S3DIS [23], and ScanNet V2 [24] datasets for semantic point cloud segmentation. The main contributions are summarized as follows: + +- We advocate the idea of GHEA to produce rich data of the semantic point clouds. +- We propose an effective component of GHEA, the generative example mixup, for combining the generated point clouds and producing the challenging examples to train a more powerful segmentation network. +- We conduct comprehensive analysis on GHEA, which achieves SOTA results on several public datasets, demonstrating effectiveness and generality of our method. + +# 2. Related Work + +We mainly introduce two different families of data augmentation for point cloud, i.e., the manipulation of semantic point cloud and the generation of point cloud without pointwise category labels, which are relevant to our method. + +# 2.1. Semantic Point Cloud Manipulation + +Many methods for augmenting the point cloud data [1, 7, 12, 13, 25-29] utilize the global or local manipulation to deform the source examples, forming the new examples for training the segmentation networks [12-14, 30-36]. Typically, Qi et al. [9, 10] and Qian et al. [11] globally rotate, translate and jitter the point clouds. Kim et al. [37] spatially deform the local structure of point clouds. These methods focus on the geometric transformations without updating the category labels of the 3D points. Note that a point may be moved from an object (or a part) region to another region whose category differs from the point's original label, thus misleading the network training. More importantly, the trivial manipulations of point clouds are less capable of producing challenging examples. + +Instead of using the above manipulations, we construct the generative network to reshape the source training example into new examples. Moreover, our network respects the spatial distribution of semantic categories to renew pointwise labels. We further mix the new examples according to their segmentation errors, producing more challenging examples to supervise segmentation network better. + +# 2.2. Point Cloud Generation + +There have many works on using the generative networks to produce new point clouds, which have more diverse shapes in contrast to the existing data [17-20, 38-42]. Zamorski et al. [43] and Luo et al. [20] use VAE [16, 44] and the diffusion model for the point cloud generation. Tang et al. [45] propose Warping-GAN, which uses pre-defined priors to generate point clouds. Li et al. [15] jointly optimize the data augmentation and segmentation networks. The above methods concentrate on generating point clouds with diverse and reasonable shapes, which lack point-wise labels for training the segmentation network. + +Our generative network not only learns to reshape the source example of a point cloud in a geometric manner but also learns the spatial distribution of semantic categories. It accurately associates each point of the generated example with a semantic label, thus addressing the problem of missing the point-wise labels for the generated point clouds. + +# 3. Method Overview + +In Figure 1, we illustrate the segmentation network with the Generative Hard Example Augmentation, which includes the iterative steps of Generative Point Cloud Reshape, Generative Example Mixup, and Network Update. + +Generative Point Cloud Reshape We illustrate the Generative Point Cloud Reshape in Figure 1(a). $\mathbf{R},\mathbf{T}\in$ $\mathbb{R}^{N\times (3 + C)}$ are source and target examples of semantic point clouds. $N$ is the number of points. Each point has the 3D coordinates and the category label ( $C$ -dimensional one-hot vector). We voxelize $\mathbf{R}$ and $\mathbf{T}$ as the grids $\mathcal{G}(\mathbf{R}),\mathcal{G}(\mathbf{T})\in$ $\mathbb{R}^{(M\times M\times M)\times (3 + C)}$ . $M\times M\times M$ represents the spatial resolution of the grid. We subtract $\mathcal{G}(\mathbf{R})$ from $\mathcal{G}(\mathbf{T})$ , yielding the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})\in \mathbb{R}^{(M\times M\times M)\times (3 + C)}$ . We employ a generative network to embed $\mathcal{D}(\mathbf{R},\mathbf{T})$ into the latent space, where $\mathcal{D}(\mathbf{R},\mathbf{T})$ is represented by a lower-dimensional discrepancy representation $\mathbf{Z}\in \mathbb{R}^D$ . The generative network randomly samples a set of discrepancy representations $\{\mathbf{Z}_o\in \mathbb{R}^D\mid o = 1,\dots,O\}$ from the latent space. Conditioned on the voxelized grid $\mathcal{G}(\mathbf{R})$ , the generative network can use $\mathbf{Z}_o$ to produce the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T}_o)$ , which reshapes source example $\mathbf{R}$ to the generated example of point cloud $\mathbf{T}_o$ . We achieve a set of generated examples $\{\mathbf{T}_o\in \mathbb{R}^{N\times (3 + C)}\mid o = 1,\dots,O\}$ for $\mathbf{R}$ . + +Generative Example Mixup The Generative Example Mixup is illustrated in Figure 1(b). Here, we construct the segmentation network that takes input as every generated example in $\{\mathbf{T}_o\in \mathbb{R}^{N\times (3 + C)}\mid o = 1,\dots,O\}$ Based on the 3D coordinates $\mathbf{T}_o^{(3)}\in \mathbb{R}^{N\times 3}$ of the $o^{th}$ generated example $\mathbf{T}_o$ , the segmentation network predicts the segmentation scores in $S(\mathbf{T}_o^{(3)})\in \mathbb{R}^{N\times C}$ . We compare the predicted scores in $S(\mathbf{T}_o^{(3)})$ with the generated labels of $\mathbf{T}_o^{(C)}\in \mathbb{R}^{N\times C}$ , computing the segmentation error $\mathbf{E}_o\in \mathbb{R}$ for measuring how difficult it is to segment the generated example $\mathbf{T}_o$ . The segmentation errors $\{\mathbf{E}_o\in$ $\mathbb{R}\mid o = 1,\ldots ,O\}$ weight the discrepancy representations $\{\mathbf{Z}_o\in \mathbb{R}^D\mid o = 1,\dots,O\}$ , forming the mixup representation $\widetilde{\mathbf{Z}}\in \mathbb{R}^D$ in the latent space. The generative network uses $\widetilde{\mathbf{Z}}$ to produce the mixup discrepancy grid $\mathcal{D}(\mathbf{R},\widetilde{\mathbf{T}})$ which reshapes the source example $\mathbf{R}$ to the hard example of point cloud $\widetilde{\mathbf{T}}\in \mathbb{R}^{N\times (3 + C)}$ + +Network Update We illustrated Network Update with the blue arrow and the dash arrow in Figure 1. We aggregate hard example $\widetilde{\mathbf{T}}$ , where each point is associated with the category label, with source examples to fine-tune the pa + +rameter of the segmentation network. Moreover, we add hard example $\widetilde{\mathbf{T}}$ to target examples, paired with any source example to update the generative network. In this way, we adjust the latent space, where hard examples have more chances to be sampled for updating segmentation network. + +# 4. Generative Hard Example Augmentation + +We elaborate the pipeline of GHEA, including the Generative Point Cloud Reshape, Generative Example Mixup, Network Update (see Section 4.1-4.3). These three steps are conducted iteratively. We leave the critical implementation details and code segments in the supplementary file. + +# 4.1. Generative Point Cloud Reshape + +We illustrate the details of the Generative Point Cloud Reshape in Figure 2. We employ the trilinear interpolation [46] to voxelize the source and target examples $\mathbf{R},\mathbf{T}$ respectively, forming the voxelized grids $\mathcal{G}(\mathbf{R}),\mathcal{G}(\mathbf{T})$ .We compute the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})$ as: + +$$ +\mathcal {G} (\mathbf {R}) = \mathcal {I} (\mathbf {R}, \mathbf {N}), +$$ + +$$ +\mathcal {G} (\mathbf {T}) = \mathcal {I} (\mathbf {T}, \mathbf {N}), \tag {1} +$$ + +$$ +\mathcal {D} (\mathbf {R}, \mathbf {T}) = \mathcal {G} (\mathbf {T}) - \mathcal {G} (\mathbf {R}), +$$ + +where $\mathcal{I}$ is the trilinear interpolation. $\mathbf{N} \in \mathbb{R}^{(M \times M \times M) \times 3}$ contains $M \times M \times M$ vertexes' coordinates, which represents a 3D grid subdivided regularly for voxelization. + +Embedding of Discrepancy Grid In Figure 2(a), the generative network embeds discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})$ into the latent space. The network structure is formulated as: + +$$ +[ \boldsymbol {\mu}, \boldsymbol {\sigma} ] = \operatorname {e n c o d e r} (\mathcal {G} (\mathbf {R}), \mathcal {D} (\mathbf {R}, \mathbf {T})), +$$ + +$$ +\mathcal {D} (\mathbf {R}, \mathbf {T} ^ {\prime}) = d e c o d e r (\mathcal {G} (\mathbf {R}), \boldsymbol {\mu} + \boldsymbol {\sigma} \odot \mathbf {Z}). +$$ + +Here, the encoder regards the voxelized grid $\mathcal{G}(\mathbf{R})$ as a condition. It embeds the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})$ into the latent space. We model the latent space by a multivariate Gaussian distribution, parameterized by the mean-value and standard-deviation vectors $\pmb{\mu},\pmb{\sigma}\in \mathbb{R}^{D}$ . Given the discrepancy representation $\mathbf{Z}$ randomly sampled from the normal distribution, we compute the latent vector $\pmb{\mu} + \pmb{\sigma}\odot \mathbf{Z}$ ( $\odot$ means the element-wise multiplication), which represents the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})$ in the latent space. By regarding the voxelized grid $\mathcal{G}(\mathbf{R})$ as a condition, the decoder uses the latent vector $\pmb{\mu} + \pmb{\sigma}\odot \mathbf{Z}$ to compute the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T}')\in \mathbb{R}^{(M\times M\times M)\times (3 + C)}$ , which estimates the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T})$ computed by Eq. (1). + +Sampling of Discrepancy Grid As illustrated in Figure 2(b), the generative network allows us to sample multiple discrepancy grids for the source example $\mathbf{R}$ as: + +$$ +[ \boldsymbol {\mu} ^ {\prime}, \boldsymbol {\sigma} ^ {\prime} ] = c o n d i t i o n (\mathcal {G} (\mathbf {R})) +$$ + +$$ +\mathcal {D} (\mathbf {R}, \mathbf {T} _ {o}) = d e c o d e r (\mathcal {G} (\mathbf {R}), \boldsymbol {\mu} ^ {\prime} + \boldsymbol {\sigma} ^ {\prime} \odot \mathbf {Z} _ {o}), +$$ + +![](images/8600e0e7f7c166bc12fe96a7155c449999c6fb9c5600aca5861af8b18e6e9a31.jpg) +Figure 2. Illustration of the generative point cloud reshape. (a) We subtract the voxelized grids of the source and target examples, achieving the discrepancy grid embedded by the generative network into the latent space. (b) The generative network samples multiple discrepancy grids from the latent space for the source example. (c) We use the sampled discrepancy grids to reshape the source example to the generated examples with various shapes. + +where condition means the condition branch of the generative network. Unlike the encoder (see Eq. (2)), the condition branch estimates the parameters of the latent space (i.e., the mean-value and standard-deviation vectors $\pmb{\mu}^{\prime},\pmb{\sigma}^{\prime}\in \mathbb{R}^{D})$ conditioned on the voxelized grid $\mathcal{G}(\mathbf{R})$ only. We randomly sample the discrepancy representations $\{\mathbf{Z}_o\in \mathbb{R}^D\mid o = 1,\dots,O\}$ from the normal distribution. The $o^{th}$ representation $\mathbf{Z}_o$ is used to compute the latent vector $\pmb{\mu}^{\prime} + \pmb{\sigma}^{\prime}\odot \mathbf{Z}_{o}$ . Based on this latent vector and $\mathcal{G}(\mathbf{R})$ , the decoder samples the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T}_o)$ . We utilize $\mathcal{D}(\mathbf{R},\mathbf{T}_o)$ to generate the new example of point cloud $\mathbf{T}_o$ . + +Reshape of Source Example We use the discrepancy grids $\{\mathcal{D}(\mathbf{R},\mathbf{T}_o)\in \mathbb{R}^{(M\times M\times M)\times (3 + C)}\mid o = 1,\dots,O\}$ to reshape the source example $\mathbf{R}$ to the new examples $\{\mathbf{T}_o\in \mathbb{R}^{N\times (3 + C)}\mid o = 1,\dots,O\}$ (see Figure 2(c)). By reformulating Eq. (1), we add the discrepancy grid $\mathcal{D}(\mathbf{R},\mathbf{T}_o)$ to the voxelized grid $\mathcal{G}(\mathbf{R})$ of the source example $\mathbf{R}$ , forming the voxelized grid $\mathcal{G}(\mathbf{T}_o)\in \mathbb{R}^{(M\times M\times M)\times (3 + C)}$ as: + +$$ +\mathcal {G} (\mathbf {T} _ {o}) = \mathcal {D} (\mathbf {R}, \mathbf {T} _ {o}) + \mathcal {G} (\mathbf {R}). \tag {4} +$$ + +Voxelized grid $\mathcal{G}(\mathbf{T}_o)$ will regress a 3D-coordinate offset for each point of source example by fully-connected layers. We add the offset to each point's coordinate as: + +$$ +\mathbf {T} _ {o} ^ {(3)} = \mathcal {F} (\mathcal {G} (\mathbf {T} _ {o})) + \mathbf {R} ^ {(3)}, \tag {5} +$$ + +$$ +\mathbf {T} _ {o} ^ {(C)} = \mathcal {I} (\mathcal {G} (\mathbf {T} _ {o}) ^ {(C)}, \mathbf {T} _ {o} ^ {(3)}), \tag {5} +$$ + +where $\mathcal{F}$ denotes the fully-connected layers. $\mathbf{R}^{(3)},\mathbf{T}_o^{(3)}\in$ $\mathbb{R}^{N\times 3}$ represents the coordinates of all points in source and generated examples $\mathbf{R}$ and $\mathbf{T}_o$ , respectively. Given the 3D coordinates in $\mathbf{T}_o^{(3)}$ , we conduct the trilinear interpolation + +$\mathcal{I}$ , which propagates the category scores in the voxelized grid $\mathcal{G}(\mathbf{T}_o^{(C)}) \in \mathbb{R}^{(M \times M \times M) \times C}$ to each point in the generated example $\mathbf{T}_o^{(C)}$ . We concatenate the coordinates in $\mathbf{T}_o^{(3)}$ and category scores in $\mathbf{T}_o^{(C)}$ as the generated example $\mathbf{T}_o$ . + +# 4.2. Generative Example Mixup + +We illustrate the Generative Example Mixup in Figure 3. We feed every generated sample to the segmentation network, which predicts the segmentation scores in $\{S(\mathbf{T}_o^{(3)})\in \mathbb{R}^{N\times C}\mid o = 1,\dots,O\}$ . + +Weighting of Hard Example In Figure 3(a), given all point coordinates $\mathbf{T}_o^{(3)}$ in the generated example $\mathbf{T}_o$ , we compare the predicted scores in $S(\mathbf{T}_o^{(3)})$ with the scores in $\mathbf{T}_o^{(C)} \in \mathbb{R}^{N \times C}$ to compute the error $\mathbf{E}_o \in \mathbb{R}$ as: + +$$ +\mathbf {E} _ {o} = \mathcal {L} _ {C} \left(S \left(\mathbf {T} _ {o} ^ {(3)}\right), \mathbf {T} _ {o} ^ {(C)}\right), \tag {6} +$$ + +where $\mathcal{L}_C$ is the cross-entropy loss. Here, we define $\mathbf{E}_o$ as the average of cross-entropy losses of all points in $\mathbf{T}_o$ . A larger segmentation error $\mathbf{E}_o$ means that $\mathbf{T}_o$ is a hard example. It plays as a larger weight for the hard example, which contributes heavily to the mixup of examples. + +Given the discrepancy representations $\{\mathbf{Z}_o\in \mathbb{R}^D\mid o = 1,\dots,O\}$ associated with the generated samples and the segmentation errors $\{\mathbf{E}_o\in \mathbb{R}\mid o = 1,\dots,O\}$ , we weight the mixup representation $\widetilde{\mathbf{Z}}\in \mathbb{R}^{D}$ for the hard example as: + +$$ +\widetilde {\mathbf {Z}} = \sum_ {o = 1} ^ {O} \mathbf {E} _ {o} \cdot \mathbf {Z} _ {o}. \tag {7} +$$ + +Generative Hard Example We show the example mixup in Figure 3(b). The mixup representation $\tilde{\mathbf{Z}}$ is used by the + +![](images/cc309779c876e4e3978f2aeb7a70432b8b51167e4c4277c903f3581162fd5121.jpg) +Figure 3. Illustration of the generative example mixup. (a) We use the segmentation errors to weight the discrepancy representations of the generated examples, yielding the mixup representation. A point-wise error with a lower/higher value is represented by a lighter/darker color. (b) The generative network uses the mixup representation to sample the hard example from the latent space. + +decoder of the generative network in place of the discrepancy representation in Eq. (3), to generate a new discrepancy grid, which reshapes the source example (see Eqs. (4) and (5)) as the hard example of point cloud $\widetilde{\mathbf{T}}$ . A more significant error $\mathbf{E}_o$ lets the shape of the hard example $\widetilde{\mathbf{T}}$ be more like the generated example $\mathbf{T}_o$ . + +# 4.3. Network Update + +We formulate the training objective $\mathcal{L}$ for updating the whole network as: + +$$ +\begin{array}{l} \mathcal {L} = \mathcal {L} _ {K} ((\boldsymbol {\mu}, \sigma), (\boldsymbol {\mu} ^ {\prime}, \sigma^ {\prime})) \\ + \mathcal {L} _ {2} \left(\mathcal {D} (\mathbf {R}, \mathbf {T}), \mathcal {D} (\mathbf {R}, \mathbf {T} ^ {\prime})\right) \\ + \mathcal {L} _ {C} \left(\mathcal {S} \left(\mathbf {R} ^ {(3)}\right), \mathbf {R} ^ {(C)}\right) \tag {8} \\ + \mathcal {L} _ {C} (\mathcal {S} (\widetilde {\mathbf {T}} ^ {(3)}), \widetilde {\mathbf {T}} ^ {(C)}). \\ \end{array} +$$ + +Update of Generative Network The first two terms of Eq. (8), i.e., $\mathcal{L}_K$ and $\mathcal{L}_2$ , denote the Kullback-Leibler divergence and L2-norm. During the network update, $\mathcal{L}_K$ enforces the latent space $(\mu', \sigma')$ conditioned on the voxelized grid $\mathcal{G}(\mathbf{R})$ only (see Eq. (3)) to estimate the latent space $(\mu, \sigma)$ conditioned on both the voxelized grid $\mathcal{G}(\mathbf{R})$ and the discrepancy grid $\mathcal{D}(\mathbf{R}, \mathbf{T})$ (see Eq. (2)). The latent space $(\mu', \sigma')$ can be used for sampling various discrepancy grids, rather than using the given discrepancy grid $\mathcal{D}(\mathbf{R}, \mathbf{T})$ to reshape the source example. We employ $\mathcal{L}_2$ to minimize the difference between the discrepancy grids $\mathcal{D}(\mathbf{R}, \mathbf{T})$ and $\mathcal{D}(\mathbf{R}, \mathbf{T}')$ . It allows the encoder to effectively embed the discrepancy grid $\mathcal{D}(\mathbf{R}, \mathbf{T})$ into the latent space as a lower-dimensional discrepancy representation, which can be successfully decoded back to the original discrepancy grid. Because the network update is conducted iteratively, the hard example $\widetilde{\mathbf{T}}$ can play the role of the target example $\mathbf{T}$ for + +updating the generative network, which reshapes the source example to more challenging examples. + +Update of Segmentation Network The segmentation network takes input as point coordinates of source and hard examples $\mathbf{R}^{(3)}, \widetilde{\mathbf{T}}^{(3)} \in \mathbb{R}^{N \times 3}$ , respectively, to predict segmentation scores $S(\mathbf{R}^{(3)}), S(\widetilde{\mathbf{T}}^{(3)}) \in \mathbb{R}^{N \times C}$ . In the last two terms of Eq. (8), we use cross-entropy losses to penalize the segmentation errors on source and hard examples. + +# 5. Experimental Results + +# 5.1. Datasets and Metrics + +We evaluate different methods on the ShapeNetPart [22], S3DIS [23], and ScanNet V2 [24] datasets, where we report the performances of part- and object-level segmentation. + +The ShapeNetPart dataset has 16,880 point clouds (12,136/1,870/2,874 for training/validation/testing) belonging to 16 object categories and 50 kinds of part labels. We use Category mean IoU (Cat. mIoU) and Instance mean IoU (Ins. mIoU) as the evaluation metrics. + +The S3DIS dataset provides 271 point clouds with 6 areas from indoor scenes, where each point has an object-level label selected from 13 categories. We report segmentation results in terms of the mean IoU (mIoU), overall pointwise accuracy (OA), and mean classwise accuracy (mAcc). + +The ScanNet V2 dataset has 1,613 scans (1,201/312/100 for training/validation/testing) about 3D indoor scenes of various rooms, which belongs to 20 semantic categories. We select validation mIoU (Val. mIoU) and test mIoU to evaluate the performance of GHEA and all baselines. + +# 5.2. Part-level Segmentation + +Impact of GHEA on Various Segmentation Backbones We remove or add GHEA to the training of the fa + +![](images/469967c2240fe30480e48902aa81a8c98709bd0d96cb2629d1bcb9b610a9e446.jpg) +Figure 4. Part-level segmentation results on the ShapeNetPart dataset. The red dash squares highlight the wrong/correct segmentation without/with the help of GHEA. + +![](images/0b0e13095d34840c60b3bb69ba7552532b72251b01a4415360fe13ddae18cb64.jpg) + +![](images/9a3fb1b6c8d45894f37d3445ea26a46fa8b40a66015e4de97ee1f0af980d0827.jpg) + +![](images/797eb062209988089e04e6784a912050af48cd14d59b7a5c7114a597de45e463.jpg) + +Table 1. Results of backbones with CDA, PointWOLF, and GHEA on the ShapeNetPart test set. + +
MethodCat. mIoUIns. mIoU
PointNet++81.284.2
w/ CDA81.985.1
w/ PW82.185.4
w/ GHEA83.386.4
PointNeXt84.886.7
w/ CDA85.287.0
w/ PW85.387.1
w/ GHEA85.987.6
PointMetaBase84.286.4
w/ CDA85.187.1
w/ PW85.487.2
w/ GHEA86.187.8
DeLA85.887.4
w/ CDA86.087.5
w/ PW86.187.5
w/ GHEA86.688.0
+ +Table 2. Various ways for reshaping the point clouds. + +
Reshape MethodCat. mIoUIns. mIoU
RandomPW85.487.2
ManipulationCDA85.187.1
DiscriminativeFC82.084.1
NetworkTF84.787.0
GenerativePL83.886.2
NetworkGHEA86.187.8
+ +mous segmentation backbones, i.e., PointNet++ [10], PointNeXt [11], PointMetaBase [33], and DeLA [47] and report the performances in Table 1. Without GHEA, we train the backbone networks with the source data only, with conventional data augmentation strategy (w/ CDA), and with PointWOLF (w/ PW) [37], respectively. In comparison, the hard examples produced by GHEA successfully enrich the training data, strengthening the segmentation abilities of these backbones. GHEA improves the segmentation performances $(0.8\sim 2.1$ Cat. mIoU and $0.6\sim 2.2$ Ins. mIoU) on the ShapeNetPart test set. In Figure 4, we compare the challenging examples to be segmented, where the backbone networks with GHEA produce more accurate segmentation results. In the ablation experiments below, we employ PointMetaBase as the segmentation backbone. + +Variants of Point Cloud Reshape We examine the effectiveness of the generative point cloud reshape in GHEA by + +![](images/c6524e5d38236843ef7e98cbd6b338fb659ebb238370c93130aa3442ac9bb572.jpg) +Figure 5. The diversity between the source and new examples generated in different epochs of the network training. + +![](images/001e70ac2c947c16700dc068bbc2c89bd082a321ff92bfa787e69e38106103db.jpg) + +changing to other alternatives (see Table 2). + +We replace the generative point cloud reshape with the random manipulation of the point cloud. We test two typical random manipulation, i.e., PointWOLF [37] (PW) and conventional data augmentation (CDA) [9, 10]. PW deforms the point cloud locally. CDA rotates and scales the entire point cloud, where the points are jittered independently. The manipulation reconfigures the point locations, whereas the points' category labels stay unchanged. It may move a point of a part to the area of another part, where the point's label without renewal could mislead the update of the segmentation network. Thus, the random manipulation achieves less improvement than our method. + +Next, we use the discriminative network for reshaping. We choose the conventional fully-connected layers (FC) or the recent PointTransformer [48] to construct the discriminative network. Note that the generative network can reshape each source example into different examples, enriching the training data's diversity. In contrast, the discriminative network only predicts a discrepancy grid for each source example. It disallows more diverse examples to appear for training a more robust segmentation network. Thus its performances fail to catch up to our generative network. + +Finally, we compare our method with another alternative (PL) for constructing the generative network, which regards the part-level category labels of the point cloud as a condition for generating novel examples. The part-level category labels are coarser information compared to the source example, with all points' coordinates and labels as the condition of our generative network. Based on too coarse information, the alternative method reshapes the source example unreasonably, generating many examples with problematic shapes and point-wise labels that harm the network training and degrade the segmentation performances. + +![](images/990902276c210ec927b70b4e4a5fc29bea8d6592099a7b8031f5b2b5d07e7ebd.jpg) +Figure 6. Visualization of reshaped examples in different epochs. + +Table 3. Various ways of example mixup. + +
Mixup MethodCat. mIoUIns. mIoU
w/o MixupPointMetaBase85.187.1
Largest85.387.3
Medium85.387.2
Smallest85.187.1
w/ MixupSame85.487.3
Random85.287.2
GHEA86.187.8
+ +In Figure 5, we evaluate the diversity of generated examples in different epochs of training stage. The diversity is measured by the difference between the source and generated examples regarding all points' coordinates and labels. Here, the difference of points' coordinates is measured by the Chamfer Distance (CD in Figure 5(a)) between 3D points of source and generated example. The difference of labels is measured by the L2 distance (L2 in Figure 5(b)) between category channels of the source and generated examples' voxelized grids. In the early epochs, we train the generative network insufficiently, producing new examples with unreasonable shapes and leading to a significant diversity of these examples. This problem is solved in the later epochs. The diversity of generated examples increases and stays at a relatively high level when the generative network is trained better. In Figure 6, we report the generated examples in different epochs, showing their remarkable differences from the source examples. + +Variants of Example Mixup We examine the impact of hard example mixup on the segmentation performances by removing or changing it to other alternatives. The results are listed in Table 3. + +Without the example mixup, the alternative of yielding the hard example is to select one of the generated examples associated with the identical source example by respecting their segmentation errors. We choose the generated example with the largest, medium, or smallest error, which is the hard example for updating the segmentation and generative network. Comparing the results of w/o Mixup in Table 3, the generated example with the largest error contributes more proper supervision than those with the medium or smallest error. Nevertheless, GHEA outperforms the above strategies because it aggregates richer examples and yields + +![](images/a895b36ff98730ca0a8690a36e18a5d128d3109d9938a4a3a8569c3fee400b8b.jpg) +Figure 7. Cross-entropy losses of the segmentation network with/without GHEA. + +![](images/1072f32973ac591cb88474abb5e95addc3b3512e6a269b79f5c5c958bc23a870.jpg) + +![](images/02e820d04a4e2978d2d1daaab634307932cae36daf0a401f4ecb0df8045a6a18.jpg) +Figure 8. Visualization of hard examples and segmentation results in different epochs. + +![](images/077d38545498cc87e2d9ffe823ea769286b3db143241d250f43e107c12d6e4ce.jpg) + +![](images/50a59fef7fb3421f1a94e1a4a5c5fabc89fabfe91c1977af9e5b31caa1f5981e.jpg) + +Table 4. Results of various strategies of using the hard examples to update the segmentation or generative network. + +
GenerativeSegmentationCat. mIoUIns. mIoU
XX85.187.1
✓X85.187.1
X✓85.687.5
✓✓86.187.8
+ +more challenging examples for network updating. + +To evaluate the effectiveness of using segmentation errors as dynamic weights for the example mixup, we change them to the same or random weights insensitive to segmenting the generated examples. The comparison between them in last three rows of Table 3 evidences the superiority of GHEA, which uses segmentation errors for example mixup. + +In Figure 7, we plot the segmentation losses (i.e., cross-entropy losses) in different epochs, where the segmentation network is updated with or without GHEA. Because the network update without GHEA only relies on the source examples, it converges faster but worse than the counterpart with GHEA. It is because the generative network is trained to allow more hard cases to appear for training the segmentation in latter epochs. In Figure 8, we provide the hard examples in different epochs and their segmentation results predicted in the final epoch. The segmentation network learns well from hard examples with good segmentation results. + +Variants of Network Update GHEA adds hard examples to the training data for updating the generative and segmentation networks. In Table 4, we enable or disable the network update based on hard examples. In the first case, we omit hard examples, which means the generative and segmentation networks are trained on the fixed data. Though the generative network learns the discrepancy between the + +![](images/697177d2beb811ca62164034e5fc8eb64557116a558e0a30d46473886042f5d5.jpg) +Figure 9. Object-level segmentation results on the S3DIS (top) and ScanNet V2 (bottom) datasets. The yellow squares highlight the wrong/correct segmentation without/with the help of GHEA. + +Table 5. Results of various strategies of adding the hard examples to the source or target examples. “+” and “\” mean adding the hard example or not for training the generative network. + +
(Source, Target)Cat. mIoUIns. mIoU
\+86.187.8
+\85.587.4
++85.287.2
+ +source and target examples, its generated examples fail to play as hard examples to update the segmentation network. This strategy lets the segmentation performances be like the results of the segmentation backbone trained alone. In the second case, we achieve unsurprising results by using hard examples to update the generative network only, whereas the segmentation network still learns from source examples. In the third case, we use hard examples to update the segmentation network, which yields better results than the above cases. But this strategy disallows the hard examples to update the generative network, which is less capable of generating more challenging examples for updating the segmentation network in the subsequent epochs. It is lower than our network update. In the experiments below, we keep using the hard examples to update the generative and segmentation networks. + +We evaluate the strategies of constructing the pair of the source and target examples for training the generative network, where we add the hard examples to the source or target examples. We report the results in Table 5. Compared to our method of adding the hard examples as the target examples only (see the first case), the strategies of regarding the hard examples as the source examples (see the last two cases) degrade the segmentation performances. This is because the hard examples, which aggregate the generated examples, may contain problematic shapes and labels that mislead the update of the generative network. + +# 5.3. Object-level Segmentation + +In Table 6, we provide the results of the object-level segmentation on S3DIS and ScanNet V2. Unlike the part-level segmentation of a single object, object-level segmentation requires augmenting the data of 3D scenes, thus leading to the high complexity of reshaping the point clouds. Despite + +Table 6. Results of different backbones with CDA, PointWOLF, and GHEA on the S3DIS and ScanNet V2 data. + +
MethodS3DIS Area5S3DIS 6-foldScanNet V2
mIoUOAmAccmIoUOAmAccVal. mIoUTest mIoU
PointNet++60.787.067.665.586.876.750.850.2
w/ CDA63.688.370.268.187.678.453.555.7
w/ PW62.288.168.366.587.277.640.839.9
w/ GHEA66.989.873.371.689.180.864.662.2
PointNeXt68.088.874.673.890.081.968.867.4
w/ CDA70.590.676.874.990.383.071.571.2
w/ PW67.489.973.473.989.982.470.770.2
w/ GHEA71.791.277.176.390.684.274.673.4
PointMetaBase69.189.8-76.591.1-69.768.1
w/ CDA71.390.8-77.091.3-72.871.4
w/ PW69.789.876.375.890.984.567.365.7
w/ GHEA72.191.677.777.891.985.174.872.6
DeLA73.092.079.176.990.684.573.872.8
w/ CDA74.192.280.078.091.585.975.974.0
w/ PW69.790.775.876.491.085.172.871.8
w/ GHEA74.992.981.379.592.387.576.675.0
+ +this challenge, GHEA consistently helps different segmentation backbones to improve performances. In Figure 9, we compare the segmentation results, where the segmentation networks are trained without or with the assistance of GHEA. We find that GHEA generally leads to better results. Notably, PW harms the results as it randomly dithers the entire scene and yields an unreasonable shape. + +# 6. Conclusion + +The current methods of augmenting point cloud data are less potent in producing diverse and challenging examples with accurate semantic labels for training a more robust segmentation network. This paper proposes the generative hard example augmentation for semantic point cloud segmentation. The methodology pipeline consists of a pair of generative and segmentation networks. The generative network reshapes the source example to new examples with various shapes, thus enriching the training data. The segmentation network evaluates the difficulty of segmenting the new examples, which are mixed as a more challenging example. We leverage the rich and challenging examples to progressively update the generative and segmentation networks, successfully improving the performances of different segmentation networks. We plan to extend our strategy to other point cloud recognition tasks (e.g., scene completion). + +Acknowledgements This work was supported in part by the National Key R&D Program of China under Grants 2023YFF0906200, in part by the Natural Science Foundation of China under Grants 62476192, in part by the Key Science and Technology Program of the Ministry of Emergency Management of the People's Republic of China under Grants 2024EMST010102, in part by the Natural Science Foundation of Tianjin under Grants 23JCQNJC02010. + +# References + +[1] Xin Lai, Jianhui Liu, Li Jiang, Liwei Wang, Hengshuang Zhao, Shu Liu, Xiaojuan Qi, and Jiaya Jia. 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(a) Given an input image and a binary object mask, our model is able to decompose the image into a clean background layer and a transparent foreground layer with preserved visual effects such as shadows and reflections. (b) Subsequently, our decomposition empowers complex and controllable layer-wise editing such as spatial, color and/or style editing. + +# Abstract + +Recent advancements in large generative models, particularly diffusion-based methods, have significantly enhanced the capabilities of image editing. However, achieving precise control over image composition tasks remains a challenge. Layered representations, which allow for independent editing of image components, are essential for user-driven content creation, yet existing approaches often struggle to decompose an image into plausible layers with accurately retained transparent visual effects such as shadows and reflections. We propose LayerDecomp, a generative framework for image layer decomposition which outputs photorealistic clean backgrounds and high-quality transparent foregrounds with faithfully preserved visual effects. To enable effective training, we first introduce a dataset preparation pipeline that automatically scales up simulated multi-layer data with synthesized visual effects. To further enhance real-world applicability, we supplement this simulated dataset with camera-captured images containing natural visual effects. Additionally, we propose a consistency loss which enforces the model to learn accurate + +representations for the transparent foreground layer when ground-truth annotations are not available. Our method achieves superior quality in layer decomposition, outperforming existing approaches in object removal and spatial editing tasks across several benchmarks and multiple user studies, unlocking various creative possibilities for layerwise image editing. + +# 1. Introduction + +The rapid advancement of large-scale text-to-image diffusion models [3, 7, 32] has greatly improved image editing capabilities, with recent studies [5, 14, 35, 51] demonstrating promising results by training on large-scale datasets of captioned images. However, achieving precise control for user-driven image composition tasks remains challenging. Layered representations, which decompose image components into independently editable layers, are essential for precise user-driven content creation. Most visual content editing software and workflows are layer-based, relying heavily on transparent or layered elements to compose and + +create content. Despite this, few existing approaches have explored layer-based representation for image editing in depth. Recently, LayerDiffusion [48] is proposed to generate transparent layer representations from text inputs; however, this approach is not well-suited for image-to-image editing tasks. Meanwhile, MULAN [38] presents a multilayer annotated dataset for controllable generation, but it often fails to preserve essential visual effects in the right layers, limiting its adaptability for seamless downstream edits. + +This work aims to fill these gaps by decomposing an input image into two layers: a highly plausible clean background layer, and a high-quality transparent foreground layer that retains natural visual effects associated with the target. These decomposed layers will support layer-constrained content modification and allow seamless blending for harmonious re-composition. Additionally, the faithfully preserved natural visual effects in the foreground layer will benefit related research areas, such as shadow detection and shadow generation. However, the lack of publicly available multi-layer datasets with realistic visual effects, such as shadows and reflections, poses a significant challenge for training high-quality layer-wise decomposition models. How to accurately decompose images into layers and learn correct representation for visual effects in the foreground layer without ground-truth data is the key problem to solve. + +To address these challenges, we first design a dataset preparation pipeline to collect data from two sources: (1) simulated image triplets consisting of composite images blended from random background and unrelated transparent foreground with generated shadow, allowing us to create a large-scale training set with ground-truth for both branches; and (2) camera-captured images for a scene with and without the target foreground object, ensuring the model can effectively adapt to real-world scenarios. Building on this dataset, we introduce Layer Decomposition with Visual Effects (LAYERDECOMP), a generative training framework that enables large-scale pretrained diffusion transformers to effectively decompose images into editable layers with correct representation of visual effects. The key to our model training lies in a consistency loss, which ensures faithful retention of natural visual effects within the foreground layer while maintaining background coherence. Specifically, for real-world data where visual effect annotations are not available, it is not feasible to directly compute diffusion loss on the foreground layer. Instead, LAYERDECOMP enforces consistency between the original input image and the re-composite result, blended from the two predicted layers, to ensure the model learns correct representation for the transparent foreground layer. + +As shown in Figure 1, LAYERDECOMP can effectively decompose an input image into a clean background and a transparent foreground with preserved visual effects. This capability supports downstream editing applications with + +out requiring additional model training or inference. Furthermore, our method exhibits superior layer decomposition quality, outperforming existing approaches in both object removal tasks and object spatial editing tasks across various benchmarks and in multiple user studies. + +In summary, our contributions are as follows: + +- We introduce a scalable pipeline to generate large-scale simulated multi-layer data with paired ground-truth visual effects for training layer decomposition models. +- We present LAYERDECOMP, a generative training framework that leverages both simulated and real-world data to enable robust layer-wise decomposition with accurate visual effect representation through a consistency loss, facilitating high-quality, training-free downstream edits. +- LAYERDECOMP surpasses existing state-of-the-arts in maintaining visual integrity during layer decomposition, excelling in object removal and object spatial editing, and enabling more creative layer-wise editing. + +# 2. Related Works + +# 2.1. Image Editing + +Image editing methods can be broadly categorized into two groups: multi-task editing and local editing. Multi-task editing allows for a wide array of image modifications based on high-level inputs, such as user instructions. For example, Emu-Edit [35] offers a flexible interface for diverse image edits. Other methods, including InstructPix2Pix [4], Prompt2Prompt [10], InstructAny2Pix [17], MagicBrush [47], Imagc [16], PhotoSwap [9], UltraEdit [51], HQ-Edit [13], MGIE [8], and OmniGen [43], focus on fine-grained, user-specific edits. These approaches achieve high precision by aligning closely with user instructions, often through fine-tuned models. However, due to the absence of region references, these methods struggle with accurately locating objects and preserving the integrity of unrelated regions. + +Local image editing focuses on tasks like inpainting and object insertion, typically guided by masks or reference images. Early GAN-based methods, such as CMGAN [53], LAMA [37], CoModGAN [52], ProFill [45], CRFill [46], and DeepFillv2 [44], use latent space manipulation for inpainting missing regions. Leveraging the success of text-to-image diffusion models, Repaint [22], SDEdit [24], ControlNet [49], BrushNet [15], and Blended Diffusion [2] combine text guidance with masks or references for customized image inpainting. Further, ObjectStitch [36], HDPainter [23], and PowerPaint [54] extend this to versatile object editing with text prompts. Beyond local object editing, recent research also focuses on spatial editing techniques that allow more interactive control over object positioning and transformations. Methods like MagicFixup [1], DiffusionHandle [27], DragGAN [26], DiffEditor [25], De + +![](images/f58f18fa70edf5f6cbe35ad573bde628cc3dd757bfb411ba58e468eae4eb1d23.jpg) +Figure 2. The framework of LAYERDECOMP. The model takes four inputs: two conditional inputs, including a composite image and an object mask, and two noisy latent representations of the background and foreground layers. During training, we use simulated image triplets alongside camera-captured background-composite image pairs. We also introduce a pixel-space consistency loss to ensure that natural visual effects such as shadows and reflections are faithfully preserved in the transparent foreground layer. + +![](images/c7e870820b606c7dc2254267142925d59605d67defbe92e243df35be08c1a97f.jpg) + +![](images/590449fe77b69040f53b2e9cd03cf2f45a15e5b681188e79400566f0f96e1d57.jpg) + +signEdit [14], and DragAnything [42] highlight a growing emphasis on user-driven, spatially aware editing. However, preserving object appearance and background integrity during spatial edits (e.g., moving and resizing) remains challenging, particularly when complex visual effects like shadows and reflections are involved. + +# 2.2. Image Layer representation + +Obtaining high-quality image layer representations is crucial for implementing accurate and diverse editing objectives. This process typically involves image decomposition, layer extraction, and image matting. PACO [21] provides a fine-grained dataset with mask annotations for parts and attributes of common objects. However, these object representations indicate only the regions of parts and objects, lacking transparent layers for flexible editing. MAGICK [6] offers a large-scale matting dataset generated by diffusion models, while MULAN [38] creates RGBA layers from COCO [18] and Laion Aesthetics 6.5 [34] using off-the-shelf detection, segmentation, and inpainting models; however, it does not capture visual effects, limiting its applicability for direct editing. LayerDiffusion [48] and Alfie [31] generate transparent image layers from text prompts, facilitating layer blending. However, text-driven generation limits object identity control in image-specific editing tasks. Once the image decomposition is performed, users typically need to execute image composition to achieve a cohesive final image. Existing methods like ObjectDrop [40] require model fine-tuning to restore visual effects, which can disrupt the original image's appearance. In contrast, LAYERDECOMP models these effects during training, inher + +ently preserving them to produce a seamless, harmonious composite image without extra fine-tuning. + +# 3. Approach + +# 3.1. Overview of LAYERDECOMP Framework + +As shown in Fig 2, the LAYERDECOMP framework builds upon Diffusion Transformers (DiTs) [29] to denoise multi-layer image outputs in the latent space encoded by the VAE encoders $g_{\phi}^{\mathrm{RGB}}(\cdot)$ and $g_{\psi}^{\mathrm{RGBA}}(\cdot)$ . Specifically, the DiT model $f_{\theta}(\cdot)$ takes two types of conditional input $\mathbf{c} = (\mathbf{y}_{\mathrm{comp}}, \mathbf{y}_{\mathrm{obj}})$ , which are the latents of the original composite image, and the decomposition object mask, respectively, i.e., $\mathbf{c} = (\mathbf{y}_{\mathrm{comp}}, \mathbf{y}_{\mathrm{obj}}) = (g_{\phi}^{\mathrm{RGB}}(\mathbf{I}_{\mathrm{comp}}^{\mathrm{RGB}}), g_{\phi}^{\mathrm{RGB}}(\mathbf{M}_{\mathrm{obj}}))$ . By taking the conditional image embeddings, the model targets to denoise the noisy latent $\mathbf{x}_t = (\mathbf{x}_t^{\mathrm{bg}}, \mathbf{x}_t^{\mathrm{fg}})$ , to recover the latents of the clean background image and the transparent foreground layer $\mathbf{x}_0 = (\mathbf{x}_0^{\mathrm{bg}}, \mathbf{x}_0^{\mathrm{fg}}) = (g_{\phi}^{\mathrm{RGB}}(\mathbf{I}_{\mathrm{bg}}^{\mathrm{RGB}}), g_{\psi}^{\mathrm{RGBA}}(\mathbf{I}_{\mathrm{fg}}^{\mathrm{RGBA}}))$ . The training loss follows the standard denoising diffusion loss [12, 19]: + +$$ +\mathcal {L} _ {\mathrm {d m}} = \mathbb {E} _ {t \sim \mathcal {U} (\{1, \dots , T \}), \boldsymbol {\epsilon}, \mathbf {x} _ {t}} \left[ \| \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}; \mathbf {c}, t) - \boldsymbol {\epsilon} \| _ {2} ^ {2} \right], \tag {1} +$$ + +$$ +s. t. \mathbf {x} _ {0} \sim q _ {\text {d a t a}} (\mathbf {x} _ {0}), \epsilon \sim \mathcal {N} (\mathbf {0}, I), \mathbf {x} _ {t} = \sqrt {\alpha_ {t}} \mathbf {x} _ {0} + \sqrt {1 - \alpha_ {t}} \epsilon . +$$ + +Specifically, the noisy input $\mathbf{x}_t$ and image conditions $\mathbf{c}$ are initially divided into non-overlapping patches and converted into patch embeddings. The patch embeddings of each type of images, such as background, foreground or any conditions, are added with a corresponding type embedding and then concatenated into a sequence. Subsequently, the model follows the standard DiT architecture, where the patch embeddings are processed through multiple + +transformer blocks. With such design, the image conditions provide comprehensive contextual information through the self-attention in the transformer blocks to enhance the denoising, and the loss is only computed on the positions corresponding to the noisy latents. + +Note that the latent of the foreground image needs to be encoded with RGBA channels, we leverage an RGBA-VAE fine-tuned from the original VAE by following LayerDiffusion [48] which makes minimal disturbance to the original latent space. Moreover, as the foreground image is not always available, e.g., in the case of real-world camera-captured data, the noisy input and output corresponding to the foreground are masked out from $\mathcal{L}_{\mathrm{dm}}$ computation if $\mathbf{I}_{\mathrm{fg}}^{\mathrm{RGBA}}$ is absent in the training stage. + +# 3.2. Consistency Loss for Visual Effects Learning + +To handle cases where real-world data lacks ground-truth annotations, we introduce a consistency loss that enables the learning of natural visual effects in the transparent foreground layer without explicit annotation. Intuitively, as shown in Fig 2, the consistency loss is applied in the decoded pixel space to encourage the predicted foreground can faithfully reconstruct the composite input after blending with the background layers. + +More specifically, given a composite image $\mathbf{I}_{\mathrm{comp}}^{\mathrm{RGB}}$ , at any denoising timestep $t$ , we reparameterize our model prediction back to the estimation of the clean latent $\mathbf{x}_0$ as: + +$$ +\hat {\mathbf {x}} _ {0} (\mathbf {x} _ {t}; \mathbf {c}, t) = \frac {1}{\sqrt {\alpha_ {t}}} \left(\mathbf {x} _ {t} - \sqrt {1 - \alpha_ {t}} \cdot \boldsymbol {\epsilon} _ {\theta} (\mathbf {x} _ {t}; \mathbf {c}, t)\right). (2) +$$ + +Given Eq. 2, we compute the estimated $\hat{\mathbf{x}}_0(\mathbf{x}_t;\mathbf{c},t) = (\hat{\mathbf{x}}_{0}^{\mathrm{bg}},\hat{\mathbf{x}}_{0}^{\mathrm{fg}})$ of background and foreground at time step $t$ and decode them into pixel space to get $\hat{\mathbf{I}}_{\mathrm{bg}}^{\mathrm{RGB}} = h_{\phi '}^{\mathrm{RGB}}(\hat{\mathbf{x}}_{0}^{\mathrm{bg}})$ and $\hat{\mathbf{I}}_{\mathrm{fg}}^{\mathrm{RGBA}} = h_{\psi '}^{\mathrm{RGBA}}(\hat{\mathbf{x}}_{0}^{\mathrm{fg}})$ , via the decoder of RGB-VAE and RGBA-VAE, respectively. The results are combined through alpha blending to produce the estimated composite image $\hat{\mathbf{I}}_{\mathrm{comp}}^{\mathrm{RGB}} = \mathcal{A}(\hat{\mathbf{I}}_{\mathrm{bg}}^{\mathrm{RGB}},\hat{\mathbf{I}}_{\mathrm{fg}}^{\mathrm{RGBA}})$ . The consistency loss is thus: + +$$ +\mathcal {L} _ {\text {c o n s i s t}} = \mathbb {E} _ {t} \sum_ {i = 1} ^ {H} \sum_ {j = 1} ^ {W} \left| \mathbf {I} _ {\operatorname {c o m p}} ^ {\mathrm {R G B}} (i, j) - \hat {\mathbf {I}} _ {\operatorname {c o m p}} ^ {\mathrm {R G B}} (i, j) \right|, \tag {3} +$$ + +where $H$ and $W$ indicates the height and the width of the composite image, respectively. + +The consistency loss enables LAYERDECOMP to learn faithful representations of transparent visual effects in the foreground layer, which is essential for accurately decomposing natural shadows and reflections in real-world data, especially in the absence of ground-truth annotations. + +# 3.3. Dataset Preparation + +To effectively train LAYERDECOMP, we curated a hybrid dataset that combines simulated and real-world data. Ideally, training LAYERDECOMP requires image triplets: an + +input image $\mathbf{I}_{\mathrm{comp}}^{\mathrm{RGB}}$ , a transparent foreground layer containing the target object and its visual effects $\mathbf{I}_{\mathrm{fg}}^{\mathrm{RGBA}}$ , and a background image without the foreground object $\mathbf{I}_{\mathrm{bg}}^{\mathrm{RGB}}$ . While collecting natural triplet images with specialized devices or through manual annotation might be feasible, it is costly and impractical for large-scale data needs. Conversely, synthesizing such triplet data directly with generative models presents significant challenges. Observations from existing approaches, such as HQ-Edit [13] and LayerDiffusion [48], indicate that generative models often inadvertently modify areas outside the target foreground, making it difficult to produce truly aligned image layers with consistent content. Additionally, accurately representing transparent visual effects, such as shadows and reflections in the foreground layer with an alpha channel for transparency, remains unexplored in existing works. To address these limitations, we developed a simulated data pipeline to create triplet images and supplemented it with a smaller portion of real-world $\mathbf{I}_{\mathrm{comp}}^{\mathrm{RGB}}$ and $\mathbf{I}_{\mathrm{bg}}^{\mathrm{RGB}}$ pairs to enhance robustness. + +Simulated Data: To create image triplets, we first collected a large-scale object assets consisting of unoccluded foreground objects with synthesized shadows. We used entity segmentation [30] to select "thing" objects from natural images, and applied depth estimation to infer occlusion relations to exclude incomplete objects. We then applied a shadow synthesis method [39] to generate a shadow intensity map for each object on a white background. By integrating the intensity map into the alpha channel, we obtained comprehensive object assets in RGBA format. During training, we adjusted the scale and position of each foreground asset to align with the properties of a randomly selected background image $\mathbf{I}_{\mathrm{bg}}^{\mathrm{RGB}}$ , resulting in a finalized foreground layer $\mathbf{I}_{\mathrm{fg}}^{\mathrm{RGBA}}$ . By blending the two layers together, we obtained a composite image $\mathbf{I}_{\mathrm{comp}}^{\mathrm{RGB}}$ , completing the triplet data needed for model training. Although the composite results may lack fully realistic geometry and harmonized content, this approach enables large-scale training and allows the model to learn the appropriate representations for the two output layers in the decomposition task. + +Camera-Captured Data: We also include a small set of real-world camera-captured image pairs, denoted as $\mathbf{I}_{\mathrm{com}}^{\mathrm{RGB}}$ and $\mathbf{I}_{\mathrm{bg}}^{\mathrm{RGB}}$ , similar to the counterfactual dataset proposed by ObjectDrop [40]. The real-world data enhances the model's ability to generalize to natural images containing authentic shadows and a broader range of visual effects, such as reflections, which are crucial for accurate foreground-background decomposition in real-world tasks. + +# 4. Experiments + +Implementation. LAYERDECOMP is finetuned from a 5B-parameter DiT model pre-trained for text-to-image genera + +![](images/79c77285144e69d76b2331b5cd04f4dffb190e317acbd26519274f89b89f7373.jpg) +Figure 3. Object removal - comparison with mask-based methods. Our model, using tight input masks, generates more visually plausible results with fewer artifacts compared to ControlNet Inpainting [49], SD-XL Inpainting [32], and PowerPaint [54], which all require loose mask input. Besides, our model delivers coherent foreground layers and supports more advanced downstream editing tasks. + +tion, with the text encoder removed for the layer decomposition task. RGBA-VAE is finetuned from the DiT VAE using L1, GAN, and perceptual losses [50]. Following LayerDiffusion [48], we extend the input/output from 3 to 4 channels and introduce an extra latent code to adapt the original VAE's latent space. It takes images with $512 \times 512$ resolution and encode them into $64 \times 64$ latent feature maps. Image type embedding is learnable through linear layers. For the simulated dataset, we use 100k foreground object images with precomputed shadows on plain backgrounds, selecting unoccluded main objects using segmentation and depth heuristics. For backgrounds, we source 5M stock images and blend the foregrounds based on object size and placement. Our camera-captured dataset consists of 6,000 image pairs. During training, we use the Adam optimizer and set the learning rate at $1e - 5$ . Training is conducted with a total batch size of 128 on 16 A100 GPUs for 80,000 iterations. During inference, all results are generated using DDIM sampling with 50 steps. + +# 4.1. Ablations + +To quantitatively assess the advantages of incorporating visual effects in the foreground layer and the effectiveness of our proposed consistency loss, we construct a held-out evaluation dataset of 635 images for ablation studies. This dataset includes camera-captured composite images with the corresponding backgrounds. Visual examples will be provided in the supplementary materials. The quality of + +Table 1. Ablation study of LAYERDECOMP on held-out test set. "BG" denotes the decomposed background, and "Comp" represents the re-composited image created by our two-layer results. + +
ModelPSNR ↑LPIPS ↓FID ↓CLIP-FID ↓
BGCompBGCompBGCompBGComp
V0:RGB-only28.21-0.0732-21.00-4.551-
V1:V0+RBA FG (obj.)28.2827.530.07080.064918.4818.832.4872.329
V2:V0+RBA FG (obj.+v.e.)28.5628.660.06910.061217.9916.872.5392.172
Ours:V2 + Lconsist29.2730.530.06180.049416.0412.751.8131.564
+ +the decomposed background layers can be directly evaluated using standard metrics, such as PSNR, LPIPS [50], FID [11, 28], and CLIP-FID [28]. To further evaluate the quality of the decomposed foreground layers, we apply alpha blending to re-composite the background and foreground together, comparing the result with the original composite image. As shown in Tab. 1, compared to a naive DiT baseline which outputs only an RGB background, adding an RGBA foreground layer not only enables decomposition but also improves background quality. Incorporating visual effects in the foreground layer and introducing a consistency loss further enhance model performance. This demonstrates the decomposition task may implicitly improve the model's understanding of the input scene, leading to superior results in both layers' predictions. + +Table 2. Comparison of LAYERDECOMP with mask-based object removal methods. Loose (L) and Tight (T) mask-based results are shown where applicable. $\mathbf{PSNR}^m$ and $\mathbf{SSIM}^m$ are computed on the shadow mask region to assess the model's shadow removal ability. + +
ModelRORD [33]MULAN [38]DESOBAv2 [20]
PSNR ↑LPIPS ↓FID ↓CLIP-FID ↓PSNR ↑LPIPS ↓FID ↓CLIP-FID ↓PSNRm ↑SSIMm ↑
CNI [49]20.45L22.01T0.235L0.182T50.40L53.71T8.853L9.262T17.790.32165.039.39636.94L0.491L
SDI [32]19.88L20.81T0.205L0.166T53.73L56.28T11.38L11.10T16.040.30365.7411.5434.21L0.527L
PP [54]20.88L21.26T0.231L0.201T39.48L56.56T8.596L11.32T17.170.31455.809.98829.33L0.369L
Ours24.56L24.79T0.133L0.132T21.77L21.73T5.735L5.778T19.130.24439.266.33238.57T0.640T
+ +![](images/801b61cc2d182d257b56b5cd55d923bf814551285df878d56b1b794657f3ecd4.jpg) +Figure 4. Object removal - comparison with ObjectDrop [21]. Based on their released examples, our model demonstrates comparable quality in photorealistic object removal in the background layer, while decomposing the foreground with intact visual effects. + +# 4.2. Comparison on Object Removal + +To assess the quality of the background layers predicted by LAYERDECOMP, we evaluate the model on the object removal task, comparing it to several state-of-the-art approaches, including mask-based methods (ControlNet Inpainting [49], SD-XL Inpainting [32], PowerPaint [54], ObjectDrop [40]) and instruction-driven models (EmuEdit [35], MGIE [8], and OmniGen [43]). + +Quantitative evaluation among mask-based inpainting methods is conducted on three public benchmarks: RORD [33], a real-world object removal dataset collected from video data with human-labeled loose and tight object masks; MULAN [38], a synthesized multi-layer dataset that provides instance-wise RGBA decompositions for COCO and LAION images; and DESOBAv2 [20], a real-world image dataset with shadow mask annotations and synthesized image pairs where instance shadows are removed. Standard metrics, including PSNR, LPIPS, FID, and CLIP-FID, are used on RORD and MULAN, while regional similarity such as masked PSNR and masked SSIM are used for shadow re + +Table 3. User study for instruction-driven object removal. + +
MethodsRemoval EffectivenessResult PlausibilityBackground IntegrityOverall
Emu-Edit [35]5.00%4.38%3.33%4.79%
Ours57.08%77.92%76.25%83.54%
OmniGen [43]4.07%3.15%2.96%3.89%
Ours67.04%80.56%84.63%87.78%
+ +moyal in DESOBAv2. More details of dataset preparation will be included in the supplementary materials. + +Most existing mask-based object removal approaches cannot automatically detect and remove visual effects associated with the target object, necessitating a loose mask input. Indeed, as shown in Tab. 2, using a loose mask introduces more inpainting area and thus hurts PSNR and LPIPS, but significantly improves result fidelity (i.e., FID and CLIP-FID) for all compared methods. In contrast, LAYERDECOMP demonstrates robustness to mask tightness and outperforms all methods by a large margin. For shadow removal on DESOBAv2, LAYERDECOMP surpasses other methods even without utilizing the shadow annotation included in the loose mask. As shown in Fig. 3, LAYERDECOMP provides substantial improvements over existing methods, generating more photorealistic background layers with fewer artifacts and minimal visual effect residues. Comparing with ObjectDrop, a leading model in object removal that can automatically eliminate visual effect with a tight input mask, we applied LAYERDECOMP to the example images released by their work. As shown in Fig. 4, LAYERDECOMP achieves similar high-quality backgrounds with effective object removal. Additionally, LAYERDECOMP decomposes the foreground with realistic visual effects, enabling further editing capabilities not supported by ObjectDrop. More visual comparisons will be included in the supplementary materials. + +To compare with instruction-driven methods, we conduct a user study on 60 randomly selected images from the Emu-Edit Remove Set [35]. We ask 17 independent researchers to compare results from LAYERDECOMP and an existing method, focusing on three quality aspects: removal effectiveness, result plausibility, and background integrity. + +Instruction + +Remove the cat from the photo. + +Remove the bottle of wine on the table. + +Input Image + +![](images/760a319f451effc9349bd83147d72ddd36965b27e896479fe9dd295b6173dbf5.jpg) +Figure 5. Object removal - comparison with instruction-driven methods. Combining with a text-based grounding method, our model can effectively remove target objects and preserve background integrity, while existing instruction-based editing methods, such as EmuEdit [35], MGIE [8], and OmniGen [43], may struggle to fully remove the target or maintain background consistency. + +Text-based Mask + +Emu-Edit + +![](images/8574ac6706d23b563ba318c09c42d1f7f4e7e06dfb4ee5b15f60b8c34b69da0f.jpg) + +MGIE + +OmniGen + +![](images/7359f576a4fae960ffaa73eb66f98573ba0eb55eb35db08c7e0d3f7f77b3aae4.jpg) + +Ours + +![](images/775b3bb15b8add1d8bd07772c27f4b0116fe64448536570a004af81692f102a8.jpg) +Figure 6. Object spatial editing. Our model enables precise object moving and resizing with seamless handling of visual effects, resulting in highly effective and realistic edits that preserve content identity. When applied to examples released by specific works, such as DiffusionHandle [27] and DesignEdit [14], our model also achieves satisfying results. + +![](images/64e5856b5edea517fd182cb871a7f09c3a0b9ecff573aa881ab2459e278c7af6.jpg) + +In cases where both methods achieve satisfactory results, users could mark it as a "tie". For a fair comparison, we use a grounding model to generate text-based masks to input to LAYERDECOMP. In total, 3060 data points are collected in this study. As shown in Tab. 3, LAYERDECOMP is clearly preferred in at least $83\%$ of the testing cases for overall quality. Example object removal results are visualized in Fig. 5. While Emu-Edit and MGIE struggle to fully remove the target object, OmniGen is more effective but does not reliably preserve the background integrity. Our model, in contrast, successfully removes the target object + +while preserving most background fine details. + +# 4.3. Comparison on Object Spatial Editing + +We further compare LAYERDECOMP for object spatial editing tasks, including object moving and resizing, against several state-of-the-art methods: DiffEditor [25], DragAnything [41], DesignEdit [14], and Diffusion Handles [27]. For user study, we select 15 editing samples using web images for each task, and ask 23 independent researchers to compare results from LAYERDECOMP and an existing method, focusing on three quality aspects: edit effective + +![](images/2a46244c8d5a9230aa771dd5a6d214920db5e6100221acaf18b6d9587cf477bb.jpg) +Figure 7. Multi-layer Decomposition and Creative layer-editing. By sequentially applying our model, we can decompose multiple foreground layers with distinct visual effects, which can then be used for further creative editing tasks. + +Table 4. User study for object spatial editing. + +
MethodsEdit EffectivenessResult PlausibilityContent IntegrityOverall
MovingDesignEdit [14]1.67%1.11%1.11%2.22%
Ours71.67%90.56%77.22%94.44%
DragAnything [41]1.82%1.21%2.42%1.21%
Ours67.88%93.33%95.15%96.36%
ResizingDesignEdit [14]2.22%3.89%3.33%3.89%
Ours69.44%82.78%71.67%87.22%
DiffEditor [25]1.11%1.11%1.21%1.11%
Ours95.15%96.36%92.21%96.36%
+ +ness, result plausibility, and content integrity. In this study, 2070 data points are collected. As shown in Tab. 4, LAYERDECOMP is at least $87\%$ more preferred in the spatial editing tasks, featuring superior plausibility in editing results. As shown in Fig. 6, LAYERDECOMP enables seamless spatial editing for objects in various scenes. By preserving intact visual effects in the transparent foreground layer, shadows and reflections move naturally with the editing targets, allowing harmonious re-composition to be effortlessly achieved through alpha blending. When compared to DiffusionHandle [27] and DesignEdit [14] on their released examples, LAYERDECOMP demonstrates comparable results in most scenarios, including graphic design examples without requiring additional fine-tuning. + +# 4.4. Multi-Layer Decomposition and Editing + +LAYERDECOMP can be applied sequentially to an original input image with different instance masks, decomposing multiple layers along with their visual effects, as examples shown in Fig. 7. This process enables creative and complex layer-based editing for each individual layer, including spatial manipulation, recoloring, and filtering. Once editing is complete, the re-composition of all layers maintains a natural and realistic appearance, as demonstrated in Fig. 7. + +# 5. Discussions + +In conclusion, our model achieves superior image layer decomposition, outperforming existing methods in object removal and spatial editing across benchmarks and user studies. By decomposing images into a realistic background and transparent foreground with preserved visual effects, it enables diverse creative editing possibilities. Our consistency loss facilitates accurate foreground representation learning even without hard-to-obtain ground truth. 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Although remarkable progress has been made in video generation models, generative inbetweening still faces challenges in maintaining temporal stability due to the ambiguous interpolation path between two key frames. This issue becomes particularly severe when there is a large motion gap between input frames. In this paper, we propose a straightforward yet highly effective Frame-wise Conditions-driven Video Generation (FCVG) method that significantly enhances the temporal stability of interpolated video frames. Specifically, our FCVG provides an explicit condition for each frame, making it much easier to identify the interpolation path between two input frames and thus ensuring temporally stable production of visually plausible video frames. To achieve this, we suggest extracting matched lines from two input frames that can then be easily interpolated frame by frame, serving as frame-wise conditions seamlessly integrated into existing video generation models. In extensive evaluations covering diverse scenarios such as natural landscapes, complex human poses, camera movements and animations, existing methods often exhibit incoherent transitions across frames. In contrast, our FCVG demonstrates the capability to generate temporally stable videos using both linear and non-linear interpolation curves. Our project page and code are available at https://fcvg-inbetween.github.io/. + +# 1. Introduction + +Given the presence of low framerate videos, the generation of high framerate videos has emerged as an active research area with a wide range of applications that demands smooth and stable visual contents. Video interpolation or inbetweening, which focuses on synthesizing intermediate frames between two given frames, has been extensively studied in the literature [7, 22, 23, 38, 61]. However, traditional video interpolation methods are inherently limited in dealing with significant motions due to their reliance on + +optical flow for modeling frame motion. Recently, generative image-to-video (I2V) models have made remarkable progress in generating coherent videos [4, 31], offering potential solutions to enhance framereates through generative inbetweening [47, 53]. Compared to traditional video interpolation, generative inbetweening leverage the creative ability of generative models and focuses more on handling scenarios with larger time intervals. + +When start and end frames are provided, it is a straightforward task to separately generate two coherent videos using an I2V model, but the challenge of inbetweening lies in the ambiguity of the interpolation path caused by large motions. To address this issue, a time reversal strategy [8] is proposed to average the fusion of bidirectional diffusion denoising steps conditioned on start and end frames. Then, temporal attention layers in the I2V model are fine-tuned to enhance motion coherence [47]. More recently, Yang et al. [53] introduced a multi-channel sampling strategy to substitute direct average fusion. However, the ambiguity of interpolation path remains severe and often results in incoherent transitions in generated videos, as shown in Fig. 1. + +In this paper, our aim is to mitigate the ambiguity in interpolation path and achieve temporal stability in video generation. We propose a straightforward yet highly effective Frame-wise Conditions-driven Video Generation (FCVG) method. Our FCVG model provides an explicit condition when generating each frame using an I2V model, making it easier to identify the interpolation path between start and end frames, and thus ensuring temporally stable production of visually plausible video frames. Firstly, we extract two conditions from the input key frames to establish robust correspondences between start and end frames using matched lines. In addition, pose skeletons can be incorporated into the conditions to better capture human poses. Subsequently, linear interpolation is employed on a frame-by-frame basis to interpolate the start and end conditions. These framewise conditions effectively alleviate ambiguity in determining the interpolation path, and can be seamlessly integrated into the I2V model as control for video frame generation. + +The linear frame-wise conditions for generative inbetweening are generally feasible from two perspectives: (i) + +![](images/ff24db13cf1a3181fb3edb0eae425adf034dc2a666fa4e28cc50e667fd030abe.jpg) +GI +Figure 1. Video results of GI [47] and our FCVG. More videos are provided in https://fcvg-inbetween.github.io/. + +In pioneering video interpolation methods [2, 19, 25], the linear assumption is commonly adopted, which may not truly align with ground-truth temporal consistency but can lead to temporally stable videos for most scenes. As depicted in Fig. 1, our FCVG demonstrates a significantly higher level of video stability compared to existing methods; (ii) As illustrated in Fig. 2(b), our frame-wise conditions provide a control path for inbetweening, while still allowing some flexibility for video generation models, whose influence can be further adjusted by tuning the fusion weight between features of condition and video generation branches. Moreover, our FCVG allows users to specify a non-linear interpolation path for frame-wise conditions to generate desired video frames, providing more flexibility in determining the interpolation path. + +Extensive experiments are conducted on the collected diverse testing samples including natural landscapes, complex human poses, camera movements and animations, where our FCVG is compared with both video interpolation methods and generative inbetweening methods. Regarding several evaluation metrics, our method outperforms existing methods in terms of frame textures and temporal stability. Particularly when dealing with large motions, unlike other methods that suffer from incoherent transitions across frames, our FCVG exhibits significantly enhanced temporal stability in the generated videos. + +# 2. Related Work + +Optical Flow-based Frame Interpolation. Video frame interpolation aims to synthesize intermediate frames between two given input frames [3, 28]. Previous methods primarily rely on optical flow-based approaches[14, 22, 23], which estimate optical flow and apply forward [27] or backward warping to generate intermediate frames. Some techniques incorporate flow reversal techniques to estimate the intermediate flows [19, 40, 50], while others concentrate on directly predicting the intermediate flows [15, 21, 55, 60]. Although these methods yield stable interpolation results in real-world scenes, they exhibit significant artifacts when + +confronted with large motion or complex scenarios, such as human motion. Moreover, they struggle with the impact of optical flow estimation accuracy [6] in varying data distributions, such as animation or line art. While some approaches have developed models tailored for animation [6, 41] or line art [37, 42, 64], restricting them for specific data types. + +Diffusion-based Frame Interpolation. In recent years, diffusion models have demonstrated remarkable capabilities in generating high-quality images and videos [1, 5, 12, 34, 43, 46]. Several studies have explored the effectiveness of diffusion models for video frame interpolation [7, 17, 38, 45], particularly in addressing complex motions that pose significant challenges for optical flow-based methods. Some approaches treat the input frames as conditions and utilize large-scale data to train a diffusion model for video frame interpolation [18, 51, 52]. Other approaches leverage pre-trained image-to-video diffusion models, incorporating new sampling strategies to achieve frame interpolation [8, 47, 53]. TRF [8] proposes a time reversal sampling strategy that fuses bidirectional motion from two parallel diffusion denoise steps conditioned on the start and end frame. Based on the time reversal strategy, Generative Inbetweening [47] fine-tunes diffusion models by utilizing temporal attention information to maintain motion consistency, while VIBIDSampler [53] introduces a bidirectional sampling approach rather than direct average fusion ensuring on-manifold generation of intermediate frames. + +Controllable Video Generation. Recent works try to introduce controllable conditions to video generation models [59], such as camera motion [9, 49] and human pose [13, 58, 63]. Among these methods, the approach utilizing lightweight adapters [26, 56] is preferred by many researchers due to its elimination of the need for pre-training the large diffusion model. ControlNet [56] uses zero convolution to connect certain trainable layers copied from pretrained large models to the original layers. To reduce the additional computational cost, ControlNeXt [31] introduces a lightweight module and fine-tunes several parameters in the diffusion model, aligning them using cross normalization. + +![](images/3ed28519400cbdba455302d0ee549ba3bd82a83db873ad0b7a6ed00f2dd7fe80.jpg) +Figure 2. (a) The ambiguity in interpolation path, where the stochastic nature of forward and backward paths leads to misalignment or even generating substantially different contents in two paths. (b) Our frame-wise conditions serve as a control path, enabling rough alignment of the forward and backward paths, thereby confining the fusion process closer to the manifold. + +![](images/2663e594e8626fa60b6050e5b4a73512786e84d05b2493236965cd33b2c45cd2.jpg) + +# 3. Method + +# 3.1. Preliminaries + +Diffusion model [12] is a type of generative model that uses a denoising network to iteratively denoise random Gaussian noise to generate a high-quality image or video. Specifically, for I2V diffusion models, such as Stable Video Diffusion (SVD) [4], given a video $\pmb{x} \in \mathbb{R}^{N \times 3 \times H \times W}$ containing $N$ frames, SVD first encode $\pmb{x}$ using an autoencoder $\mathcal{E}(\cdot)$ to get latent representation $\pmb{z} \in \mathbb{R}^{N \times C \times H \times W}$ [20]. The forward process of diffuse gradually adds noise to latent representation $\pmb{z}$ as follows + +$$ +\boldsymbol {z} _ {t} = \alpha_ {t} \boldsymbol {z} + \sigma_ {t} \boldsymbol {\epsilon}, \tag {1} +$$ + +where $\epsilon \sim \mathcal{N}(\mathbf{0},\mathbf{I})$ , $\alpha_{t}$ and $\sigma_{t}$ represent the noise level for denoising time $t$ , defined by the noise schedule. As for backward process, a 3D UNet [35] denoiser $f_{\theta}$ is used for iteratively denoising under the image condition $c_{\mathrm{image}}$ . The optimization objective is formulated as + +$$ +\mathcal {L} = \mathbb {E} _ {\boldsymbol {z}, \boldsymbol {c} _ {\text {i m a g e}}, \boldsymbol {\epsilon} \sim \mathcal {N} (\boldsymbol {0}, I), t} \left[ \| \boldsymbol {v} - f _ {\theta} \left(\boldsymbol {z} _ {t}, \boldsymbol {c} _ {\text {i m a g e}}, t\right) \| _ {2} ^ {2} \right], \tag {2} +$$ + +where $\pmb{v} = \alpha_{t}\pmb{\epsilon}_{t} - \sigma_{t}\pmb{z}_{t}$ is referred as v-prediction [36]. Finally, the generated videos are obtained through the VAE decoder $\hat{x} = \mathcal{D}(z_0)$ . + +Inspired by the strong capability of diffusion models in video generation, several studies have endeavored to integrate diffusion models into video inbetweening to tackle challenges posed by intricate and extensive motions that are difficult to address using optical flow-based methods [7, 8, 17]. A direct approach for applying diffusion models in video inbetweening involves utilizing key frames as conditions for retraining the diffusion model. However, this often necessitates substantial data and computational resources and may also be influenced by discrepancies in data distribution. Consequently, some approaches leverage pretrained diffusion models for video inbetweening [8, 47, 53]. + +![](images/cdafe6f205a2197dcd28f5dc42f33c2bb8399fcc6fe1be468f813952ca34dc78.jpg) +Figure 3. The process for acquiring forward and backward frame-wise conditions $c_{1 \to N}$ and $c_{N \to 1}$ . Two initial conditions $c_{1}$ and $c_{N}$ can be obtained by establishing correspondence between start frame $I_{\mathrm{start}}$ and end frame $I_{\mathrm{end}}$ , where the same color indicates corresponding matches. Then, frame-wise conditions are obtained by interpolating $c_{1}$ and $c_{N}$ . + +The fundamental concept behind these methods is to fuse the temporal forward path and backward path after each denoising step conditioned on start and end frames, respectively, i.e., a process referred to "time reversal" [8, 47]. + +# 3.2. Motivation of Frame-wise Conditions + +Although time reversal provides a means to directly utilize pre-trained video generations for inbetweening, it exhibits certain limitations [8] that are summarized as follows: (i) The motion generated by I2V models tends to be diverse rather than stable. While this diversity is advantageous for pure I2V tasks, it introduces significant ambiguity when applying the time reversal strategy for video inbetweening. As depicted in Fig. 2(a), the stochastic nature of generating forward and backward paths leads to misalignment and even substantially different contents in two paths, resulting in an unstable and unrealistic videos. (ii) T tedious tuning of hyper-parameters related to temporal conditioning within the I2V model is required for each input pair, such as motion bucket ID and frames per second. (iii) Inference efficiency is constrained by certain techniques, e.g., noise reinjection [8], aimed at mitigating the ambiguity but significantly increasing inference time (approximately 1.5 to 3 times longer). + +Indeed, if the first fundamental limitation in ambiguity can be addressed, the subsequent two issues can also be readily resolved. To this end, several studies have made significant efforts in mitigating the misalignment between forward and backward paths [47, 53]. Nevertheless, as depicted in Fig. 2(b), there still exists considerable stochasticity between these paths, thereby constraining the effectiveness of these methods in handling scenarios involving large motions such as rapid changes in human poses. The ambiguity in the interpolation path primarily arises from insufficient conditions for intermediate frames, since two input images only provide conditions for start and end frames. Therefore, in this work, we suggest offering an explicit condition for each frame, which significantly alleviates the am + +![](images/6033ce8d3ac8390bcd0fe95c2c71b9c9662adf7b99b2e4b3701c7d80e9a72f05.jpg) +Figure 4. Inference of FCVG at time $t$ . + +biguity of the interpolation path. As shown in Fig. 2(b), frame-wise conditions ensure that the forward and backward paths are relatively aligned during the denoising process, thereby rendering a simple fusion method adequate to confine the fusion process closer to the manifold. + +# 3.3. Proposed FCVG + +Given two input frames $I_{\mathrm{start}}$ and $I_{\mathrm{end}}$ , our FCVG aims to generate $N$ video frames, whose start and end frames should be consistent with $I_{\mathrm{start}}$ and $I_{\mathrm{end}}$ , respectively. As shown in Fig. 4, our FCVG provides frame-wise conditions for video generation model to make the generated frames be temporally stable. Based on the time reversal strategy, our FCVG at time $t$ can be specifically formulated as + +$$ +\tilde {\boldsymbol {z}} _ {t} = f _ {\theta} \left(\boldsymbol {z} _ {t + 1}, \boldsymbol {I} _ {\text {s t a r t}}, \boldsymbol {c} _ {1 \rightarrow N}, t\right), \tag {3} +$$ + +$$ +\tilde {z} _ {t} ^ {\prime} = f _ {\theta} (\operatorname {f l i p} \left(\boldsymbol {z} _ {t + 1}\right), \boldsymbol {I} _ {\text {e n d}}, \boldsymbol {c} _ {N \rightarrow 1}, t), \tag {4} +$$ + +$$ +\boldsymbol {z} _ {t} = \boldsymbol {\lambda} \cdot \tilde {\boldsymbol {z}} _ {t} + (1 - \boldsymbol {\lambda}) \cdot \operatorname {f l i p} \left(\tilde {\boldsymbol {z}} _ {t} ^ {\prime}\right), \tag {5} +$$ + +where $\pmb{z}_{t + 1}\in \mathbb{R}^{N\times C\times H\times W}$ is diffusion noises from time $t + 1$ , $f_{\theta}$ is the pre-trained denoiser model with control module, $\pmb{c}_{1\rightarrow N},\pmb{c}_{N\rightarrow 1}\in \mathbb{R}^{N\times 3\times H\times W}$ are temporal aligned forward and backward frame-wise conditions, $\mathrm{flip}(\cdot)$ denotes flipping the sample along the time dimension, and $\lambda \in \mathbb{R}^N$ is fusion weights with $\lambda_{i} = 1 - \frac{i - 1}{N - 1},i\in \{1,\dots,N\}$ . The symbol $\cdot$ denotes frame-wise multiplication, i.e., $\lambda_{i}$ is multiplied with noises for $i$ -th frame. By iteratively denoising until time $t = 0$ , final inbetweening video frames can be obtained by $\hat{\pmb{x}}_0 = \mathcal{D}(\pmb {z}_0)$ . + +# 3.3.1 Frame-wise Conditions + +Currently, we only have access to two image conditions, i.e., $I_{\mathrm{start}}$ and $I_{\mathrm{end}}$ . However, extending them as framewise conditions is infeasible. In order to acquire framewise conditions, the initial conditions should satisfy two properties that can effectively capture frame motion, and + +Algorithm 1: Inference of FCVG +Input: $\pmb{I}_{\mathrm{start}},\pmb{I}_{\mathrm{end}},f_{\theta},\mathcal{D},\pmb{z}_T\sim \mathcal{N}(\pmb {0},\pmb {I})$ Computing $\lambda$ with $\lambda_{i} = 1 - \frac{i - 1}{N - 1}$ $i\in \{1,\dots,N\}$ Extracting conditions $c_{1},c_{N}$ from $\pmb{I}_{\mathrm{start}},\pmb{I}_{\mathrm{end}}$ .. + $c_{1\rightarrow N} =$ interpolate $(c_{1},c_{N})$ . + $c_{N\rightarrow 1} =$ flip $(c_{1\rightarrow N})$ . +for $t\gets T:1$ do + $\tilde{\pmb{z}}_t = f_\theta (\pmb {z}_t,\pmb{I}_{\mathrm{start}},\pmb {c}_1\to N,t);$ $\pmb{z}_{t,f} =$ flip $(z_{t})$ $\tilde{\pmb{z}}_t^{\prime} = f_\theta (\pmb {z}_{t,f},\pmb{I}_{\mathrm{end}},\pmb {c}_{N\to 1},t);$ $\tilde{\pmb{z}}_{t,f}^{\prime} =$ flip $(\tilde{\pmb{z}}_t^{\prime})$ $z_{t - 1} = \lambda \cdot \tilde{z}_t + (1 - \lambda)\cdot \tilde{z}_{t,f}^{\prime};$ +end +Return: $\mathcal{D}(\pmb {z}_0)$ + +are amenable for extension as frame-wise. Drawing inspiration from prior works [23, 64] that showcase the robustness of global matching in handling large motions and complex scenes, we propose to employ the line matching model to extract the initial conditions from $I_{\mathrm{start}}$ and $I_{\mathrm{end}}$ . Compared to conditioning on optical flow, which is often erroneous in certain regions, using line matches as conditions focuses on the most stable regions, avoiding the introduction of erroneous conditions that could disrupt the generation process. Specifically, we utilize the pre-trained Glue-Stick [30] as our line matching model to establish correspondences between $I_{\mathrm{start}}$ and $I_{\mathrm{end}}$ , and subsequently visualize these matches as images with distinct colors representing different line matches, resulting in two initial conditions $c_1$ and $c_N$ . Moreover, to further improve human motions, we extract human poses that can be directly added into $c_1$ and $c_N$ . + +As shown in Fig. 3, the control condition $c_{i}$ for $i$ -th frame can be obtained by accordingly interpolating $c_{1}$ and $c_{N}$ , where the forward frame-wise conditions $c_{1 \to N}$ are the concatenation of $\{c_{i}\}_{i=1}^{N}$ along the time dimension, and backward frame-wise conditions $c_{N \to 1}$ are the flip of $c_{1 \to N}$ along the time dimension. We empirically found that linear interpolation is sufficient for most cases to guarantee temporal stability in inbetweening videos, and our method allows users to specify non-linear interpolation paths for generating desired videos. + +# 3.3.2 Injection to Video Generation Model + +We follow ControlNeXt [31] to inject frame-wise conditions into the I2V model. We choose SVD [4] as our base I2V model. Compared to other controllable video generation methods, ControlNeXt is light-weight and does not significantly increase inference time. Specifically, the control conditions are first encoded by a lightweight module composed of multiple ResNet [10] blocks. These encoded conditions are first processed using cross normalization to + +![](images/ae4ff7ceb7206ea0a09d274f9a6be575e059d8c53348a378b5690bda2af79841.jpg) +Figure 5. Overview of injecting frame-wise conditions into SVD. To make frame-wise conditions better fit pre-trained SVD, we only need to fine-tune a small set of parameters including the value and output projection matrices within the attention layers, and the lightweight ResNet blocks. + +align the distributions of $\pmb{y}^{\mathrm{Con}}$ and $\pmb{y}^{\mathrm{SVD}}$ from the condition and SVD branches. Then at denoising time $t$ , frame-wise conditions can be injected into SVD as follows + +$$ +\hat {\boldsymbol {y}} _ {t} = \boldsymbol {y} _ {t} ^ {\mathrm {S V D}} + \gamma \boldsymbol {y} _ {t} ^ {\mathrm {C o n}}, \tag {6} +$$ + +where $\gamma$ is a tunable weight for controlling the significance of $y^{\mathrm{Con}}$ . The inference of FCVG is detailed in Algorithm 1. Moreover, in order to enhance the compatibility of pretrained SVD with our frame-wise conditions, we employ a small set of videos for fine-tuning. We freeze the majority of SVD parameters and solely optimize the value and output projection matrices within attention layers, along with lightweight ResNet blocks, as shown in Fig. 5. + +The limitations in Sec. 3.2 have been largely resolved in FCVG: (i) By explicitly specifying the condition for each frame, the ambiguity between forward and backward paths is significantly alleviated; (ii) Only one tunable parameter $\gamma$ is introduced, and setting it to 1, while keeping hyperparameters in SVD as default, yields favorable results in most scenarios; (iii) A simple average fusion, without noise re-injection, is adequate in FCVG, and the inference steps can be substantially reduced by $50\%$ compared to GI [47]. + +# 4. Experiments + +# 4.1. Experimental Setup + +Datasets. To verify the performance of our FCVG across diverse scenes, we collect a dataset encompassing a variety of scenes, such as natural environments, indoor/outdoor scenes, and human poses, where diverse motion types are encompassed such as camera movements, object motion, human dance actions, and facial expression transitions. Specifically, our dataset consists of 524 video clips, each containing 25 frames, selected from the DAVIS dataset [32] + +and RealEstate10K dataset [62], supplemented by high-frame-rate videos from Pexels1. We randomly split the dataset in a 4:1 ratio for fine-tuning and testing respectively. Evaluation Metrics. Following previous works [8, 47], we adopt LPIPS [57] and Fréchet Inception Distance (FID) [11, 29] to evaluate the quality of individual frames, while employing Fréchet Video Distance (FVD) [44] to assess the overall quality of videos. Additionally, we take two recently proposed metrics VBench [16] and FVMD [24] to assist the evaluation, where VBench assesses videos across multiple dimensions based on pre-trained models, while FVMD refines FVD by emphasizing more on motion consistency. Furthermore, it should be noted that all these metrics are not capable of precisely evaluating temporal stability of generated videos, and thus we highly recommend directly observing more video results provided in our project page. + +Implementation Details. For obtaining initial conditions, we utilize the pre-trained GlueStick [30] for line matching and DWPose [54] for estimating human poses. The fine-tuning is performed on ResNet blocks, and the value and output projection matrices within the attention layer of SVD. The fine-tuning process is conducted for 70k iterations using the AdamW optimizer on an NVIDIA A800 GPU, with a learning rate of $1 \times 10^{-6}$ and $\beta_{1} = 0.9$ , $\beta_{2} = 0.999$ . For fine-tuning, we crop the frames to patches with resolution $512 \times 320$ . The inference of FCVG is done in $T = 25$ steps without noise re-injection. Without specific clarity, the balancing weight $\gamma = 1$ is set for all the experiments. Due to the robustness of our FCVG, all the hyperparameters in SVD adopt the default settings. + +# 4.2. Comparison with State-of-the-arts + +We compare FCVG with state-of-the-art optical flow-based interpolation method FILM [33], and diffusion-based methods including DynamiCrafter [52], TRF [8] and GI [47]. + +Quantitative evaluation. To evaluate performance under different motion conditions, we conduct assessments with frame gaps setting to 23 and 12, respectively. As shown in Tab. 1, our method achieves the best performance among four generative approaches across all the metrics. Regarding the LPIPS comparison with FILM, our FCVG is marginally inferior, while demonstrating superior performance in other metrics. Considering the absence of temporal information in LPIPS, it may be more appropriate to prioritize other metrics and visual observation. Moreover, by comparing the results under different frame gaps, FILM may work well when the gap is small, while generative methods are more suitable for large gap. Among these generative methods, our FCVG exhibits significant superiority owing to its explicit frame-wise conditions. + +Qualitative evaluation. The visual comparison in Fig. 6 il + +Table 1. Quantitative comparison on different interpolation gaps. Our primary focus lies in generative approaches, with FILM being the sole method that employs optical flow. Bold refer to the best results. All these metrics are not capable of precisely evaluating temporal stability of generated videos, and thus we highly recommend directly observing video results. + +
MethodFrame Gap = 23Frame Gap = 12
LPIPS (↓)FID (↓)VBenchmark (↑)FVMD (↓)FVD (↓)LPIPS (↓)FID (↓)VBenchmark (↑)FVMD (↓)FVD (↓)
FILM[33]0.154025.000.86158208.7543.40.198024.440.86676975.9495.4
DynamiCrafter[52]0.388652.660.841013221.9978.90.383937.490.845811810.7652.5
TRF[8]0.368742.760.843810458.0823.40.374239.010.847810076.6818.4
GI[47]0.215531.390.86065682.6524.00.261532.370.86514721.0565.8
Ours0.183224.050.86195607.2437.90.237822.770.86724537.4465.6
+ +![](images/4d3f1d1f76f5c0d7f13c96fc7c5c8264c42ebba4650b8684912980e091dbaeb3.jpg) +Figure 6. Qualitative evaluation on diverse scenes, where our FCVG is superior in texture details and coherent intermediate motions. + +lustrates the superior performance of our method compared to other counterparts in terms of motion stability, consistency, and overall quality. While FILM produces smooth interpolation results for small motion scenarios, it struggles with large scale motion due to inherent limitations of optical flow, resulting in noticeable artifacts such as back + +ground and hand movement (in the first case). Generative models like TRF and GI suffer from ambiguities in fusion paths leading to unstable intermediate motion, particularly evident in complex scenes involving human and object motion. In contrast, our method consistently delivers satisfactory results across various scenarios. Even when significant + +![](images/567f97c1e99be95c697e90f95303ec8739917b9f2346603170c8b7f59f788560.jpg) +Figure 7. The effect of control weight $\gamma$ . Red arrows indicate the movement directions. As the value of $\gamma$ decreases, the diversity of intermediate motion increases, e.g., up-and-down swinging of the arm, while temporal stability is guaranteed for two cases. The videos are available in the project page. + +![](images/fc74773e19b88c328292929cb6e96185b183df191917072a9f5ea54410e430a5.jpg) + +![](images/d1349a10837245106667751900e36871f1fce75682248ff659510f295a6c8708.jpg) + +![](images/414d7de16b5d4ac003f85b8ebd5c18dc9d5d48d109ee29cf7366f30a988dc8ed.jpg) + +![](images/a60e6946b2073a438c495d877ec3fcfe5e8d594446a87b0d37be2c6657289007.jpg) + +occlusion is present (in the second case and sixth case), our method can still capture reasonable motion. Furthermore, our approach exhibits robustness for complex human actions (in the last case). + +Computational efficiency. In Tab. 2, we evaluate the inference time of diffusion-based methods. DynamiCrafter generates 16 frames at resolution of $512 \times 320$ , while the other methods generate 25 frames at resolution of $1024 \times 576$ . DynamiCrafter exhibits advantages in inference time due to its single-pass denoising process. In comparison to TRF and GI, our FCVG facilitates easier alignment between forward and backward paths, ensuring that the results remain within the manifold as in Sec. 3.2. Consequently, although FCVG requires slightly less extra time for conditions extraction, it eliminates noise re-injection step and achieves satisfactory results with only 25 steps, in contrast to the requirement of 50 steps by the other methods. Real-time applications still pose challenges for generative inbetweening due to the high inference cost of pre-trained video generation models. + +Table 2. Evaluation of computational efficiency. + +
MethodsN × (H, W)TTime (s)
DynamiCrafter [52]16×(512, 320)5037
TRF [8]25×(1024, 576)501230
GI [47]25×(1024, 576)50975
Ours25×(1024, 576)25523
+ +# 4.3. Flexibility of Frame-wise Conditions + +Our FCVG allows some flexibility to SVD by setting different values for $\gamma$ . In Fig. 7, one can see that adjusting $\gamma$ within a certain range has little impact on video stability but can lead to different directions of movement. Albeit fine-tuned for linear frame-wise conditions, FCVG enables users to specify non-linear motion trajectories, such as ease-in and ease-out motion trajectories. The video examples can be found in our project page. + +# 4.4. Generalization to Animation Videos + +We further evaluate the generalization ability of FCVG to hangle animation and linear videos, whose data types do not appear in the fine-tuning dataset. As depicted in Fig. 8, our FCVG consistently produces visually appealing results, even for challenging scenarios such as head turns, liquid flow, and object deformations. This can be attributed to the robust guidance provided by frame-wise conditions that are beneficial for interpolation involving large motion in line-arts and animations [23, 64]. + +Table 3. Ablation study on condition components. + +
LPIPS (↓)FID (↓)FVMD (↓)FVD (↓)
w/o Control0.248527.557217.5536.5
w/o Pose0.184324.705520.9446.1
w/o Matching0.212424.176546.8498.8
Full Model0.183224.055607.2437.9
+ +# 4.5. Ablation Study + +We conduct ablations to discuss the components of conditions and control weight $\gamma$ . + +Condition components. In Tab. 3, 'w/o Control' denotes the exclusion of the entire frame-wise conditions control, while 'w/o Pose' and 'w/o Matching' indicate the removal of human pose and line matching conditions, respectively. The visual results are presented in Fig. 9, from which one can see that the line matching condition governs the overall motion of the scene, and the pose condition benefits details with human movements. + +Control weight $\gamma$ . The impact of $\gamma$ has been discussed in Sec. 4.3. Based on the findings in Figure 7 and Table 4, FCVG is not very sensitive to the value of $\gamma$ , and the weight $\gamma = 1$ proves to be suitable for the majority of scenarios. + +# 5. Limitations and Future Work + +Due to the dependence on line matching, incorrect matching results may arise when two input frames exhibit highly similar features, thereby impacting the quality of generated + +![](images/6263c4788921deb8a1ab9ba9cb281da044c5a046c6d621664e57bdab3b89286a.jpg) + +![](images/221bd9bd74b457243febf32670356bc54b9eadfe3d50a19541677e242fab8286.jpg) + +![](images/dc50827c46b5f1348c54522eedc505417c1933d2de093b6dbdec53a3fba4399d.jpg) +Start Frame + +![](images/f34600c8ba0a843ce0db32160d4b3aa5fc2bb9c161078cfffda8302e18def753.jpg) + +![](images/54f09b96c634f7482d830f78d4396269da965570278ce70c34fd8799e8b3fed6.jpg) + +![](images/56003e29d06d42cb18d5445ec73aa60d8d9fff7fdad41b6cdeee7b71e3221d8a.jpg) + +![](images/b5482a53549cb251894ed9a1580db7a630f3a2d0e993b13db75073ffcde5cc90.jpg) +Inbetweening + +![](images/42dc157c819ad2b5542511898f9c15d93edbcc2074679d3dd2aff6b6c1655ac5.jpg) +Figure 8. Inbetweening results on animations and linearts. FCVG exhibits favorable performance without fine-tuning on these data types. + +![](images/13a2f7f2778f3325e395c7f0bbfc9e34f8d89bd762e56d7f6fe0a609d75d9a75.jpg) + +![](images/39408e87a33f17d268fed47262aa6643a119eca89c1af14dd5bb900db10e59ab.jpg) + +![](images/f9c9b1f467886437aa3200d73bd0389aee533b57cd8551db76964a04fb0ecc43.jpg) + +![](images/030814d1536aea8410dfad317b694a373c042a70e1747d6f0d927fe454552b2a.jpg) + +![](images/0d1bb370e5396724141b0187456abdd73cc948590743e493af657c4d3a223b0c.jpg) + +![](images/eb3e022775b4c768f73fd86c3325d9799dd7bbccf91549136378eecf2adf80b2.jpg) + +![](images/4ee0e3c6f618b6702a23f0e577c094b982741fffe89142494b443961b33a5a8f.jpg) + +![](images/122bbd5995b6b4d27df73957178b57be0d8e06eb75aa4f0a1676be0d50a7e42c.jpg) +screening + +![](images/ec8e4156b727cca0008529754fb653d739c1566371f2f6ac4933ef847205cbc4.jpg) + +![](images/4e6562d7284947427750e244f4e723e00cea6a9d0d68f9a0a38c13f176f9d0df.jpg) + +![](images/f0a0d3cc903b069ae945e15b071c7116f6ce361c73568d40774427d25a577a30.jpg) + +![](images/28cfac6c28f27bf52d947062acacb789587138c76d423f7d978f7ec66269bab7.jpg) + +![](images/dd2fffbdac09236cb36f1d27e5489d7ac0f86e98fd7a427641dd43d8bd1bc791.jpg) + +![](images/953d4fdef4b728d5ca4b7f7e95353218b1f2ff3f2374cfa8e64c59592147affb.jpg) + +![](images/45bbb9848ddb24ba6cd21037cf56c9767344daaec96eba8d741614e65bfce946.jpg) + +![](images/5c3df0439e461e4e055f16dbb9d1667c2ba2db859c69ea36d5e8d5c272ab8f68.jpg) + +![](images/576b6a48f642fa3211143f19654f7a13ed7f60c87aa2bdcf9ae7b24dd31067b7.jpg) +End Frame + +![](images/61a57369a22e1f5ef44c1b5e98d2b8774d8f1090c501608b553a1c3130768999.jpg) +w/o Control + +![](images/1157bf785ed14ab414ac5a54dff117f9c71418b5fac5525fef65e5e0c9233351.jpg) +w/o Matching + +![](images/dcec2e7d9329fae40f97d3b2fd330aa2ff59526e5a9b6a122e67606efb93b034.jpg) +w/o Pose +Figure 9. Ablation study on condition components. + +![](images/b1cb5fe554143001fbe66ad1007cd6daa8207d0dab374761f21de9c37d347037.jpg) +Ours + +Table 4. Quantitative analysis on control weight $\gamma$ . + +
LPIPS (↓)FID (↓)FVMD (↓)FVD (↓)
γ = 0.50.191223.805920.0431.4
γ = 1.00.183224.055607.2437.9
γ = 2.00.186124.665726.9441.1
+ +frames. This limitation can be alleviated by manually reducing the control weight, as exemplified in the first instance in Fig. 10. However, when there is a significant difference between the two input frames, matched lines may be sparse, making simple adjustment of the control weight ineffective, as the second example in Fig. 10. This limitation could potentially be addressed in future research by replacing SVD with more robust I2V models. Furthermore, enhancing the interpolation process through diverse control conditions could offer improvements, e.g., incorporating user-specified drag effects like Dragdiffusion [39] or generating control conditions based on generative models using user-defined text inputs [48]. + +![](images/197e587f556d761619a0cde2835e1071844dcbdad8fb2ad3a815eb1d04341058.jpg) +Start Frame +Figure 10. Failure cases. Incorrect matches and significant difference between input frames lead to intermediate artifacts, some of which can be mitigated by adjusting the control weight. + +![](images/4a23eb40d5492d1dbcbdbf41a0fb25631931a07efd2153ea738171d8a0ab9245.jpg) +End Frame + +![](images/732adff8b038436d8230c01c44dc208542716c229ee13233e495940efeeb5708.jpg) +$\pmb{\gamma} = 1.0$ + +![](images/76fe000202fcc5839addb3bffa6ab65e2786cb298ffcc5bd0643e9334ce574db.jpg) +$\gamma = 0.5$ + +# 6. Conclusion + +In this paper, we propose a frame-wise conditions-driven video generation method, FCVG, for generative inbetweening. To fully exploit the potential of a video generation model in producing temporally stable videos, an explicit condition is provided for each frame. Specifically, framewise conditions can be obtained by interpolating two initial conditions that contain matched lines extracted from two input frames, and subsequently injecting them into the video generation model alleviates the ambiguity of inbetweening path. Our FCVG is not very sensitive to the introduced control weight, and thus exhibits robustness across diverse scenes with a fixed weight setting. Moreover, FCVG is able to handle specific interpolation paths defined by users. + +# Acknowledgements + +This work was supported in part by the National Key Research and Development Project (2022YFA1004100), the National Natural Science Foundation of China (62172127 and U22B2035), the Natural Science Foundation of Heilongjiang Province (YQ2022F004). + +# References + +[1] Liu Anan, Su Yuting, Wang Lanjun, Li Bin, Qian Zhenxing, Zhang Weiming, Zhou Linna, Zhang Xinpeng, Zhang Yongdong, Huang Jiwu, and Yu Nenghai. 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Thin-plate spline-based interpolation for animation line in-between. arXiv preprint arXiv:2408.09131, 2024. 2, 4, 7 \ No newline at end of file diff --git a/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/images.zip b/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..e6cff1f21e171d985465c62446768c3235ce19ba --- /dev/null +++ b/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:76199766e4431142bee64c84038bb61e360b57ccb2ffec701a6241eeeee9c6a3 +size 926895 diff --git a/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/layout.json b/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..f3f441f316a471399ec9eac28cd2617232ea017c --- /dev/null +++ b/CVPR/2025/Generative Inbetweening through Frame-wise Conditions-Driven Video Generation/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b12971fd0de6a894eccd6184fc49663a4930d23485b154898e97df96856f75f0 +size 470671 diff --git a/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_content_list.json b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7a5a9730effcfb67f4a436ee910b22ae3b1d7f5c --- /dev/null +++ b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:8c6c6c35b1096414a3d00b0e245629841c828e95ddc026ff9c338987dd82fff0 +size 78585 diff --git a/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_model.json b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_model.json new file mode 100644 index 0000000000000000000000000000000000000000..143bef800559bcc311761b417aeb2490db4dabc8 --- /dev/null +++ b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:6dd482bc7221a8dea77a58210c2615c9fba87ecf1d7ddedc43d1259b8fbcf2cf +size 100213 diff --git a/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_origin.pdf b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..f753b4d4e1e62ba205fedaad208afb9bb8ccf08b --- /dev/null +++ b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/36370215-ddbe-432c-8353-c63d16f3f636_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c892fb7f3c90dc70aab252f01ce2a087083b3da3273e205231faf34c63cf79ca +size 1843178 diff --git a/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/full.md b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..b1352e3adfe7a2b8618a11f8152e0a6e294f5840 --- /dev/null +++ b/CVPR/2025/Generative Map Priors for Collaborative BEV Semantic Segmentation/full.md @@ -0,0 +1,333 @@ +# Generative Map Priors for Collaborative BEV Semantic Segmentation + +Jiahui Fu $^{1}$ , Yue Gong $^{1}$ , Luting Wang $^{1}$ , Shifeng Zhang $^{2}$ , Xu Zhou $^{2}$ , Si Liu $^{1}$ † + +$^{1}$ Institute of Artificial Intelligence, Beihang University $^{2}$ Sangfor Technologies Inc. + +# Abstract + +Collaborative perception aims to address the constraint of single-agent perception by exchanging information among multiple agents. Previous works primarily focus on collaborative object detection, exploring compressed transmission and fusion prediction tailored to sparse object features. However, these strategies are not well-suited for dense features in collaborative BEV semantic segmentation. Therefore, we propose CoGMP, a novel Collaborative framework that leverages Generative Map Priors to achieve efficient compression and robust fusion. CoGMP introduces two key innovations: Element Format Feature Compression (EFFC) and Structure Guided Feature Fusion (SGFF). Specifically, EFFC leverages map element priors from codebook to encode BEV features as discrete element indices for transmitted information compression. Meanwhile, SGFF utilizes a diffusion model with structural priors to coherently integrate multi-agent features, thereby achieving consistent fusion predictions. Evaluations on the OPV2V dataset show that CoGMP achieves a 6.89/7.64 Road/Lane IoU improvement and a 32-fold reduction in communication volume. + +# 1. Introduction + +Collaborative perception aims to achieve global optimal perception with minimal message exchange between multi-agents. It has notable applications in fields such as vehicle-to-everything [54, 63] and autonomous drone swarms [45, 53]. In scenarios with multi-agents, they exchange complementary information to overcome individual constraints like restricted viewpoints [7] and occlusions [10], thereby enhancing perceptual ability. Specifically, senders need to adopt compression strategies to retain local information as much as possible under limited transmission bandwidth. Meanwhile, receivers are committed to aggregating information from senders to achieve global perception despite conflicts caused by pose errors and prediction discrepancies. To this end, collaborative perception methods focus on achieving efficient information compression on sender side and robust information fusion on receiver side. + +![](images/8500c2df407a2bc82e4f995db44f9dbaacf3e63778ce74279ef7807aaf7f0fe4.jpg) +Figure 1. (a) Sender's compression suffers from information degradation, deteriorating the compressed prediction. The receiver's fusion struggles to handle information conflicts, leading to the suboptimal fusion prediction. (b) Our method leverages the generative map priors for compression in element format and fusion under structure guidance, facilitating better fusion prediction. + +Existing methods [6, 17, 26, 32, 43, 49-52] primarily address the 3D object detection task in Bird's Eye View (BEV). However, accurate environment understanding requires perceiving not only surrounding objects but also scene layouts [4, 19, 23]. Therefore, we explore the compression and fusion strategies for collaborative BEV semantic segmentation, which has not been explored. Designing appropriate strategies for dense features presents significant challenges as shown in Fig. 1 (a). During the sender compresses BEV features with spatial mask and dimensionality reduction, information degradation inevitably occurs, resulting in inferior perception quality. On the receiver side, when features from multi-agents are fused, conflicting semantic estimations in overlapping regions present a substantial obstacle and lead to erroneous fusion predictions. Existing strategies tailored to collaborative detection fail to address the above challenges due to their dependency on object-level sparsity, which is absent in the dense BEV segmentation task because of non-negligible feature representation differences. + +Therefore, we propose CoGMP, a novel Collaborative framework with Generative Map Priors for BEV semantic + +segmentation, aiming at efficient information compression and robust information fusion. Our method leverages the inherent Map Priors (e.g., layout structure, road shapes, and lane continuity) from generative models to help collaborative perception. As illustrated in Fig. 1 (b), on the sender side, we introduce an innovative Element Format Feature Compression (EFFC) method, which utilizes element priors to represent continuous BEV features as discrete map element indices. Specifically, we first construct map element priors contained in the codebook by training the VQVAE [41] on BEV maps. Then, we determine the indices in the codebook by predicting the element type based on BEV features. During message transmission, replacing continuous BEV features with discrete element indices efficiently reduces communication volumes. Furthermore, senders select the critical element indices to be transmitted, which can be used by receivers to reconstruct the dropped elements. Compared with reconstructing complex high-dimensional BEV features, element priors enable easier information recovery by estimating element types. By abstracting BEV features based on element priors, EFFC significantly reduces communication volume. + +On the receiver side, we propose an innovative Structure Guided Feature Fusion (SGFF) method, which robustly fuses features from senders under the guidance of global structural priors. In particular, SGFF progressively injects conditions from multi-agents into diffusion process [16], with the ego's preliminary perception as the initial state. Benefiting from the map structure prior learned through diffusion training, SGFF can adaptively select complementary information and resolve conflicts among agents based on implicit map structure priors. Moreover, considering the efficiency limitations of diffusion-based models when applied to perception tasks, we design an uncertainty adaptive time scheduler to enable high-quality fusion prediction with fewer iterations. By reformulating the multi-agent feature fusion as a conditional diffusion process, SGFF achieves global consistent fusion predictions. + +In summary, our approach efficiently compresses information by sharing codebook element priors and leverages structure priors in the diffusion model to aggregate elements from multi-agents in appropriate regions. We validate the effectiveness of our method on the OPV2V [47] dataset, and comprehensive experiments demonstrate that CoGMP achieves state-of-the-art performance-communication trade-off. Compared to previous methods, CoGMP achieves 6.89/7.64 Road/Lane IoU improvements and a 32-fold communication volume reduction simultaneously. Additionally, improvements reach up to 10.59/11.17 Road/Lane IoU under the similar transmission bandwidth, and communication volume is further reduced by 512 factor while still maintaining superior performances. Overall, our main contributions are as follows: + +- We propose a novel collaborative BEV segmentation method CoGMP that leverages generative map priors for efficient compression and robust fusion. +- We introduce EFFC for compression in the form of discrete map element indices and an SGFF process to fuse elements using a conditional diffusion model. +- We conduct extensive experiments on the OPV2V dataset, demonstrating that our method achieves a state-of-the-art performance-communication trade-off. + +# 2. Related Works + +Collaborative perception. Existing researches primarily focus on efficient information compression and robust information fusion within the collaboration process. Regarding information compression, previous methods reduce communication volume by limiting transmission targets [11, 29, 30, 57], reducing feature channels [20, 27], and using spatial filtering maps based on objectness scores [17, 18] or mutual information [50]. For robust information fusion, previous approaches employ various techniques, such as attention mechanism [26, 49, 52], graph optimization [32, 44], neural reasoning [40], and multi-scale interactions [43, 51] for multi-agent features integration. However, most methods are specifically designed for object detection task, which can not apply to BEV segmentation task. Although some studies [28, 42, 48] have developed collaborative BEV segmentation frameworks, their works typically employ task-driven compression while overlooking the utilization of structural prior information specific to maps. To fill this gap, our work introduces rich map priors from generative models, to achieve efficient information compression via element priors and robust information fusion with structure priors. + +Diffusion models for perception. The recent achievements of diffusion models [16, 35] in generative tasks have sparked a growing interest in adapting for discriminative tasks. Recent works apply diffusion models to various perception tasks, including image segmentation [1, 5, 9, 21, 60], depth estimation [13, 14, 24], and object detection [8, 15, 34, 46, 56]. These studies demonstrate the effectiveness of diffusion models in addressing classical perception tasks, inspiring us to apply them to collaborative perception. + +BEV segmentation. The BEV segmentation task utilizes sensor data as inputs and outputs a BEV segmentation map containing road structures such as drivable areas and lane markings. Previous approaches have mostly employed discriminative models based on CNNs [31, 37, 58] or transformers [2, 33, 61], performing per-pixel classification on BEV maps. Recently, some studies [22, 25, 59, 62, 64] have attempted to introduce generative models into BEV + +![](images/00ae8c6863d5853222e0757a4e69775369eade307f32d98a4d06d0818b22f585.jpg) +Figure 2. The overall framework of CoGMP. After extracting BEV features from surrounding multi-view images, senders perform EFFC to convert BEV features into element types and select critical elements indices as messages for transmission. These indices are used by the receiver to obtain selected element features and recover dropped element features. Next, the receiver employs SGFF to progressively refine its own element features through multiple iterations conditioned on senders' information. The fused features are finally processed by a VAE decoder to produce the collaborative BEV segmentation prediction. + +segmentation. However, they are limited to the refinement of perception in a single-agent setting. In this work, we further explore the effects of generative models in multi-agent collaboration, applying them to the compression and fusion of transmitted information. + +# 3. Method + +# 3.1. Overview + +Problem formulation. We focus on the BEV semantic segmentation task. Consider a scene with an ego agent denoted as $e$ and $N_{a}$ other agents. Let $\mathbf{X}_i$ represent the input data collected by the $i$ -th agent's sensors (e.g., multi-view cameras), and $\mathbf{Y}$ be the global ground-truth semantic label obtained from BEV maps under the ego's perspective. Our objective is to maximize the collaborative perception performance within a given communication budget $B$ . To achieve this, the goal can be formalized as: + +$$ +\begin{array}{l} \max _ {\theta , \mathcal {M}} g \left(\Phi_ {\theta} \left(\mathbf {X} _ {e}, \{\mathcal {M} _ {i \rightarrow e} \} _ {i = 1} ^ {N _ {a}}\right), \mathbf {Y}\right) \\ \text {s . t .} \quad \sum_ {i = 1} ^ {N _ {a}} b \left(\mathcal {M} _ {i \rightarrow e}\right) \leq B \tag {1} \\ \end{array} +$$ + +Here, $g(\cdot, \cdot)$ represents the evaluation metric, $\Phi_{\theta}(\cdot)$ is the collaborative perception model with trainable parameters $\theta$ , $\mathcal{M}_{i \to e}$ denotes the message transmitted from agent $i$ to the ego agent $e$ , and $b(\cdot)$ measures the communication volume associated with each message. The core challenge lies in determining how to select critical information to be transmitted as messages and how to utilize messages from multi-agents to enhance the ego agent's perception performance. + +Framework. As shown in Fig. 2, our method utilizes a BEV encoder to generate BEV features for each agent. + +Then, for other agents acting as senders, we apply Element Format Feature Compression to use discrete key element indices as transmission units, thereby reducing communication volume. Specifically, we utilize the Element Type Inference module to compress the original continuous BEV features into discrete type indices and Element Code Mapping module to convert the indices to element features. Subsequently, the Critical Element Selection module is used to select the key elements, which enables Masked Element Recovery module to maximize the restoration of map information after the transmission. Leveraging the prior of diverse map elements, we can represent the entire map's information using a limited set of element indices. Further details can be found in Sec. 3.2. + +For the ego agent acting as the receiver, we integrate the elements from other agents into the ego prediction through Structure Guided Feature Fusion. In particular, the receiver obtains element features from its own BEV features as mentioned above. Moreover, to aggregate element features from senders, we employ a conditional latent diffusion model which incorporates global structure priors of BEV maps. Through the diffusion reverse process, we use the features from senders as a condition to guide the progressive enhancement of the ego features. Finally, a VAE decoder is utilized to predict the segmentation result based on the fused features. Refer to Sec. 3.3 for more details. + +# 3.2. Element Format Feature Compression + +Given multi-view camera input, we use a BEV encoder following CVT [61] to extract the BEV feature map $\mathbf{F}_{\text {bev }}$ by aggregating image features via learnable queries with the assistance of intrinsic and extrinsic camera parameters. + +Previous works directly transmit the continuous representation $\mathbf{F}_{bev}$ between agents, which consumes much bandwidth due to the continuous characteristic. Therefore, + +![](images/8df49dc4e31a60628fc4fa7078381d94ec0e63eb7990b8c8d5194e766bf561df.jpg) +(a) Discrete Map Element Representation Learning +(b) Masked Map Element Reconstruction Learning + +![](images/116746203c5e9aa0ce6cac7c93523ddbe8e97d72cc9e22df94d12e1916455ec5.jpg) +Figure 3. (a) ETI module converts BEV features into discrete element indices, enabling retrieval of map element features from the pre-built codebook via ECM module. (b) CES module selects critical elements, which are then used by the MER module to reconstruct the masked elements. + +we propose Element Format Feature Compression (EFFC) to compress the continuous $\mathbf{F}_{bev}$ into masked discrete element indices $\tilde{\mathbf{E}}$ as message, which can be recovered into complete element feature $\hat{\mathbf{F}}_{elm}$ after the transmission. To achieve efficient compression based on element representation, we propose a Discrete Map Element Representation Learning process (seen in Fig. 3 (a)) to convert the continuous $\mathbf{F}_{bev}$ into a discrete element indices $\mathbf{E}$ . Furthermore, we employ a Masked Map Element Reconstruction Learning process (seen in Fig. 3 (b)) to adaptively select the $\tilde{\mathbf{E}}$ of most informative elements for transmission and recover the masked elements to get $\hat{\mathbf{F}}_{elm}$ . + +Discrete map element representation learning. To define the map elements, we train a VQ-VAE model on the segmentation labels $\mathbf{Y}$ . Similar to the original VQ-VAE, the codebook $\mathcal{C} = \{e_1,\dots,e_{N_c}\}$ contains $N_{c}$ vectors, where each vector is the embedding of a particular map element. The training process is almost the same as the original VQ-VAE, except that we convert the $\mathbf{Y}$ into a multi-channel binary mask image and use BCE loss as $\mathcal{L}_{rec}$ to supervise reconstruction, intending to better preserve the semantics information. + +Building on the VQ-VAE model, map element priors are incorporated into the codebook vectors as element embeddings. Next, we need to learn the conversion from BEV + +features to element features, which can be divided into two stages: Element Type Inference (ETI) and Element Code Mapping (ECM) as shown in Fig. 3 (a). For learning ETI, we first encode the $\mathbf{Y}$ to a one-hot distribution $P_{elm}(\mathbf{H}|\mathbf{Y})\in \mathbb{R}^{h\times w\times N_c}$ as: + +$$ +\mathcal {Q} (f) = \arg \min _ {j} \| f - \mathcal {C} [ j ] \|, \tag {2} +$$ + +$$ +P _ {e l m} (\mathbf {H} | \mathbf {Y}) = \operatorname {o n e - h o t} \left(\mathcal {Q} \left(\mathcal {E} _ {v a e} (\mathbf {Y})\right)\right). +$$ + +Then, we employed the ETI module to infer the corresponding element type indices based on BEV features. Specifically, given a BEV feature $F_{bev} \in \mathbb{R}^{h \times w \times c}$ , we applied a convolutional block $\mathcal{E}_{pri}$ to obtain a element type probability distribution $P_{elm}(\mathbf{H}|\mathbf{F}_{bev}) \in \mathbb{R}^{h \times w \times N_c}$ , from which an indices map $\mathbf{E}$ is generated by selecting the highest probability. This can be formulated as: + +$$ +P _ {e l m} (\mathbf {H} | \mathbf {F} _ {b e v}) = \mathcal {E} _ {p r i} (\mathbf {F} _ {b e v}), +$$ + +$$ +\mathbf {E} = \arg \max _ {j} P _ {e l m} (\mathbf {H} | \mathbf {F} _ {b e v}) [ j ]. \tag {3} +$$ + +Optimized by $\mathcal{L}_{pri} = \mathrm{CE}(P_{elm}(\mathbf{H}|\mathbf{Y}), P_{elm}(\mathbf{H}|\mathbf{F}_{bev}))$ , where $\mathrm{CE}(\cdot)$ is the cross-entropy loss, we can associate the continuous BEV features with the indices of specific element type in the codebook. + +Subsequently, in the ECM stage, we can directly use the indices map $\mathbf{E}$ to retrieve the corresponding embeddings from the codebook $\mathcal{C}$ to obtain the element features $\mathbf{F}_{elm} \in \mathbb{R}^{h \times w \times d}$ . Utilizing the element priors contained in the codebook optimized through the VQ-VAE map reconstruction process, we achieve efficient information compression using element indices as transmission units. + +Masked map element reconstruction learning. The previous compression converts the continuous BEV features to discrete element indices, significantly reducing the communication volume. However, the elements still suffer from spatial redundancy (i.e., background and repetitive elements can be predicted by nearby features). Therefore, we adopt the Critical Element Selection (CES) and Masked Element Recovery (MER) as Fig. 3 (b) to avoid the waste of bandwidth for redundant elements transmission. + +For CES in the sender side, we apply a self-attention module over $F_{bev}$ to obtain score map $\mathbf{S} \in \mathbb{R}^{h \times w \times 2}$ as: + +$$ +\mathbf {S} = \operatorname {M L P} (\text {S e l f - A t t e n t i o n} (\mathbf {F} _ {b e v})), \tag {4} +$$ + +A higher value in $\mathbf{S}^{(0)}$ (i.e., 0-th dimension of $\mathbf{S}$ ) indicates that the corresponding region contains more informative and unique features. Based on $\mathbf{S}$ , we derive a selection mask $\mathbf{M} \in \{0,1\}^{h \times w}$ , which identifies critical elements located in regions with high values that need to be transmitted. Specifically, the $\mathbf{M}$ can be obtained as follows: + +$$ +\left\{ \begin{array}{l l} \mathbf {M} = \operatorname {G u m b e l - S o f t m a x} (\mathbf {S}) ^ {(0)} & \text {i n} \\ \mathbf {M} = \mathbb {I} \left((i, j) \in \operatorname {T o p K} (\mathbf {S} ^ {(0)}, K)\right) & \text {i n} \end{array} \right. \tag {5} +$$ + +here the indicator function $\mathbb{I}(\cdot)$ assigns $M_{i,j} = 1$ if the position $(i,j)$ is in the top-K set, and $M_{i,j} = 0$ otherwise. + +Subsequently, we determine the masked discrete element indices $\tilde{\mathbf{E}} = \mathbf{E} \odot \mathbf{M}$ for transmission. Once the receiver acquires these indices, the MER module is used to recover the masked element. MER first derive $\tilde{\mathbf{F}}_{elm}$ based on $\tilde{\mathbf{E}}$ from codebook, followed by filling the masked regions with a learnable mask token embedding $\mathbf{F}_{mask} \in \mathbb{R}^{1 \times C}$ . Then, a self-attention module is employed to predict the probability distribution of element indices corresponding to the masked tokens as follows: + +$$ +\tilde {\mathbf {F}} _ {e l m} = \mathbf {C} [ \tilde {\mathbf {E}} ] \odot \mathbf {M} + \mathbf {F} _ {m a s k} \odot (1 - \mathbf {M}), +$$ + +$$ +\begin{array}{r} P _ {e l m} (\mathbf {H} | \tilde {\mathbf {F}} _ {e l m}) = \mathrm {M L P} (\text {S e l f - A t t e n t i o n} (\tilde {\mathbf {F}} _ {e l m})), \\ \hat {\mathbf {E}} = \tilde {\mathbf {E}} \odot \mathbf {M} + \end{array} \tag {6} +$$ + +$$ +\arg \max _ {j} P _ {e l m} (\mathbf {H} | \tilde {\mathbf {F}} _ {e l m}) [ j ] \odot (1 - \mathbf {M}), +$$ + +Based on the predicted indices $\hat{\mathbf{E}}$ , MER recovers masked element features by retrieving the corresponding embeddings from the codebook to get recovered features $\hat{\mathbf{F}}_{elm}$ . Regarding supervision, the CES and MER modules are both optimized by the $\mathcal{L}_{mask} = \mathrm{CE}(P_{elm}(\mathbf{H}|\mathbf{Y}), P_{elm}(\mathbf{H}|\tilde{\mathbf{F}}_{elm})) \odot (1 - \mathbf{M}) + \| \mathbf{M}\|_1$ , where $\| \mathbf{M}\|_1$ is used as a regularization term to prevent the CES module from degenerating into trivially selecting all elements. + +By optimizing the learnable mask during the reconstruction training process, we can select the most suitable elements for transmission on the sender side. These selected critical elements possess the potential to reconstruct the global information maximally on the receiver side. + +# 3.3. Structure Guided Feature Fusion + +With messages derived from multi-agents, previous methods achieve feature fusion through various techniques (e.g., GNN [44], CNN [17], transformer [48]). However, these approaches struggle to handle cross-agent conflicts arising from the limitations of individual perception. To address the above issues, we propose a novel Structure Guided Feature Fusion (SGFF) method. Our approach utilizes a diffusion model to capture the global map structure prior for generating BEV segmentation results. By progressively injecting the perceived information of multi-agents as conditions for various regions, our method produces more consistent and realistic predictions under the guidance of structural priors. In the following exposition, we first introduce the preliminaries of the diffusion model briefly, then present our Diffusion-driven Progressive Fusion process tailored to the collaborative BEV segmentation task. + +Conditional latent diffusion model. The CLDM is designed to learn a latent space distribution $p(z|c)$ . This + +![](images/ac4fe72eadf63934b0ace8aefed7a53af5a31dccd3e584cc822d3e3fdb4c331d.jpg) +Figure 4. SGFF process pipeline. In the diffusion process, Gaussian noise is added in the forward process, and $z_{t}$ is predicted by U-Net with condition features for the next reverse step. The UATS adjusts time scheduler for inference, with fewer steps required for lower uncertainty. + +model assumes a forward process by gradually adding noise to the latent feature, transforming the $z_0$ into a noisy $z_{t}$ as: + +$$ +q \left(\boldsymbol {z} _ {t} \mid \boldsymbol {z} _ {0}\right) \sim \mathcal {N} \left(\boldsymbol {z} _ {t}; \sqrt {\bar {\alpha} _ {t}} \boldsymbol {z} _ {0}, (1 - \bar {\alpha} _ {t}) \mathbf {I}\right), \tag {7} +$$ + +where $\bar{\alpha}_{t} = \prod_{s=1}^{t}\left(1 - \beta_{s}\right)$ , and $\beta_{s}$ is the noise schedule. + +During training, the model $f_{\theta}(z_t, c, t)$ is trained to predict the noise $\epsilon_t$ added at each time step from $z_t$ under the guidance of the conditional input $c$ , by minimizing the training objective function (i.e., $l_2$ loss with the true noise). + +At the inference stage, the $z_0$ is reconstructed from random noise $z_T$ using the model $f_{\theta}$ , the conditional input $c$ , and a translation rule in a Markovian manner, expressed as: + +$$ +p _ {\theta} \left(\boldsymbol {z} _ {0: T} | \boldsymbol {c}\right) = p \left(\boldsymbol {z} _ {T}\right) \prod_ {t = 1} ^ {T} p _ {\theta} \left(\boldsymbol {z} _ {t - 1} | \boldsymbol {z} _ {t}, \boldsymbol {c}\right). \tag {8} +$$ + +During the reverse process, at each step $t$ , the model $f_{\theta}$ predicts the noise $\epsilon_{t}$ which is then used to obtain $z_{t-1}$ by denoising $z_{t}$ according to the reverse diffusion equation. + +Diffusion-driven progressive fusion. Based on CLDM, we design a progressive fusion process for integrating element features from senders into the receiver features under the guidance of structure prior. As illustrated in Fig. 4, we first construct a diffusion forward process in the latent space of ground-truth semantic labels, transitioning the element features from clean $z_0 = \mathcal{E}_{vae}(\mathbf{Y})$ to noisy $z_T$ by sequentially adding Gaussian noise as Eq. (7). This process models the gradual corruption of BEV maps, simulating the incompleteness of perception information in various regions. + +Inspired by previous works [3, 38], instead of adopting $\epsilon$ -prediction for loss computation widely used in image generation, we train a lightweight U-Net [36] $f_{\theta}$ to directly predict the denoised feature $z_0$ from the noisy feature $z_{t}$ conditioned on $c$ at $t$ -th step, which can avoid the harmful variance commonly associated with $\epsilon_t$ prediction. Here, the condition $c$ refers specifically to the complete recovered element features $\hat{\mathbf{F}}_{elm}$ derived from senders after randomly permuting the agent order. These features are then transformed by $\mathcal{T}$ according to relative poses and processed through a convolutional block to extract the conditional features. We adopt an approach similar to ControlNet [55] to incorporate conditions, integrating them into the decoder process of U-Net. The training phase can be formalized as: + +$$ +\begin{array}{l} \boldsymbol {c} = \operatorname {C o n v} \left(\operatorname {C o n c a t} \left(\left\{\mathcal {T} \left(\hat {\mathbf {F}} _ {e l m} ^ {i}\right) \right\} _ {i = 1} ^ {N _ {a}}\right)\right), \tag {9} \\ \mathcal {L} _ {l d m} = \left\| \boldsymbol {z} _ {0} - f _ {\theta} \left(\boldsymbol {z} _ {t}, \boldsymbol {c}, t\right) \right\| ^ {2}. \\ \end{array} +$$ + +In the diffusion reverse process, $\mathbf{z}_{t-1}$ is derived from the predicted $\mathbf{z}_0$ following [38] for next step. To accelerate the inference, we adopt the DDIM [39] sampler to reduce the number of iteration steps. Additionally, we implement various improvements to meet the efficiency requirements of perception tasks. Rather than initializing from random noise, we start from the ego agent's element representation $\mathbf{F}_{elm}^e$ , since it shares the same latent space of codebook with $\mathbf{z}_t$ . This initialization enables inference process to utilize the ego's local perception, providing a more informed initial state. Moreover, we propose an Uncertainty Adaptive Time Scheduler (UATS) to dynamically adjust the number of iterations based on the uncertainty of ego prediction. Our design considers varying fusion complexity across scenarios (e.g., multiple iterations are not necessary when ego achieves satisfactory predictions). Specifically, the uncertainty is determined by the probability distribution from ego's ETI module, and the reverse process is early-stopped when uncertainty is relatively low. This improvement significantly reduces the number of iterations required to achieve similar accuracy as shown in Tab. 3. + +# 4. Experiments + +We conduct experiments on the camera-track BEV segmentation task of the OPV2V collaborative perception dataset. We demonstrate the effectiveness and robustness of our method through quantitative evaluations in Sec. 4.2. We conduct ablation experiments to validate the impact of our proposed modules in Sec. 4.3 and performed experimental result visualization in Sec. 4.4. + +# 4.1. Experimental Setup + +Datasets. OPV2V [47] is a widely used, large-scale open simulated collaborative perception dataset. Data for OPV2V is collected from 8 towns within CARLA [12]. It + +comprises 73 scenes with a total of 11464 frames, with each scene lasting average 25 seconds. Each scene features 2-7 autonomous vehicles, each equipped with four directional cameras that together provide a 360-degree field of view. During testing, one autonomous vehicle is designated as the ego vehicle, with evaluations focused on a $100m \times 100m$ area centered around it and a map resolution of $39cm$ . + +Evaluation metric. We use Intersection-over-Union (IoU) of Road and Lane categories as our evaluation metrics, which measure segmentation accuracy by quantifying the overlap between predicted and ground-truth areas. Following previous works [18, 20, 47], communication volume is measured in terms of the number of bytes transmitted per message as $\log_2(b(\mathcal{M}) / 8)$ . + +Implementation details. Following [44], we assume that all agents have a communication range of 70 meters, and agents beyond the ego's communication range do not participate in collaboration. Our training process can be divided into three stages. Firstly, we perform map-based VQ-VAE training, using latent features with a resolution of $32 \times 32$ , and a codebook containing 128 element types, each with a 64-dimensional feature vector. Then, referring to the common training procedure [48], we secondly conduct single-agent training with additional $\mathcal{L}_{pri}$ and $\mathcal{L}_{mask}$ to optimize EFFC. Based on the frozen single-agent model, we thirdly train U-Net of SGFF by $\mathcal{L}_{ldm}$ to achieve multi-agent fusion. Unless otherwise specified, we use 10 iterations in SGFF. + +Baseline methods. We compare with the previous state-of-the-art methods: F-Cooper [6], AttFuse [47], V2VNet [44], DiscoNet [27], and CoBEVT [48]. In order to make a fair comparison under the same communication volume cost, we adopted a BEV feature-oriented compression transmission strategy [17] for the baselines. + +# 4.2.Quantitative Evaluation + +Efficiency of EFFC compression. As shown in Fig. 5 (a), our CoGMP achieves significantly better IoU scores than previous works. To simulate various bandwidths, we conduct experiments with the communication volume ranging from 6 to 15. The experimental results demonstrate that our method achieves the best performance-bandwidth trade-off, with a SOTA performance of 66.19/52.92 Road/Lane IoU. When transmitting all intermediate features, our method improves upon the previous SOTA performance by 6.89/7.64. Under the maximum bandwidth constraint, our method achieves improvements of 8.93/10.40. Even with a bandwidth that is only $\frac{1}{512}$ of previous methods, our method still achieves accuracy gains of 3.03/4.33. + +Robustness of SGFF fusion. We follow CoAlign [32] to add Gaussian noises $\varepsilon \in \mathcal{N}(0,\sigma)$ to the pose of each agent. The variance $\sigma$ ranges from 0 to 1 and the corresponding + +![](images/a6a67fa68f8c53090fa0d986ce0c26597fadec8878a5dc99421b42a530d6bde1.jpg) +(a) Our CoGMP achieves the best performance-bandwidth trade-off. + +![](images/166df6006f62c0b82cc30555791faca2581e9cb76c270aa9792ca2010f2d241c.jpg) + +![](images/743a77f8c01581bc519bd0a3b705ed3a03b35ae2ce1ced258a53ae6626781410.jpg) +Figure 5. Comparison of the performances between our CoGMP and baselines under various communication volume and pose error. + +![](images/11bab3b709e85a43c22f2dce854787b6bafb37fdce000557c6e6651ee1886ebd.jpg) +(b) Our CoGMP exhibits the best performance under arbitrary pose error. + +segmentation IoU scores are plotted in Fig. 5 (b). As $\sigma$ increases from 0 to 1, the road and lane IoU of our GoGMP consistently outperforms previous methods. As $\sigma$ reaches 1, the IoU score of our CoGMP drops slightly to 63.76/48.21 (dropped 2.43/4.71 IoU scores), but our method still outperforms previous methods by a larger margin, with the performance gap widening to 9.96/9.52. These results suggest that our CoGMP is more robust to pose errors. + +# 4.3. Ablation Studies + +Effectiveness of SGFF. The SGFF module enhances the element feature of the ego agent by integrating elements from other agents. Without SGFF, the ego's element feature is directly decoded without fusion, resulting in Road IoU and Lane IoU scores of only 58.76 and 43.92, as shown in Tab. 1. With SGFF to fuse other agents' element features, Road IoU improves to 66.19 (+7.43), and Lane IoU rises to 52.92 (+9), demonstrating the effectiveness of SGFF. To further assess the robustness of SGFF, we vary the number of other agents (denoted as $N_{a}$ ). As $N_{a}$ increases from 0 to 4, the IoU scores also rise, suggesting that SGFF effectively leverages additional agent information. Even without other agents ( $N_{a} = 0$ ), SGFF contributes gains of 2.17 and 3.9 to Road IoU and Lane IoU, respectively. The absence of other agents changes SGFF from a conditional to an unconditional module. This result supports our claim that SGFF not only integrates external information but also uses internal map priors to refine the element feature effectively. + +Number of iteration steps in SGFF. SGFF incorporates an iterative approach to refine the element feature. We examine the impact of iteration steps $N_{s}$ on performance, as reported in Tab. 2. Gradually increasing $N_{s}$ from 1 to 20 leads to consistent improvements in performance. Notably, Road IoU increases by 5.68 when $N_{s}$ goes from 1 to 2, reaching a score of 65.28, which significantly outperforms previous methods. However, the performance gains diminish with higher values of $N_{s}$ . At $N_{s} = 10$ , doubling it to 20 yields only marginal gains of 0.13 in Road IoU and 0.02 + +Table 1. Ablation studies on SGFF and conditions from $N_{a}$ agents. + +
SGFFNaIoU(↑)
RoadLane
X-58.7643.92
060.9347.82
✓265.3752.18
466.1952.92
+ +Table 2. Ablation studies on the iteration step $N_{s}$ + +
NsIoU(↑)
RoadLane
159.6045.40
265.2851.82
565.9752.53
1066.1352.75
2066.3252.94
+ +in Lane IoU. This finding suggests that SGFF can achieve strong performance with relatively few iteration steps. + +Effectiveness of UATS. Although the maximum number of iteration steps in SGFF is set to 10, the results in Tab. 2 indicate that fewer steps are often sufficient to achieve high IoU scores. Based on this insight, we develop the UATS strategy, which dynamically adjusts the number of iteration steps in SGFF according to the uncertainty score in the ego-perception results. As shown in Tab. 3, this adaptive early-stopping strategy significantly reduces the average number of iteration steps by 4.76, with minimal impact on IoU scores. In fact, UATS slightly improves IoU scores by mitigating data drift, thus enhancing model stability. + +Effectiveness of EFFC. For the compression module, we compare the codebook features obtained through generative training with those directly optimized for the task [20]. Under the same communication constraint of $2^{8}$ bytes, our method achieves 65.48/52.07, outperforming 63.03/49.92 with the task-oriented codebook. The CES module selects the most critical elements by learned mask for transmission at the sender while discarding elements that are easier to recover by the receiver's MER module. Tab. 4 shows the performance improvement of our method with CES. On the sender side, we discarded $75\%$ of the elements, leaving the remaining $25\%$ as critical elements sent to the receiver. The + +Table 3. Ablation studies on UATS strategy. + +
UATSIoU(↑)Ns
RoadLane
66.1352.7510
✓66.1952.925.24
+ +Table 4. Ablation studies on Selection Mask. + +
MIoU(↑)
RoadLane
rand.62.7749.58
learn.65.4852.07
+ +first row in the table indicates random mask, while the second row represents our learned mask. Experimental results show that the CES module improved the performance of our method by 2.71/2.49, indicating that our selection strategy can significantly compress the transmission volume while minimizing information loss in transmission. + +# 4.4. Qualitative Results + +SGFF visualization. SGFF uses a diffusion-driven approach to progressively refine the element feature of the ego agent by incorporating both external information from other agents and internal map priors. This dual integration helps produce complete, high-fidelity predictions. As shown in the first row of Fig. 6, the initial prediction $\hat{Y}_{ego}$ displays shaky lane boundaries, while the final prediction $\hat{Y}_0$ is significantly clearer. This refinement primarily relies on SGFF's map priors, which provide essential road and lane structure knowledge. The second row of Fig. 6 illustrates SGFF's ability to enhance predictions using information from other agents. Here, the ego agent is located between two intersections, with agent $a_1$ positioned at the upper crossing and perceiving more details about it in $\hat{Y}_{other}$ . SGFF leverages this external input to fill in missing details in $\hat{Y}_{ego}$ , resulting in $\hat{Y}_0$ , which successfully captures the four lanes of the upper crossing while showing only two to three lanes of the lower crossing. The third row of Fig. 6 demonstrates SGFF's capability to resolve conflicts among varying perceptions from multiple agents. In this case, the ego agent perceives the crossing as a vertical road, agent $a_1$ as a T-junction, and agent $a_2$ as a horizontal road. SGFF uses its internal map priors to synthesize these conflicting views, recognizing them as partial perceptions of a crossing. Consequently, the final prediction $\hat{Y}_0$ forms a complete crossing that closely aligns with the ground truth $Y$ . + +Visualization compared with previous methods. We show our visualization comparison in Fig. 7. Compared to other methods, the BEV map segmentation results obtained by our CoGMP demonstrate higher realism. Our model can generate clearly distinguishable map elements and coherent structures, such as smooth and uninterrupted drivable areas, as well as lane markings that are parallel, evenly spaced, and clearly distinguishable. In contrast, the perception results obtained from baselines are often ambiguous, with discontinuities or missing segments in drivable areas. Moreover, + +![](images/fb9ac69735b5aa4fd5dfb803d681f9c3f8e6108661096df175819bc95a070b54.jpg) +Figure 6. Visualization of SGFF. $\hat{Y}_{\text{other}}$ with a red border is the observation of other agents. Images with blue borders depict the diffusion-driven progressive fusion of SGFF, where $\hat{Y}_{\text{ego}}$ is the input, $\hat{Y}_{t_2}$ and $\hat{Y}_{t_1}$ are intermediate steps, and $\hat{Y}_0$ is the final prediction. The rightmost column labeled $Y$ is the Ground Truth. + +![](images/b282fb939f74aa2d06ab91dae2f51522e5a74fd039d412a1ae6a02e37c2c13b7.jpg) +Figure 7. Qualitative comparison of BEV semantic segmentation. We show the prediction of previous methods, our CoGMP, and Ground Truth from left to right. Compared with methods without map prior, our CoGMP produce more realistic elements and reasonable structure (e.g., parallel lanes and continuous roads) + +the lane markings are unclear with inconsistent lane widths, making it difficult to distinguish the lanes. + +# 5. Conclusion + +This paper introduces CoGMP, a novel collaborative perception framework for BEV semantic segmentation. The core idea of the method is to leverage generative models to learn the element and structure priors of BEV maps. Benefiting from informative map priors, our method significantly reduces the communication volume during the multiagent collaboration via efficient feature compression and achieves consistent and realistic predictions by employing a robust fusion process based on diffusion models. Our experiments show that our method achieves SOTA performance-bandwidth trade-off compared to previous methods. + +# 6. Acknowledgement + +This research is supported in part by National Key R&D Program of China (2022ZD0115502), National Natural Science Foundation of China (NO. 62461160308, U23B2010), "Pioneer" and "Leading Goose" R&D Program of Zhejiang(No. 2024C01161). + +# References + +[1] Tomer Amit, Eliya Nachmani, Tal Shaharbany, and Lior Wolf. 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However, conventional approaches such as contrastive learning often struggle with modality discrepancies, leading to potential misalignments. In this paper, we propose a novel class anchor alignment approach that leverages class probability distributions for multi-modal representation learning. Our method, Class-anchor-ALigned generative Modeling (CALM), encodes class anchors as prompts to generate and align class probability distributions for each modality, enabling more effective alignment. Furthermore, we introduce a cross-modal probabilistic variational autoencoder to model uncertainty in the alignment, enhancing the ability to capture deeper relationships between modalities and data variations. Extensive experiments on four benchmark datasets demonstrate that our approach significantly outperforms state-of-the-art methods, especially in out-of-domain evaluations. This highlights its superior generalization capabilities in multi-modal representation learning. + +# 1. Introduction + +Multi-modal understanding has emerged as a crucial area of research in deep learning, enabling models to jointly comprehend inputs from diverse modalities, such as image, audio, video, and text. One of the most widely used approaches in this domain is contrastive learning [32], which aligns features from different modalities by projecting them into a shared embedding space. By minimizing the distance between features of corresponding modality pairs while maximizing the distance between non-corresponding pairs in a shared latent space, this metric learning approach effectively captures semantic relationships across modalities, + +![](images/d25f7e54804ab7def0aba46d098a5b926f112b6142cbfc52894a87322c348c1a.jpg) +Figure 1. (a) Videos contain subtle semantic information, whereas textual descriptions often have limited expressive capacity. This mismatch leads to an information imbalance and modality discrepancy between video and text, resulting in the collapse of diverse video features to a limited textual representation scope. (b) To address this issue, we propose a class-anchor-aligned generative modeling approach. Our method generates class probability distributions by aligning prompts with inputs from each modality, effectively bridging the modality gap and preserving the diverse semantics of video content. + +![](images/52b5c4fa17c26f4f85268eb072fddf19a63b8f55d799e0e0f1feb0fedb36eb3e.jpg) + +leading to advancements in real-world tasks, such as videotext retrieval [29] and captioning [35]. + +Despite these successes, multimodal representation learning still faces significant challenges in aligning features from different modalities. A notable issue is the modality discrepancy and information imbalance arising from information disparity between inputs of different modalities [7]. To address these issues, existing works for image-text alignment proposed semantic reasoning methods [6,9,21]. However, a video contains much more complex information, as it requires understanding both spatial information and temporal dynamics. For instance, as illustrated in Fig. 1-(a), given the text "a judge is talking to a contestant", the modality discrepancy arises as multiple videos could match this description, each depicting different judges, contestants, and contexts. This leads to an + +information imbalance, as each video contains visual and temporal details that the brief text description cannot fully capture. + +As contrastive learning approaches [14, 29] rely on pairing each input with both its matching positive pair and nonmatching negative pairs, they face significant challenges when dealing with information imbalance. The discriminative nature of contrastive learning requires rigid definitions of positive and negative pairs. However, when videos and texts share only partial information, defining these pairs can overlook the inherent uncertainty and partial relationships between modalities. As a result, contrastive learning often fails to model the underlying data distribution effectively [19, 23, 40], leading to misaligned representations and hindering robust multimodal understanding. + +Recent advancements in video-text retrieval have explored methods beyond contrastive learning. These methods aim to model the probability distribution [5, 19] to capture the latent characteristics of each modality better. Some studies adopt uncertainty-aware models to align probabilistic embeddings [5] or generative models to generate joint distributions for improved modal alignment [19]. Although these approaches have made progress, they still depend heavily on direct matching between positive and negative pairs. This reliance makes them vulnerable to misalignment and limits their effectiveness in modeling the complexities of multi-modal information. + +In this paper, we propose a novel Class-anchor-ALigned generative Modeling (CALM) approach to address these challenges by leveraging class anchors for enhanced cross-modal alignment. We utilize class labels from an independent dataset that represent general categories. As illustrated in Fig. 1-(b), each class label is transformed into a prompt, which serves as a class anchor. We achieve effective alignment that handles ambiguity and partial information by calculating probability distributions between each modality input and these anchors. + +Our intuition is based on the observation that intramodality relationships are less complex to model than intermodality relationships, as latent spaces within the same modality share similar statistical features [17, 22]. The probability distribution between text and the class anchor captures the abstraction of textual data. By aligning the video-prompt probability distribution (an inter-modal distribution) with the text-prompt probability distribution (an intra-modal distribution) over the same set of class anchors, our approach offers two advantages. First, by introducing class anchors independent of the modality inputs, our method enriches the joint embedding space with supplementary semantic cues. This approach enhances the ability of the model to learn underlying data distributions and capture variations within each modality. Second, our approach effectively handles modality discrepancy and uncertainty. + +Our generative alignment enables the model to capture variability in inter and intra-modalities by generating a probabilistic representation of each modality. Unlike discriminative approaches that focus on direct pairwise comparisons [18, 27, 29], the presented alignment generates intramodal probabilistic representations from inter-modal probabilistic representations, effectively considering the distributional properties of inter and intra-modality relationships. This approach adapts flexibly to subtle variations in video and text inputs and aligns partial or ambiguous information to enhance the generalizability of cross-modal learning. Specifically, we augment each class label with descriptive sentences to create class anchors and generate probability distributions for each modality. A cross-modal probability model then aligns these distributions, forming a joint probabilistic representation between video and text. + +We evaluate our model on four widely used video-text benchmarks, MSR-VTT [41], DiDeMo [13], MSVD [4], and LSMDC [33]. We assess the performance across two tasks: video retrieval and video captioning. We evaluate the generalizability of our approach in both in-domain and out-of-domain scenarios. The results show significant improvements over the previous state-of-the-art methods, particularly in the out-of-domain scenario. In summary, our main contributions are as follows + +- We propose a Class-anchor-ALigned generative Modeling (CALM) framework, introducing a novel alignment approach that leverages class anchors to bridge the modality gap. +- We present a cross-modal probabilistic variational autoencoder to model uncertainty in video-text alignment to capture deeper relationships between modalities. +- We demonstrate that the proposed method significantly outperforms existing approaches on four benchmarks, showcasing superior generalization capabilities. + +# 2. Related Works + +# 2.1. Multi-Modal Representation Learning + +The challenge of learning joint representations from multiple modalities has been extensively studied, particularly in the context of video and text alignment. Our work builds upon the pretrained image-text model CLIP [32], taking advantage of its semantic extraction capabilities. Building on CLIP, existing methods focused on improving video and text representations for real-world tasks [5,10,18,27,29, 39]. CLIP4Clip [29] was the first to transfer CLIP knowledge to multi-modal tasks. TS2-NET [27] introduced a method to capture fine-grained temporal visual cues. X-pool [10] used text-conditioned feature fusion across frames to enhance alignment. EMCL-Net [18] sought to bridge the + +modality gap using expectation maximization-based feature decomposition. T-MASS [39] proposed a stochastic text embedding technique to facilitate the interaction between text and video by treating text as a stochastic mass. UATVR [5] proposed a distribution matching approach, modeling modality features as probabilistic distributions and minimizing the distance between corresponding probabilistic embeddings. Recent approaches have focused on enhancing the pre-training process to improve the representation ability of models for video and text. VideoCLIP [14] enhanced CLIP by incorporating temporal alignment for improved video-text representation learning. OmniVL [38] introduced a unified framework capable of addressing various visual-linguistic tasks simultaneously. Flamingo [1] extended pre-training transformers to large visual-language models to capture cross-modal interactions with few-shot learning capabilities. CLIP-ViP [42] proposed a cross-modal learning method by generating auxiliary captions and enabling frame-wise interaction. + +Despite these advancements, the aforementioned methods for pre-training and finetuning primarily focus on aligning video and text features through direct matching. Our approach, on the other hand, aligns probability distributions between each modality and a set of class anchors, providing a more generalizable alignment mechanism. + +# 2.2. Generative Models for Cross-Modal Alignment + +Generative modeling has emerged as a powerful approach for cross-modal alignment, enabling the capture of complex relationships between different modalities. Popular generative models, such as variational autoencoders (VAE) [20] and generative adversarial networks (GAN) [8] were widely used for this purpose. Cross-modal VAE [36] uses latent variables to learn a joint representation of text and visual data, effectively capturing the uncertainty inherent in multi-modal tasks. DiffusionRet [19] introduced a diffusion model to establish a shared latent space between video and text, improving alignment quality by modeling the distributions of both modalities. These generative modeling approaches offer flexibility in learning cross-modal interactions compared to discriminative methods [10, 18, 27, 29], as they better capture variations and uncertainties in the data. Recent advancements have introduced even more sophisticated generative modeling approaches for cross-modal alignment [3, 15]. Uni-Diffuser [3] proposes a unified diffusion framework for multi-modal generative tasks, allowing simultaneous generation and alignment across modalities. DiffDis [15] combines cross-modal generative and discriminative pretraining under the diffusion process. Machine Vision Therapy [16] proposes a in-context learning approach that leverages large language models to identify and correct errors. + +Unlike existing works generating a match probability + +distribution between each pair of modality inputs, the proposed method aims to align class probability distributions based on a generative model, providing a more comprehensive capture of uncertainties across modalities. + +# 3. Method + +As illustrated in Fig. 2, our framework first leverages pre-trained CLIP encoders for feature extraction and utilizes class anchors as prompts. We generate probability distributions between modality inputs and prompt features and employ a cross-modal variational autoencoder for the probabilistic alignment of video and text modalities. + +# 3.1. Preliminary + +To extract features from videos, we uniformly sample $T$ frames as $\mathbf{v} = \{f_1,f_2,\dots ,f_T\}$ . Each frame $f_{t}$ is processed by the pre-trained CLIP image encoder, $\mathrm{CLIP}_v$ . The frame-level features are then aggregated using a temporal fusion module, $\Psi_{\mathrm{TE}}$ , resulting in a video-level feature representation as + +$$ +\mathbf {h} _ {t} ^ {v} = \operatorname {C L I P} _ {v} \left(f _ {t}\right), \quad t = 1, \dots , T, \tag {1} +$$ + +$$ +\mathbf {V} = \Psi_ {\mathrm {T E}} \left(\mathbf {h} _ {1} ^ {v}, \mathbf {h} _ {2} ^ {v}, \dots , \mathbf {h} _ {T} ^ {v}\right). \tag {2} +$$ + +$\mathbf{h}_t^v$ represents the visual feature of $t$ -th frame and $\mathbf{V}$ represents the aggregated video feature, incorporating temporal semantics across frames. + +For textual description consisting of $L$ tokens, $\mathbf{s} = \{w_1^s,w_2^s,\dots ,w_L^s\}$ , we use the pre-trained CLIP text encoder, $\mathrm{CLIP}_s$ , to process each token, generating token-level features as + +$$ +\mathbf {S} = \operatorname {C L I P} _ {s} (\mathbf {s}) = \left[ \mathbf {h} _ {1} ^ {s}, \mathbf {h} _ {2} ^ {s}, \dots , \mathbf {h} _ {L} ^ {s} \right]. \tag {3} +$$ + +We use the embedding of the special [CLS] token, $\mathbf{h}_{\mathrm{CLS}}^s$ , as the sentence-level representation to capture the contextual feature of the sentence. + +# 3.2. Class-Prompt Probability Distribution + +Class Anchor Extraction. We define a set of $K$ class labels as $\mathbf{p} = \{w_1^p, w_2^p, \ldots, w_K^p\}$ where $w_k^p$ is the $k$ -th class label obtained from an independent classification dataset $p$ . Each class label represents a general semantic category as classification datasets are typically designed to cover a wide range of categories. With these class labels, we adopt a prompt template [26] for each class as + +$$ +h _ {k} ^ {p} = \text {" T h e c o n t e n t o f [ l a b e l} _ {k} ] "} , \quad k = 1, \dots , K. \tag {4} +$$ + +$h_k^p$ denotes the class-specific prompt in a natural language format, and we process it through the CLIP text encoder to generate a class anchor as + +$$ +\mathbf {p} _ {k} = \operatorname {C L I P} _ {s} \left(h _ {k} ^ {p}\right) + \mathbf {e} _ {k} ^ {\text {D O S}}, \tag {5} +$$ + +![](images/23cf79632530783270f3cd5e26616e9d876731181d68d5ff89e253f780048cfc.jpg) +Figure 2. An overview of our framework. We employ class labels from an independent dataset, transform them into prompts, and extract their linguistic features to serve as class anchors. We then compute class probability distributions for video and text features by measuring the similarities between their features and the class anchors, effectively representing intra-modal and inter-modal relationships. For modality alignment, we employ a cross-modal probabilistic variational autoencoder that takes the inter-modal probability distribution as input and reconstructs the intra-modal probability distribution to align the modalities in a shared latent space. + +where $\mathbf{e}_k^{\mathrm{pos}}$ is a learnable positional embedding for each prompt, allowing the model to differentiate between anchors. The class anchors are represented as $\mathbf{P} = [\mathbf{p}_1,\mathbf{p}_2,\dots ,\mathbf{p}_K]$ + +Probability Distribution Over Anchors. To capture semantic relationships between video or text features and class anchors, we compute their cosine similarity. We then apply a softmax function to the similarity vector to obtain the probability distribution over anchors for each modality. The class probability distributions $\mathbf{V}_p$ for video and $\mathbf{S}_p$ for text are generated as follows: + +$$ +\mathbf {V} _ {p} = \operatorname {s o f t m a x} \left(\tau \mathbf {c} ^ {V}\right), \quad \mathbf {S} _ {p} = \operatorname {s o f t m a x} \left(\tau \mathbf {c} ^ {S}\right), \tag {6} +$$ + +where + +$$ +\mathbf {c} ^ {V} = \cos \left(\frac {1}{T} \sum_ {t = 1} ^ {T} \mathbf {h} _ {t} ^ {v}, \mathbf {P}\right), \quad \mathbf {c} ^ {S} = \cos \left(\mathbf {h} _ {\mathrm {C L S}} ^ {s}, \mathbf {P}\right). \tag {7} +$$ + +$\tau$ is a temperature parameter that controls the sharpness of the distribution. These distributions $\mathbf{V}_p$ and $\mathbf{S}_p$ represent the semantic relationships between the modality inputs and the class anchors. Specifically, $\mathbf{S}_p$ captures the intra-modal relationships between text and class anchors, while $\mathbf{V}_p$ captures the inter-modal relationships between video features and class anchors. Since the class anchors are independent of the input data, the probabilistic distributions provide supplementary semantic cues to enrich the representations. Aligning these distributions bridges the modality + +gap by mapping video and text inputs to a shared semantic space defined by class anchors. This approach captures shared and distinct semantic cues to reduce discrepancies and handle uncertainty, effectively aligning partial information across modalities. + +# 3.3. Cross-Modal Probabilistic Modeling + +To align the video and text modalities, we propose a cross-modal probability variational autoencoder (VAE) that reconstructs the text-anchor distribution $\mathbf{S}_p$ from the video-anchor distribution $\mathbf{V}_p$ . It models the conditional distribution $p(\mathbf{S}_p|\mathbf{V}_p)$ via a latent variable $\mathbf{z}$ to capture semantic relationships and uncertainties between the modalities. + +The encoder network encodes the video-anchor distribution $\mathbf{V}_p$ into the latent space by modeling the approximate posterior $q_{\phi}(\mathbf{z}|\mathbf{V}_p)$ as a Gaussian distribution with $\boldsymbol{\mu} = f_{\mathrm{enc}}^{\mu}(\mathbf{V}_p)$ and $\sigma^2 = f_{\mathrm{enc}}^\sigma (\mathbf{V}_p)$ , where $f_{\mathrm{enc}}^{\mu}$ and $f_{\mathrm{enc}}^{\sigma}$ are fully connected layers. Here, $\boldsymbol{\mu}$ captures the deterministic features of $\mathbf{V}_p$ , and $\sigma^2$ models the uncertainty associated with these features. To sample $\mathbf{z}$ from the approximate posterior while allowing backpropagation, we employ the reparameterization trick [20]. We have + +$$ +\mathbf {z} = \boldsymbol {\mu} + \boldsymbol {\sigma} \odot \epsilon , \quad \epsilon \sim \mathcal {N} (\mathbf {0}, \mathbf {I}), \tag {8} +$$ + +where $\odot$ denotes element-wise multiplication. The decoder network reconstructs the text-prompt distribution from the latent variable $\mathbf{z}$ as + +$$ +\hat {\mathbf {S}} _ {p} = f _ {\mathrm {d e c}} (\mathbf {z}), \tag {9} +$$ + +where $\hat{\mathbf{S}}_p$ is the reconstructed probability distribution and $f_{\mathrm{dec}}$ is a fully connected network. + +To model $p_{\theta}(\mathbf{S}_p|\mathbf{z})$ suitable for representing probability distributions, the marginal likelihood can be expressed as + +$$ +\begin{array}{l} \log p _ {\theta} \left(\mathbf {S} _ {p} \mid \mathbf {V} _ {p}\right) = \log \int p \left(\mathbf {S} _ {p}, \mathbf {z} \mid \mathbf {V} _ {p}\right) d \mathbf {z} (10) \\ = \log \int p (\mathbf {S} _ {p} | \mathbf {z}) p (\mathbf {z} | \mathbf {V} _ {p}) d \mathbf {z}. (11) \\ \end{array} +$$ + +However, computing this integral directly is intractable due to the continuous latent variable $\mathbf{z}$ . To address this, we use an approximate posterior distribution $q_{\phi}(\mathbf{z}|\mathbf{V}_p)$ parameterized by $\phi$ . We assume the prior $p(\mathbf{z}|\mathbf{V}_p)$ is independent of $\mathbf{V}_p$ , i.e., $p(\mathbf{z}|\mathbf{V}_p) = p(\mathbf{z}) = \mathcal{N}(\mathbf{0},\mathbf{I})$ . This assumption simplifies the computation and allows the encoder to extract modality-specific features into the latent space without being constrained by a complex prior dependent on $\mathbf{V}_p$ . + +Using variational inference [43], we derive the Evidence Lower Bound (ELBO) for the marginal likelihood as $\log p(\mathbf{S}_p|\mathbf{V}_p)\geq \mathbb{E}_{q_\phi}\left[\log p(\mathbf{S}_p|\mathbf{z})\right] - \mathrm{KL}(q_\phi \| p(\mathbf{z}))$ where the inequality follows the Jensen's inequality. The first term encourages the model to reconstruct $\mathbf{S}_p$ from $\mathbf{z}$ , while the second term regularizes the approximate posterior to be close to the prior $p(\mathbf{z})$ . While our primary focus is on modeling the conditional distribution $p(\mathbf{S}_p|\mathbf{V}_p)$ , it implicitly captures the joint distribution through the shared latent variable $\mathbf{z}$ . By modeling the relationship between each modality and $\mathbf{z}$ , the model learns a joint representation that expresses the shared semantics between video and text, enhancing the alignment and capturing deeper relationships. + +# 3.4. Training Objective + +Maximizing the ELBO yields the training objective, comprising two main components: the reconstruction loss and the KL divergence regularization term. The reconstruction loss, $\mathcal{L}_{\mathrm{rec}}$ , guides the model to generate probability distribution $\hat{\mathbf{S}}_p$ closer to $\mathbf{S}_p$ , and is expressed as + +$$ +\mathcal {L} _ {\mathrm {r e c}} = - \mathbb {E} _ {q _ {\phi}} \left[ \log p _ {\theta} \left(\mathbf {S} _ {p} \mid \mathbf {z}\right) \right] \approx - \sum_ {k = 1} ^ {K} \mathbf {S} _ {p} ^ {(k)} \log \hat {\mathbf {S}} _ {p} ^ {(k)}, \tag {12} +$$ + +where $\hat{\mathbf{S}}_p^{(k)}$ is the predicted probability for the class anchor $k$ , and $\mathbf{S}_p^{(k)}$ is the true probability from the text modality. The KL divergence regularizes the approximate posterior to be close to the prior, preventing overfitting and encouraging a smooth latent space as + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {K L}} = \mathrm {K L} \left(q _ {\phi} \| p (\mathbf {z})\right) (13) \\ = \int q _ {\phi} (\mathbf {z} \mid \mathbf {V} _ {p}) \left[ \log q _ {\phi} (\mathbf {z} \mid \mathbf {V} _ {p}) - \log p (\mathbf {z}) \right] d \mathbf {z} (14) \\ \approx \frac {1}{2} \sum_ {i = 1} ^ {d} \left(\mu_ {i} ^ {2} + \sigma_ {i} ^ {2} - \log \sigma_ {i} ^ {2} - 1\right), (15) \\ \end{array} +$$ + +where $d$ is the dimensionality of the latent space. + +Our final loss for multi-modal representation learning is as follows + +$$ +\mathcal {L} = \mathcal {L} _ {\text {r e c}} + \alpha \mathcal {L} _ {\mathrm {K L}} + \mathcal {L} _ {\text {t a s k}}, \tag {16} +$$ + +where $\alpha$ is the hyperparameter balancing the reconstruction loss and the KL divergence. $\mathcal{L}_{\mathrm{task}}$ represents an objective function for a multi-modal task. + +# 4. Experiments + +# 4.1. Datasets + +We evaluate CALM using four benchmark datasets. MSR-VTT [41] contains 10,000 online video clips (10-30 seconds each), annotated with 200,000 captions across various topics. LSMDC [33] includes 118,081 clips from 200 movies, each paired with a sentence from scripts and audio descriptions. DiDeMo [13] comprises 10,642 personal videos with 40,543 temporally localized sentences. MSVD [4] features 1,970 online video clips, each with about 40 diverse English annotations. + +# 4.2. Tasks and Metrics + +We assess CALM on two tasks, video retrieval and video captioning. Video Retrieval retrieves relevant videos based on textual queries, measured by Recall at N (R@N) indicating retrieval accuracy within top N results, and mean rank (MnR) for overall retrieval performance. Video Captioning generates descriptive sentences for videos, evaluated using BLEU-4 [30] (B), ROUGE-L [24] (R), METEOR [2] (M) and CIDEr [37] (C) metrics, assessing n-gram overlap, semantic relevance, and consensus with human annotations, respectively. + +# 4.3. Implementation Details + +We use class labels from the Charades dataset [12] as class anchors, providing diverse, dynamic action and event categories. The number of class labels, $K$ , is set to 157, ensuring broad category coverage. We implement our CALM framework using the ViT-B/32 CLIP model [32]. In the cross-modal probabilistic modeling, we set the dimensionality of the latent space $d$ to 256. The hyperparameter $\alpha$ in the loss function is set to 0.1. We train our models using the AdamW optimizer [28] with a learning rate of $10^{-5}$ . We employ a batch size of 128 and train for five epochs for the retrieval task and 20 epochs for the captioning task. To prevent overfitting, we apply dropout with a rate of 0.1 in the encoder and decoder networks of the VAE. For video processing, we uniformly sample 12 frames from each video and resize them to $224 \times 224$ . For a fair evaluation, we re-implement existing methods that build upon a pretrained model (CLIP) [5, 11, 18, 19, 29, 31, 34, 35, 39] and evaluate their performance under our experimental setup. Note that results from our re-implemented models may differ from + +Table 1. Experimental results of video retrieval trained on MSR-VTT. “→” indicates the out-of-distribution evaluation. + +
MSR-VTT→ DiDeMo→ LSMDC
R@1R@5R@10MnRR@1R@5R@10MnRR@1R@5R@10MnR
CLIP4Clip [29]43.172.781.515.732.459.968.837.915.930.538.3115.1
EMCL [18]47.873.583.613.634.259.769.531.815.227.736.5119.7
UATVR [5]47.073.183.512.724.944.953.879.110.721.928.6153.1
DiffusionRet [19]49.075.282.712.136.865.072.130.917.233.039.7110.3
T-MASS [39]48.976.385.311.737.364.874.226.319.637.046.487.5
CALM (Ours)50.877.585.811.741.266.376.316.121.439.747.880.9
+ +Table 2. Experimental results of video retrieval trained on DiDeMo. + +
DiDeMo→LSMDC→MSR-VTT
R@1R@5R@10MnRR@1R@5R@10MnRR@1R@5R@10MnR
CLIP4Clip [29]42.868.579.218.914.528.836.2119.435.459.069.425.5
EMCL [18]47.874.184.812.214.327.735.1127.834.360.671.426.7
UATVR [5]43.171.882.315.19.920.526.9171.630.253.063.135.8
DiffusionRet [19]46.674.782.714.313.926.134.2125.631.756.467.230.6
T-MASS [39]46.773.182.414.220.437.846.081.339.766.376.617.4
CALM (Ours)51.177.384.212.822.140.548.778.941.766.579.016.0
+ +Table 3. Experimental results of video retrieval trained on LSMDC. + +
LSMDC→ DiDeMo→ MSR-VTT
R@1R@5R@10MnRR@1R@5R@10MnRR@1R@5R@10MnR
CLIP4Clip [29]22.641.049.161.030.155.266.037.728.953.662.733.6
EMCL [18]22.440.649.258.829.055.464.835.830.153.463.439.9
UATVR [5]21.941.449.358.330.555.966.236.130.453.864.234.9
DiffusionRet [19]24.443.154.340.731.557.967.132.530.453.565.633.4
T-MASS [39]26.047.556.446.227.251.963.134.928.552.965.231.3
CALM (Ours)27.547.956.345.433.459.368.331.932.555.566.230.2
+ +the original papers due to variations in training and evaluation settings. While some methods evaluate only at the end of each epoch, others evaluate multiple times within each epoch. To ensure a fair comparison, we standardize the procedure by evaluating all methods at the end of each epoch. + +# 4.4. Performance Comparison + +We evaluate the effectiveness of CALM by comparing it with state-of-the-art methods for video retrieval on three datasets (MSR-VTT, DiDeMo, and LSMDC) and video captioning on two datasets (MSR-VTT and MSVD). We evaluate on in-domain and out-of-domain scenarios to assess the generalization capabilities of our model. In the out-of-domain evaluation, we train the model on the training set of one dataset and measure its performance on the test set of another dataset, which remains unseen during training. + +# 4.4.1 Video Retrieval Results + +In-Domain Evaluation. CALM consistently outperforms existing state-of-the-art methods across all datasets and metrics, demonstrating its effectiveness in capturing cross-modal relationships. Specifically, on the MSR-VTT dataset + +(Table 1), CALM attains an R@1 of $50.8\%$ , surpassing the previous best result of $49.0\%$ from DiffusionRet by a margin of $1.8\%$ . On DiDeMo (Table 2), CALM achieves an R@1 of $51.1\%$ , exceeding the previous best result of $47.8\%$ by EMCL by $3.3\%$ . For LSMDC (Table 3), CALM achieves an R@1 of $27.5\%$ , improving the result of T-MASS by $1.5\%$ . + +Out-of-Domain Evaluation. To assess generalization performance, we evaluate the models in out-of-domain scenarios and report the results in Tables 1, 2 and 3. We study the performance results from two perspectives: the performance increase of our method compared to previous works and the average performance drop from in-domain to out-of-domain evaluations. When trained on MSR-VTT, DiDeMo, and LSMDC, CALM achieves average performance improvements of $2.9\%$ , $1.9\%$ , and $2.0\%$ in $\mathbb{R}@\mathbb{1}$ , respectively. For the average performance drop, we calculate it as the performance decrease in $\mathbb{R}@\mathbb{1}$ from in-domain to out-of-domain evaluations. CALM exhibits drops of $13.7\%$ , $13.8\%$ , and $5.8\%$ when evaluated on the test sets of MSR-VTT, DiDeMo, and LSMDC, respectively. For MSR-VTT and DiDeMo, CLIP4Clip shows slightly lower average performance drops of $11.0\%$ and $11.6\%$ , respec + +Table 4. Experimental results of video captioning trained on MSR-VTT. "MSVD $\rightarrow$ MSR-VTT" indicates out-of-domain results, where the model is trained on MSVD and evaluated on MSR-VTT. + +
MSR-VTTBMCR
SemSynAN [31]46.430.451.954.7
TextKG [11]43.729.652.462.4
CoCAP [34]43.129.856.262.7
CLIP4Caption [35]46.130.757.064.1
CALM (Ours)47.831.159.365.0
MSVD → MSR-VTTBMCR
CoCAP [34]28.122.629.154.8
CLIP4Caption [35]30.123.530.555.6
CALM (Ours)34.226.135.658.9
+ +tively. However, this may be attributed to the comparatively lower in-domain performance of CLIP4Clip. For LSMDC, CALM shows the lowest average performance drop. Overall, CALM demonstrates superior generalization abilities, with higher R@1 scores and competitive average performance drops compared to other methods. This suggests that our model learns more generalized representations due to the introduction of class anchors and probabilistic modeling. + +Complexity and Time. Our approach slightly increases computational cost compared to the baseline, T-MASS, adding only 0.5M parameters (from 152.6M to 153.1M) and 0.08 seconds to the training time per batch (from 1.06s to 1.14s). This minimal overhead results from the shallow encoder-decoder structure of our VAE. Importantly, the cross-modal probabilistic modeling used during training enhances modal alignment without introducing extra computational costs during inference. + +# 4.4.2 Video Captioning Results + +As shown in Tables 4 and 5, our model achieves significant improvements over state-of-the-art methods on both the MSR-VTT and MSVD datasets. For in-domain evaluations on MSR-VTT, CALM surpasses existing methods by 1.4, 0.4, 2.3, and 0.9 in BLEU-4, METEOR, CIDEr, and ROUGE-L metrics, respectively. On the MSVD dataset, CALM demonstrates comparable performance to SemSynAN [31] in BLEU-4, METEOR, and ROUGE-L, while achieving a substantial increase of 2.7 in CIDEr, indicating better alignment with human annotations. In our out-of-domain evaluations, we compare CALM with CLIP4Cap and CoCAP as these methods have achieved the highest CIDEr scores in in-domain settings among existing approaches, providing strong baselines for assessing the performance of our method. On MSR-VTT trained on MSVD, CALM outperforms these methods with improvements of 4.1, 2.6, 5.5, and 3.3 in BLEU-4, METEOR, CIDEr, and ROUGE-L, respectively. Similarly, for MSVD trained on + +Table 5. Experimental results of video captioning trained on MSVD. "MSR-VTT $\rightarrow$ MSVD" indicates out-of-domain results. + +
MSVDBMCR
SemSynAN [31]64.441.9111.579.5
TextKG [11]60.838.5105.275.1
CoCAP [34]55.939.9113.076.8
CLIP4Caption [35]63.040.6114.677.3
CALM (Ours)64.441.2115.777.8
MSR-VTT → MSVDBMCR
CoCAP [34]39.134.369.869.8
CLIP4Caption [35]39.932.967.863.7
CALM (Ours)44.235.670.371.0
+ +Table 6. Comparison of the number of class anchors on video retrieval performance on MSR-VTT. + +
Class anchorsTypeR@1R@5MnR
0 (Baseline)Charades48.976.311.7
50Charades48.174.012.1
100Charades49.776.511.5
157Charades50.877.511.7
91COCO50.376.011.7
258Charades+COCO51.175.710.7
+ +MSR-VTT, CALM attains gains of 4.3, 1.3, 0.5, and 1.2 in the same metrics. These consistent gains across different metrics, datasets, and evaluation scenarios underscore the ability to handle modality discrepancies and information imbalance effectively, capturing nuanced semantic relationships between video and text and generating high-quality captions with strong generalization performance. + +# 4.5. Ablation Analysis + +Effect of Class Anchors. Table 6 presents the impact of varying the number and quality of class anchors on video retrieval performance using the MSR-VTT dataset. We randomly select class anchors, train and evaluate performance with 0 anchors as the baseline, followed by 50, 100, and 157 anchors. When using 50 anchors, the model achieves an R@1 of $48.1\%$ , slightly below the baseline $(48.9\%)$ , suggesting that a limited anchor set can introduce bias and negatively impact performance. Increasing to 100 anchors raises performance to an R@1 of $49.7\%$ , indicating that greater diversity among anchors improves semantic alignment. Employing the complete set of 157 anchors yields an even higher R@1 of $50.8\%$ , demonstrating the advantage of comprehensive anchor coverage for capturing richer semantic information. Additionally, we replace Charades anchors with 91 object-centric COCO image labels [25], which lack explicit descriptions of actions or events. Despite this domain mismatch, employing COCO anchors still outperform the baseline. This suggests that the model effectively adapts to anchor relevance, using even seemingly irrelevant anchors to guide modal alignment. Further, com + +![](images/2573dc007f6121275bd9b656371baed5aa8a7ca363266199efc27c241cc3e9a9.jpg) +(a) + +![](images/cf07ac52d035fd5d8cd4b61a28f875357ad01f30da8665cd093f60526d7ea00f.jpg) +(b) +Figure 3. Qualitative video retrieval results on the MSR-VTT dataset. Selected anchors capture distinct semantic cues, either aligning shared content (a) or highlighting complementary information to address modality imbalance (b). Inter-modal and intra-modal relationships serve as supplementary semantic cues, enhancing the semantic alignment between video and text and improving retrieval performance. + +Table 7. Comparison of generative and discriminative learning approaches on video retrieval performance on MSR-VTT for indomain and DiDeMo for out-of-domain evaluation. + +
MSR-VTT→ DiDeMo
LossR@1R@5R@1R@5
Baseline48.976.337.364.8
KL Divergence Loss49.575.038.865.7
Cross-Entropy Loss50.175.538.365.5
MSE Loss48.774.237.365.4
CALM (Ours)50.877.541.266.3
+ +bining Charades and COCO anchors lead to the best performance improvements in R@1, emphasizing that the model benefits significantly from integrating both domain-specific and general semantic cues. + +Generative Modeling. In Table 7, we study the effect of our generative modeling by replacing the variational autoencoder with discriminative loss functions, such as KL divergence, cross-entropy, and mean squared error (MSE) losses between the class probability distributions. By minimizing the distance between the class probability distributions of the video and text modalities, these loss functions align them without employing our approach. CALM, employing the variational autoencoder, achieves the highest R@1 of $50.8\%$ , outperforming the discriminative methods. It also outperforms those methods in out-of-domain evaluation, achieving the highest R@1 of $41.2\%$ . This underscores the effectiveness of our VAE-based method in modeling uncertainty and capturing the underlying data distribution, resulting in improved cross-modal alignment. + +# 4.6. Qualitative Analysis + +Fig. 3 visualizes two results from the video retrieval task on MSR-VTT. In each example, the green boxes highlight the two most related class anchors, while the red boxes in + +dicate the two least related class anchors. In Fig. 3-(a), our model effectively associates the video with the class anchor "Holding a laptop", which closely aligns with the text-matched anchor "Putting a laptop somewhere". This demonstrates that class anchors successfully capture semantic cues within each input modality. In Fig. 3-(b), we present another case where the video contains complex actions that are not explicitly described in the accompanying text. The video aligns with class anchors corresponding to these intricate actions, while the text aligns with anchors related to the general activities of "a man is talking on stage". This highlights the information imbalance between the modalities. Our model effectively handles this imbalance by aligning probability distributions in a generative manner rather than directly matching input features. By doing so, it addresses uncertainty and partial alignments, thus enhancing both inter-modal and intra-modal understanding through underlying semantic relationships. + +# 5. Conclusion + +In this work, we present CALM, Class-anchor-ALigned generative Modeling, to address modality discrepancies and information imbalance in multi-modal representation learning. By leveraging class anchors as prompts and aligning class probability distributions across modalities, CALM effectively bridges the modality gap and captures deeper semantic relationships between video and text. Our cross-modal probabilistic variational autoencoder models uncertainty and accommodates variations across modalities by reconstructing the intra-modal distribution from the inter-modal distribution. Extensive experiments on four benchmark datasets demonstrate that CALM consistently outperforms state-of-the-art methods, with significant improvements in out-of-domain evaluations, highlighting its superior generalization capabilities. + +# Acknowledgment + +This work was supported in part by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (RS-2023-00279019) and in part by the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant funded by Korea Government (MSIT) (2021-0-01341, Artificial Intelligence Graduate School Program (Chung-Ang University)). + +# References + +[1] Jean-Baptiste Alayrac et al. Flamingo: a visual language model for few-shot learning. 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Advances in variational inference. 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Existing approaches rely on spatial visual tokens, where image patches are encoded and arranged according to a spatial order (e.g., raster scan). However, we show that spatial tokens lack the recursive structure inherent to languages, hence form an impossible language for LLM to master. In this paper, we build a proper visual language by leveraging diffusion timesteps to learn discrete, recursive visual tokens. Our proposed tokens recursively compensate for the progressive attribute loss in noisy images as timesteps increase, enabling the diffusion model to reconstruct the original image at any timestep. This approach allows us to effectively integrate the strengths of LLMs in autoregressive reasoning and diffusion models in precise image generation, achieving seamless multimodal comprehension and generation within a unified framework. Extensive experiments show that we achieve a new SOTA for multimodal comprehension and generation simultaneously compared with other MLLMs. Project Page: https://DDT-LLaMA.github.io/. + +# 1. Introduction + +Multimodal Large Language Models (MLLMs) [20, 55] strive to unify the comprehension and generation of data across various modalities within the same next-token prediction paradigm of LLM [38, 53]. Specifically, given a user query about comprehension—“What kind of dog is in this picture [IMG]”, or generation—“Turning the picture [IMG] into a sketch”, the model can complete the task by sequentially predicting the appropriate text or image tokens. + +The challenge lies in the conflicting objectives of the two + +![](images/9b5bcfc595f51dc71e58d3baf5cfbded0a6c441a3527f9d2166e5c9c21d6384a.jpg) +Figure 1. Auto-regressive training curves of diffusion timestep tokens (left) and spatial tokens (right) under different degrees of sequence perturbation. + +![](images/b2bc758aae663aa83889fbd3c28adc1b8cd57de7f363969a485ca303899074c0.jpg) + +tasks. Comprehension pursues a many-to-one mapping that abstracts visual details (e.g., many photos of corgi dogs result in recognition of "corgi"). On the other hand, generation finds a one-to-one mapping that preserves visual details (e.g., the sketched image specific to the query image). To bridge these conflicting objectives, the most straightforward way is to combine LLMs and diffusion models (DMs), which excel in comprehension and generation respectively. There are two main integration strategies. One approach is cascading [35], where the LLM understands user queries and plans instructions, which are then passed to the DM for generation. The other approach involves quantizing [15, 28, 60, 66, 68] or mapping [12] the continuous visual modalities into discrete tokens for LLM processing, followed by decoding these tokens into images using the DM. Recently, Transfusion [67] aims to combine the LLM and DM into a single model, creating a unified framework for both understanding and generating multimodal content. + +Notably, all existing methods are based on spatial visual tokens, which are extracted from image patches and arranged in a spatial order (e.g., row by row in raster scan order). However, following the evaluation in [26], we find that spatial token sequences lack the traits of human language, and essentially form an impossible language [26] for LLM to master. Specifically, the performance of LLMs on language tokens should degrade rapidly when their order is disrupted. However, when we train an LLM to model spatial token sequences in Figure 1 right, the order of tokens has + +minimal impact on the convergence of the LLM, deviating from phenomenons observed in human language. This finding is perhaps non-surprising, as spatial tokens lack the recursive structure that characterizes languages. For example, one can extend "a man" by recursively embedding phrases to get "a man [[walking] in the park]". + +To address the limitation of spatial tokens, we propose to learn tokens with recursive structure by Discrete Diffusion Timestep (DDT) tokenization. Specifically, the forward process of a Diffusion Model (DM) incrementally adds Gaussian noise to images at each time-step $t$ , which collapses different images into similar ones by gradually losing the visual attributes that differentiate them. We aim to learn an expanding sequence of discrete tokens to make up for the incremental attribute loss as $t$ increases. For example, given a noise-free image $\mathbf{x}_0$ , we obtain its $t$ -specific token sequence $f_{t}(\mathbf{x}_{0})$ by an encoder $f$ , with an initial condition $f_{0}(\mathbf{x}_{0}) = \emptyset$ (i.e., no attribute loss). At $t$ , the noised image is given by $\mathbf{x}_t$ . We train the DM to reconstruct $\mathbf{x}_0$ given $\mathbf{x}_t$ and $f_{t}(\mathbf{x}_{0})$ , so that the tokens compensate for the attribute loss in $\mathbf{x}_t$ . As $t$ increases, we learn a recursive sequence given by $f_{t + 1}(\mathbf{x}_0) = (f_t(\mathbf{x}_0),\mathbf{V}_{t + 1})$ , where the appended visual token $\mathrm{V}_{t + 1}$ accounts for the increased attribute loss in $\mathbf{x}_{t + 1}$ over $\mathbf{x}_t$ . Until at $t = T$ , $x_{T}$ becomes pure noise where all attributes are lost. We output $f_{T}(\mathbf{x}_{0})$ as the final token sequence for the image $\mathbf{x}_0$ , which encodes all its visual attributes. We do the same language verification on our DDT tokens in Figure 1 left. With our recursive tokens, we observe findings similar to those on languages. + +Using a DDT tokenizer trained on ImageNet [11], we build an MLLM that simultaneously unseals the potential of LLM in language modeling and DM in image generation. First, we transform images into DDT tokens. Then we train an MLLM with a unified next-token-prediction objective on a vast corpus of image-text pairs (see Section 3), where the model essentially learns to translate between human language and the visual language using DDT tokens. Finally in inference, when MLLM outputs visual tokens, they are mapped to images using our trained DM as decoder. This leads to a unified framework for comprehension and generation. Our main contributions are three-fold: + +- We propose DDT to learn discrete, recursive visual tokens by recovering visual attributes lost in the diffusion process that can subsequently drive an MLLM. +- We propose a novel way to integrate LLMs and diffusion models with our DDT tokens, producing an effective MLLM for both visual comprehension and generation. +- Despite using a tokenizer trained on just ImageNet, we achieve a new SOTA for multimodal comprehension and generation (i.e., image generation, image editing, visual comprehension), surpassing MLLMs that use tokenizers trained on large-scale data (e.g., Laion [46] and Coyo [6]). + +# 2. Related Work + +Research on achieving unified understanding and generation in multimodal models has primarily focused on two main strategies: cascading architectures and tokenization-based methods. Cascading architectures [19, 20, 25, 49] integrate separate modality-specific encoders and decoders, each pre-trained independently, and then fuse their representations through projection layers to create combined models for multimodal tasks. Notable examples include models such as EMU2 [49], which uses pre-trained language models [53] augmented with EVA-02-CLIP-E-plus [48] for comprehension tasks, and cascade an SDXL-initialized [41] diffusion model for visual generation tasks. In contrast, tokenization-based methods [9, 32, 39, 51, 55–57, 69] aim to create a unified framework by converting visual and textual inputs into a discrete space, and then jointly training a single transformer based solely on next-token prediction, thereby eliminating the need for diffusion or compositional approaches entirely. Moreover, recent advances, such as TransFusion [67] and Show-o [58], explore a blend of diffusion and autoregressive models within a single transformer for enhanced performance. However, although these methods provide a step towards unification, most of them focus on spatial tokens for vision, which are extracted from image patches and arranged in a spatial order (e.g., row by row in raster scan order). These spatial tokens lack the traits of human language, resulting in an inability to seamlessly integrate with human natural language within an MLLM to mutually enhance each other. Consequently, existing MLLMs still lag behind specialized architectures like SDXL [41] in visual generation tasks and LLaVA-1.6 [34] in visual comprehension tasks. These indicate the need for further exploration into more holistic tokenization methods that go beyond spatial representations to achieve more comprehensive multimodal comprehension and generation. + +# 3. Diffusion Timestep Tokenizer + +Our goal is to train an image tokenizer that encodes an image to a recursive sequence of discrete tokens—to effectively train an MLLM—and decode the tokens back to the image—to render the image tokens predicted by the MLLM during inference. The model consists of 1) an encoder $f$ that maps a noise-free image $\mathbf{x}_0$ to a sequence of continuous features $(\hat{\mathrm{V}}_1, \dots, \hat{\mathrm{V}}_T)$ ; 2) a quantizer that assigns each continuous feature $\hat{\mathrm{V}}_i$ to its token embedding $\mathrm{V}_i \in \mathcal{C}$ in a fixed size dictionary $\mathcal{C}$ ; 3) a Diffusion Model (DM) $d$ as a decoder that reconstructs $\hat{\mathbf{x}}_0 = d(\mathbf{x}_t, t, (\mathrm{V}_1, \dots, \mathrm{V}_t))$ , where $\mathbf{x}_t$ is a sampled noised image at timestep $t$ and the tuple denotes the first $t$ tokens from the quantizer. The model is trained end-to-end with (primarily) a reconstruction loss. And then we provide details on each part below. + +Encoder. As shown in Figure 2(a) left, we use a + +![](images/39c42ef6af1c6a9ef59b3b17db375ebd45eb45b3e657e3c15b3afd84b5cb7afd.jpg) +Figure 2. The overview of our methods. (a): The architecture of diffusion timestep tokenizer encodes an image to a recursive sequence of discrete tokens. (b): An MLLM architecture that unifies comprehension and generation based on next token prediction. + +![](images/704cc995365d0bdd56ff5bf85fd252d8a90009824d5e79b5cfa667ea64b54312.jpg) + +transformer-based model with learnable query tokens as our encoder. The input to the encoder is a noise-free image (patchified and flattened into image tokens similar to ViT [13]) and the set of $T$ learnable query tokens. Note that the input query tokens have the same size $T$ as the desired output tokens. We first apply 1D and 2D sinusoidal position embedding on the query and image tokens, respectively. Following SD3 [16], we then use two independent transformers to process the query and image tokens, and join them for the attention operation. Finally, only the transformed query tokens are kept as the output $(\hat{\mathrm{V}}_1,\dots ,\hat{\mathrm{V}}_T)$ , where $\hat{\mathrm{V}}_i\in \mathbb{R}^n$ is an $n$ -dimensional feature vector. + +Quantizer. We feed the encoder output to a standard Vector Quantization (VQ) module [54]. Specifically, the VQ has a fixed size dictionary $\mathcal{C}$ ( $|\mathcal{C}| = 65536$ in our experiments), where each entry is a vector of dimension $m$ . We first use a linear layer to project the encoder output from $\mathbb{R}^n$ to $\mathbb{R}^m$ , and then find $\mathrm{V}_i$ in $\mathcal{C}$ with the largest cosine similarity with each $\hat{\mathrm{V}}_i$ . Note that we use an EMA-variant of VQ to improve training stability, i.e., updating $\mathcal{C}$ by gradually moving each entry towards the cluster center of its matched encoder outputs. To improve codebook usage, we use two tricks: 1) We use a small $m = 16$ based on the empirical results in [60]; 2) Inspired from [62], we monitor dead entries in $\mathcal{C}$ at each training step (i.e., rarely matched with any $\mathrm{V}_i$ ) and setting them to random $\mathrm{V}_i$ in a training batch. + +Decoder. Our decoder is a DM. As shown in Figure 2(a) right, we use the same MMDiT [16] architecture for our decoder $d$ with slight modifications: 1) Instead of inputting text tokens, we input a sequence of quantized tokens; 2) We use a linear layer to project the $m$ -dimensional vector to the latent dimension of the MMDiT; 3) We do not use pooled token embedding as in SD3. Given a timestep $t$ , a sampled noisy image $\mathbf{x}_t$ from $\mathbf{x}_0$ , a sequence of tokens from the quantizer, $d$ is trained to output a reconstructed $\mathbf{x}_0$ as shown below. + +Training. Recall that we aim to learn a recursive sequence + +in the form $f_{t}(\mathbf{x}_{0}) = (f_{t - 1}(\mathbf{x}_{0}),\mathrm{V}_{t})$ at each $t$ , such that $f_{t}(\mathbf{x}_{0})$ makes up for the attribute loss in the noisy image $\mathbf{x}_t$ . Hence we use an expanding set of tokens $(\mathrm{V}_1,\dots ,\mathrm{V}_t)$ as the input to the decoder $d$ , and train everything end-to-end with the reconstruction loss: + +$$ +\mathcal {L} = \underset {t, \mathbf {x} _ {0}, \epsilon} {\mathbb {E}} \underbrace {\left[ \| d (t \epsilon + (1 - t) \mathbf {x} _ {0} , t , (\mathrm {V} _ {1} , \dots , \mathrm {V} _ {t})) - \mathbf {x} _ {0} \| ^ {2} \right]} _ {\mathcal {L} _ {t}}, \tag {1} +$$ + +where we follow Rectified Flow [36] to sample the noisy $\mathbf{x}_t = t\epsilon + (1 - t)\mathbf{x}_0$ with the Gaussian noise $\epsilon$ . We also use a standard commitment loss $\sum_{i=1}^{T} \|\hat{\mathrm{V}}_i - \mathrm{V}_i\|^2$ to regularize the encoder output (continuous vector) to be similar with the matched quantized vector. + +# 4. DDT-LLaMA + +The process begins by converting images into a 1D recursive discrete sequence like a foreign language that LLM can read. This transformation allows us to pursue a unified next-token-prediction training objective across a vast array of image-text data. To achieve this, visual tokens are concatenated with text tokens to form a multi-modal sequence. Special tokens, [BOV] and [EOV], are strategically placed at the beginning and end of the visual sequence to distinguish between modalities. We Initialize the MLLM from a pre-trained LLM, specifically the LLaMA3-8B [14] model, with an expansion of its vocabulary by 65,536 visual codes. Then MLLM adopts the general Language Modeling (LM) objective to directly maximize the likelihood of each multimodal sequence in an auto-regressive manner: + +$$ +p (y) = \sum_ {y \in \mathcal {D}} \sum_ {i = 1} ^ {S} \log P _ {\theta} \left(y _ {i} \mid y _ {< i}\right). \tag {2} +$$ + +where $y$ is the text or visual token with $S$ as the sequence length. Since both image and text are represented as discrete token IDs, we can use the cross-entropy to supervise the + +Table 1. Comparison with state-of-the-art models on GenEval, T2I CompBench and DrawBench on zero-shot text-to-image generation. The best results among MLLM-based Generalists are in bold fonts. And the best results among all methods are underline. + +
MethodGenEvalT2I-CompBenchDrawBench
Overall↑SingObj↑TwoObj↑Counting↑Colors↑Position↑ColorAttri↑Color↑Shape↑Texture↑Spatial↑NonSpatial↑Complex↑Clip-T↑
Diffusion-based T2I Specialists
DALL-E 2 [43]0.520.940.660.490.770.100.190.5750.5460.6370.1280.3040.370-
SDv1.5 [44]0.430.970.380.350.760.040.060.3730.3650.4220.131---
SDv2.1 [44]0.500.980.510.440.850.070.170.5690.4500.4980.174---
SDXL [41]0.550.980.740.390.850.150.230.6370.5410.5640.2030.3110.409-
PixArt-alpha [7]0.480.980.500.440.800.080.070.6890.5580.7040.2080.3180.412-
DALL-E 3 [4]0.670.960.870.470.830.430.450.8110.6750.807----
SD3 [16]0.740.990.940.720.890.330.60-------
MLLM-based Generalist
SEED-LLaMA [19]0.330.890.170.250.590.020.030.1760.1840.2020.0680.2890.2270.220
LaVIT [25]0.510.930.700.430.670.170.180.4390.4570.5750.1510.3110.3200.259
Emu2-Gen [49]0.350.930.280.140.700.050.020.3380.3590.4000.0990.2990.2850.235
SEED-X [20]0.490.960.570.290.820.140.150.6570.4920.6030.1720.3060.3610.265
VILA-U [57]0.400.880.420.250.690.080.090.5680.4330.5010.1540.3070.3340.262
Lumina-mGPT [32]0.520.990.700.340.850.080.170.5560.4650.5880.1760.3120.3430.267
Transfusion [67]0.63-------------
Emu3 [55]0.540.980.710.340.810.170.210.6110.4730.6180.1370.3000.3450.265
Ours0.660.990.640.560.870.390.480.7280.5140.6420.1760.3140.3450.267
+ +token prediction at each position for both modalities with a shared prediction head. The training regimen is composed of two stages, during which all parameters of the MLLM are meticulously fine-tuned. + +Stage1: Pre-training. In the first stage, we aim to enhance the alignment between DDT tokens and text tokens, transitioning from LLM to MLLM. Our pre-training dataset, sourced from Laion [46] and Coyo [6], consists of 200M text-to-image pairs. Each pair is structured in the format "[BOS] [BOV] [EOV] [EOS]", where [BOS] and [EOS] are special tokens from the text tokenizer. Moreover, to prevent the forgetting of textual capabilities, we also incorporate pure text data at a fusion ratio of $10\%$ . The pre-training is conducted on 512 Ascend 910B NPUs, lasting for nearly two weeks. + +Stage2: Instruction Tuning. In the second stage, we perform multimodal instruction tuning to align our MLLM with human instructions through supervised fine-tuning on public image-text datasets. To enhance the MLLM's comprehension and generation capabilities in complex scenarios, we employ supervised training data from visual comprehension and generation tasks. We use the instruction format as "USER: ASSISTANT: " and only the content of is accounted for loss. See Appendix A and B for more details. + +Inference. After DDT-LLaMA predicts [BOV] token, it consecutively performs $T$ next-token-predictions to generate a set of discrete DDT tokens $\{V_1,\dots,V_T\}$ . We then feed these tokens into the decoder to guide the denoising of random noise into an image over $T$ timesteps through a DDPM process. Similar to the training procedure, at timestep $t$ during inference, we provide only the first $t$ tokens as the guidance, while the remaining $(T - t)$ tokens are masked as 0. + +Table 2. Zero-shot image editing results. + +
MethodEVRMA5KMagicBrush
L1↓CVS↑L1↓LPIPS↓L1↓CVS↑
Image editing Specialist
InsPix2Pix [5]18.981.417.635.910.185.2
MGIE [18]16.381.713.329.88.291.1
UltraEdit [65]14.481.616.535.26.688.4
MLLM-based Generalist
GILL [27]31.865.027.444.328.375.2
Emu2-Gen [49]22.880.320.536.419.985.7
SEED-LLaMA [19]28.472.324.639.024.580.9
LaVIT [25]26.873.825.136.925.381.1
SEED-X-Edit [20]16.781.914.632.718.486.1
Ours14.585.514.229.67.192.4
+ +# 5. Experiment + +# 5.1. Text-to-Image Generation + +Automated Metric Evaluation. To evaluate our model's capabilities in zero-shot image synthesis, we first conduct an automated metric evaluation on 3 popular text-to-image benchmarks: GenEval [21], T2I-CompBench [23], and DrawBench [45]. The comparison results of DDT-LLaMA against Diffusion-based T2I Specialists, and MLLM-based generalists are shown in Table 1. In most settings, our method surpasses other MLLMs and is even competitive with several diffusion-based models. For example, in the overall GenEval score, DDT-LLaMA significantly outperforms SEED-X [20], Emu3 [55], and the specialist method, SDXL [41]. This highlights that our model facilitates better vision-text alignment. + +Furthermore, through detailed analysis of the results, we find that compared to other MLLMs, DDT-LLaMA achieves higher scores in tasks related to color, counting, and position. It excels in understanding object attributes such as color, quantity, and the spatial relationships between objects. However, it underperforms in tasks of 'TwoObj', which simply requires generating two objects with no additional constraints. This is largely due to the fact that the image-text captions in our training data rarely include this straightforward prompt format. + +![](images/83551c31acc25878cb379d739a6caafbffd8b6e472353d658c088aab35f107b9.jpg) +Figure 3. Qualitative results of DDT-LLaMA text-to-image generation. + +![](images/96a7686535bfd80b9880f46ae98dd881d0b48d00ec8e7c3d335e03c5770d8f6e.jpg) +Figure 4. Qualitative comparison with EMU3 on T2I generation. DDT-LLaMA better responses to prompts related to counting or position. + +Qualitative Examples. In Figure 3, we present some qualitative examples of DDT-LLaMA on image synthesis tasks. It can be observed that DDT-LLaMA effectively follows various types of instructions, including complex ones such as generating surreal images and multi-condition combined prompts, to generate semantically consistent images. Of course, we acknowledge that there is room for improvement in the aesthetic quality of the images. This limitation stems from the fact that our current tokenizer was only trained on ImageNet with a resolution of $256 \times 256$ . So its performance in reconstructing open-domain images is inferior to that of baseline methods (e.g., the EMU3 tokenizer MOVQ), which restricts our capability in T2I generation. More qualitative examples are in Appendix C. + +Moreover, Figure 4 presents a direct comparison between DDT-LLaMA and Emu3 on prompts involving + +counting, color, and position. Though Emu3 generates images with higher aesthetic quality, it struggles to accurately respond to such prompts. In contrast, DDT-LLaMA generates images that better align with the object attributes and the spatial relationships specified in the prompt. + +# 5.2. Image Editing + +Automated Metric Evaluation. We evaluate our model in zero-shot instruction-based image editing across three datasets: EVR [50], MA5k [47], and MagicBrush [63]. Following [18], for EVR and MagicBrush, we treat L1 and CVS (Clip-Visual-Similarity) as the evaluation metrics. For MA5K, we utilize L1 and LPIPS [64]) for evaluation. The results are shown in Table 2. + +We find that DDT-LLaMA demonstrates significant superiority over existing MLLMs across all test datasets and + +![](images/af755357bdbcffa185ad51e607c0685751cd68cb08c4a6054f2788cddb7bf020.jpg) +Figure 5. Qualitative comparison on image editing. + +metrics. It not only effectively comprehends the instruction to execute editing, but also excels at preserving image fidelity, which is rarely seen in prior work. Furthermore, when compared with specialist models, DDT-LLaMA still shows stronger performance. It consistently outperforms InsPix2Pix [5], also showing greater effectiveness than MGIE [18] and UltraEdit [65] across most datasets. + +Qualitative Examples. Figure 5 shows some qualitative image editing examples of DDT-LLaMA and baselines[20, 65]. DDT-LLaMA supports a wide spectrum of editing op + +erations including both local change (e.g., removal, replacement) and global change (change time, manipulation). For each case, our output images not only resemble the source image to a high degree but also are coherent with the instruction, demonstrating that DDT-LLaMA achieves a great trade-off between fidelity and editability. + +# 5.3. Vision-Language Comprehension + +We also evaluate the vision-language comprehension capabilities across various public benchmarks [1, 2, 17, 22, 24, 29, 30, 37, 40]. The primary results, detailed in Ta + +Table 3. Comparison for multimodal comprehension on vision-language benchmarks. + +
ModelsSizeImage GenImage captionVQAMLLM Bench
NoCapsFlickr30KVQAGQAOKVQAVizWizMMESEEDBenchPOPE
Specialized Visual Comprehension MLLMs
InstructBlip [10]7BX123.182.4-49.2-34.51212.858.8-
QWenVL-Chat [3]7BX120.281.078.257.556.638.91487.5758.2-
LLaVA-1.5 [33]7BX105.5-78.562.053.450.01510.764.385.9
mPLUG-Owl2 [59]7BX-85.179.456.157.754.51450.357.886.2
ShareGPT4V [8]7BX--80.663.3-57.21567.469.7-
LLaVA-1.6(HD) [34]7BX88.3-80.664.244.360.6-64.786.5
VILA [31]7BX--79.962.3-57.91533.061.185.5
MLLMs for both Visual Comprehension and Generation
Emu2-Chat [49]37B-119.886.084.965.164.854.91315.762.8-
SEED-LLaMA [19]8B✓90.466.766.234.845.955.1736.751.5-
VILA-U [57]7B✓95.470.375.358.359.635.31336.256.383.9
LaVIT [25]7B✓114.283.066.046.854.638.5997.957.382.2
Emu3 [55]8B-117.582.575.160.361.250.5-68.285.2
Ours8B✓124.288.576.466.365.957.31378.967.986.9
+ +Table 4. Reconstruction quality on ImageNet validation split and FID score comparison for autoregressive class-conditional synthesis on $256 \times 256$ ImageNet. + +
MethodReconstruction (PSNR) ↑Class-cond (FID) ↓
VQGAN [15]18.915.8
VQGAN-LC [68]20.815.4
RQ-Transformer [28]-7.6
MoVQ [66]21.57.1
Ours21.76.1
+ +ble 3, compare two categories of methods: specialized visual comprehension MLLMs [3, 8, 10, 31, 34, 35, 59] and MLLMs designed for both visual comprehension and generation [20, 25, 49, 55, 57]. Notably, DDT-LLaMA is an encoder-free MLLM without pretrained encoders such as CLIP [42]. Compared to other MLLMs, it significantly surpasses its counterparts across multiple benchmarks, even without relying on a specialized pretrained CLIP. It also outperforms many MLLMs that focus solely on comprehension tasks, highlighting the inherent capabilities and promising potential of DDT tokens in multimodal understanding. + +# 5.4. In-Depth Analysis + +# 5.4.1. Class-conditional Generation of DDT + +Our tokenizer is trained on $256 \times 256$ images from the ImageNet train split. The PSNR between the reconstructed and original images from the validation split reaches 21.7, outperforming spatial tokenizers trained on ImageNet (using a comparable number of tokens). + +To directly compare the performance of DDT tokens with other spatial tokens for image generation, we also train an autoregressive GPT model for class-conditional image generation, following [15]. We compare our model with several previous SOTA spatial tokenizers [15, 28, 66] for autoregressive modeling of class-conditional image synthesis on ImageNet. As shown in Table 4, under the same autoregressive paradigm, our method achieves a superior FID score, demonstrating stronger performance than tokenizers that generate spatially-based visual tokens. + +![](images/f7d14c1abe183c29da5045984fb1ff5754cf8dad25e73f409081ae9f5e3523c2.jpg) +Figure 6. Results of Counterfactual Interpolation with DDT tokens and VQGAN tokens. + +# 5.4.2. DDT Tokens are Recursive + +Counterfactual Interpolation. To directly show that DDT tokens are recursive and decouple visual attributes at various granularities, we first conduct counterfactual interpolation with both DDT tokens and VQGAN tokens. Specifically, for the token sequence derived from an image, we replace a subset of tokens with those from another image, while keeping the remaining tokens fixed, with the resulting sequence fed into the decoder for image generation. + +As shown in Figure 6, for VQGAN tokens, counterfactual interpolation actually performs CutMix [61], where regions from two images are concatenated. In contrast, DDT tokens, with their disentangled representation, ensure that only the attributes captured by the substituted tokens change in the generated counterfactuals, which allows for a seamless semantic blending of the two images. + +Decoding Image with an expanding subset of DDT tokens. To further illustrate the recursive nature of DDT tokens, we only input a subset of the first $t$ timestep tokens that are autoregressively sampled by DDT-LLaMA, into the decoder for image synthesis ( $t$ ranges from 1 to + +![](images/48e6da19f2a7af5392210ff244a586b4418aa42bced8a9c6f8872626d1de3421.jpg) +Scaling up training compute $C$ + +![](images/931389d0a27f8e21ea4eb143ec5b179b55c21f324eca1c9ac6d916abeb8f4c04.jpg) +Figure 7. Scaling MLLM size (2B, 8B) and training compute (50%, 75%, 100% of total tokens) improves visual quality. +Figure 8. Decoding images with an expanding subset of autoregressive-sampled DDT tokens. + +480). As shown in Figure 8, with the number of tokens increasing, the image's attributes are progressively recovered. Initially, the decoder reconstructs fine details, with contours and color information gradually completed until the full structure of the image is outlined. This finding further demonstrates that DDT tokens are recursive, and DDT-LLaMA effectively disentangles visual attributes, progressively inferring visual features at varying granularities based on textual instructions. This behavior aligns with our expectations for the DDT token design. + +# 5.4.3. Perplexity of Text Generation + +To further demonstrate that our recursive DDT tokens can facilitate the synergism between comprehension and generation, we record the perplexity of text prediction during auto-regressive multimodal pre-training, with VQGAN tokens and DDT tokens, respectively. As shown in Figure 9(a), training with DDT tokens results in a decrease in perplexity for text generation, whereas training with VQGAN tokens yields the opposite conclusion. This highlights that our DDT tokens are better suited for unified autoregressive modeling with text tokens, much like a foreign language that LLMs can read. + +# 5.4.4. A/B Test on Image Editing + +By disentangling visual attributes, DDT tokens hold an advantage over spatial tokens for tasks that require attribute modifying, such as image editing. To demonstrate this, we first use Gemma2-2B [52] as the backbone and leverage both DDT tokens and MoVQ tokens on the same 200M image-text dataset for pre-training, respectively. We then fine-tuned both models on the same image editing training set for consistent training steps. For evaluation, we manually collect a set of image editing test data and conduct an A/B test for human assessment. As shown in Fig- + +![](images/e16d21f43c8e56f80d797518e1dc5f53989b61b9d6868a97016307d35019d1ae.jpg) +Figure 9. (a) Perplexity of MLLM in text generation during image-generation training. (b) A/B test on image editing. + +ure 9(b), DDT-Gemma outperforms MoVQ-Gemma in 65 editing cases in total, showing a notable advantage in both global and local editing instructions. While MoVQ-Gemma surpasses DDT-Gemma in only 10 cases. It further underscores the superiority of DDT tokens. + +# 5.4.5. Scaling Laws of DDT-based MLLM + +We have also observed preliminary indications of scaling laws in our DDT-based MLLM. As mentioned in Sec 5.4.4, we also leverage Gemma2-2B for pre-training. And we further compare the performance of T2I generation with two model sizes (2B,8B) at three different training stages (50%, 75%, and 100% of total training tokens), as shown in Figure 7. The observed improvements in visual quality align with scaling laws, which suggest that larger transformers trained on more extensive datasets can learn more detailed and fine-grained image distributions. + +# 6. Conclusion + +In this work, we propose Discrete Diffusion Timestep (DDT) tokenizer to learn discrete, recursive visual tokens, which recursively compensate for the progressive attribute loss in noisy images as timesteps increase. With image decoding as DDT tokens, we train DDT-LLaMA on a vast corpus of image-text pairs for vision-language alignment. Extensive experiments showcase the immense potential of DDT-LLaMA across various tasks, e.g., T2I generation, image editing, and vision-language understanding. We are currently working on scaling up the training of our DDT tokenizer and the MLLM. In the near future, we will release a more powerful version of DDT-LLaMA, along with a more detailed technical report. Stay tuned! + +# Acknowledgements + +# References + +[1] Harsh Agrawal, Karan Desai, Yufei Wang, Xinlei Chen, Rishabh Jain, Mark Johnson, Dhruv Batra, Devi Parikh, Stefan Lee, and Peter Anderson. Nocaps: Novel object captioning at scale. In Proceedings of the IEEE/CVF international conference on computer vision, pages 8948-8957, 2019. 6 +[2] Stanislaw Antol, Aishwarya Agrawal, Jiasen Lu, Margaret Mitchell, Dhruv Batra, C Lawrence Zitnick, and Devi Parikh. Vqa: Visual question answering. 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Barron $^{1}$ Jia-Bin Huang $^{2}$ Pratul P. Srinivasan $^{1}$ Dor Verbin $^{1}$ + +$^{1}$ Google $^{2}$ University of Maryland, College Park + +https://relight-to-reconstruct.github.io/ + +![](images/56a9cc3092bd9f6ad0cd8c2206d067c76e5040150b5c09714405b6ba4c59205f.jpg) +Figure 1. 3D reconstruction under extreme illumination variation. We propose a method for 3D reconstruction from a set of images captured under strongly varying illumination. Our method recovers high-fidelity appearance details including specular highlights that prior state-of-the-art approaches cannot recover (top baseline: NeRF-Casting [47] with appearance embeddings, bottom baseline: NeROIC [25]). + +# Abstract + +Reconstructing the geometry and appearance of objects from photographs taken in different environments is difficult as the illumination and, therefore, the object appearance vary across captured images. This is particularly challenging for specular objects whose appearance strongly depends on the viewing direction. Some prior approaches model appearance variation across images using a per-image embedding vector, while others use physically-based rendering to recover the materials and per-image illumination. Such approaches fail at faithfully recovering view-dependent appearance given the significant variation in input illumination and tend to produce mostly diffuse results. We present an approach that reconstructs objects from images taken under different illuminations by first relighting the images under a single reference illumination with a mul + +tiview relighting diffusion model and then reconstructing the object's geometry and appearance with a radiance field architecture that is robust to the minor remaining inconsistencies among the relit images. We validate our approach on synthetic and real datasets and demonstrate that it outperforms existing techniques at reconstructing high-fidelity appearance from images taken under extreme illumination variation. Moreover, our approach is particularly effective at recovering view-dependent "shiny" appearance which cannot be reconstructed by prior methods. + +# 1. Introduction + +A common strategy for performing novel view synthesis is to recover a 3D representation from a collection of photographs of a scene and then use it to render novel views from unseen viewpoints. Most view synthesis approaches + +assume that the input images are all taken under the same illumination conditions, i.e., the scene's appearance is assumed to be static. However, this assumption is frequently violated during capture: moving clouds may cause the intensity of the sun to vary, artificial light sources may turn on or off, and even the shadows cast by the photographer may interfere with the scene. This issue becomes even more severe when dealing with unstructured photograph collections such as those scraped from the Internet, where an object may be imaged in environments with extremely different illumination conditions, such as the case shown in Figure 1. + +One strategy for addressing illumination variation is to use a view synthesis model capable of representing appearance changes across captured images. A simple and popular approach is to parameterize the view-dependent radiance of the scene as a function of a per-image "latent code" [9, 34]. Such an approach is effective for modeling changes (i.e. the "base" color and texture of the object). However, the additional expressivity comes at a cost because it tends to "explain away" all view-dependent appearances (not just those due to variable illumination). For non-diffuse (shiny) objects, we find that methods using per-image latent code often produce unrealistic, mostly-diffuse reconstructions. + +Other physics-based approaches explicitly recover the spatially-varying material properties of the scene in addition to a per-image representation of illumination [10, 25]. While inverse rendering provides a more physically meaningful image formation model than a view-dependent latent encoding, it suffers from the same ambiguities: appearance variation can be attributed to either a change in lighting or a change in viewing direction, and these models often mix up the two. + +Recent works [24, 58] attempt to circumvent these ambiguities by training image diffusion models that relight an individual image to appear as if it were lit by a specified illumination condition. Though diffusion models can leverage strong priors on natural image appearance to assist in material/lighting disambiguation, single-image relighting is fundamentally ill-posed. As such, independently applying these models to relight multiple images to a single reference illumination often yields samples corresponding to completely different, mutually-incompatible explanations of object materials. + +In this work, we first use a multiview image diffusion model to jointly relight all input images to match the lighting of a reference image selected from the set of input images. This produces relit images that are significantly more consistent than those from prior single-image relighting diffusion models. We then design a novel 3D reconstruction model based on NeRF [35, 47] to fit a 3D representation to those relit images, which enables rendering from novel viewpoints. Our 3D reconstruction model is designed to be robust to inconsistencies that may still be present in the + +output of the relit samples. Since the diffusion model has to implicitly estimate 3D shape to relight the input images, any errors in its shape estimation would translate to specular highlights not appearing at the correct locations. To resolve this, we use a per-image vector which we call "shading embedding". This vector is used to encode per-image perturbations to the surface normal vectors used by the shading model of the NeRF, which allows the model to account for errors in the model's underlying estimated shape. + +We validate the method on both synthetic (Objaverse [13]) and real (NAVI [22]) datasets. We showcase the capability of reconstructing accurate geometry and accurate view-dependent appearance from images captured under extreme illumination variation. Extensive quantitative and qualitative evaluation shows that the proposed approach significantly outperforms state-of-the-art methods both qualitatively and quantitatively. + +# 2. Related Work + +3D Reconstruction and View Synthesis. Neural radiance fields (NeRF) [35] is a successful approach for reconstructing a 3D scene under a fixed illumination. Many improvements to NeRF have been developed to improve the modeling of effects such as refractions and reflections [1, 6, 28, 32, 46, 47, 50], but all of these approaches also rely on static lighting. NeRF-W [34] achieved high-quality 3D reconstructions from unconstrained "in the wild" images taken from the internet, which tend to exhibit a variety of inconsistencies in lighting, appearance, and geometry. One aspect of this approach was using per-image appearance embeddings within the learned mapping from spatial coordinates and viewing direction to color (but not volumetric density). This parameterization forces optimization to recover a single consistent 3D geometry model while allowing appearance to vary across input images. This allows per-image appearance variation to be explained away, but also allows many view-dependent effects to be incorrectly attributed to per-image variation, often resulting in diffuse and erroneous reconstructions. Due to its simplicity (in that it does not contain a physically-based image formation model), per-image appearance embeddings are frequently used in settings where lighting only varies slightly [3, 4, 45]. + +Inverse Rendering. Decomposing an image into its constituent physical components has been a central problem in computer vision for nearly half a century [5]. Most modern approaches leverage the success of the computer graphics community, which has produced accurate and efficient models for the "forward" problem of rendering an image from an underlying 3D model [36]. Many modern inverse rendering techniques use radiance fields that, rather than mapping a 3D location and viewing direction to an outgoing color, map a 3D location to material properties and sur + +face normals, which are then rendered according to some estimate of incident illumination [2, 7, 10, 11, 14, 23, 29-31, 33, 43, 44]. Because this problem is ill-posed, these techniques often critically rely on analytical priors to regularize the estimated scene decomposition. Although these models fully decompose the scene into its components and thereby enable editing and relighting, their rigidly specified rendering models tend to constrain the solution space of the recovered model and result in lower rendering quality than models designed solely for view synthesis. + +Many prior approaches to inverse rendering depend critically on modeling illumination and material properties using low-frequency parameterizations such as spherical harmonics [25], spherical Gaussians [55], or MLPs that are strongly biased to produce smoothly-varying outputs [57]. All of these parametrizations necessarily limit the model's ability to recover and render high-frequency (i.e., nonsmooth) color variations caused by glossy surfaces. This limitation is avoided by NeRF-Casting [47], which models incident illumination by explicitly reflecting secondary rays into the volumetric representation, thereby enabling the reconstruction of extremely specular objects. The 3D representation used by our model builds upon NeRF-Casting. + +Lighting Estimation. Because estimating every aspect of a 3D scene is a challenging task with a broad scope, many prior works have instead attempted to only reconstruct a model of illumination from input images [16, 17, 26, 42]. Though this problem is still fundamentally underconstrained, it can be made tractable by learning a model from datasets containing light probes [27] or by relying on accidental light probes in the scene [51]. Modern generative approaches in this vein have shown that diffusion models are capable of developing an internal understanding of illumination [37], which is further validated by our work. + +Generative Relighting. Diffusion-based generative models have recently been used for relighting individual images [52] and, closer to our approach, for 3D relighting [24, 38, 58]. This process circumvents the need to decompose the scene into physically-meaningful components and instead relies on a diffusion model to re-synthesize an input image as if it were illuminated by some reference illumination. Unlike our method, these approaches require the set of input images to have constant illumination, which is used in the first step to recover the 3D geometry of the object before relighting it. IllumiNeRF [58] samples a diffusion model multiple times to generate a collection of plausible results, while Neural Gaffer [24] iteratively refines a set of relit images alongside a NeRF. Crucially, both models independently relight each input image given a reference illumination, which can lead to inconsistent relit images. Concurrent to our work, RelitLRM [56] uses a large reconstruction model to jointly reconstruct and relight an object + +from multiple images, but it also assumes that the input images are consistently lit. Additionally, all of these methods require a reference environment map as input, while we address a more general problem where we only have access to images. Our model works by relighting a set of differently-lit input images simultaneously to match the appearance of one of the input images, and it does not require any additional information, including constantly-lit input images or a reference environment map. We show that our approach not only yields significantly more consistent 3D reconstructions than prior work, but is also more practically applicable to a broader variety of inputs and capture settings. + +# 3. Method + +We aim to recover a 3D model from an collection of (posed) images of an object, where each image is illuminated by arbitrarily-varying lights. We use a two-step solution: in Section 3.1 we describe a relighting diffusion model that "harmonizes" the input images by making their illumination constant, and in Section 3.2, we describe a NeRF-based approach to convert the relit images produced by that diffusion model into a consistent 3D model. Our full pipeline is illustrated in Figure 2. + +# 3.1. Relighting model + +Our relighting model takes a set of $N$ input images $I_{1},\ldots ,I_{N}$ of an object from multiple known camera poses $\pi_1,\dots,\pi_N$ , each of which is assumed to have been taken under a different illumination (see Figure 2, leftmost pane). The relighting model's aim is to generate a set of images of the same object from the same viewpoints, relit under the illumination from a designated reference image in the input set, which we arbitrarily select as the first image, $I_{1}$ + +We build our relighting model using image diffusion, which can leverage strong natural image priors from large amounts of data. While recent works have used image diffusion models to relight individual input images based on a reference environment map [24, 52, 58], we argue that it is essential to relight the entire set of input images jointly. As demonstrated by the success of photometric stereo [19], leveraging multiple observations of the same material under varying lights reduces the inherent ambiguity between material properties and illumination, and it provides a strong cue for estimating shape. Using this same insight in the context of modern diffusion models leads to significantly more consistent relit images, as each sample from our model represents a unified interpretation of the object's material. Consequently, our method does not require ad-hoc solutions to address the issue of extremely inconsistent relit images, such as the use of appearance embeddings [58] or refinement of the relit images during reconstruction [24]. + +Our model's architecture follows prior work on view synthesis that extends image generative models to the mul + +![](images/2bbf5216e503878dae2ecf1d780b4ee548a535387fc61b6b26472c0358894766.jpg) +Figure 2. Method overview. We first apply a relighting diffusion model that converts $N$ images $I_{1}, \ldots, I_{N}$ with known camera poses $\pi_{1}, \ldots, \pi_{N}$ , captured under extremely different illuminations, to a set of images with the same poses, but rendered under the illumination of the reference image $I_{1}$ (highlighted in orange). We then optimize a neural radiance field to obtain a consistent 3D representation with a novel per-image shading embedding, which can be used to render new views of the scene from unobserved poses. + +tiview or video case [8, 15, 21] — we will analogously extend a single-image relighting model to multiple views, each with a distinct light. + +We construct our relighting diffusion model as a multiview latent model that denoises a set of $N$ latent codes $\mathbf{z}_1,\dots ,\mathbf{z}_N$ , one for each input image. Unlike generative models that synthesize images from only random noise, the observed images $I_{1},\ldots ,I_{N}$ contain a significant amount of valuable information about geometry and illumination. As such, when denoising the $i$ th latent code, $\mathbf{z}_i$ , the denoising network should use the geometry encoded in image $I_{i}$ as well as the lighting of the reference image $I_{1}$ . To accom + +plish this, we pass the "clean" latent corresponding to the $i$ th image $I_{i}$ and an encoding of its pose $\pi_{i}$ into the network that denoises the $i$ th latent $\mathbf{z}_{i}$ . To jointly reason about the reference lighting, we use 3D self-attention blocks [15] for the latent codes, and we use cross-attention in between them and the camera poses. This structure allows the geometry and camera pose of the $i$ th image and the lighting of the reference image to be directly observed by the network denoising the $i$ th latent $\mathbf{z}_{i}$ . + +Because our input is an unordered set of images, we follow CAT3D's approach [15] of replacing temporal embeddings with camera poses which we encode as raymaps [41, 49]. To inform the network which image should be used as the reference, we concatenate the reference image with a "reference map" consisting of a single-channel image of ones, and we concatenate all other images with a single-channel image of zeros. See the supplement for a full description of this process. Results from this relighting model component are shown in Figure 3. + +# 3.2. 3D Reconstruction + +Applying the relighting model from Section 3.1 to the input images yields a set of "harmonized" input images that appear to have been lit under a single consistent illumination. With these images we can recover a 3D model without solving the difficult problem of handling variable illumination within a 3D reconstruction pipeline. We build our reconstruction model on NeRF-Casting [47], a view synthesis technique that achieves state-of-the-art results for reconstructing highly specular objects under constant illumination. + +Although the relit images produced by our relighting diffusion model appear largely consistent when visually inspecting individual images, they still exhibit slight inconsistencies. As we will demonstrate, if the outputs of our diffusion model are used to naively train a NeRF that is not robust to this subtle variation (such as the common appearance-embedding based approach of NeRF-W [34]), these inconsistencies may be absorbed into the view-dependent parameterization of the NeRF, which results in novel view synthesis results with highly unrealistic and distracting "flickering" temporal artifacts as the camera moves. We must, therefore, be careful to parameterize appearance such that optimization is robust to this variation — resolving these inconsistencies is a primary goal of 3D reconstruction. + +We address this problem by observing that the subtle inter-image errors made by the diffusion model are usually due to the specular highlights being slightly "warped" relative to the ground truth. This suggests that the diffusion model has small errors in its implicit estimate of the surface normals of the object, which causes the specular reflections to be tilted in slightly incorrect directions. We therefore re + +![](images/298736cd04528b74e35fe78c8930a34c26aa6155e92834c6f66f8985b9765f42.jpg) +Figure 3. A comparison of our multiview relighting with prior work on single-image relighting. Our method first relights a set of inconsistently-lit images (one of which is shown in (a)) to match the illumination of a selected reference image (b) in that set. Single-image relighting techniques such as IllumiNeRF [58] (c) struggle to disambiguate geometry, lighting, and materials, leading to an inaccurate relighting. In contrast, our model jointly relights a set of inconsistently-lit frames, which reduces ambiguities and results in a significantly more accurate result (d) when compared with the ground truth (e). + +![](images/b22ad84f3bf3ec8932c79df2084f06110d8aec4e26f4b9f4cbe781bbc3ca2cb4.jpg) + +solve this by using a per-image "shading embedding": an embedding vector $\mathbf{v}_i$ is used to warp the normal vectors of the corresponding $i$ th training image, and those warped normal vectors are provided as input to the network that models the shading (and therefore, appearance) of the image. More concretely, the normals of the $i$ th image at a 3D coordinate $\mathbf{x}$ are computed as: + +$$ +\mathbf {n} _ {i} (\mathbf {x}) = \text {n o r m a l i z e} \left(\operatorname {M L P} \left(\mathbf {f} (\mathbf {x}), \mathbf {v} _ {i}\right)\right), \tag {1} +$$ + +where $\mathrm{MLP}(\cdot)$ is a multi-layer perceptron with 3 layers each with 128 hidden units, $\mathbf{f}(\mathbf{x})$ is a spatially-varying feature parameterizing the normals (identical to the one used by NeRF-Casting), and the normalize $(\cdot)$ operator turns the output of the MLP to a unit-length vector. + +The per-image surface normals defined in Equation 1 can slightly alter the directions in which secondary rays are reflected by the model, which allows optimization to account for errors in the output of the relighting diffusion model. We prevent the normals from changing significantly between different images by tying them to the normals corresponding to the underlying NeRF density field, as in NeRF-Casting [47]. See NeRF-Casting and our supplement for more details. As we will demonstrate later, this shading embedding yields more accurate reconstructions and renderings than the standard appearance embedding approach [34] used in prior work for relighting [24, 58]. + +# 4. Architecture and Training + +Training Data. The relighting model's training dataset is key to its ability to generalize across different illumination conditions, materials, and geometries. Due to the ease of rendering a large set of synthetic data, we rely solely on synthetic data for training, and we experimentally verify that our method generalizes to real captured photographs. We render our dataset using assets from a dataset of $\sim 300\mathrm{K}$ high-quality objects, similar in appearance to Objaverse but with more diverse materials. We additionally augment this dataset by rendering another copy after replacing all materials with perfect mirrors, which we found improved reconstruction quality for both highly-specular objects and (perhaps surprisingly) for standard mostly-diffuse objects. We render the objects using about 700 environment maps taken from Poly Haven [39], which we augment by randomly rotating azimuthally. + +Diffusion Model. We initialize our model using an image generation latent diffusion model similar in architecture to Stable Diffusion 1.5 [40] that had been trained on a large dataset of images. The image input of our diffusion model is a $512 \times 512 \times 3$ resolution image that is encoded into $64 \times 64 \times 8$ latents. To enable classifier-free guidance (CFG) [20], we randomly mask out the attention to the reference image to force the model to do "unconditional re + +lighting" and relight the input views with an arbitrary lighting. For all our experiments, we use a CFG value of 3. Because the speed and memory requirements of training the model are inversely proportional to the number of synthesized views, we train our model in stages: We first train the model to relight 8 frames for $200\mathrm{K}$ steps, then 16 frames for $100\mathrm{K}$ steps, then 32 frames for $50\mathrm{K}$ steps, and finally 64 frames for another $50\mathrm{K}$ steps. Note that our model parameters are independent of the number of input views, since the cross-attention operation can scale to an arbitrary number of images. Our model was trained on 64 5th-generation TPUs with a total batch size of 64, which took approximately two weeks. At inference, we set the number of images that our diffusion model simultaneously relights to $N = 64$ + +3D Reconstruction. The optimization of each radiance field uses a similar number of parameters to those used in NeRF-Casting [47]. Optimizing a model from a set of harmonized images takes roughly 30 minutes on 16 NVIDIA A100 GPUs, and rendering a single $512 \times 512$ image takes about 0.5 seconds on the same hardware. See supplement for details and a full description of all hyperparameters. + +# 5. Results + +We evaluate our method on two datasets: synthetic objects from Objaverse [13] and real captured objects from NAVI [22]. The synthetic dataset comprises two components: 8 standard textured assets whose materials range from mostly-diffuse to glossy, and 12 shiny assets containing objects with perfectly-reflective materials, designed to highlight the challenge of recovering accurate view-dependent effects. We render the synthetic Objaverse dataset using environment maps from HDRIMaps [18]. Each scene contains 64 training images and 36 testing images, all with different random poses. Each training image was rendered with distinct illumination, and the test set was rendered using the illumination of the reference image from the training set. Please see the supplemental material for additional results and videos. + +# 5.1. Comparisons to State-of-the-Art Methods + +We compare our approach with two methods designed for 3D reconstruction "in the wild": NeROIC [25] and NeRF-Casting [47] with standard appearance embeddings for each image (which we call "NeRF-Casting + AE" or "NeRFCast + AE" for short). We also compare our approach with the recent diffusion-based relighting method IllumiNeRF [58]. IllumiNeRF requires a target environment map for relighting and we provide it with the ground truth illumination, which is a significant advantage over other techniques as the full environment map contains more information than the reference image. For methods with appearance embeddings (ours and NeRF-Casting + AE), we render novel views us + +ing the same embedding as the reference image. Similarly, when rendering test images using NeROIC, we use the estimated illumination of the reference image. + +Synthetic Results. In Figure 4, we qualitatively compare our method's novel view synthesis results with prior state-of-the-art approaches. Our results appear significantly more accurate, and all baselines struggle to recover specular highlights. This is particularly apparent in the first and third rows, demonstrating the recovery of fine details in the reflections of perfectly specular objects. The quantitative results in Table 1 show that our method significantly outperforms all baselines on both splits of the dataset, even when we provide the IllumiNeRF [58] baseline with true environment maps corresponding to the reference image. + +Table 1. Novel view relighting on Objaverse. Our approach of relighting and robustly optimizing a radiance field outperforms previous state-of-the-art methods in rendering novel views under target lighting. We outperform prior work despite giving the baseline a significant advantage by providing it the true lighting. + +
Standard AssetsShiny Assets
MethodPSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
NeROIC [25]26.130.9350.08822.140.8800.113
NeRFCast [47] + AE27.530.9410.06721.800.8740.108
IllumiNeRF [58] w/ known light29.220.9580.05723.460.8810.095
Ours31.340.9660.05326.540.9110.090
+ +Real Photographs. The top row of Figure 1 shows photographs we captured of a chrome-plated figurine in different environments. The resulting synthesized novel views show that our method can render accurate images corresponding to the selected reference illumination. In the bottom of Figure 1 and in Figure 5 we show reconstruction results on captured photographs from NAVI. The results show that our method can preserve shadows and specular highlights. Since NAVI also provides multiview data for each illumination, we can quantitatively evaluate the novel view synthesis performance on held-out views under the same illumination as the reference. We evaluate the method on all of the 18 NAVI scenes with at least 64 frames, and we show that our method also achieves the best quantitative results across all prior methods, as shown in Table 2. Since NAVI does not provide ground truth environment maps, we could not evaluate IllumiNeRF on this dataset. + +Table 2. Novel view relighting on real photos from NAVI. We show that we outperform prior work on synthesizing novel views from "in-the-wild" images. + +
MethodPSNR↑SSIM↑LPIPS↓
NeRF-Casting [47] + AE23.590.9160.066
NeROIC [25]24.010.9180.079
Our Model25.550.9290.060
+ +![](images/09b5c07ea70fa8e5e77b413a149876cb3ed4ca7f8027c68e08a2bde6b44e738e.jpg) +Figure 4. Visual comparison of novel view renderings on the Objaverse dataset. (b) We show sample input images under extreme illumination variation. (c) Adding a per-image latent code to NeRF-Casting [47] ("NeRFCast + AE") cannot accurately explain away the variations, leading to erroneous reconstruction. (d) Due to the ill-posed nature of the problem, inverse rendering-based methods such as NeROIC [25] tend to produce lower-quality renderings with mostly diffuse appearance. (e) IllumiNeRF [58] leverages diffusion prior for single-image relighting but produces inconsistent output samples, resulting in excessive blur in rendered novel views. Note that IllumiNeRF requires access to the target illumination's environment map as input. We provide IllumiNeRF with the ground truth environment map corresponding to the reference image (a), while other methods only have access to the reference image itself. (f) Our method renders accurate appearance with specular highlights close to those in the ground truth images (g). + +![](images/60cec098889a5add566075ed062f067c3e107fbbc639760e4877e7a57d38c65e.jpg) + +![](images/e30e503a11512ea99c514dedb0f7c3aa819b951ad92975d782066692245c5f41.jpg) + +![](images/9762c99f2fa127449d47d6c92fd9da5f7d7c991764bee327530cf69b886bbae2.jpg) + +![](images/0e4ebf1d7dc702ed4edcc77f9771cb0fb62a4e21614665f2cd25ba0758f57ce4.jpg) + +![](images/0b2f098800ea3671647548c90ac0abfb167af3bd4e21deec5cc8eaa0b9aa7a40.jpg) + +# 5.2. Ablation Studies + +Here, we provide ablations designed to test the different components of our model. + +Number of Frames. A major benefit of our approach is that it jointly relights all frames. Table 3 shows our view synthesis results when relighting the images using different numbers of simultaneously-predicted frames $N$ . Increasing the number of predicted frames improves 3D reconstruction, hence our choice for predicting $N = 64$ images. + +Table 3. The effect of the number of frames $N$ output simultaneously by our model. Increasing the number of frames simultaneously processed by our model improves its performance, therefore we use $N = 64$ . + +
Standard AssetsShiny Assets
# frames NPSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
1 frame28.390.9430.07923.850.8890.105
8 frames30.430.9560.06725.620.9010.095
16 frames30.490.9580.06325.520.9000.097
32 frames30.720.9610.06026.140.9080.090
64 frames (ours)31.340.9660.05326.540.9110.090
+ +Dataset. Next, we demonstrate the importance of including purely-specular objects in our training data. To do this, we train two 16-frame versions of our model for 70K steps, with and without the purely specular data augmentation described in Section 4. Table 4 shows that including the specular materials in the training set improves performance on specular objects and, perhaps surprisingly, that it is also beneficial for our general less-specular (but not perfectly-diffuse) dataset. + +Table 4. Training dataset ablation. We show that training on assets with standard materials as well as objects with highly reflective materials improves performance for both types of assets. + +
Standard AssetsShiny Assets
Training dataPSNR↑SSIM↑LPIPS↓PSNR↑SSIM↑LPIPS↓
Standard assets29.160.9380.06622.340.8740.113
Standard + shiny assets29.260.9390.06622.910.8770.111
+ +Shading Embeddings. Table 5 demonstrates the effect of our shading embeddings on the 3D reconstruction of the shiny synthetic scenes harmonized by our relighting model. As explained in Section 3.2, the shading embeddings allow the model to slightly shift the normal vectors used for com + +![](images/09b520ab8d053bd736416071c23ffe4906167046191ccf186c589863c22a8b18.jpg) + +![](images/4349bb001a53bf51f35ed5a1921638a36b2e79acd11d09992a9aa98fd6e5b171.jpg) + +![](images/735c3726f29588f8f4fef7ad5c025d4f2260cb6e18a09d3973f2f27f703f3035.jpg) + +![](images/2a5e8441383f4af38e2fcd464d89f617dcb222042da1726d34ef4f156849455d.jpg) + +![](images/4ecc1047f4e5d7e8080bb971a8cab84ccf4780f56feea9d57a2ddc8eee4bec54.jpg) +(a) Reference + +![](images/f77f000d10dc11bed8b821cbe5e26d32020cdd5e92261b37017bc9eb1d9cc7ea.jpg) +(b) Input Samples + +![](images/aba3c6bfbcf14eaf9caf12c2c7f665ca5063920f3044c7ca48c263c085875aa2.jpg) + +![](images/6a03747c0c87e107707a361a5a1feef558b909b834922ca5dc87e8dfb6526867.jpg) + +![](images/a66d81db02ae20ffaaa93ce4b7b90bd90a7f1fcfb9f4c156be6265448e1fa3ae.jpg) +(c) NeRFCast + AE + +![](images/99d8fc35efef49413cb89d74ca25c66f5fc1b3348c92b79f21ae46317f5d56e4.jpg) + +![](images/723790154b5da6d5e00c29801602e11f728b07fd492c9fad9aeaa83dcd5c1f22.jpg) + +![](images/bd3927f09ff02ccbdd0fd7ff00c0d8b71b1729147f967f71cfb41fc019a89bfa.jpg) +(d) NeROIC +Figure 5. Comparison on real world photos. We use our method to reconstruct objects from in-the-wild photos taken in different environments. Our method can render novel views under the illumination conditions of any input image we select as the reference. Unlike prior work, our technique accurately preserves shadows (e.g. the bunny's ear shadow in the first row) and reflections (e.g. the box's handle in the second row and the car's specularities in the last row) that appear in the reference image we would like to match. + +![](images/8bb032cf77e04bfea920e4e73d0d934870b12cb0c78daacfa404d2ca3961ab81.jpg) + +![](images/e803c72a3c735b96e8e3c5f0ba66925e6f64a4ba0b3f32fb2411ee4dd38c9d1a.jpg) + +![](images/b940d7cf3c3f50c32299d7034c7669d40375b9d53ad04349aab33ab46a7c5721.jpg) +(e) Ours + +![](images/cefe31490c3173771eedc4eaf48d80cc3693a6b42c24a0a540453da55efa214d.jpg) + +![](images/55bfbf8dba97240240aae486986eca1b7f0072d183565a75acc8684814ce717e.jpg) + +![](images/de20e5f141e0fcc499695d2d30d750f3284deebbeabc9f4657ae71f78be81859.jpg) +(f) Ground Truth + +puting appearance separately for each image, which enables absorbing small inconsistencies in the relit images. This improves upon the same NeRF model with no per-image embeddings ("No embeddings"). In contrast, using standard embeddings as in NeRF-W [34] ("Shading embeddings") has an adverse effect: the per-image codes allow the model to encode specularities as per-image diffuse color, which results in unrealistic and poor reconstructions. + +Table 5. Per-image embedding ablation. We show that our shading embeddings improve performance compared to NeRF-Casting without any per-image code and that standard appearance embeddings have an adverse effect on reconstruction quality. + +
MethodPSNR↑SSIM ↑LPIPS↓
No embeddings26.020.9070.094
Appearance embeddings24.380.8960.096
Shading embeddings (ours)26.540.9110.090
+ +# 6. Discussions and Conclusions + +Limitations. Our approach requires object masks and accurate camera poses as inputs. Camera poses, in particular, can be challenging to compute from images of highly reflective objects that do not have reliable features for matching, but are required by most 3D reconstruction methods. However, there has been significant recent + +progress in camera pose estimation using learning-based techniques [12, 48, 53, 54] which do not rely on explicit feature matching. We believe that leveraging strong generative priors for joint pose estimation and 3D reconstruction is an exciting direction for future research. + +Conclusions. In this paper, we address the challenge of reconstructing 3D objects from images captured under extreme illumination variation. Our core insight is to simultaneously relight all input images to match the illumination of a chosen reference image, thereby harmonizing lighting conditions among input images. We achieve this by training a diffusion-based multiview relighting model. Using these relit images, we apply a 3D reconstruction model that is robust to residual inconsistencies, enabling accurate reconstruction of the object's shape and view-dependent appearance. Our method effectively reconstructs objects with complex shapes and materials from images taken under drastically different lighting conditions. Our work highlights a promising direction for leveraging strong generative priors to tackle the ill-posed problems of 3D reconstruction. + +Acknowledgements. We thank Matthew Burruss, Xiaoming Zhao, Ben Poole, Alex Trevithick, Stan Szymanowicz, Rundi Wu, David Charatan, Jiapeng Tang, Matthew Levine, Ruiqi Gao, Ricardo Martin-Brualla, and Aleksander Holski for help and fruitful discussions. + +# References + +[1] Benjamin Attal, Jia-Bin Huang, Michael Zollhöfer, Johannes Kopf, and Changil Kim. Learning neural light fields with ray-space embedding. 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Generative Omnimatte. Our method decomposes a video into a set of RGBA omnimatte layers, where each layer consists of a fully-visible object and its associated effects like shadows and reflections. We improve upon existing work by adding a generative video prior, allowing our method to complete occluded regions (top, middle) and handle dynamic backgrounds (bottom). + +![](images/9aa64a93b810cb3094dae3902dbcc5b624a291bb7effdf855f18e01635f949a8.jpg) + +![](images/9cad9adba3604934d3a0fa559a46c485433b5c5d3e93f0bdacd7810b8546fd3a.jpg) + +![](images/cdb283bc8bac8101db67105c8383ba71879db5be0c74772032abafa3e04cf8f6.jpg) +Layer editing + +# Abstract + +Given a video and a set of input object masks, an omnimatte method aims to decompose the video into semantically meaningful layers containing individual objects along with their associated effects, such as shadows and reflections. Existing omnimatte methods assume a static background or accurate pose and depth estimation and produce poor decompositions when these assumptions are violated. Furthermore, due to the lack of generative prior on natural videos, existing methods cannot complete dynamic occluded regions. We present a novel generative layered video decomposition framework to address the omnimatte problem. Our method does not assume a stationary scene or require camera pose or depth information and produces clean, complete layers, including convincing completions + +of occluded dynamic regions. Our core idea is to train a video diffusion model to identify and remove scene effects caused by a specific object. We show that this model can be finetuned from an existing video inpainting model with a small, carefully curated dataset, and demonstrate high-quality decompositions and editing results for a wide range of casually captured videos containing soft shadows, glossy reflections, splashing water, and more. + +# 1. Introduction + +Natural videos typically intertwine complex signals about our dynamic world, such as camera motion, articulated object movement, intricate scene effects, and time-varying interaction between objects. Mid-level representations that + +model this complexity are vital for intuitive interaction and editing of video content. One such representation is a decomposition of video into a set of semantically meaningful, semi-transparent layers, typically with one layer for each foreground object and the background. The utility of layers in creating visual effects has fueled interest in generating them from casually-captured video. + +Omnimatte [19, 29, 35-37, 47] methods produce semantically meaningful layers that contain individual objects along with their associated effects, such as shadows and reflections. To infer the complex space-time correlations between objects and their effects, existing methods rely heavily on restrictive assumptions such as a stationary background or accurate camera and depth estimation. These methods fail when these assumptions are violated. Furthermore, existing methods cannot complete occluded regions, limiting their potential applications (Fig. 2). + +In this work, we present a novel generative layered video decomposition framework that overcomes previous limitations by leveraging the strong generative prior of a pretrained video diffusion model [7]. The video prior serves two purposes. First, the model's internal features reveal connections between objects and their effects (Fig. 5) that can be exposed through finetuning, similar to recent works that apply the internal features of video diffusion models for analysis tasks [22, 44]. Second, the model can directly complete occluded areas in the layer decomposition, including dynamic regions. This prior is a key factor that enables our method to dispense with the ad-hoc, limited priors of previous works [19, 29, 36, 47] and the restrictions they place on the input video. + +However, existing video inpainting models are not directly applicable to the omnimatte task — because they inpaint only the region indicated by a binary mask, they lack the flexibility to remove associated effects outside of the mask region (Fig. 3). Instead, we finetune the video inpainting model to create an object-effect-removal model, and apply it as a core component of a layer-decomposition system (Fig. 4). The model produces a "clean-plate" RGB background layer and initialization for the foreground layers. The final RGBA foreground layers are optimized to reconstruct the input video while remaining sparse. Since the pretrained model's features already connect objects and their effects, a small, carefully curated dataset of real and synthetic examples of object-effect associations is sufficient for finetuning. + +Our method advances video layer decomposition in two directions: (i) it operates on casual videos where previous methods fail, without relying on a stationary background or camera poses, and (ii) it generates realistic, dynamic layers for both fully occluded regions and regions partially occluded by shadows or reflections. These capabilities unlock various creative editing tasks such as object removal, move- + +![](images/be54ed05c1d7c857a8b5ad121bc144289bb2189cbf8c9430ae1f741d80e1cd6a.jpg) +Figure 2. Limitations of existing Omnimatte methods. Omnimatte methods [19, 29, 36, 47] rely on restrictive motion assumptions, such as stationary background, resulting in dynamic background elements becoming entangled with foreground object layers. Furthermore, these methods lack a generative and semantic prior for completing occluded pixels and accurately associating effects with their corresponding objects. + +![](images/8973a84ffd95f5f642616bb5bee7985c60c97435750581c214b7a6720ab6d86a.jpg) +Figure 3. Limitations of inpainting models for object removal. While video inpainting models (e.g., [66]) can complete plausible background pixels in the input mask region, they preserve the removed objects' shadows and reflections outside the mask. + +ment retiming, and foreground stylization (Fig. 1). We will release the dataset of real and synthetic layered videos used to finetune the video inpainting model. + +# 2. Related Work + +Transparent Images and Matting. Transparent (RGBA) images and videos are widely used in various applications, including rotoscoping and visual effects synthesis. The matting problem [40, 50] aims to extract foreground RGBAs and background layers from the given images or videos. In the visual effects industry, this layer decomposition is traditionally achieved by green-screen chroma keying, requiring complex filming setups and manual postprocessing [34]. Deep learning methods [24, 26, 30, 52] approach this problem by training on large-scale alpha matte + +groundtruth [26, 30]. These studies focus on estimating fine-level alpha mattes for foregrounds but cannot capture the correlated effects. Recent advancements [62] have enabled text-to-RGBA image generation with plausible effects by finetuning Stable Diffusion [42] on a transparent image dataset. Nonetheless, decomposing videos into layers with effect association is a different problem domain and remains under-explored. + +Video Layer Decomposition. Decomposing a video into a set of semantically meaningful layers enables a wide range of applications, including video editing [5, 23, 25, 45], motion re-timing [35], view synthesis [43, 67], game deconstruction [46], and obstruction removal [2, 3, 33]. Our work focuses on synthesizing fully-visible layers of individual objects and their associated effects from a video. + +Video Matting with Associated Effects. Omnimatte [35, 36], inspired by early flow-based methods [1, 9, 51], leverages motion cues to decompose a video into RGBA matte layers, each comprising an object and its associated effects. It assumes a static background, modeled by planar homographies, and groups the time-varying residual (moving objects and effects) into foreground layers through a test-time optimization step. Recent works extend Omnimatte by enhancing the deep image priors [19, 37] and relaxing the planar homography constraint to non-rigid warping [35, 59] or 3D scene representations [29, 47]. However, these approaches are limited to restrictive motion assumptions (e.g., static backgrounds, accurate pose estimation) and lack generative capabilities and semantic understanding for completing occluded areas and detecting precise object-effect associations (Fig. 2). Our method, in contrast, requires no motion assumption and leverages the generative and semantic priors of our object-effect-removal model to obtain a set of fully-visible layers with accurately associated effects. + +Video Generation and Inpainting. Recent advancements in diffusion models have significantly improved the capabilities of text-to-video generation. These models [7, 8, 12, 16, 17, 21, 48, 56, 58, 60, 65] are trained on massive datasets of video-text pairs, enabling them to generate visually appealing videos from text descriptions. + +Text-to-video models have been adapted for the task of inpainting (e.g., [38, 64, 68]), in which they synthesize content in a user-specified mask region, conditioned on the surrounding visual context. While existing video inpainting methods [11, 15, 28, 31, 54, 61, 64] are often employed for object removal, these models cannot handle the effects that extend beyond mask boundaries, leaving undesired shadows and reflections in the output frames (Fig. 3). + +Object Effect Removal. Work [13, 32] in video shadow removal focuses specifically on removing cast shadows, but does not aim to perform object-shadow association, object removal, or background completion. Recent meth + +ods [4, 53] fine-tune image diffusion models for object and effect removal. However, they are unsuitable for video object removal because they lack temporal coherence when run on individual frames. Moreover, our goal extends beyond object removal; we aim to decompose a video into an entire set of omnimatte's to enable layer-based video editing tasks. + +# 3. Method + +Given an RGB video $\mathcal{I}$ and $N$ object masks $\{m_i\}_{i = 1}^N$ our goal is to generate $N + 1$ video layers: a clean-plate RGB background $\mathcal{I}_{\mathrm{bg}}$ and $N$ foreground RGBA omnitimates $\{\mathcal{O}_i\}_{i = 1}^N$ , each containing one object and its associated effects (such as shadows or reflections). + +Since ground-truth layered video data is scarce, we aim to apply an existing video diffusion model (Sec. 3.1) with minimal modifications. Large, pretrained video models have already learned the required associations between objects and their effects as part of their generative task (Sec. 3.3), so we aim to bring out this ability by finetuning the model with a small dataset of layered videos (Sec. 3.4). + +The diffusion model produces RGB (without alpha), and retraining to produce alpha maps would require a large dataset of RGBA layers [62]. To avoid changing the output space of the model, we employ a two-step process (Fig. 4): (1) creation of the clean-plate video $\mathcal{I}_{\mathrm{bg}}$ and $N$ "soloed" or single-object videos $\mathcal{I}_i$ containing only object $i$ and the background, and (2) reconstruction of the foreground layers $\mathcal{O}_i$ from the pairs $(\mathcal{I}_i,\mathcal{I}_{\mathrm{bg}})$ (Fig. 4). To construct the background $\mathcal{I}_{\mathrm{bg}}$ and solo videos $\mathcal{I}_i$ , we train a new video object-effect-removal model, which we dub "Casper"*, guided by a trimask (Sec. 3.2). We then reconstruct the layers $\mathcal{O}_i$ via test-time optimization (Sec. 3.5). + +# 3.1. Base Video Diffusion Model + +Our object-effect-removal model, Casper, builds upon the inpainting variant of the video diffusion model, Lumiere [7]. Lumiere is a text-to-video generator with a two-stage cascade of pixel-based diffusion models. The first-stage base model generates an 80-frame video at $128 \times 128\mathrm{px}$ resolution from a text prompt. The second stage, a spatial super-resolution (SSR) model, upsamples the output of the base model to $1024 \times 1024\mathrm{px}$ resolution. + +The Lumiere inpainting model [7, 38], finetuned from the original text-to-video base model, takes two additional conditions: a masked RGB video with zeroed-out inpainting regions and a binary mask video $m$ . The base inpainting model is followed by the same SSR to achieve high-resolution quality. + +Casper is finetuned from the inpainting model to perform object-and-effect removal. While Casper keeps the same + +![](images/7882d0cf6a525b6a6ebd55587fb42bf5c52e29a4d3b84e805bfab0ef8e050a54.jpg) +Figure 4. Generative omnimatte framework. Given an input video and binary object masks, we first apply our object-effect-removal model, Casper, to generate a clean-plate background $\mathcal{I}_{\mathrm{bg}}$ and a set of single-object (solo) videos $\mathcal{I}_i$ applying different trimask conditions. The trimasks specify regions to preserve (white), remove (black), and regions that potentially contain uncertain object effects (gray). In Stage 2, a test-time optimization reconstructs the omnimatte layers $\mathcal{O}_i$ from pairs of $\mathcal{I}_i$ and $\mathcal{I}_{\mathrm{bg}}$ . + +![](images/f99b7821a4c11010b6b3fa38e1449d2a727a180185966a9da417ddd5d4c92d46.jpg) + +model architecture as the base inpainting model, our decomposition framework introduces novel strategies for input object masking (Sec. 3.2). + +# 3.2. Object and Effect Removal with Trimask + +The original Lumiere inpainting model is conditioned on a binary mask $m$ that indicates regions to be inpainted ( $m = 0$ ) and preserved ( $m = 1$ ). Our object-effect-removal task introduces extra ambiguity: the "preservation" region may not be completely preserved, but instead can be potentially changed (e.g., to erase shadows). + +To address the ambiguity, we propose a trimask condition $\mathcal{M}$ , derived from the binary object masks $\{m_i\}_{i=1}^N$ . The trimask explicitly marks three regions: the objects to remove $(\mathcal{M} = 0)$ , objects to preserve $(\mathcal{M} = 1)$ , and background areas $(\mathcal{M} = 0.5)$ that may contain effects to be removed or preserved (Fig. 4). To obtain the clean-plate background video $\mathcal{I}_{\mathrm{bg}}$ , we use a background trimask $\mathcal{M}_{bg}$ that marks all objects as areas to remove and the background as an area to potentially modify. To associate effects with their corresponding $N$ objects, we aim to produce $N$ solo (single-object) videos $\mathcal{I}_i$ that contain a single object and its correlated effects. The $N$ input trimasks $\{\mathcal{M}_i\}_{i=1}^N$ mark the object $i$ as a preservation area and the remaining $N - 1$ objects as removal areas. The set of $N + 1$ trimasks $(\mathcal{M}_{bg}$ and $\{\mathcal{M}_i\}_{i=1}^N)$ are fed into Casper separately, each with the same noise initialization, to generate $N$ solo videos $\mathcal{I}_i$ and the background video $\mathcal{I}_{\mathrm{bg}}$ . We obtain the binary object masks $m_i$ using SegmentAnything2 [41]. + +Additionally, instead of a masking the RGB values in the input video, we follow ObjectDrop [53] and keep the RGB values of the removal regions $(\mathcal{M} = 0)$ in the input video + +![](images/8b1b1dc37a5ad77fbfdd2d213516ae9b5ed90e8a7c5e9fd1812efa9eabd58709.jpg) +Figure 5. Effect association prior in a pretrained video generation model. We input a video to a pretrained text-to-video generator [7] using an SDEdit approach [39] and analyze the spatial self-attention weights. By measuring the attention weights between query tokens and key tokens located within target object areas, we observe that the generator can effectively associate effects with target objects. In this specific example, we re-noise the video to $t = 0.5$ and visualize the attention in the middle bottleneck of the U-Net at the sampling step $t = 0.125$ . + +condition, allowing the model to associate the content inside the mask with the corresponding effects outside the mask. + +During inference, the inputs to Casper are a text prompt describing the target removal scene, and a concatenation of the input video, trimask, and noisy video at a $128\mathrm{px}$ resolution (e.g., $224\times 128\mathrm{px}$ ). The model takes 256 DDPM [20] sampling steps without classifier-free guidance for inference ( $\sim 12$ minutes for an 80-frame video). We adopt temporal multidiffusion [6] to handle longer videos. + +# 3.3. Effect Association Prior in Video Generator + +To investigate Lumiere's inherent understanding of object-effect associations, we analyze the self-attention pattern during denoising of a given video using SDEdit [39]. We focus on the spatial self-attention within the frame since it is the strongest indicator of the model's prior on object-effect associations. Specifically, we measure the self-attention weights between the query tokens and key tokens associated with the object of interest. For a query at the spatial location $p$ in the $j^{\mathrm{th}}$ frame $\mathcal{I}^j$ , the response to the object is calculated as: + +$$ +r (p) = \frac {\sum_ {y \in m ^ {j}} \mathbf {W} _ {p , y}}{\sum_ {x \in \mathcal {I} ^ {j}} \mathbf {W} _ {p , x}}, \tag {1} +$$ + +where $\mathbf{W}$ is the attention weight matrix obtained by the attention operation [49], and $\mathbf{W}_{p,x}$ denotes the weight between the query at $p$ and the key token at $x$ . The numerator sums the weights between the query and all the keys within object mask $m^j$ , and the denominator normalizes this sum by the total weight across the entire image space $\mathcal{I}^j$ . + +As visualized in Fig. 5, we observe that the query tokens in the shadow areas exhibit attention to the object region. This suggests that the pretrained model [7] can associate objects and their effects. Leveraging this prior knowledge, we hypothesize that a relatively small training dataset can be sufficient to train an effective object-effect-removal model. + +# 3.4. Training Data for Object and Effect Removal + +We curate a training dataset of real and synthetic video examples (Fig. 6) from the following four categories: + +Omnimatte. We collect 31 scenes from successful results of existing omnimatte methods [29, 36, 47] to form the training tuples of input video, input trimask, and target background video. These scenes, mostly from the DAVIS [10] dataset, feature static backgrounds and single objects, providing basic examples of shadows and reflections in real-world videos. + +Tripod. We supplement our dataset with 15 in-the-wild videos from the web, captured by stationary cameras. These videos contain objects moving in and out of the scenes, which can be segmented into pseudo tuples of videos with and without the objects. These videos include examples of water effects (e.g., reflections, splashing, ripples) and ambient background motion. We augment these videos with Ken Burns effects to simulate camera motion. + +Kubric. While the real-world videos provide valuable object-effect examples, they primarily depict single-object scenes, limiting the model's ability to learn effect association with multiple objects. Hence, we incorporate 569 synthetic videos generated using Kubric [18]. By rendering multi-object scenes in Blender [14] and making objects transparent, we create ground-truth removal videos that preserve the physical interactions and motion of the remain- + +![](images/8a38ad40f83242ac284b7d1b14d82eadf35538c96d3229f9f4d9f8a9e1014354.jpg) + +![](images/d508361860050ef6b32c3033ecc9ae4245a5f3cbb5fb56b61f73508fd1e074fe.jpg) + +![](images/74d745baba5872baedb0f8fa4696b2596f9f3596c5c071c3a84d02da9ddd197d.jpg) +(a) Omnimatte + +![](images/856e20604d185a37550d37c914b9ab8d5796cd06e1d52157005e901dfb4dfe4e.jpg) + +![](images/62e9c725b98ef2a8c96bdb626b38115eae306db6e8e9facb4cd86c48e1acc651.jpg) + +![](images/84f5b8bb80df0f6df071170103f7a721481ad99ec4f622e54a74a68a74740036.jpg) +(b) Tripod + +![](images/873c8241d37674c9159b0a7bfa471b872dd97827d37d1d94b627e08e5146a4f7.jpg) + +![](images/1b8006f3721024c7055089d6f94f62eb290cbd1998d9edacd967cf6a92b0983f.jpg) + +![](images/61113b173252c276e590adea7ff8536949809896af2bf5f5cb2025bcd46e1c17.jpg) +(c) Kubric +(d) Object-Paste + +![](images/44f5d98bd0d83d7fe6eb17b45dad16222072bebda663b6c0b97fe310cfa86410.jpg) + +![](images/cf61ddb972aafbca476fc70f7161c7e866b2b0336341c698c67dc9defade783f.jpg) + +![](images/92cdfa18749343cae097a8e50b54fcc9f054f726779f3403b498f50bf1ea5545.jpg) +Figure 6. Training data for object and effect removal. (a) We collect omnimatte results from existing omnimatte methods to provide examples of cause-and-effect relationships in real videos. (b) The Tripod dataset consists of videos captured with stationary cameras, providing pseudo-examples of more complex real-world scenarios, such as water effects and dynamic backgrounds. (c) We use Kubric [18] to synthesize multi-object scenes with diverse reflections and shadows. (d) We segment objects from real videos and paste them onto target real videos [57] to strengthen the model's inpainting capabilities and background preservation. + +ing scene elements. Moreover, we observe that many real-world scenarios exhibit multiple instances of the same object type in a scene, such as dogs, pedestrians, or vehicles. Therefore, we generate scenes with duplicated objects to train the model to handle multiple similar objects. We also insert reflective surfaces in the scenes to simulate water and glass reflections. + +Object-Paste. We synthesize 1024 video tuples from real videos in the YouTube-VOS Dataset [57], using SegmentAnything2 [41] to crop objects from a random video and paste them onto a target video. The training input and target are the composited video and original video, respectively. Training on this data strengthens the model's inpainting and background preservation abilities. + +The text prompts of the training data are captioned by BLIP-2 [27], describing the target video that the object-effect-removal model should learn to generate. We augment the dataset with spatial horizontal flipping, temporal flipping, and random cropping to a $128 \times 128$ px resolution. We balance the four data categories with different ratios, using approximately equal proportions (50%) of real and synthesized data. Please refer to the Supplementary Material for the training details. + +# 3.5. Omnimatte Optimization + +As described in Sec. 3.2, we obtain solo videos $\{\mathcal{I}_i\}_{i=1}^N$ and the background $\mathcal{I}_{\mathrm{bg}}$ from an $N$ -object video input. Given each pair of $(\mathcal{I}_i, \mathcal{I}_{\mathrm{bg}})$ , the goal is to reconstruct an omn + +imatte layer, $\mathcal{O}_i$ , such that its composition with the background, $\mathcal{I}_{\mathrm{bg}}$ , matches the solo video, $\mathcal{I}_i$ : + +$$ +\mathcal {I} _ {i} \approx C o m p \left(\mathcal {I} _ {\mathrm {b g}}, \mathcal {I} _ {i, \mathrm {f g}}, \alpha_ {i}\right) = \alpha_ {i} \mathcal {I} _ {i, \mathrm {f g}} + (1 - \alpha_ {i}) \mathcal {I} _ {\mathrm {b g}}, \tag {2} +$$ + +where $\mathcal{I}_{i,\mathrm{fg}}$ and $\alpha_{i}$ are the RGB and alpha channels of the omnimatte $\mathcal{O}_i$ . + +Variables. Unlike previous methods [19, 29, 36, 47] that jointly optimize the background scene model with the foreground omnimatte, our method first produces a clean background video which is kept constant during the optimization. Therefore, the variables to optimize are the foreground RGB $\mathcal{I}_{i,\mathrm{fg}}$ and alpha $\alpha_{i}$ . Following existing methods [29, 36, 47], we use a U-Net to generate smooth alphas from the inputs $\mathcal{I}_i$ and error map $\Delta_i = |\mathcal{I}_i - \mathcal{I}_{\mathrm{bg}}|$ . We directly optimize the pixel values of the RGB $\mathcal{I}_{i,\mathrm{fg}}$ for efficiency, with a sigmoid to constrain the range to [0, 1]. + +Loss function. Similar to [29, 36, 47], we use a reconstruction loss, $\mathcal{L}_{\mathrm{recon}}$ (the difference between the target $\mathcal{I}$ and the composited video) to drive the optimization: + +$$ +\mathcal {L} _ {\text {r e c o n}} = \left\| \mathcal {I} _ {i} - \operatorname {C o m p} \left(\mathcal {I} _ {\mathrm {b g}}, \mathcal {I} _ {i, \mathrm {f g}}, \alpha_ {i}\right) \right\| _ {2}. \tag {3} +$$ + +To prevent the foreground omnimatte from being overly sensitive to reconstruction error, we add $L_{0}$ and $L_{1}$ -sparsity regularization on the alpha map: + +$$ +\mathcal {L} _ {\text {s p a r s i t y}} = \beta_ {1} \| \alpha_ {i} \| _ {1} + \beta_ {0} \Phi_ {0} (\alpha_ {i}), \tag {4} +$$ + +where $\Phi_0$ denotes an approximate $L_{0}$ proposed in [36], and $\beta_{1}$ and $\beta_0$ are the hyper-parameters balancing the loss. + +To optimize the alpha network from scratch, a mask supervision loss, $\mathcal{L}_{\mathrm{mask}} = \| m_i - \alpha_i\| _2$ , is used to guide the learning of alpha $\alpha_{i}$ from the input object mask $m_{i}$ . The loss is gradually reduced over the optimization iterations. The final omnimatte $\mathcal{O}_i$ is obtained by minimizing the total loss of $\mathcal{L}_{\mathrm{recon}} + \lambda_{\mathrm{sparsity}}\mathcal{L}_{\mathrm{sparsity}} + \lambda_{\mathrm{mask}}\mathcal{L}_{\mathrm{mask}}$ . + +Upsampling and Detail Transfer. The Casper model has a resolution of $128\mathrm{px}$ (e.g., $224\times 128$ ) inherited from the Lumiere base stage. Lumiere's SSR stage [7] is used to upsample the base model outputs to the target resolution $640\times 384$ . The RGBA omnimatte layers $\mathcal{O}_i$ are first optimized at the base resolution, then upsampled and optimized further at the target resolution. Finally, a detail transfer step [35, 36, 47] is applied to fully opaque regions. Please see SM for further details. + +# 4. Results + +We compare our method with SOTA omnimatte methods [29, 47]. We also compare Casper with video inpainting models [7, 66] and ObjectDrop [53] on object-removal tasks. Note that ObjectDrop is an image-based model, and thus, it processes each video frame independently. We obtain the results of [47, 53] from the respective authors. + +![](images/01d8a516f4503a3014122fb294ae95886b85779a0791e8caed9292bda5139c24.jpg) +Figure 7. Qualitative comparisons with omnimatte methods. For each example, we show the background layer and foreground omnimatte generated by different methods in the top and bottom rows, respectively. Existing methods [29, 36, 47] struggle with relatively stationary foregrounds ("boat"), and struggle to complete heavily occluded objects ("horses"). While [29, 47] can handle scenes with parallax ("horses"), the background layer appears blurry due to imperfect camera pose and depth estimation. + +# 4.1. Qualitative Results + +We compare omnimatte methods in Fig. 7. In "boat", existing approaches fail to separate the boat's wake from the background layer, while our method correctly places it in the boat's layer. For "horses", Omnimatte3D [47] and OmnimatteRF [29] produce blurry background layers because their 3D-aware background representations are sensitive to camera pose estimation quality. Furthermore, none of the existing Omnimatte methods can disocclude the horse in the last row. In contrast, our method does not require camera pose information and can inpaint heavily occluded objects. + +Fig. 8 compares our Casper model with existing methods for object removal. Video inpainting models [7, 66] fail to remove soft shadows and reflections outside the input masks. ObjectDrop [53] can remove shadows in "cartoon" and "parkour", but it processes frames independently and inpaints regions without global context. This leads to inconsistent hallucinations, such as a missing car in "parkour", and inconsistent background trees in "car-puddle". Our model effectively removes soft shadows ("cartoon"), handles shadows cast on complex structures ("parkour"), and excels at multi-object removal ("penguins"). We encourage readers to view SM for video comparisons. + +![](images/a5517e96951fc2397711498a86f6ffddbd4b7acda25cacabc914a08ed006cfe6.jpg) +Figure 8. Visual comparison on object removal. We compare our removal model with state-of-the-art video inpainting models [7, 66] and per-frame ObjectDrop [53]. Inpainting models fail to remove effects that extend beyond the provided mask boundaries. ObjectDrop processes video frames independently, lacking temporal information to preserve backgrounds and produce temporally coherent results. We encourage readers to view the supplementary material for video comparisons. + +Table 1. Quantitative comparison. Following the benchmark established in OmnimatteRF [29], we evaluate the removal quality on background videos of 10 synthetic scenes in two categories. Our method achieves the best overall scores in both PSNR and LPIPS metrics. We adopt the numbers of [23, 29, 36] reported in [29]. Best results are highlighted in red and second-best in yellow. Results marked as “.” indicate failures in some scenes (e.g., all-zero outputs in [47]). We present the per-scene scores in SM. + +
Scene MetricMovieKubricAverage
PSNR↑LPIPS↓PSNR↑LPIPS↓PSNR↑LPIPS↓
ObjectDrop [53]28.050.12434.220.08331.140.104
Propainter [66]27.440.11434.670.05631.060.085
Lumiere inpainting [7]26.620.14831.460.15729.040.153
Ominatte [36]21.760.23926.810.20724.290.223
LNA [23]23.100.129----
Omnimatte3D [47]------
OmnimatteRF [29]33.860.01740.910.02837.380.023
Ours32.690.03044.070.01038.380.020
+ +# 4.2. Quantitative comparison + +We adopt the evaluation protocol from OmnimatteRF [29] to assess background layer reconstruction on ten synthetic scenes. The synthetic dataset comprises 5 Movie scenes and 5 Kubric scenes generated by [55]. Each scene has a corresponding ground-truth background without foreground objects and effects. We use PSNR and LPIPS [63] as evaluation metrics. We confirm that our Kubric training data does not overlap with the Kubric scenes used in the evaluation. + +The quantitative results are presented in Table 1. Existing layer decomposition methods perform a global static scene optimization for each video. Omnimatte [36] and Layered Neural Atlas [23] utilize 2D motion models and thus struggle to handle parallax. Omnimatte3D [47] fails to construct a background scene model in two cases and struggles with stationary foreground objects in the Movie scenes. + +![](images/f8c88a9a0f83978906c09eec548ca0cdc4534469e2cf47b2abaced99bb302801.jpg) + +![](images/f79fc2e0ad5bf4bc3c6cf849b2b3e6be507c2d7f56d7ad7cd4251e090e715302.jpg) +Figure 9. Ablation study. (a) We ablate four different categories of training examples to validate their individual contributions. (b) The proposed trimask allows for greater control over defining regions to preserve or alter. Models trained with binary masks lack this flexibility and may remove objects that are intended to be kept (e.g., the umbrella). (c) Optimizing the foreground RGB of omni-mattes rather than using pixels directly from the input video results in cleaner foreground layers. Best viewed zoomed-in on a display. + +OmnimatteRF [29] applies an additional background retraining step to further improve removal results and, in some cases, can complete the inpainting regions more accurately due to the global scene model optimization. Overall, our method achieves the best performance in both metrics. We provide visual comparisons of the evaluation scenes in SM. + +# 4.3. Ablation study. + +Training data. We assess the individual contributions of each dataset category to our model's performance in Fig. 9a. + +![](images/cb772c9021d21cfeac918a72d345b5293fe4936579f22ba832fa257ba8962b7f.jpg) +Figure 10. Applications. Our omnimatte uses enable diverse video editing tasks. Please refer to SM for full video demonstrations. + +The Omnimatte data provides real-world shadow and reflection scenes. The Tripod data complements Omnimatte by providing additional real-world scenarios, including specific examples of water reflections, to better handle water effects. Our Kubric synthetic data strengthens the model's ability to handle multi-object scenes. Object-Paste, synthesized by overlaying objects onto real videos, reduces undesired background changes and improves inpainting quality. Mask condition. As shown in Fig. 9b, the proposed trimask explicitly defines the regions to be removed or preserved, thereby enabling more accurate handling of multi-object scenarios. In contrast, the model trained on binary masks is susceptible to ambiguity, potentially leading to undesired removal of objects meant to be preserved. + +Omnimatte optimization. The omnimatte reconstruction optimizes both foreground RGB and alpha channels. If the foreground RGB channel is not optimized and instead fixed as the input foreground video, the resulting omnimatte may exhibit increased background color contamination and hinder the generation of soft alpha mattes. (Fig. 9c). + +# 4.4. Applications + +As showcased in Fig. 1 and Fig. 10, our omnimatteles enable a wide range of video editing for users, such as layer insertion and replacement. Each layer can also be independently edited with different transformations, stylizations, and time offsets for motion retiming [35]. The edited layers can then be recomposed seamlessly to generate novel videos. + +# 5. Discussion and Limitations + +Our method overcomes the limitations of existing omnimatte approaches by incorporating a finetuned video inpainting model that performs object and effect removal. This is achieved by finetuning a pretrained inpainting model on a small training set, without modifying the architecture to generate an additional alpha channel. The RGB outputs of the video model are then used to reconstruct the RGBA omnimatte layers using an optimization step. + +The finetuned model inherits the original diffusion model's learned prior on natural videos, allowing for strong generalization to scenarios not present in the training set + +![](images/c18c82d440487b99169faebe6284488b136af0f6888f1edb902785d1e0b372ec.jpg) +Figure 11. Limitations. (a) Casper effectively removes objects and their associated shadows and reflections, while keeping shape deformation in the outputs. (b) In challenging multi-object cases, Casper may struggle to accurately separate individual effects. + +![](images/f04d70802cf5d7f1d79e9b04eda76c92770c53c22ea5eabd2f168a84a08297c0.jpg) +Figure 12. User-specified trimask. Casper may introduce undesired changes to dynamic background elements (e.g., wave details). To mitigate this, users may specify a coarse preservation region to merge with the trimasks. The zoomed-in boxes show precise detail preservation in the specified background area. + +(e.g., human hands in "lego," "cartoon"). However, this reliance on a data-driven prior can also limit the range of effects the method can handle. For example, since we did not include training data capturing physical deformations, our current model does not remove effects such as bending poles or trampolines (Fig. 11a). However, our ablation experiments (Fig. 9) indicate the model responds well to small additions to the training data, suggesting that it may be possible capture these effects by curating additional data. + +We also observed challenging multi-object cases where, despite apparently appropriate training data, our model fails to correctly remove effects (Fig. 11b). We hypothesize the model may need to be trained with additional information (e.g., instance segmentation) to disambiguate objects and their effects when multiple, very similar objects are present. + +Finally, we observe some cases where Casper will associate unrelated background effects with a foreground layer, such as the waves in Fig. 12. Our system allows the user to modify the trimask to preserve background areas in simple cases (Fig. 12, mid). In future work, such lightweight user input can be used to enlarge and improve the training set. + +We present a new, generative approach to video layer decomposition. The current method already outperforms previous methods based on more limited priors, and will continue to improve as more ground-truth layered video data becomes available and generative video priors gain strength. + +Acknowledgments. We would like to thank Charles Herrmann, Daniel Geng, Junhwa Hur, Hadi Alzayer, Deqing Sun, Daniel Vlasic, Miki Rubinstein, and Bill Freeman for their insightful discussions and generous support. We sincerely appreciate Ray Li, Scott Wisdom, Andrei Kapishnikov, Matthew Grimes, AJ Maschinot, and Shu-Jung Han for their invaluable help in filming testing videos and contributing creative editing ideas. + +# References + +[1] Edward H Adelson. Layered representations for vision and video. In Proceedings IEEE Workshop on Representation of Visual Scenes (In Conjunction with ICCV'95), 1995. 3 +[2] Jean-Baptiste Alayrac, Joao Carreira, Relja Arandjelovic, and Andrew Zisserman. Controllable attention for structured layered video decomposition. In ICCV, 2019. 3 +[3] Jean-Baptiste Alayrac, Joao Carreira, and Andrew Zisserman. The visual centrifuge: Model-free layered video representations. 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with bokeh blur parameter \*\* +2 + +![](images/f1ceb54159d69dcc2f0e71e273e710cc09fc1012495dc619ac38df9f7fd6a3da.jpg) +8 + +![](images/e96f9e5e3a21ca46ad4f7d285e81fe41c74ae14b3bc3f16c10d4dc8266f9dfb9.jpg) +17 + +![](images/ed944be769d626852fa2bd2729905b13cc1db9dd29f1ba24963ba1bbd6c99dd1.jpg) +2 + +![](images/81a76f0698e9dfca86299e70ef021254d999876dfa5c204e2b44cf4a1c150a10.jpg) +Ours +8 + +![](images/cffa6502737d52190969af61dd8aa3ec5e443b272ac46ee63612cfd7c700d2b7.jpg) +17 + +![](images/441501752ff8c2a672ee1fbb6688924b7d0ae3efe8d18e7ca0bce6dd7c47eb5a.jpg) +(b) Focal length +A quiet mountain trail +with rocks and pine +trees lining the path; +with ** lens +24mm + +![](images/126e7d30508790501a72a8f1f1c4bf61b1bd5e9ba26f0b5027fccc9442e59e28.jpg) +44mm + +![](images/d3fc60281ddffe25a782017a804ca9c47281fb18f75a16ad63ad8476c8aae31b.jpg) +70mm + +![](images/58b11f79dbff708be398e080f35edf882b7e657330561054ffc68ad33c678da0.jpg) +24mm + +![](images/c1c56ba26f8fa5bae7008460e1c4fade0324105d8cea1b6caa6af7fb58147362.jpg) +44mm + +![](images/babc19290cadd8f84db7e3e9b71218a321feb290de1ef32df6ae1bab4318ab4a.jpg) +70mm + +![](images/124c94d15b6916bfaaf247d6c162b8db4549ce40cb6e7ebe54749cf0b737a29b.jpg) +(c) Shutter speed A brown and orange leather handbag with a paw print on it sits: with shutter speed \*\* +0.2 second + +![](images/ffd29bb02cce1d46906614eaaf48b00abbab4564629c6dcf66767cec636ba39d.jpg) +0.5 second + +![](images/47f6025da3543adca4f036adc9a6679a607d28c72900e1122d24c559270803ef.jpg) +0.9 second + +![](images/b5da992655350ebb4bc7817d7c6d8e5f0f86947cb38c3677192c88f4ca21960a.jpg) +0.2 second + +![](images/70b2d1df7d834182795492ddf0eeeb2209613d40edcb63d6458551fa65ed0d44.jpg) +0.5 second + +![](images/124e8ba462e7faf66aec6f0ce2e0b25329ce8a92352adfdd6b226ea7f3052696.jpg) +0.9 second + +![](images/15732b0c89b943e83ac1d66c5c82054b6d7dd46ff6c789623c3640f61701a490.jpg) +(d) Color temperature A beautiful blue sky with a mountain range in the background; with temperature \*\* +2000K +Figure 1. This paper introduces generative photography, a new paradigm for text-to-image generation that maintains a consistent base scene while modifying only the camera settings to achieve varied photographic effects. Current state-of-the-art text-to-image generation models like Stable Diffusion 3 (SD3) [3] and FLUX [1] face two major limitations: failure to accurately interpret camera-specific settings and difficulties in maintaining consistency in the base scene. This paper introduces a novel approach that addresses these issues, enabling precise camera setting control and maintaining scene consistency in generative models. + +![](images/5ddcfaf4a139059ac0a836a3e254f9a49f1e21b3891dbf008cae7ea49bec2534.jpg) +4000K + +![](images/0fd5043658c1ea61444f4cd1aa814dcfcec840849161731cc3564a94c6edf8c8.jpg) +5155K + +![](images/f06ae78ed2a0857c76caa3bfde8c9d9a9246c8b159f1a1ad7d0808dba6be0fe4.jpg) +2000K + +![](images/0ce3e2a1bafa2ae7ead464d9b74d60ff529c4570cc55d5b560efc4f41bf7aeb6.jpg) +4000K + +![](images/9e17f790aaed9a3e5010950c10565f5c1226b539fbdb0f530b216f9f011bcc76.jpg) +5155K + +# Abstract + +Image generation today can produce somewhat realistic images from text prompts. However, if one asks the generator to synthesize a specific camera setting such as creating different fields of view using a 24mm lens versus a 70mm lens, the generator will not be able to interpret and generate scene-consistent images. This limitation not only hinders the adoption of generative tools in professional photography but also highlights the broader challenge of aligning data-driven models with real-world physical settings. In this paper, we introduce Generative Photography, a framework that allows controlling camera intrinsic settings during content generation. The core innovation of this work + +are the concepts of Dimensionality Lifting and Differential Camera Intrinsic Learning, enabling smooth and consistent transitions across different camera settings. Experimental results show that our method produces significantly more scene-consistent photorealistic images than state-of-the-art models such as Stable Diffusion 3 and FLUX. Our code and additional results are available at https://generative-photography.github.io/project. + +# 1. Introduction + +Since the breakthrough of probabilistic diffusion models in the early 2020's [13, 22, 48, 56], foundational vision + +models have created unprecedented opportunities for artificially generated content [1, 3, 4, 6, 16, 19, 32, 41, 46, 48–50, 69, 70]. Content generation processes that would have taken days of human labor in the past are now possible by machines in just a few seconds. Although current text-to-image models can produce perceptually realistic images, professional photographers remain skeptical, as these tools still cannot reliably replicate even basic camera effects. For example, the prompt “quiet mountain trail, $24\mathrm{mm}$ lens” and another prompt “quiet mountain trail, $70\mathrm{mm}$ lens” will have no differences in the field of view (FoV) but different rocks and trees, as illustrated in Fig. 1 (b). + +The inability of current diffusion models to accurately interpret camera settings reflects not merely limitations of scaling laws [28], but a fundamental gap between data-driven models and physical-world principles. Recent research [27] demonstrates that increasing training data and model parameters are insufficient for generation models to capture essential physics principles. To bridge this gap in photography context, we aim to teach camera physics to the models. However, teaching camera physics is not a trivial task due to the lack of training data and the fundamental problem of existing image/video generation foundation models [27]. This paper introduces a novel framework, jointly designed through data curation and network architecture, to enable Generative Photography—specifically targeting image generation with camera intrinsics controls. + +Why do Existing Generative Models Fail to Understand Camera Physics? There are two primary reasons why existing generative models fail: (1) The available training data is very limited. To train a generative photography model, we need sets of images captured under different camera settings, such as varying apertures or focal lengths. Apart from the fact that acquiring these paired images is tedious and time/manpower-consuming, there is also a lack of textual labels. Therefore, in the absence of sufficient training data, it is challenging to train or fine-tune existing visual models; (2) Even if we have the training data, it remains unclear how one can disentangle the information of scene embeddings from the camera embeddings. If we cannot disentangle these embeddings, then it will be impossible to keep the scene unchanged while altering the camera settings. This would lead to severe scene consistency problems as illustrated in Fig. 1. + +What is Generative Photography? Generative photography is an emerging approach in photography where content is generated instead of physically captured. Generative photography stresses camera-awareness. On top of an existing text-to-image generation process, we demand the model to comprehend the typical camera settings: adjusting the aperture, shutter speed, focal length, and color temperature. By adjusting these camera settings, we can generate a vari + +ety of photorealistic effects such as different bokeh effects, exposure, color, and zoom, unlocking new applications in photography. A successful generative photography method should satisfy three objectives: (1) the camera effects are realistically rendered; (2) by changing the camera settings, the content of the scene is not altered, e.g., the buildings remain the same buildings and persons remain the same persons; (3) adding camera awareness does not degrade the image quality when compared to the baseline models that do not possess this property. + +In this paper, we highlight the importance of maintaining scene consistency across varying camera settings. For example, transitioning from a "24mm lens" to a "70mm lens" should result in a smooth and consistent change in the field of view (FoV). This seamless transition between different camera intrinsics introduces the concept of a camera dimension. Analogous to spatial and temporal dimensions, generative photography is to solve consistency problem in spatial and camera dimensions. To handle this camera dimension effectively, we propose two complementary approaches: Dimensionality Lifting, transforming text-to-image generation from a purely spatial problem into a joint space-camera domain for improved camera intrinsics disentanglement and spatial consistency; and Differential Camera Infrinsics Learning, a strategy designed to explicitly capture differences in camera intrinsic settings, operating simultaneously at both data and network architecture levels to reinforce consistent scene representation. + +In summary, the contribution of this paper is two-fold: + +1. We introduce the concept of Generative Photography, a new paradigm focusing on enabling text-to-image diffusion models with precise and consistent controllability over camera intrinsic settings. +2. To support generative photography, we present two new techniques, dimensionality lifting and differential camera intrinsics learning, to allow scene-consistent camera control for realistic text-to-image generation. This framework can be used on various camera effects, producing appealing camera control with consistent scenes. + +# 2. Prior Work and Limitations + +# 2.1. Text-to-image Generation + +Diffusion models [13, 22, 48, 56] have emerged as a powerful framework in the field of generative AI, primarily due to their robustness and versatility in generating high-quality images from textual descriptions. Tutorials such as [8, 31, 37] have provided comprehensive coverage of the foundations of these diffusion models. + +Notable implementations of text-to-image generation utilizing diffusion models include DALL-E [46], Stable Diffusion [3], DreamBooth [49], IMAGEN [50], FLUX [1], and others [16, 41, 48]. DALL-E pioneered the generation of + +novel images by combining concepts, attributes, and styles derived from textual input, demonstrating an advanced capability for understanding and creatively interpreting descriptions. Stable Diffusion further enhances this by generating high-resolution images in a latent space, significantly improving both computational efficiency and output quality. + +# 2.2. Camera-Awareness + +When we think about camera-aware content generation, a fundamental question is how to control the diffusion model so that it respects the camera settings. The following three families of approaches are the most relevant ones to us: + +Camera-Awareness Via Guidance. In theory, camera awareness can be done by integrating the control signals into the generation process through guidance. Methods such as ControlNet [70], T2I-Adapter [40], and GLIGEN [34] belong to this category where they use depth maps, edge maps, semantic maps, and object-bounding boxes to guide the diffusion process. However, this guidance is mostly about the scene, not the camera. We are interested in the latter. + +Camera External Parameters. Existing work related to our work mostly focuses on controlling the camera external parameters such as its pose and trajectory [5, 10, 11, 21, 24, 26, 33, 39, 59, 65, 66]. Approaches like CameraCtrl [21] and CamCo [66] incorporate these external parameters into pre-trained generative models by leveraging an additional camera encoder network. However, these methods are limited to single-camera trajectories, leading to significant inconsistencies in content and dynamics when generating multiple videos. Collaborative video diffusion (CVD) [33] and Civia [65] improve consistency by aligning features across multi-view video generation branches. + +Camera Intrinsic Settings. When it comes to intrinsic camera settings, there is very limited work except for some basic zoom-in/out effects [2, 6, 15, 19, 57]. One of the main challenges is that most datasets used for training vision models often lack comprehensive camera settings. Even when some camera metadata is included, there is typically an absence of multi-setting metadata for the same scene [15]. This lack of parameter variation means that the available metadata cannot fully capture the true physical meaning of these settings. For instance, for a given scene, having only a single $50\mathrm{mm}$ f/8 setting makes it difficult to infer how the depth of field (DoF) and field of view (FoV) would change under a $16\mathrm{mm}$ f/4 setting for the same scene. + +# 2.3. Information Disentanglement + +Beyond the previous related works, a major difficulty in camera-aware content generation is the user-computer interface. In today's text-to-image generation, a user needs to modify the prompt to control the image attributes. However, once the camera prompt is modified, the overall image + +structure can be severely distorted due to the sensitivity of outputs to the prompt-seed combination [17, 30, 49, 63]. This happens because we are not able to disentangle the camera embeddings and scene embeddings. + +GAN-based Disentanglement. Information disentanglement can be done in many ways. In the pre-diffusion era, generative adversarial networks (GANs) [18] have shown potential for highly disentangled control in their latent spaces, enabling precise manipulation of facial attributes without affecting others [29, 51-53, 58]. For example, StyleGAN [29, 58] allows detailed control over image properties through linear editing of its latent space, isolating specific attributes while preserving others. + +Diffusion-based Disentanglement. There is increasing evidence that diffusion models can perform some degree of latent space information disentanglement. For example, Wu et al. [63] did a case study about Stable Diffusion [3] and consequently proposed to optimize the text embeddings during inference to maintain image coherence. There are new mechanisms to explicitly enforce information disentanglement, e.g., Wu et al. [62] used contrastive guidance by sending two prompts to disentangle the information, and Rohit et al. [17] minimized interference by identifying a low-rank direction. The general problem of these approaches is that they are mostly tailored to facial attributes. When applying them to generic image content, they struggle with shapes and colors. Additionally, they primarily focus on optimizing the text embeddings during inference without considering any joint strategies to decouple data and models. + +In this paper, we introduce the task of generative photography. We propose a framework consisting of two concepts: dimensionality lifting and differential camera intrinsics learning, which disentangle camera and scene embeddings. Our framework enables precise control over various camera settings, such as shutter speed, aperture, focal length, and color temperature, while maintaining scene consistency, allowing for exposure, bokeh rendering, zoom, and color control in generated images. These aspects will be detailed in the proposed methods section. + +# 3. Proposed Methods + +# 3.1. Dimensionality Lifting + +A critical question in generative photography is how to disentangle the camera embedding from the scene embedding. Without this disentanglement, it becomes challenging to maintain consistency in the scene. In this paper, we first propose the idea of dimensionality lifting to achieve this. Figure 2 (a) illustrates the low consistency between generated images in existing text-to-image (T2I) generation processes, where only part of the prompt is modified (in this case, the camera focal length). This paper addresses this issue within a higher-dimensional text-to-video (T2V) + +![](images/aacc8fe85fd71d17f6995e5ee13f563cb4c92e6f6e2159e569f838ea12f6f9e1.jpg) +(a) Existing Pipelines + +![](images/ab6ee46e938898da3ecaaada12b9ee9bc75a5c722f3af07ad30c53922396feec.jpg) +(b) Our Proposed Framework +Figure 2. (a) Existing text-to-image (T2I) models struggle to perceive physical camera settings and maintain consistency across multiple settings, even when the random seed is fixed. (b) We solve this problem by lifting camera-controlled text-to-image (T2I) generation into text-to-video (T2V) generation, thereby decoupling scene description from camera settings and achieving better scene consistency. + +paradigm. As shown in Fig. 2 (b), we lift multi-camera setting image generation with video generation. Within the T2V framework, we decouple the invariant scene description from camera settings: the scene description is used to establish a foundational scene, while the camera settings provide extra constraints for each corresponding frame. + +There are several reasons why dimensionality lifting could solve our problem: (i) Variations in camera settings are important factors to consider; thus, we should elevate our base problem from a space-only problem to a space-camera joint problem. (ii) This approach allows for a modular separation between scene elements and camera settings, enabling more flexible and accurate manipulations of camera-related aspects without impacting the underlying scene structure. (iii) Video generation models, due to their spatiotemporal attention design, are inherently better at maintaining consistency across frames [6, 23, 55, 64]. (iv) We can leverage the powerful generative capabilities of pre-trained T2V models to ensure high-quality image generation. + +# 3.2. Differential Camera Infrinsics Learning + +Another challenge in generative photography is teaching the model to comprehend the physical settings of a camera. To address this, we introduce a differential camera intrinsics learning approach comprising two key components: differential data and a differential camera encoder. On the data side, we construct a differential dataset containing image-text pairs of a fixed scene captured under varying camera settings. At the network level, we incorporate the differences between adjacent camera settings to enhance the model's understanding of their effects. + +# 3.2.1 Differential Data + +The differential dataset provides data-driven support for camera settings understanding in generative tasks. + +What is Differential Data and Why is it Useful? Differential data involves creating pairs or sets of images that highlight specific differences, such as varying camera set + +tings, while keeping other elements constant. Differential data is advantageous as it enables models to focus on and learn from the differences between images, rather than being overwhelmed by the vast diversity of real-world data. Here is a simple example of differential data. + +Example. If the images vary by color temperature, their corresponding textual labels are: + +Invariant scene description: "A squirrel eating a leaf from a tree." + +Color temperature for each frame: $< 9933K$ ; 3626K; 6302K; 4039K; 2400K> + +How is the Differential Data Constructed? We propose to construct a differential dataset in three steps following the outline shown in Fig. 3. + +![](images/da6f6c173f1d11d945a498c76e5fd8c20d4ebc66f79d76d11556a3612e3e8105.jpg) +Figure 3. The pipeline of building differential data. + +(i). Vision Language Model Captioning for Base Images: To ensure that the data we generate can be used for training, we first need to collect base images and obtain their textual labels. The base images we select must be of high quality and meet specific requirements for camera generation tasks. For example, for shutter speed control, the base images should have a wide dynamic range and appropriate exposure; for color temperature control, all base images should lean towards a neutral color temperature; for bokeh rendering tasks, the base images should be all-in-focus images; and for focal length control, the base images need to have sufficiently high resolution. We employ a vision language model + +(VLM) LLaVA [36] to generate scene captions for a base image, which we use as the invariant scene descriptions for this differential set. + +(ii). Random Sampling on Continuous Camera Space: Camera settings are typically treated as continuous variables, such as focal length, shutter speed, and color temperature. We argue that each value on the camera setting scale is crucial, as it embodies a deeper physical understanding rather than merely representing a few discrete values. Continuous sampling supports continuous-scale training [7, 9, 61], which enhances the model's ability to perform across any value on the scale. Therefore, when constructing differential data, we perform random sampling across the continuous camera setting scale to gather multiple values. Specifically, as shown in Fig. 3, we assume an invariant scene description on a continuous camera setting scale (here exemplified by color temperature, with the vertical axis representing color temperature). For each instance, we sample several (5 here) points along the horizontal axis and use this collection of points as a set to describe camera setting variations. We did not order the randomly collected data points in each set, ensuring that our network does not merely fit a specific directional pattern (such as simple zoom in/out for focal length) but instead learns the numerical values themselves. For the camera's color temperature, we collect a range from 2,000 to 10,000 Kelvin. For shutter speed, we re-normalize it to a scale of 0.1 to 1.0 (where larger values correspond to brighter images). For focal length, we sample values between $24\mathrm{mm}$ and $70\mathrm{mm}$ . Regarding bokeh rendering, we sample blur parameter values from 1 to 30, with larger values corresponding to stronger blur effects. + +(iii). Physically-based Simulation: In the context of physically-based simulation, after obtaining the randomly sampled camera settings, we render the corresponding frames based on physical simulation for the base image. + +- Bokeh rendering [43, 44, 54]: We first extract the base image's depth map using a depth estimation model Depth Anything [67, 68] and convert it to a disparity map, which, together with the base image and the sampled blur parameter, is input to the bokeh rendering module [43]. During this process, the refocused disparity remains fixed at the foreground depth, ensuring the foreground subject remains sharp while only adjusting the background blur. +- Focal length: We draw on Level-of-Detail methods [38, 60]; specifically, for a given high-resolution base image, we calculate the field of view (FoV) ratio [47] corresponding to the sampled focal length relative to the original focal length (thus the sampled focal length must exceed the base focal length). Based on this ratio, we center-crop the corresponding region from the base image and subsequently resize all images captured at different focal lengths to the same resolution. +- Shutter speed: We obtain images at different exposure + +![](images/7f62d0ce81bf96985e021211187cd44e537d8bfd0d58395798b8d56159c17bd5.jpg) +Figure 4. The overall architecture of differential camera encoder. + +levels by adjusting the captured image irradiance and converting it back to RGB images using a simulated image signal processor (ISP) [35]. + +- Color temperature: We adjust the RGB channel ratios according to the relationship between blackbody radiation and color temperature using empirical approximation [12] to fit various color temperatures. + +Through the aforementioned steps, we obtain multiple frames corresponding to variations in camera settings, along with the associated invariant scene description and camera settings. For further details, please refer to the appendix. + +# 3.2.2 Differential Camera Encoder + +As shown in Fig 2 (b), after dimensionality lifting, we use the scene description as the primary input to the T2V model to represent the base scene, with the camera settings as additional conditions. These settings are fed into the Differential Camera Encoder, which injects them into the foundation models to control the camera effects for each frame. In the differential camera encoder, we enhance the network's ability to understand and generate camera settings by embedding camera settings and providing additional differential information. + +As illustrated in Fig. 4, for each frame's camera setting, we first create a coarse embedding, which incorporates a physical prior at the multi-channel pixel level (details in Appendix), similar to our physically-based simulation approach. Additionally, we capture inter-frame differences among camera settings as an auxiliary input to introduce finer-grained semantic difference information. Specifically, we utilize a frozen CLIP text encoder [45] to generate camera features for each frame and compute the feature differences between adjacent values of camera settings. + +We then concatenate the coarse embedding with these differential features and feed them into an embedding encoder specifically designed for videos, similar to the T2I-Adaptor [40]. The embedding encoder and the T2V foundation encoder are structurally similar, which facilitates the integration of the multi-level features obtained from the embedding encoder into the foundation models. Following recommendations from CameraCtrl [21], we avoid using ControlNet + +[70] to mitigate information leakage issues. + +We propose that the Differential Camera Encoder enhances the model's ability to differentiate camera settings by focusing on comparative effects between them. This approach moves beyond a solely data-driven paradigm, significantly reducing the training data requirements and computational costs, while providing the network with more robust and precise control capabilities. + +# 4. Experiments + +In this section, we evaluate the application of our proposed framework in generative photography. Section 4.1 presents implementation details, Section 4.2 compares our framework with other potential methods, and Section 4.3 discusses the results of ablation studies. + +# 4.1. Implementation Details + +Datasets. As mentioned in Sub-section 3.2.1, we need high-quality base images with task-related features to simulate camera effects. For the exposure and white balance conditioning tasks, our base images are sourced from our own photography as well as public image datasets [42, 72]. For the bokeh rendering task, we collected all-in-focus base images from our own photography and [14, 20, 73], ensuring they contained a well-defined foreground subject with a distinguishable background. For the focal length task, our base images were sourced from our own photography and [14, 72], with all images captured using a full-frame camera equipped with a $24\mathrm{mm}$ lens. The base images for focal task have a minimum resolution of 3,000 on the shorter side to ensure high quality and detailed high-frequency information, even after partial central cropping. + +Each task includes 1,000 images with diverse scenes and varied shooting conditions. Note that these datasets are scalable, though we found 1,000 images sufficient to achieve the desired camera control effects. + +Training and Inference. In this work, we select AnimateDiff [19] as our T2V base model, reducing the generated video frames to 5 to decrease computational costs for both training and inference. During training, most parameters of AnimateDiff are kept frozen, with only the motion LoRA [25] and our differential camera encoder being finetuned/trained. We use a learning rate of 1e-4 with the Adam optimizer. The video resolution for training is set to $256 \times 384$ . For each task, we train with a batch size of 8 for 25,000 epochs, taking approximately 10 hours on an Nvidia A100 80GB GPU. + +During inference, we input a prompt along with a set of camera settings to generate multiple frames. It's worth noting that inference can also be conducted with a single camera setting by replicating this value across multiple frames, which results in a static output across frames. For bokeh rendering inference, no depth map is required. + +Metrics. Our proposed evaluation metrics primarily focus on accuracy to physical laws and scene consistency. The accuracy of generated images with respect to camera physical settings is evaluated using the Pearson correlation coefficient (CorrCoef) of trend changes between the generated images and the reference video. For scene consistency, we use frame-wise Learned Perceptual Image Patch Similarity (LPIPS) [71] to calculate the perceptual feature distance between frames generated with different camera settings. Additionally, to evaluate the impact of added camera controls on generation following, we use CLIP [45] to compute the similarity score between generated images and the text prompt. For more details on the metrics, please refer to the supplementary material. + +For each task, we chose 75 sets of camera settings for testing. These sets emphasize a wide range settings to enhance the robustness and persuasiveness of the evaluation. + +# 4.2. Comparisons with Other Methods + +To evaluate our method, we conduct comparisons against three categories of approaches: first, the state-of-the-art text-to-image generation models, Stable Diffusion 3 (SD3) [3] and FLUX [1]; second, the text-to-video generation model,AnimateDiff [19], fine-tuned on our differential dataset to assess the performance of a purely data-driven approach; and finally, CameraCtrl [21], where we adapt the model to control intrinsic camera settings instead of external ones, and train it on our dataset. Together, these baseline models form a comprehensive evaluation framework, encompassing image and video generation, external camera parameter control, and other related aspects. + +Fig. 5 demonstrates that our method preserves excellent scene consistency while realistically simulating camera effects for any given setting. Notably, in bokeh rendering, although no depth information was provided during inference, the rendered scenes appear to exhibit depth awareness, consistently keeping the foreground sharp while only the background varies according to the bokeh blur parameter. In color temperature control, our model also shows fine-grained control capabilities, producing images at 3,000K and 3,002K with only minimal differences in color temperature. From Table 1, although SD3 and FLUX demonstrate a clear advantage in prompt following, it exhibits lower consistency and accuracy between frames with different camera settings. After fine-tuning using our comparative dataset, both AnimateDiff and CameraCtrl showed obvious improvements in accuracy. Our method shows a significant advantage in both the accuracy and consistency of generated camera settings. It also performs well in prompt following, suggesting that our approach maintains the model's overall generative capabilities without significant compromise. Here, a lower LPIPS score is not always better, as variations in color temperature, exposure, focal length, and bokeh can affect frame differ + +![](images/333cdfcbb0d713231ba941c8c9995ed0f04d493978dbe60e7567ced64fa412dc.jpg) +(a) Bokeh rendering: A variety of potted plants are displayed on a window sill; with bokeh blur parameter \*\* + +![](images/fc710849be7da602423adfa13d327fd81b3a43e8fd725feb34a74deaf1a6ce58.jpg) +(b) Focal length: A large office space with a carpeted floor and white walls; with \*\* lens + +![](images/09c26b47eea863a2e6a19acf2a808b438758996c3146aea1478512d9164a0fb5.jpg) +(c) Shutter speed: A modern bathroom with a mirror and soft lighting; with shutter speed \*\* + +![](images/96f96e508f05221fdbc713f8b42028b04fe350dac24949b834e606afb7765abb.jpg) +(d) Color temperature: A cozy living room with a white sheep ottoman, a bookshelf, and a rug; with temperature \*\* +Figure 5. Visual comparisons between different generative methods. Our method is capable of generating realistic camera effects for any given camera setting scale, while maintaining high scene consistency across images corresponding to different scales. BothAnimateDiff [19] and CameraCtrl [21] have been fine-tuned on our data. We highlight the discontinuities in the scene with red arrows. + +
MethodsBokeh RenderingFocal LengthShuttle SpeedColor Temperature
Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑
Reference1.00000.05270.39741.00000.47090.38531.00000.05110.37831.00000.03980.4053
SD3 [3]0.24920.7253—0.23560.7108—0.27310.6937—0.23120.6891—
FLUX [1]0.20060.6770—0.20030.6461—0.23980.6403—0.23630.6155—
AnimateDiff [19] (w/o FT)0.29600.10050.27530.26130.12080.25320.18430.10020.26310.18340.08050.2659
AnimateDiff [19] (w/ FT)0.37140.02550.29840.25970.22880.27390.21980.09480.29360.28970.02050.2839
CameraCtrl [21] (w/o FT)0.33030.14470.28040.29130.11440.26440.18960.09860.29120.17730.09350.2753
CameraCtrl [21] (w/ FT)0.60250.11580.30170.86710.46060.28650.75260.07750.29810.58120.06510.2885
Ours0.86260.07880.30070.96950.46470.28710.92640.06950.30150.89700.04990.2910
+ +Table 1. Quantitative comparison with different generative methods. Accuracy is computed by comparing with reference videos; Consistency by frame-wise LPIPS; Prompt following by CLIP. Reference refers to the results obtained from physical simulations. $FT$ denotes fine-tuning on our differential data. We highlight the best and second-best values for each metric. + +
MethodsBokeh RenderingFocal LengthShuttle SpeedColor Temperature
Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑Accuracy CorrCoef ↑Consistency LPIPSFollowing CLIP ↑
Reference1.00000.05270.39741.00000.47090.38531.00000.05110.37831.00000.03980.4053
w/o differential0.76310.12390.29640.85940.49430.28850.88640.06980.30070.85860.06990.2904
Discrete0.67740.08540.29480.72540.41730.28330.83840.05840.29760.81400.05240.2946
Ours (3 frames)0.83550.08140.28950.92730.39210.28570.90730.06850.28730.88480.08350.2955
Ours (5 frames)0.86260.07880.30070.96950.46470.28710.92640.06950.30150.89700.04990.2980
Ours (7 frames)0.88350.07470.29880.97830.48130.29090.92940.05350.30340.90950.05810.2985
+ +Table 2. Quantitative results of ablation study. + +ences. The key metric is proximity to the reference videos. Compared to other base models, our approach still excels in prompt following, indicating that the additional camera control does not compromise generative performance. + +# 4.3. Ablation study + +Differential Camera Encoder. To assess the impact of differential network design, we removed inter-frame differences in the differential camera encoder. Table 2 (w/o differential) suggests that incorporating different information enhances the model's accuracy and consistency. + +Data Sampling Strategy. To evaluate the impact of continuous data sampling in constructing the dataset, we compared it with the discrete (uniform) sampling method using 100 data points. Table 2 (Discrete) demonstrates that continuous sampling of data points better facilitates the network's understanding of these physical values. + +Number of Frames. Our model can perform training and inference across different frame counts. To assess the potential impact of varying training frames, we trained our model using 3, 5, and 7 frames. As shown in Table 2, increasing the frame number tends to improve the model's accuracy and consistency. This also highlights a trade-off: while a higher number of camera settings offers users more options and improved performance, it also increases computational cost and processing time. + +Dataset Scaling. In Fig. 6, we present training dataset scaling experiments for shutter speed control. The results indicate that performance improves as the training data increases; however, beyond 1000 samples, the gains plateau. This suggests that our carefully designed dataset, combined + +with joint network optimization, is sufficient for understanding physical parameters and efficiently capturing fundamental principles with relatively little data. + +![](images/0b29188300cdb3277e7ad410b532de27f2c81e974dfb58d27ae206f80159b244.jpg) +Figure 6. Ablation study on dataset scaling characteristic. + +# 5. Conclusions + +Generative photography opens the door to a new paradigm in photography where the generated contents are consistent with the intrinsic camera physics. Our solution is based on two concepts: dimensionality lifting and differential camera intrinsics learning. It generates physically realistic camera effects while maintaining a high degree of scene consistency. Generative photography has the potential to reduce the post-processing burden in human-operated photography fundamentally. In addition, it offers a fresh perspective for generative models to understand the world better. + +Acknowledgements. This work is supported, in part, by the National Science Foundation under grants 2133032, 2134209, 2030570, and 2431505. + +# References + +[1] FLUX. https://github.com/black-forest-labs/flux. 1, 2, 6, 8 +[2] Creating with camera control on gen-3 alpha turbo. https://help.runwayml.com/hc/en-us/articles/34926468947347-Creating-with-Camera-Control-on-Gen-3-Alpha-Turbo.3 +[3] Stable Diffusion. https://github.com/Stability-AI/StableDiffusion. 1, 2, 3, 6, 8 +[4] Video generation models as world simulators. https://openai.com/index/video-generation-models-as-world-simulators/.2 +[5] Sherwin Bahmani, Ivan Skorokhodov, Aliaksandr Siarohin, Willi Menapace, Guocheng Qian, Michael Vasilkovsky, Hsin-Ying Lee, Chaoyang Wang, Jiaxu Zou, Andrea Tagliasacchi, David B. Lindell, and Sergey Tulyakov. 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Liu1 + +Nupur Kumari1 + +Ariel Shamir2 + +Jun-Yan Zhu + +$^{1}$ Carnegie Mellon University + +$^{2}$ Reichman University + +![](images/6cac4f342e75c3b3dd96425af39991e7c9b392457767dc4e98b61fc78f490699.jpg) + +![](images/0585796942ad9492fe0c0203b154bad08a315314aebe744cd0fbc4637fa6edfd.jpg) + +![](images/e3c177e1a70e7e1d29ca1f9e07da836030ba1e8e44ea629c407339ebc450aa89.jpg) +(b) + +![](images/3f1c59e1f396a515a2af422827fe4b65ab4d4e4514287ee68d60de85bdd65fb0.jpg) +ControlNet Input ControlNet Output $^+$ User strokes + +![](images/4511324d2a2be6159fdec2167be427ca6a25f1a8d9db1fe06722dfa8d131a8b4.jpg) + +![](images/6783688d8dd6a8025e3b3c3d64bd313eec61a8c062af8d23307384fe6e2060ee.jpg) + +![](images/555f4a3dfe572438c70202ace7cd22746df5d662f44250a6d2187dc29e6f114d.jpg) + +![](images/9c88070ee994446daebf41de3276f6e67376c825f77f9a78bcc494f526bbbc5a.jpg) +Our Output + +![](images/b01274e07430617d38f1bdeeedc6fe62ea3cf0599e9b918953712e28b7d9ab5b.jpg) + +![](images/5aaad8b8f241253adf1842545c9247ca0cfe52f93c1061d1ec4657d9fa9f60b4.jpg) + +![](images/5b08b59cc65fb5e0d157c9134315d5d5226b1b387fb59edb43408d379f4cdee4.jpg) + +![](images/5404a609144a069692078c7a94de7985652f7b6e002e2cbf3f711d388901dce3.jpg) + +![](images/96e11d0ce8291dd67b574dc5170c7555ddeeca196911b2bd66159961cc3a1147.jpg) +Figure 1. We introduce Generative Photomontage, a framework that allows users to create their desired image by composing multiple generated images. Given a stack of ControlNet-generated images using the same input condition and different seeds, users select desired regions from different images within the stack. Our method takes in the user strokes, solves for a segmentation across the stack using diffusion features, and then composites them using a new feature-space blending method. Our method offers users fine-grained control over the final image and enables various applications, such as generating unseen appearance combinations (a, c), correcting shapes and removing artifacts (b, d). + +![](images/0d2b463bfb1d2fe9720491fd72c85a8613f6bcfb15c7e24f7eac3d6f1140c696.jpg) + +![](images/e07fcef833eab609afd9d8b39092ccb7d1f5e4cd554f0885f8b517b8afd8fbbe.jpg) +(d) + +![](images/e8fde41e20b24b65babb65bd69e07a04695be65e68d384cd62442681fe011c6f.jpg) + +# Abstract + +Text-to-image models are powerful tools for image creation. However, the generation process is akin to a dice roll and makes it difficult to achieve a single image that captures everything a user wants. In this paper, we propose a framework for creating the desired image by compositing it from various parts of generated images, in essence forming a Generative Photomontage. Given a stack of images generated by ControlNet using the same input condition and different seeds, we let users select desired parts from the generated results using a brush stroke interface. We introduce a novel technique that takes in the user's brush strokes, segments the generated images using a graph-based optimization in diffusion feature space, and then composites the segmented regions via a new feature-space blending method. Our method faithfully preserves the user-selected regions while compositing them harmoniously. We demonstrate that our flexible framework can be used for many applications, including generating new appearance combinations, fixing incorrect shapes and + +artifacts, and improving prompt alignment. We show compelling results for each application and demonstrate that our method outperforms existing image blending methods and various baselines. + +# 1. Introduction + +Text-to-image models [54, 75] can generate visually compelling images from simple input conditions, such as text prompts and sketches, making them a powerful tool for image synthesis and creative exploration. + +However, these models may not achieve exactly what a user envisions, due to the ambiguity in mapping from lower-dimensional input space (e.g., text, sketch) to high-dimensional pixel space. For example, the prompt "a robot from the future" can map to any sample in a large space of robot images, that is usually sampled using different random seeds in the diffusion process. From the user's perspective, this procedure is akin to a dice roll. In particular, it is often challenging to achieve a single image that includes every- + +thing the user wants: the user may like one part of the robot from one result and another part in a different result. They may also like the background in yet a third result. + +Many works add various conditions to text-to-image models for greater user control [46, 75], such as edges and depth maps. While these approaches restrict the output space to better match the additional user inputs, the process is still akin to a dice roll (albeit with a constrained die). For example, using the same edge map and text prompt, ControlNet [75] can generate a range of outputs that differ in lighting, appearance, and backgrounds. Some results might contain desirable visual elements, while others could contain artifacts or fail to adhere closely to the input conditions. While one can create numerous variations using different random seeds (i.e., re-roll the dice), such a trial-and-error process offers limited user control and makes it challenging to achieve a completely satisfactory result. + +In this paper, we propose a different approach – we suggest the possibility of synthesizing the desired image by composing it from different parts of generated images. We refer to the final result as a Generative Photomontage, inspired by the seminal work of Interactive Digital Photomontage [1]. In our approach, users can first generate many results (roll the dice first) and then choose exactly what they want (composite across the dice rolls), which gives users fine-grained control over the final output and significantly increases the likelihood of achieving their desired result. Our key idea is to treat generated images as intermediate outputs, let users select desired parts from the generated results, and then compose the user-selected regions to form the final image. + +Our framework begins with a stack of images from ControlNet, generated by using the same input condition and different seeds, and lets users choose parts they like from different images via simple brush strokes. Our key insight is that these images share common spatial structures from the same input condition, which can be leveraged for composition. We propose a novel technique that takes in the user's brush strokes, segments the image parts in diffusion feature space, and then composites these parts during a final denoising process. Specifically, given users' sparse scribbles, we formulate a multi-label graph-based optimization in diffusion feature space, grouping regions with similar diffusion features while satisfying user inputs. We then introduce a new feature injection and mixing method to composite the segmented regions. Our method accurately preserves the user-selected regions while harmoniously blending them together. + +The advantages of using our approach are two-fold. First is the user interaction. Our approach strikes a balance between exploration and control: by treating the model's generated images as intermediate outputs and allowing users to select and composite across them, users can take advantage of the model's generative capabilities and use it as an expo + +ration tool, while also retaining fine-grained control over the final result. This is especially helpful in cases where users may not know what they want until they see it. Second is the ability to correct undesired artifacts in resulting images. With our method, users can replace undesired regions with more visually appealing regions from other images and build towards their desired result. Compared to the trial-and-error process, where users "re-roll the dice" in hopes of getting a satisfactory image, our approach combinatorially improves the chances of success: users can combine a few images, each one containing a good region. + +We show visually compelling results on various applications and user workflows, including creating new appearance combinations, correcting shape misalignment, reducing artifacts, and improving prompt alignment. Our method outperforms existing pixel-space blending methods in preserving the realism and fidelity of local regions. Our code and data will be available upon publication. We include a breadth of results and ablation experiments in supplemental materials. + +# 2. Related Work + +Text-to-image generative models aim to learn the real image distribution conditioned on textual inputs [47, 65, 79]. In recent years, we have seen rapid progress with works on different training objectives, such as diffusion [29, 34, 35, 61, 62], GANs [33, 58, 59], and autoregressive models [15, 73], as well as new architectures [18, 19, 51, 54]. However, these models may still fall short of generating what the user wants in one go and often fail to follow all instructions in the text prompt, despite recent efforts [16, 21, 43]. In this work, we aim to bridge this gap by allowing users to compose desirable regions from multiple generated images. + +Image editing. Text-to-image diffusion models have enabled various editing tasks given reference images and text-instructions [24, 28, 31, 45, 71, 72, 77]. This is usually achieved through fine-tuning the model [11, 36] or modifying the denoising process of the diffusion model [2, 13, 27, 32, 45, 48, 67]. These methods often focus on the attention mechanism in the text-to-image model, which is crucial for determining the structure and text alignment of generated images [27, 50]. While we take inspiration from these works, our tasks and methods are different. Notably, MasaCtrl [13], Cross-Image Attention [2], and StyleAligned [28] focus on high-level style transfer, where local appearances are expected to change. We focus on blending a multi-image stack and preserving local appearances for greater user control. We show that our proposed technique performs better for this new task. + +Controllable image generation. Improving controllability and adherence to text instructions is critical for using these models as a collaborative tool. As a result, many recent + +![](images/920b810e0cf1734710a0fd06315f303b3189473e1157643c4e72dc795a12e57b.jpg) +Figure 2. Overview. (a) ControlNet-generated images using the same prompt and sketch with different seeds. (b) Upon inspecting the stack, the user wishes to remove the extra rock from the first image and add in the red leaf from the third image. The user draws strokes to select desired regions from each image. Our method finds a segmentation across the stack by performing multi-label graph cut in diffusion feature space ( $K$ features). (c) The graph-cut result is then used to form composite $Q$ , $K$ , $V$ features, which are then injected into the self-attention layers. The final result is a harmonious composite of the user-selected regions. + +works increase user control in the form of input conditions, such as sketch, depth map, bounding box, segmentation map, and reference image [4, 8, 25, 37, 42, 44, 49, 53, 75, 78]. Another line of work improves the existing text conditioning [6, 16, 21], constrains internal features [5, 66], or augments it through a rich text editor [23]. However, these works aim to create a single correct image by directly constraining the output space of solutions. In contrast, we offer a complementary approach – we allow users to pick and choose exactly what they want from multiple generated images, giving them more fine-grained control without relying solely on the model to create a single perfect image in one shot. + +Image blending aims to combine multiple images in a seamless manner [12, 20, 52, 64]. Our work draws inspiration from Interactive Digital Photomontage [1], a seminal work that employs graph cut [9, 10, 39, 55] for blending multiple images given sparse user strokes. This method allows us to "capture the moment" [17] or create new visual effects. Many other works also use graph-cut optimization for textures [40] and videos [56]. Our method follows these graph-cut frameworks but performs the optimization in diffusion feature space, which captures more semantic information compared to pixel colors or edges. More recent image blending methods use generative models like GANs [70, 74] or diffusion models [3, 3, 7, 41, 57, 60, 63]. However, our method is specifically designed for compositing a spatially aligned image stack and is better at preserving user-selected regions and blending them harmoniously. We also provide additional support for multi-image segmentation with sparse user strokes. + +# 3. Method + +Our method takes in a stack of generated images and produces a final image based on sparse user strokes. In our + +image stack, images are generated through ControlNet [75], using one or more prompts (Figure 2a). The generated images share common spatial structures, as they are produced using the same input condition (e.g., edge maps or depth maps). + +Upon browsing the image stack, the user selects desired objects and regions via broad brush strokes on the images. For example, in Figure 2b, the user wishes to remove the rock at the Apple bite in the first image and add the red leaf from the third image. To do so, the user draws strokes on the base rock in the first image, the patch of grass in the second image, and the red leaf in the third image. Our algorithm takes the user input and performs a multi-label graph cut optimization in feature space to find a segmentation of image regions across the stack that minimizes seams. Finally, using a new injection scheme, our method composites the segmented regions during the denoising process (Figure 2c). The final composite image seamlessly blends the user-selected regions while faithfully preserving the local appearances. + +Below, we first give a brief overview of image space graph-cut segmentation in Section 3.1, and then introduce our feature-based multi-image segmentation (Section 3.2) and blending algorithms (Section 3.3) in more detail. + +# 3.1. Preliminaries: Segmentation with Graph Cut + +Graph cut [9, 10, 39] has been widely used in several image synthesis and analysis tasks, including texture synthesis [40], image synthesis [1], segmentation [55], and stereo [68]. + +Here, we describe multi-label graph cut in image space [1, 10]. Suppose we have an image stack of $N$ images, labeled 1 to $N$ . For each 2D pixel location $p$ in the output image $I_{o}$ , the goal is to assign an image label $i \in [1 \dots N]$ . If a pixel $I_{o}(p)$ in the output image is assigned the image label $i$ , then $I_{o}(p) = I_{i}(p)$ . The optimization seeks to find an optimal image label assignment for all output pixels such that + +a given energy cost function is minimized. We can define the energy cost function to encourage the label assignments to have desired properties, such as placing seams in less noticeable regions. An output image of size $(W,H)$ means the optimization has to solve for $W\times H$ variables, where each variable has $N$ candidate labels. To solve the optimization, researchers have adopted max-flow min-cut algorithms for binary cases $(N = 2)$ [22], or $\alpha$ -expansion for multi-label cases $(N > 2)$ [10]. + +# 3.2. Segmentation with Feature-Space Graph Cut + +Given user strokes, our goal is to find a segmentation across the generated image stack and select image regions that adhere to the user strokes while minimizing seams. To achieve this, we also employ a multi-label graph cut optimization. + +However, in contrast to prior image-space graph cut approaches [1, 10], we perform the optimization in feature space, using the key features $K \in \mathbb{R}^{w \times h \times d}$ from the self-attention layers of the diffusion model. $K$ serves as a compact, lower-resolution representation of the generated image, where $(w, h)$ are smaller than the original image resolution $(W, H)$ and $d$ is the number of hidden dimensions. Prior works show that these features capture rich appearance and semantic information of the generated image [2, 13], which makes them better candidates than raw pixel values for finding good seams. Moreover, subsequent blending in feature space gives us more natural and seamless composites than in pixel space, without additional post-processing as in Agarwala et al. [1]. See Figure 3 for comparison. + +Instead of solving for each pixel location $(W, H)$ , our optimization assigns a label $i \in [1 \dots N]$ to each spatial location $p = (x, y)$ in key features $K$ , for $x \in \{1 \dots w\}$ and $y \in \{1 \dots h\}$ . During the blending stage, we use the label assignment to create composite self-attention features, which are then injected into ControlNet [75] to form the final result (Section 3.3). + +As users generate the initial image stack, we store the query, key, and value features $Q, K, V$ of each image for all layers and time steps on disk. After the user marks desired image regions with strokes, our system performs a multilabel graph cut using the stored key features $K$ from the first encoding layer, where $(w, h) = \frac{1}{8} (W, H)$ , at the final time step, when the generated content is mostly formed. + +Energy cost. To create a good composite, we design the energy cost function to ensure that the label assignment 1) satisfies user-designated strokes and 2) picks good (unnoticeable) seams to join regions from different images. The energy function is composed of unary and pairwise costs [9, 10, 39]: + +$$ +E _ {\text {t o t a l}} (L) = \sum_ {p} E (p, L _ {p}) + \sum_ {p, q} E (p, q, L _ {p}, L _ {q}), \tag {1} +$$ + +where $p$ and $q$ are neighboring spatial locations in key fea + +![](images/9284ce5923d88493ea17b28a39710cb75ef21512b81cd21f113b4c1b2aa4e89d.jpg) +(b) + +![](images/35f3d632a289e2bb3a5e42ba34106cdd5bf9ca27a2b812ad06dc1c13f42fafe6.jpg) +Figure 3. Ours vs. Interactive Digital Photomontage [1]. (a) Pixel-space graph cut may be more sensitive to low-level changes in color, whereas our diffusion feature-based graph cut selects seams that are more aligned with semantic features. (b) Due to large variations in color across the stack, gradient-domain blending [52] may alter local appearances, such as the red leaf. + +![](images/3214d01a64d25514234cffb2ca7f9828e36f7ce51715dc6f360eac468c65b436.jpg) + +tures $K$ . $L_{p}$ and $L_{q}$ are image labels to be optimized. + +Unary term. Unary costs are the cost of assigning a label $L_{p}$ at feature location $p$ . Here, we assign a high penalty if there is a user stroke at the corresponding pixel location of $p$ , and the label is not the image that the user has designated: + +$$ +E (p, L _ {p}) = \left\{ \begin{array}{l l} C & \text {i f} S (p, i) = 1 \text {a n d} L _ {p} \neq i \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {2} +$$ + +where $S(p, i)$ is an indicator function of whether there is a user stroke at the corresponding pixel location of $p$ in image $i$ , and $C$ is a large constant. We use $C = 10^6$ in our results. + +Pairwise term. Pairwise costs are the cost of assigning neighboring feature locations a pair of labels. Because we want seams to be less noticeable, we encourage seams to fall on edges (lower cost), where the neighboring features are significantly different: + +$$ +E (p, q, L _ {p}, L _ {q}) = \left\{ \begin{array}{l l} \sum_ {i = 1} ^ {N} \lambda e ^ {- \frac {\left| f _ {i} (p) - f _ {i} (q) \right|}{2 \sigma}} & \text {i f} L _ {p} \neq L _ {q} \\ 0 & \text {o t h e r w i s e ,} \end{array} \right. \tag {3} +$$ + +where $f_{i}(p)$ is a feature vector derived from the key features $K$ of image $i$ at location $p$ . To capture the most important features, $f_{i}(p)$ consists of the top-10 PCA components of $K$ at location $p$ , computed across hidden dimensions and heads. + +The cost is low if the features of $p$ and $q$ are dissimilar for all images within the stack; in other words, we encourage seams where $p$ and $q$ straddle an edge in all the images. $\sigma$ controls how quickly the penalty falls off as feature distance increases, and $\lambda$ is a constant scale for the cost range. We use $\lambda = 100$ and $\sigma = 10$ in all our results. + +Discussion. While it is possible to segment each image individually using off-the-shelf methods (e.g., SAM [38]), it often requires extra user intervention to resolve conflicts where objects overlap and to maintain coverage. Instead, our multi-label graph cut optimization can automatically account for all images within the stack, assigning a unique label to each location. + +# 3.3. Composition with Self-Attention Feature Injection + +The above optimization gives us an image label assignment per feature location for the output image. We use this assignment to make composite features $Q^{\mathrm{comp}}$ , $K^{\mathrm{comp}}$ and $V^{\mathrm{comp}}$ from the respective features $Q$ , $K$ , $V$ of the image stack, for each self-attention layer in ControlNet. We then inject these composite features $Q^{\mathrm{comp}}$ , $K^{\mathrm{comp}}$ and $V^{\mathrm{comp}}$ into ControlNet to form the final result. + +When users input strokes, they designate one image within the stack as the base image (usually the one whose background region is selected). During the blending stage, we use the seed and prompt of this base image when injecting the composite features. + +Specifically, we resize the label assignment map $L$ into the respective sizes of each self-attention layer $l$ . Then, we make composite features $Q^{\mathrm{comp}}$ , $K^{\mathrm{comp}}$ and $V^{\mathrm{comp}}$ as follows: + +$$ +Q _ {l} ^ {\text {c o m p}} = M _ {l} ^ {B} \odot Q _ {l} ^ {\text {m o d e l}} + \sum_ {i \neq B} M _ {l} ^ {i} \odot Q _ {l} ^ {i}, \tag {4} +$$ + +$$ +K _ {l} ^ {\text {c o m p}} = \sum_ {i} M _ {l} ^ {i} \odot K _ {l} ^ {i}, \tag {5} +$$ + +$$ +V _ {l} ^ {\text {c o m p}} = \sum_ {i} M _ {l} ^ {i} \odot V _ {l} ^ {i}, \tag {6} +$$ + +where $M_{l}^{i}$ is the binary mask of feature locations with the label assignment $i$ , resized to layer $l$ . $M^{B}$ represents the mask of the base image, where $B$ is the base image index. $Q_{l}^{i}$ are the query features $Q$ from image $i$ at layer $l$ (stored during initial generation), and similarly for $K_{l}^{i}$ and $V_{l}^{i}$ . $Q^{\mathrm{model}}$ are the query features generated from the model during the blending stage, which are different from those during the initial generation. These composite features are injected into the U-Net's self-attention maps for all layers and time steps. + +Note that we inject the initially generated self-attention features for all images except for $Q^B$ , the query features of the base image. If we inject the initial $Q^B$ features, we often observe suboptimal blending at the seams. As noted in previous literature [2, 13], $Q$ influences the image structure, while $K$ and $V$ influence the appearance. Hence, injecting $Q^B$ (and thus completely overwriting the $Q$ features) eliminates the opportunity for the model to adapt the image structure near the seams. Allowing $Q$ within the mask $M^B$ to change over time allows the model to adapt to the different graph-cut regions when blending (Figure 4a). It also adjusts the low-resolution graph cut boundaries to align with semantic features in high-resolution pixel space (Figure 4b). + +# 4. Results + +By supporting the ability to combine generated images, our method allows users to achieve a wider range of results with more flexibility and control. Here, we highlight some use + +![](images/b72d4bb932e78448d3cd3ec7b7bde709dbda5e1fafa071ad587d3104e0dff26d.jpg) +Figure 4. Using $Q^B$ vs. $Q^{\mathrm{model}}$ . $Q^B$ : query features of the base image from initial generation. $Q^{\mathrm{model}}$ : query features generated from the model during the blending stage. Leftmost column: visualization of diffusion-feature graph cut results, resized to image dimensions and combined in image space. (a) Injecting $Q^B$ does not leave room for the model to adapt its image structure near seams, causing the shadow from the input image to remain. (b) Injecting $Q^B$ causes the image to strictly adhere to low-resolution graph cut boundaries, whereas using $Q^{\mathrm{model}}$ adjusts the boundaries to align with semantic features in high-resolution image space. + +cases and show compelling results for each application. Due to space constraints, we refer readers to supplemental materials for additional results. We created the results using various pre-trained ControlNet models [75] with Stable Diffusion 1.5, such as canny edge, scribble map, Openpose [14], and depth map. + +Appearance Mixing. First, we show applications in creative and artistic design, where users refine images based on subjective preference. This is useful in cases where the user may not realize what they want until they see it (e.g., creative exploration). For example, users may use our method for exploring architectural designs, by combining the roofs, windows, and doors from different images (Figure 1c), or for creating fashion designs, by mixing different features of shoes (Figure 5b). Additionally, users can composite different components to create something new. For example, we can combine the body, ear, and arm of a robot to form a new robot (Figure 1a). This strategy can also be applied to other subjects, e.g., to combine new colors in a bird's feathers (Figure 5a). + +Shape and Artifacts Correction. While users can provide a sketch to guide ControlNet's output, ControlNet may fail to adhere to the user's input condition, especially when asked to generate objects with uncommon shapes. In such cases, our method can be used to "correct" object shapes and scene layouts, given a replaceable image patch within the stack. + +For example, suppose the user wishes to create an Apple-logo-shaped rock and prompts ControlNet with "A rock on grass" alongside an Apple-logo sketch. Since Apple-logoshaped rocks are not commonly seen in real life (and thus out-of-training distribution), the model fails to produce the desired image. Figure 2 shows an additional rock piece covering the apple bite. To correct it, the user can use our framework to replace it with a patch of grass from another image in the stack (Figure 2b). Similarly, users can correct Control- + +![](images/551d633a8bcf0b543531ae6aaa1a05b25152319461d4bf7bfd6fd3b83d8b8a56.jpg) +Figure 5. Appearance Mixing and Shape Correction. Our method can be used to mix appearances for creative exploration and design (a, b). Our method can also fix incorrect shapes and artifacts from ControlNet's outputs (c, d), which often occur for uncommon input shapes. + +![](images/23ee99359c7f90c60d21ea6b2e8b89dc0e1d82d08f7e557f4c27690bf5a3aff5.jpg) +Figure 6. Prompt Alignment. Our method can be used to increase alignment to long, complicated prompts. (a) Example where vanilla ControlNet's outputs do not adhere to the prompt. (b) With Generative Photomontage, users can create the desired image by combining the outputs from shorter, simpler prompts. + +![](images/ae4a62f3044259ab6b5e3ab54eb23b67be63969fc12840f565b861b16e9ef346.jpg) + +Net's output to create waffles in the shape of famous architectural buildings (Figure 5c), which is difficult to achieve with ControlNet alone due to the rare object-shape combination. Finally, we show other correction examples, such as correcting a dancer's pose (Figure 5d), or replacing an unrealistic-looking dog with a different one (Figure 1d). + +Prompt Alignment. In addition, our method can be used to increase prompt alignment in cases where the generated output does not accurately follow the input prompt. For example, text-to-image with ControlNet can often fail to follow all aspects of a long complicated prompt, such as "A red fairy, a green fairy, and a blue fairy sitting from left to right in a brown boat" (Figure 6a). Using our method, users can create the desired image by breaking it up into simpler prompts and selectively combining the outputs (Figure 6b). Since our results depend on the availability of at least one "correct" candidate per region within the generated stack, we encourage our method to be used in conjunction with + +existing methods [16, 21] for greater accuracy and control. + +# 5. Evaluation + +For a comprehensive evaluation, we created 20 test examples, spanning the use cases in Section 4. Below, we compare our method against several baselines. We include the full list of test examples, additional details, and ablations in the supplemental materials. + +Baselines. We select baselines that perform blending in pixel space: Interactive Digital Photomontage (IDP) [1]; noise space: Blended Latent Diffusion (BLD) [3]; and attention space: MasaCtrl with ControlNet [13]. We also compare with CollageDiffusion [57], Cross-Domain Compositing (CDC) [26], GP-GAN [70], and Deep Image Blending [74]. In addition, we compare with a modified version of BLD with greater noise overlap, inspired by MultiDiffusion [7]. Please see supp. material for implementation details. When running comparisons, we use user strokes as input for + +![](images/c16041f282e3c20c3e3f9d1df878504cddcdd0d5d7bfeed0db9d805a5ac1160a.jpg) +Figure 7. Qualitative Comparison. Leftmost column: Image regions to blend (output of graph-cut optimization). Graph-cut in diffusion feature space is visualized on the left, and the image-space composite of that graph-cut is visualized on the right. Interactive Digital Photomontage [1]: its pixel-space graph-cut may cause seams to fall on undesired edges (see Figure 3 also), and their gradient-domain blending often fails to preserve color. Blended Latent Diffusion [3] and MasaCtrl+ControlNet [13] may lead to color and structure changes. + +
Masked LPIPS ↓Masked SSIM ↑PSNR ↑Seam Gradient Score min, avg, max 0.255, 0.340, 0.425
Ours0.1230.81522.460.339
IDP [1]0.1040.88820.130.306
BLD [3]0.2220.77220.270.393
BLD+Multi [7]0.2240.76619.790.318
MasaCtrl+CtrlNet [13]0.2300.68018.340.341
Deep Img Blending [74]0.2700.76617.330.313
GP-GAN [70]0.2260.82017.450.220*
CDC [26]0.3760.58420.010.456*
CollageDiffusion [57]0.2430.60520.570.559*
+ +Table 1. Quantitative Results. To measure fidelity of local image regions, we report masked LPIPS and SSIM and PSNR. To measure blending quality of seams, we compute a seam gradient (SG) score, which is the mean gradient magnitude along seams that join different image regions. For reference, we also compute the minimum, average, and maximum SG scores of each image stack and report their averages on the top. Methods with SG scores that fall outside of this range (*) exhibit significant seam artifacts. + +IDP and our graph cut masks as input for the other baselines. + +Quantitative Metrics. To measure local appearance fidelity, we computed masked LPIPS [76], masked SSIM [69], and PSNR [30]. For LPIPS and SSIM, we use the masks from our feature-based graph cut, resized to image dimensions. For PSNR, we compare each blended result with the image-space composite (also created with the graph cut masks). Note that the image-space composites contain noticeable seams (e.g., the first column in Figure 7) and only serve as a proxy in the absence of groundtruth data. + +To measure seam artifacts, we compute the average gradient magnitude along seams, called the seam gradient (SG) score. Since some seams fall on object boundaries, the gradient is not expected to be zero. Rather, it should be within range of the SG scores of images in the stack. For reference, we compute the minimum, average, and maximum SG scores of each image stack and report their averages in Table 1. + +Quantitative Results. As shown in Table 1, our method achieves the highest PSNR score, the second-best LPIPS loss, and the third-best SSIM score across all the baselines, indicating good preservation of local image appearance. While IDP achieved the best LPIPS and SSIM scores, it often exhibits significant color changes, leading to a lower PSNR score than ours. Our method's SG score is within range and close to the average SG score. Though CollageDiffusion and GP-GAN achieved the second-best PSNR and SSIM, respectively, they have large SG scores, denoting major seam artifacts. Deep Image Blending and Cross-Domain Compositing have relatively large LPIPS losses, which correlates with larger changes in image appearances. BLD has the third-highest PSNR score and outperforms its variant, BLD+MultiDiffusion. Please see supplemental files for examples. + +Qualitative Comparison. In Figure 7, we show qualitative comparisons with IDP, BLD, and MasaCtrl+ControlNet. As + +![](images/ffb34edc8545c3a7121d4ea8691526c7953919042e2599df6b2f23bb9005060c.jpg) +Figure 8. User Survey Results. For each test scene, we asked participants to select the best image produced by four methods. The results suggest that our method has the best blending quality while being comparable to MasaCtrl+CtrlNet in realism. + +![](images/566b0ae10088318ad4a8f04ad0ffdafe69f2599a431d66c964e8fcd266a539e7.jpg) + +
Masked LPIPS ↓Masked SSIM ↑PSNR ↑Seam Gradient Score min, avg, max 0.255, 0.340, 0.425
Ours0.1230.81522.460.339
w/ Kconcat, Vconcat0.2430.67718.370.354
w/ Kmodel, Vmodel0.2680.66918.850.332
+ +Table 2. Ablation of Self-Attention Injection Schemes. + +shown, IDP often leads to changes in color due to gradient-domain blending, such as the marked regions in Figure 7. BLD [3] and MasaCtrl+ControlNet [13] may lead to structural changes or local appearance changes. The other baselines exhibit significant artifacts in blended regions or at seams. Please see supplemental materials for qualitative results of these other baselines. + +User Survey. Finally, we conduct two user surveys to compare our results with the most competitive baseline in each domain: Interactive Digital Photomontage (pixel-space), BLD (noise-based), and MasaCtrl+ControlNet (attention-based). Across 12 test scenes, we ask participants to select the best image produced by the four methods: (1) Which image appears most realistic to you? and (2) Which image is the best at blending all the selected regions? Out of 192 and 120 responses, respectively, results show that our method is comparable to MasaCtrl+ControlNet in terms of realism and has the best blending quality among the baselines by a wide margin (Figure 8). + +# 5.1. Ablation + +Here, we ablate our self-attention injection scheme with alternative injection strategies, adapted to our use case. First, we consider using shared (concatenated) key and value features, i.e., $K^{\mathrm{concat}} = [K^{1},K^{2},\dots,K^{N}]$ and $V^{\mathrm{concat}} = [V^{1},V^{2},\dots,V^{N}]$ , which StyleAligned [28] used to transfer style across different images. Next, we consider using $K^{\mathrm{model}}$ and $V^{\mathrm{model}}$ for the base image, similar to Equation 4. Both alternative injection schemes lead to changes in the appearance of user-selected image regions, whereas our method is able to preserve them. Table 2 reflects this change quantitatively. Please see supp. materials for qualitative examples and additional ablations on attention injection. + +# 5.2. Multi-image Segmentation + +Here, we compare our multi-label graph cut with a modified version of SAM [38] and pixel-space graph cut in IDP [1]. + +![](images/bf64b9a9e4050fa9f57cbeb7cec941b3698896e573363262bb71b1252a6cd54a.jpg) +Figure 9. Our Graph Cut vs. SAM [38]. We adapted SAM to an image stack and compared it with our graph cut. As shown, SAM may output noisy, incongruent labels within an object, such as the building (a) and fairies (c). SAM may also fail to follow user strokes, such as the bird interior (b) and the boat (c). Our graph cut takes into account the entire image stack during optimization and outputs labels that are congruent and satisfy user strokes. + +Since SAM is trained to segment single images, adapting it to a multi-image stack while maintaining coverage and avoiding overlaps is not straightforward. As a baseline, we use the following setup: given an input image stack, we run SAM on each image, with the user strokes on the image as positive and strokes on other images as negative samples. SAM outputs logits per pixel per image. For each pixel in the composite image, we assign the image label with the highest logit score. As shown in Figure 9, we observe two major types of artifacts here: 1) incongruent (noisy) labels within an object; 2) the segmentation does not follow user strokes. Pixel-space graph cut, as shown in Figure 3, may be sensitive to low-level changes in color and select seams that fall on undesired edges. Our graph cut, which operates in feature space, selects seams that are more aligned with semantic features. Please see supplemental materials for ablations of these methods and other graph cut features. + +# 6. Discussion + +In this work, we proposed a new approach for generating images: by compositing it from multiple ControlNet-generated images. At a broader level, our work suggests a new user workflow for interacting with text-to-image models: rather than trying to get the model to output the final end-product (i.e., a single image that contains everything the user wants, which is often difficult), we treat the model's output as an intermediate step, from which users provide further input to create their final end-product. Our approach not only gives users more fine-grained control over the final output, but also allows us to fully utilize the model's generative capabilities in creating diverse candidates. We hope this work inspires new ways of interacting with generative models. + +Acknowledgments We are grateful to Kangle Deng for his help with setting up the user survey. We also thank Maxwell Jones, Gaurav Parmar, Sheng-Yu Wang, and Or Patashnik for helpful comments and suggestions. This project is partly supported by the Amazon Faculty Research Award, DARPA ECOLE, the Packard Fellowship, the IITP grant funded by the Korean Government (MSIT) (No. RS-2024-00457882, National AI Research Lab Project), and a joint NSFC-ISF Research Grant no. 3077/23. + +# References + +[1] Aseem Agarwala, Mira Dontcheva, Maneesh Agrawala, Steven Drucker, Alex Colburn, Brian Curless, David Salesin, and Michael Cohen. Interactive digital photomontage. In ACM SIGGRAPH, 2004. 2, 3, 4, 6, 7, 8 +[2] Yuval Alaluf, Daniel Garibi, Or Patashnik, Hadar Averbuch-Elor, and Daniel Cohen-Or. Cross-image attention for zero-shot appearance transfer. In ACM SIGGRAPH, 2024. 2, 4, 5 +[3] Omri Avrahami, Ohad Fried, and Dani Lischinski. Blended latent diffusion. ACM Transactions on Graphics (TOG), 42 (4), 2023. 3, 6, 7, 8 +[4] Omri Avrahami, Thomas Hayes, Oran Gafni, Sonal Gupta, Yaniv Taigman, Devi Parikh, Dani Lischinski, Ohad Fried, and Xi Yin. 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Our proposed Generative Sparse-view Gaussian Splatting (GS-GS) achieves high-fidelity quality with only three training views. 1) GS-GS is a general pipeline for static and dynamic scene reconstruction with sparse camera views (left: vanilla GS model, right: ours). 2) Quantitative comparisons with other state-of-the-art methods on the LLFF [22] dataset. + +# Abstract + +Novel view synthesis from limited observations remains a significant challenge due to the lack of information in undersampled regions, often resulting in noticeable artifacts. We introduce Generative Sparse-view Gaussian Splatting (GS-GS), a general pipeline designed to enhance the rendering quality of 3D/4D Gaussian Splatting (GS) when training views are sparse. Our method generates unseen views using generative models, specifically leveraging pre-trained image diffusion models to iteratively refine view consistency and hallucinate additional images at pseudo views. This approach improves 3D/4D scene reconstruction by explicitly enforcing semantic correspondences during the generation of unseen views, thereby enhancing geometric consistency—unlike purely generative methods that often fail to maintain view consistency. Extensive evaluations on various 3D/4D datasets—including Blender, LLFF, Mip-NeRF360, and Neural 3D Video—demonstrate that our GS-GS outperforms existing state-of-the-art methods in rendering quality without sacrificing efficiency. + +# 1. Introduction + +Gaussian splatting [15], known for its efficiency in representing 3D scenes using Gaussian primitives, has achieved + +impressive results in generating high-quality renderings from dense input views. However, when input views are sparse, this approach struggles to maintain scene fidelity. The lack of sufficient view constraints leads to severe ambiguities in reconstructing scene geometry and appearance, causing degraded performance with visible artifacts, such as incorrect depth estimation, floating structures, and inconsistent colors. + +This problem is fundamentally ill-posed due to the underconstrained nature of sparse-view scenarios. Without enough observations, it becomes exceedingly difficult to accurately infer the 3D structure and appearance of a scene. As a result, existing methods either rely heavily on the large multi-view training datasets [5-7, 36, 41, 43, 48] or introduce regularization strategies [8, 18, 27, 51] that are often insufficient to address the inherent limitations posed by sparse views. The challenge is exacerbated in textureless or color-inconsistent areas [15, 23], where traditional reconstruction methods fail to establish reliable correspondences between views. + +Our intuition is to leverage generative models to compensate for the missing information in under-sampled regions. Specifically, we propose GS-GS, a pipeline designed to enhance the quality of 3D/4D Gaussian splatting reconstructions from sparse inputs. + +At the core of our approach is the integration of pretrained image diffusion models, which are used to generate unseen views and iteratively refine the view consistency of + +the reconstructed scene. Unlike conventional generative solutions that often struggle with maintaining geometric consistency, our method incorporates explicit geometric constraints to guide the generation process. By enforcing semantic correspondences when generating new views, we ensure that the synthesized content aligns well with the underlying scene structure, preserving both geometric and photometric accuracy. + +GS-GS introduces three key innovations: First, we propose a joint optimization approach for both the pre-trained diffusion model and the Gaussian Splatting model. The training datasets for both models are iteratively updated, with the images generated by the diffusion model at novel views improving the quality of Gaussian Splatting, and the rendered images from Gaussian Splatting enhancing the diffusion model to generate more scene-specific outputs. Second, we introduce a geometry-aware diffusion fine-tuning strategy to ensure geometry consistency across camera views, which is essential for producing consistent and realistic reconstructions by aligning the generative model's outputs with the true scene structure. Finally, we incorporate a depth regularization term when optimizing the Gaussian Splatting model, enabling more detailed and accurate geometry information. + +To evaluate the effectiveness of our approach, we conducted extensive experiments on a variety of benchmarks, including the Blender, LLFF, Mip-NeRF360, and Neural 3D Video datasets. Our results demonstrate that GS-GS outperforms state-of-the-art methods in terms of both visual quality and reconstruction accuracy. This performance is achieved without sacrificing efficiency, as our method retains the speed and scalability benefits of Gaussian splatting. In summary, our contributions are as follows: + +1. We introduce GS-GS, a novel pipeline that significantly improves 3D/4D Gaussian splatting reconstructions from sparse input views by leveraging pre-trained diffusion models for view generation. +2. We enforce geometric consistency through semantic correspondences, ensuring that generated views align accurately with the scene's structure, which addresses common issues of view inconsistency in generative methods. +3. We demonstrate that GS-GS achieves state-of-the-art performance across multiple datasets, producing high-quality novel view synthesis with minimal input views and achieving results comparable to models trained with dense input data. + +# 2. Related Works + +Novel view synthesis. Recent advancements in neural rendering, such as Neural Radiance Fields (NeRFs)[23], have significantly improved novel view synthesis. Many studies[1-3, 25] have focused on enhancing the quality and efficiency of differentiable volume rendering. More recently, 3D Gaussian Splatting (3DGS)[15] has enabled + +real-time, high-fidelity view synthesis for various scenes, including objects and unbounded environments. Extensions of 3DGS [9, 17, 20, 35, 42, 46, 49] have been developed for dynamic scenes. Despite these advances, reconstructing scenes from sparse camera views remains challenging, and creating a general pipeline for 3DGS/4DGS methods in sparse-view settings is still an open area of research. + +Sparse-view novel view synthesis. Few-shot novel view synthesis aims to generate novel views from a sparse set of input views. Various methods [18, 27, 39, 44, 51] address this challenge by adding regularization to NeRF [23] and 3DGS [15] to enhance geometry under sparse inputs. For example, the depth regularization [8, 18, 26] is one of the most widely used techniques. In addition, feed-forward models [5-7, 36, 41, 43, 48] have been developed for sparse-view reconstruction, often trained on large multi-view datasets [21, 50]. Despite promising results, these models often struggle when input images largely differ from the training data, leading to reduced performance. + +Lifting 2D diffusion models for 3D/4D generation. Leveraging 2D diffusion priors for generating 3D/4D content [28, 34, 37, 47] has seen significant advancements with pre-trained text-to-image/video diffusion models [4, 31]. For instance, DreamFusion [28] uses Score Distillation Sampling (SDS) to generate 3D objects from text prompts. Later methods [10, 11, 40, 45] enhance temporal and multi-view modeling by adding control signals to diffusion models. Although these approaches achieve high-quality results, they are designed for content generation and lack precision for accurate scene reconstruction. In contrast, our method focuses on improving 3D/4D reconstruction from sparse views, offering greater generalizability and reliability. + +# 3. Preliminary + +# 3.1. Gaussian Splitting + +3D Gaussian Splatting [15] (3DGS) optimizes a set of 3D Gaussians through differentiable rasterization to represent a static 3D scene using images captured from multiple camera views with known extrinsic parameters. The process starts with 3D point clouds reconstructed through Structure-from-Motion (SfM). Each Gaussian primitive $G(\pmb{x})$ is described by a position $\pmb{\mu}_i$ , a scaling factor $s$ , and a rotation quaternion $q$ . The basic function of the $i$ -th Gaussian primitive is defined as: + +$$ +G (\boldsymbol {x}) = e ^ {- \frac {1}{2} (\boldsymbol {x} - \boldsymbol {\mu}) ^ {T} \boldsymbol {\Sigma} ^ {- 1} (\boldsymbol {x} - \boldsymbol {\mu})}, \tag {1} +$$ + +where $\pmb{x}$ is a 3D point location within the 3D scene. $\pmb{\Sigma}$ is formulated using a scaling matrix $S$ and rotation matrix $\pmb{R}$ : + +$$ +\boldsymbol {\Sigma} = \boldsymbol {R} \boldsymbol {S} \boldsymbol {S} ^ {T} \boldsymbol {R} ^ {T}. \tag {2} +$$ + +![](images/cc89eb35804aa196289e7329e628a26cbc2280a7fbf761a1232bb9fb6ccd0352.jpg) +Figure 2. The pipeline of our method. Our method jointly optimizes the vanilla 3D/4D Gaussian Splitting model and the LoRA modules inserted to the pre-trained diffusion model by iteratively generating the pseudo-view images. 1) an image is rendered from an arbitrary pseudo viewpoint, 2) the depth map of the image is estimated by a depth estimation model, 3) depth-guided hallucination image at the pseudo view is generated by the pre-trained diffusion model and the depth adjater, 4) the hallucinated images are set as additional training dataset for training 3D/4DGS model and the parameters of inserted LoRA module of diffusion model are optimized based on the images at the training and pseudo views. For generating images with geometry consistency across various camera views, we constrain the diffusion features to be the same by warping images with known camera extrinsics. Specifically, an image rendered at a pseudo camera view is firstly warped to a training camera view with known camera poses $\{R,T\}$ . The warped image and the ground-truth image at the training view are fed into the pseudo view hallucination pipeline to obtain the their corresponding diffusion feature $f_{train}$ and $f_{train}^{\prime}$ . The parameters of LoRA module are optimized with the additional geometry-aware feature loss. + +To render an image from the given view, 3D Gaussians are first projected to 2D, and the rendered pixel value $C$ is formulated as: + +$$ +\boldsymbol {C} = \sum_ {i \in N} c _ {i} \alpha_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {i}), \tag {3} +$$ + +where $c_{i}$ and $\alpha_{i}$ denote the color and density of the point, and $N$ is the number of sorted Gaussians contributing to the rendering process. + +To represent 4D dynamic scenes, various strategies have been proposed to model the attributes of each Gaussian over time [20, 35, 42, 49]. In this work, we use vanilla 3DGS [15] for static scenes and SpacetimeGS [20], a state-of-the-art multi-view 4DGS method, as the base models for dynamic scenes. + +# 3.2. Diffusion Models + +A diffusion model [12] consists of a forward noising process, which gradually adds noise to an image, and a denoising process that iteratively removes the noise to reconstruct a valid image. In this work, we leverage Stable Diffusion [31] (SD), a text-conditioned latent diffusion model (LDM). SD + +employs an autoencoder [16] to map images to a latent space and a modified UNet [32] denoising network, $\epsilon_{\Theta}$ , parameterized by $\Theta$ , to perform denoising in the latent space. The encoder $\mathcal{E}$ embeds an input image $I$ into a latent representation $z = \mathcal{E}(I)$ , and the decoder $\mathcal{D}$ reconstructs the image from $z$ as $I' = \mathcal{D}(z)$ . The LDM is optimized using the following equation: + +$$ +\mathcal {L} _ {\mathrm {L D M}} (I, y; \Theta) = \mathbb {E} _ {\epsilon \sim \mathcal {N} (0, 1), t} \| \epsilon - \epsilon_ {\Theta} (z _ {t}, t, \tau (y)) \| _ {2} ^ {2}, (4) +$$ + +where $y$ is the text prompts, $\tau$ is the text encoder (e.g., CLIP [29]), and $t$ is the timestep. + +DreamBooth [33] is a subject-driven method for SD, which fine-tuning all parameters of the UNet or insert low rank adaptation [13] (LoRA) to generate personalized images. + +T2I-adapter [24] is a lightweight module to align internal knowledge in SD with external control signals, achieving rich control and editing effects in the color and structure of the generation results. In this work, we apply a pre-trained depth T2I-adapter [24] as the foundation module of our pipeline. + +# 4. Generative Sparse-View Gaussian Splitting + +# 4.1. Overview + +Problem Definition. Given a set of input images $\mathcal{I} = \{I_1, I_2, \dots, I_N\}$ with known camera poses $\mathcal{P} = \{P_1, P_2, \dots, P_N\}$ , the goal is to generate a set of images $\tilde{\mathcal{I}} = \{\tilde{I}_1, \tilde{I}_2, \dots, \tilde{I}_{\tilde{N}}\}$ from pseudo-novel views $\tilde{\mathcal{P}} = \{\tilde{P}_1, \tilde{P}_2, \dots, \tilde{P}_{\tilde{N}}\}$ . These pseudo-novel views are interpolated from the original camera poses $\mathcal{P}$ . Using a pre-trained text-to-image diffusion model, we generate the images $\tilde{\mathcal{I}}$ for these interpolated views, which are then used to update the 3D/4D scene representation. + +Alternating Optimization. Consider a conditional diffusion model from which we can sample images using $I = \text{sample}[\epsilon_{\Theta}(y)]$ , where $y$ is the conditioning input and $\epsilon_{\Theta}$ represents the diffusion model parameterized by $\Theta$ . Our ultimate objective is to optimize the 3D/4D representation parameterized by $\theta$ . The above problem can be reformulated as a bi-level optimization problem as: + +$$ +\boldsymbol {\theta} ^ {*} = \arg \min _ {\boldsymbol {\theta}} \sum_ {i = 1} ^ {N} \mathcal {L} _ {\mathrm {G S}} \left(R (P _ {i}; \boldsymbol {\theta}), I _ {i}\right) + \sum_ {j = 1} ^ {\tilde {N}} \mathcal {L} _ {\mathrm {G S}} \left(R (\tilde {P} _ {j}; \boldsymbol {\theta}), \tilde {I} _ {j}\right) +$$ + +[Scene Reconstruction] + +s.t. $\Theta^{*} = \arg \min_{\Theta}\sum_{i = 1}^{N}L_{\mathrm{LDM}}(I_{i},y_{i};\Theta),$ [Model Adaptation] + +$\tilde{I}_j = \mathrm{sample}[\pmb {\epsilon}_{\Theta^*}(\tilde{y}_j)]$ [View Generation] (5) + +where $R(\cdot ;\theta)$ is the rendering function, and $\mathcal{L}_{\mathrm{GS}}$ is the reconstruction loss between the rendered images and the observations. The variables $P_{i}$ and $\tilde{P}_j$ denote the original and pseudo-novel camera poses, respectively. + +To solve the optimization problem above, we alternating between 3 steps. We start by adapting the diffusion model to the available views. Using the pre-trained depth adapter [24], we generate new training images at pseudo-novel views. These images are then used to optimize the parameters of the 3D/4D GS model. + +We loop over these three steps iteratively. In each iteration, the 3D/4D representation renders new images, which serve as supplementary data for further fine-tuning the diffusion model. This iterative process gradually improves the quality of the 3D/4D reconstruction as more data becomes available. + +# 4.2. Geometry-aware Pseudo View Hallucination + +Our goal is to hallucinate the images for novel pseudo views, which facilitates the optimization of 3D/4D scene reconstruction under sparse-view setting. To achieve this, we need to guarantee that the pre-trained diffusion model can generate scene-specific images with camera-view-related condition. Specifically, we use LoRA [13] and a pre-trained + +depth adapter [24] to train the diffusion model. This setup allows us to generate scene-specific images based on the given depth image. An overview of the entire pipeline is shown in Fig. 2. + +As shown in Sec. 4.1, our pipeline involves a joint optimization, in which the training dataset for LoRA and 3D/4DGS model are iteratively updated by each other. This iterative process allows for gradual percolation of the diffusion priors to static or dynamic scene and personalize the diffusion model to the specific scene. + +When optimization begins, we optimize the GS model based on the sparse training view to initialize a coarse 3D/4D scene. Then we update the training images for LoRA model and GS model, iteratively. Specifically, 3D/4DGS models firstly render all images at training views $\{P_1, P_2, \dots, P_N\}$ and pseudo views $\{\tilde{P}_1, \tilde{P}_2, \dots, \tilde{P}_{\tilde{N}}\}$ . All the rendered images serve as the training dataset for fine-tuning LoRA model. After the LoRA parameters optimized for several iterations, we generate the images $\{\tilde{I}_1, \tilde{I}_2, \dots, \tilde{I}_{\tilde{N}}\}$ by the fine-tuned diffusion model given the estimated depth maps at pseudo views $\{\tilde{P}_1, \tilde{P}_2, \dots, \tilde{P}_{\tilde{N}}\}$ . The GS model are further optimized by the ground truth images $\{I_1, I_2, \dots, I_N\}$ and the hallucinated images $\{\tilde{I}_1, \tilde{I}_2, \dots, \tilde{I}_{\tilde{N}}\}$ . The overall procedure is illustrated in Alg. 1. + +Algorithm 1 Joint Optimization for 3D/4DGS with Diffusion Prior + +1: Input: Sparse-view images $\mathcal{I}$ at views $\mathcal{P}$ , pseudo views $\hat{\mathcal{P}}$ , pre-trained diffusion model, depth adapter, LoRA module. +2: for initialize iteration do +3: Train GS with $\mathcal{I}$ at views $\mathcal{P}$ +4: end for +5: for training iteration do +6: Render images $\mathcal{I}$ and $\tilde{\mathcal{I}}$ from GS at views $\mathcal{P}$ and $\tilde{\mathcal{P}}$ . +7: for fine-tuning LoRA do +8: Optimize LoRA parameters with $\mathcal{I}$ and $\tilde{\mathcal{I}}$ . +9: end for +10: Update refined pseudo-view images $\tilde{\mathcal{L}}$ at views $\mathcal{P}$ by the fine-tuned diffusion model. +11: for optimizing GS do +12: Optimize GS model with $\mathcal{I}$ and $\tilde{\mathcal{I}}$ . +13: end for +14: end for +15: Output: Optimized 3D/4DGS model. + +# 4.3. Geometry-aware Diffusion Fine-Tuning + +The main challenge in hallucinating images at pseudo views is maintaining geometry consistency across views. While the LoRA module personalizes the pre-trained diffusion model + +![](images/26dd5d71d5fad78633749d3f34847365ccd0a08c53d66f619f425a91b92aede7.jpg) +Figure 3. Dataset Evolution. We illustrate the dataset evolution process for the horn scene using the LLFF [22] dataset. Starting with two camera views, the diffusion model generates geometry-consistent image pairs as the training dataset is updated iteratively. + +to a specific scene, ensuring geometry consistency remains difficult, especially with depth maps from two camera views. Recent work by DIFT [38] demonstrates that the intermediate features of diffusion models contain strong semantic information and can establish correspondences between images. To address this, we propose a geometry-aware fin-tuning strategy for updating the LoRA parameters of the diffusion model. + +The geometry-aware diffusion fine-tuning pipeline is illustrated in Fig. 2. Given a image $\tilde{I}$ rendered by 3D/4DGS at the pseudo view $\tilde{P} \in \{\tilde{P}_1, \tilde{P}_2, \dots, \tilde{P}_{\tilde{N}}\}$ , we first warp it to the known training view $P \in \{P_1, P_2, \dots, P_N\}$ with known camera intrinsic parameter $\{R, T\}$ , denoting $\tilde{I}_{R,T}$ . The depth maps of the ground-truth image $I$ at view $P$ and the warped image $\tilde{I}_{R,T}$ are estimated by the pre-trained Dense Prediction Transformer (DPT) [30], serving the condition of the diffusion model. The diffusion features of images $I$ and $\tilde{I}_{R,T}$ , denoting $f_{train}$ and $f_{train}'$ are extracted by the diffusion model with the inserted fine-tuned LoRA module. Ideally, the diffusion features $f_{train}$ and $f_{train}'$ should be the same since the camera extrinsic parameters of $I$ and $\tilde{I}_{R,T}$ are the same. To this end, we calculate the L1 loss for $f_{train}$ and $f_{train}'$ as the regularization term when fine-tuning LoRA parameters. The loss function for fine-tuning LoRA module formulate as: + +$$ +\begin{array}{l} \mathcal {L} _ {\Theta} = \mathcal {L} _ {L D M} (I, y; \Theta) + \mathcal {L} _ {L D M} (\tilde {I} _ {R, T}, y; \Theta) \tag {6} \\ + \lambda_ {g e o} \| f _ {\text {t r a i n}}, f _ {\text {t r a i n}} ^ {\prime} \|, \\ \end{array} +$$ + +where $\mathcal{L}_{LDM}(\cdot ,y;\Theta)$ is the optimization loss for LDM with optimized parameters $\Theta$ , as depict in Eq. (4). $\lambda_{geo}$ represents the geometric regularization term for fine-tuning LoRA module. We set $\lambda_{geo} = 0.1$ in all experiments. + +We visualize the evolution of hallucinated images generated by the fine-tuned diffusion model in Fig. 3. Specifically, we show the ground-truth images, estimated depth maps, and hallucinated images at different training iterations for + +two camera views. Initially, the generated images at pseudo views are inconsistent across camera views. However, as training progresses, the hallucinated images become more geometry-consistent. The high-fidelity, 3D-consistent images at pseudo views facilitate the optimization of 3D and 4D scene representations in a sparse-view setting. + +# 4.4. Depth Regularization for Gaussian Optimization + +Although the pseudo-view hallucination pipeline generates additional images with geometry awareness, the resulting images are not perfectly aligned with the scene, leading to blurring in the rendered results. To inject richer geometric information into the Gaussian optimization, we incorporate pixel-level geometric correspondences as regularization during 3D/4DGS training. Specifically, for each camera view $P$ in the training views $\mathcal{P}$ and pseudo views $\tilde{\mathcal{P}}$ , we first render an image $I$ at view $P$ . We then compute the structural similarity between the rasterized depth $D_{\text{render}}$ at view $\mathcal{P}$ and the estimated monocular depth of the rendered image $I$ . This structural similarity serves as a regularization term when optimizing the 3D/4DGS model. We now detail this procedure. + +Similar to the differentiable rasterization for RGB images in Eq. (3), the rendered depth map $D_{\mathrm{GS}}$ at camera views $\mathcal{P}$ and $\widetilde{\mathcal{P}}$ are calculated by: + +$$ +D _ {\mathrm {G S}} = \sum_ {i \in N} d _ {i} \alpha_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \alpha_ {i}), \tag {7} +$$ + +where $d_{i}$ and $\alpha_{i}$ denote the z-buffer and density of the Gaussian point, and $N$ is identical to that in Eq. (3). + +For each image $I$ at either the ground-truth training views $\mathcal{P}$ or the generated pseudo views $\tilde{\mathcal{P}}$ , we first estimate its monocular depth map $D_{\mathrm{DPT}}$ by the pre-trained Dense Prediction Transformer (DPT) [30]. To mitigate depth ambiguity between the estimated depth $D_{\mathrm{DPT}}$ and the rasterized depth + +map $D_{\mathrm{GS}}$ , $D_{\mathrm{DPT}}$ and $D_{\mathrm{GS}}$ are further normalized by the following equation: + +$$ +D _ {\mathrm {G S}} ^ {\text {n o r m}} = \frac {D _ {\mathrm {G S}} - \mu_ {D _ {\mathrm {G S}}}}{\sigma_ {D _ {\mathrm {G S}}}}, \tag {8} +$$ + +and + +$$ +D _ {\mathrm {D P T}} ^ {\text {n o r m}} = \frac {D _ {\mathrm {D P T}} - \mu_ {D _ {\mathrm {D P T}}}}{\sigma_ {D _ {\mathrm {D P T}}}}, \tag {9} +$$ + +where $\mu_{D^{*}}$ and the $\sigma_{D^{*}}$ are the mean and variance values of $D_{\mathrm{DPT}}$ and $D_{\mathrm{GS}}$ , respectively. + +Rather than previous methods [18, 51] which calculate L1 or L2 distance between $D_{\mathrm{DPT}}$ and $D_{\mathrm{GS}}$ , we calculate the multi-scale structural similarity (MS-SSIM) between $D_{\mathrm{DPT}}$ and $D_{\mathrm{GS}}$ by + +$$ +\mathcal {L} _ {\text {r e g}} = - \mathrm {M S} - \mathrm {S S I M} \left(D _ {\mathrm {D P T}} ^ {\text {n o r m}}, D _ {\mathrm {G S}} ^ {\text {n o r m}}\right). \tag {10} +$$ + +# 4.5. Optimization + +The 3D/4DGS model is optimized by the regular photometric loss terms with depth regularization. + +$$ +\begin{array}{l} \mathcal {L} _ {\mathrm {G S}} \big (R (\cdot ; \boldsymbol {\theta}) \big) = \mathcal {L} _ {1} \big (R (\mathcal {P}; \boldsymbol {\theta}), \mathcal {I} \big) + \mathcal {L} _ {1} \big (R (\tilde {\mathcal {P}}; \boldsymbol {\theta}), \tilde {\mathcal {I}} \big) \\ + \lambda \mathcal {L} _ {\mathrm {D - S S I M}} (R (\mathcal {P}; \boldsymbol {\theta}), \mathcal {I}) + \lambda \mathcal {L} _ {\mathrm {D - S S I M}} (R (\hat {\mathcal {P}}; \boldsymbol {\theta}), \tilde {\mathcal {I}}) \\ + \lambda_ {\text {r e g}} \mathcal {L} _ {\text {r e g}}, \tag {11} \\ \end{array} +$$ + +where, $R(\cdot; \theta)$ is the rendering function, $\theta$ is the parameter of 3D/4D Gaussian representation. $\mathcal{L}_1$ and $\mathcal{L}_{\mathrm{D - SSIM}}$ are the L1 reconstruction loss and D-SSIM loss, respectively. + +# 5. Experiments + +# 5.1. Datasets + +We conduct our experiments on four datasets: the NeRF Blender Synthetic dataset (Blender) [23], the LLFF dataset [22], the Mip-NeRF-360 dataset [2], and the Neural 3D Video dataset [19]. + +NeRF Blender Synthetic dataset (Blender) [23] consists of 8 object with realistic images rendered by Blender. Aligned with [14, 18, 51], we use 8 views for training and 25 views for testing. + +LLFF dataset [22] consists of eight real-world scenes. Following baseline methods [18, 27, 51], we select every $8^{th}$ image as the test set, and sample 3 views from the remaining views for training evenly. + +Mip-NeRF360 dataset [2] consists of 9 real-world complex ourdoor scenes. Following [51], the test images are selected the same as the LLFF dataset [22] and the training views are 24. + +Neural 3D Video dataset [19] contains six indoor multiview video sequences captured by 18 to 21 cameras. Following other methods [20, 35], the first camera is set for evaluation. Since there are no method designed specifically for sparse dynamic scene generation, we evenly sample 3 views from the all other views for training. + +# 5.2. Experimental Settings + +Baselines. We compare our method with several state-of-the-art methods on these datasets, including Mip-NeRF [1], DietNeRF[14], RegNeRF [27], FreeNeRF [44], SparseNeRF [39], 3DGS [15], DNGaussian [18], and FSGS [51]. We report PSNR, SSIM, and LPIPS scores to evaluate the reconstruction performance quantitatively. For sparse view dynamic scene reconstruction, we conduct experiments based on SpacetimeGS [20] under sparse-view setting. + +Implementation details. We build our pipeline based on the official 3DGS [15] and SpacetimeGS [20] for sparse-view 3D and 4D scene reconstruction, respectively. We train the overall pipeline with 10,000 iteration for all datasets. We apply pre-trained DPT [30] to estimate monocular depth for all training and pseudo views. The initial point clouds for each scene are reconstructed by Structure-from-Motion (SfM) with the sparse training views. Please refer to the supplementary material for details. + +# 5.3. Few-shot 3D Reconstruction + +Table 1. Quantitative comparisons on the Blender, LLFF, and Mip-NeRF360 datasets. We color each cell as the best, second best, and third best. + +
MethodPSNR↑Blender SSIM↑LPIPS↓PSNR↑LLFF SSIM↑LPIPS↓Mip-NeRF360
PSNR↑SSIM↑LPIPS↓
Mip-NeRF [1]20.890.8300.16816.110.4010.46019.510.5170.413
3DGS [15]21.560.8470.13017.430.5220.32120.890.5880.401
DietNeRF [14]22.500.8230.12414.940.3700.49620.210.4820.452
RegNeRF [27]23.860.8520.10519.080.5870.33622.190.5460.398
FreeNeRF [44]24.260.8830.09819.630.6120.30822.780.5870.377
SparseNeRF [39]24.040.8760.11319.860.3280.32822.850.6000.389
DNGaussian [18]24.310.8860.08819.120.5910.13223.090.6370.322
FSGS [51]24.640.8950.09520.310.6520.28823.700.6930.293
Ours28.570.9230.05524.820.7370.10525.870.7450.182
+ +Blender dataset. The quantitative results on the Blender dataset [23] with 8-view setting are reported in Tab. 1. Our method outperforms all other approaches on the Blender dataset [23] across all three evaluation metrics—PSNR, SSIM, and LPIPS. Specifically, it achieves a substantial improvement in PSNR with a value of 28.57, surpassing the second-best method, FSGS, by more than 3 dB. Additionally, our method demonstrates the highest SSIM score of 0.923, reflecting superior structural similarity between the reconstructed and ground-truth images. These results highlight the effectiveness of our approach in accurately reconstructing 3D scenes with high fidelity, both in terms of geometry and visual quality. + +LLFF dataset. The evaluation results on the LLFF dataset [22] are shown in Tab. 3. Our method leads in all three metrics, achieving a PSNR of 24.82, SSIM of 0.737, and LPIPS of 0.105, significantly outperforming the $2^{nd}$ -best method, FSGS [51]. The PSNR improvement over FSGS is approximately 4.5 dB, demonstrating the robustness of our approach in sparse-view reconstruction. Additionally, + +![](images/35a59a680b89c1b820a66ad0d69a5d48c2a0a433fe8a26d2c35ba5bd0bef67ce.jpg) +Figure 4. The visualization results on the Blender [23], LLFF [22], and Mip-NeRF360 datasets. Our method produces detailed foreground geometry and renders high-quality novel views with sparse camera views. Please refer to the supplementary material for more visualization results. + +our SSIM score of 0.737 indicates superior structural alignment, while our LPIPS score of 0.105 reflects the lowest perceptual discrepancy, highlighting the visual quality of our method. These results confirm that our method excels in both geometric accuracy and perceptual realism on the LLFF dataset. + +Mip-NeRF360 dataset. The performance of our method on the Mip-NeRF360 dataset [2] is also exceptional, with a PSNR of 25.87, SSIM of 0.745, and LPIPS of 0.182. These results mark the highest scores across all three metrics, outperforming the second-best method, FSGS [51], by a substantial margin. Notably, our PSNR score is the highest, indicating that our method produces the sharpest reconstructions. The SSIM score further confirms the high level of structural consistency with ground-truth images, and our LPIPS score of 0.182 is the best, showing minimal perceptual deviation. These results reinforce the effectiveness of our method in handling the complex, large-scale reconstructions in the Mip-NeRF360 dataset. We visualize the rendering results in Fig. 4. We observe that both 3DGS [15] and DNGaussian [18] fail to capture the geometry and the intricate details of scenes. In comparisons, our method recovers the fine-grained details, such as the Lego in the kitchen scene, aligning well with the ground truth. + +# 5.4. Few-shot Dynamic Scene Reconstruction + +Due to there are no proper baselines for sparse-view dynamic scene reconstruction, we compare our method with the baseline 4DGS method, i.e., SpacetimeGS [20]. The evaluation results are listed in Tab. 2. Our method outperforms the baseline SpacetimeGS across all camera view configurations in the Neural 3D Video dataset. Even with just 3 views, our method achieves a PSNR of 27.13, which is over 12 dB higher than SpacetimeGS's 14.98. The SSIM score also reflects this improvement, with our method scoring 0.907 compared to SpacetimeGS's 0.774. Furthermore, our LPIPS score of 0.135 demonstrates a significant reduction in perceptual discrepancy. As the number of views increases to 6 and 9, the gap between our method and SpacetimeGS continues to widen, with our method achieving a PSNR of 30.21, an SSIM of 0.928, and an LPIPS of 0.082 at 9 views. Notably, even when comparing our results with just 3 views to SpacetimeGS's performance with 9 views, our method still outperforms them in all metrics, highlighting the efficiency and effectiveness of our approach in sparse view 4D scene generation. We visualize the rendering results for both SpacetimeGS [20] and our method with 3, 6, and 9 camera views in Fig. 5. SpacetimeGS suffers from + +![](images/f6a3a20f3a2c545b3eac363f9c6d20c352bd2d9afcd825416777ecf3cd0081b0.jpg) +Figure 5. The visualization results on the Neural 3D Video dataset. Comparisons are conducted with SpacetimeGS [20] with 3, 6, and 9 training views. Please refer to the supplementary material for more results. + +poor results and inaccurate RGB values with only 3 views. Our method achieves much better rendering results, with a high-fidelity appearance. Though both SpacetimeGS and our method improve the rendering results with more training views, our method still achieves higher results with various camera views. + +Table 2. Quantitative comparisons on the Neural 3D Video dataset. Our proposed pipeline is general for both 3D and 4D scene reconstructions. We set SpacetimeGS [20] as the baseline model for dynamic scene reconstruction and evaluate the performance with different number of camera views. + +
Method3 Views6 Views9 Views
PSNRSSIMLPIPSPSNRSSIMLPIPSPSNRSSIMLPIPS
SpacetimeGS [20]14.980.7740.32725.150.8950.16326.720.9130.165
Ours27.130.9070.13529.200.9160.11730.210.9280.082
+ +# 5.5. Ablation Studies and Analysis + +![](images/9de14fb856809173eee40f79803baa1674f26582c838bd44c4c3e507608076d4.jpg) +Figure 6. Ablation studies for the proposed modules. We ablate for each component of our GS-GS. + +Diffusion Hallucination. To demonstrate the effectiveness of our diffusion hallucination strategy, we conduct an ablation study by removing the diffusion prior from the pseudoview hallucination pipeline. As shown in Tab. 3 and Fig. 6, without the diffusion prior, the 3DGS model struggles to render high-quality novel views due to the limited number of camera views. + +Geometry-Aware Fine-Tuning. Introducing the diffusion hallucination pipeline into the optimization of the 3DGS model leads to improved rendering results. As shown in Tab. 3, the PSNR score increases from 17.43 to 22.71 on the LLFF dataset [22]. The flowers depicted in Fig. 6 exhibit better appearance. However, compared to the full model, the rendering results still appear blurry, and the details are not as refined. This is because, although the diffusion process helps hallucinate images at pseudo views, the generated images lack geometry consistency, which negatively impacts scene reconstruction. + +Depth Regularization. As shown in Fig. 6, incorporating depth regularization further enhances geometric details, such as the edges of the flowers. With the addition of the depth regularization term, the PSNR score on the LLFF dataset increases from 24.09 to 24.82. + +Table 3. Ablation studies on the proposed components. + +
w/o diffusion hallucinationdiffusion w/o geometry-aware fine-tuningw/o depth reg.full model
Mip-NeRF360 [2]20.8923.2325.2825.87
LLFF [22]17.4322.7124.0924.82
+ +# 6. Conclusion + +In this work, we present Generative Sparse-view Gaussian Splatting (GS-GS), a general pipeline designed to enhance the quality of 3D/4D Gaussian Splatting (GS) with sparse-view inputs. By leveraging pre-trained diffusion models to hallucinate additional views while maintaining semantic and geometric consistency, GS-GS enhances the quality of 3D/4D Gaussian splatting even in under-sampled regions. Through extensive experiments on diverse datasets, we demonstrate that our method significantly outperforms existing state-of-the-art techniques in both reconstruction accuracy and rendering performance, offering a promising solution for high-quality view synthesis in sparse-view settings. + +# Acknowledgement + +# References + +[1] Jonathan T Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P Srinivasan. Mip-nerf: A multiscale representation for anti-aliasing neural radiance fields. 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GenProp. We propose a generative video propagation framework (GenProp), which can seamlessly propagate any first frame edit through the video. GenProp supports a wide range of video applications, including (a) complete object removal with effects such as shadows and reflections, (b) background replacement with realistic effects, (c) object insertion where inserted objects have physically plausible motion (i.e., blueberries falling while spoon goes up), (d) tracking of objects and their associated effects, and (e) multiple edits (outpainting, insertion, removal) at a single inference run. + +# Abstract + +Large-scale video generation models have the inherent ability to realistically model natural scenes. In this paper, we demonstrate that through a careful design of a generative video propagation framework, various video tasks can be addressed in a unified way by leveraging the generative + +power of such models. Specifically, our framework, GenProp, encodes the original video with a selective content encoder and propagates the changes made to the first frame using an image-to-video generation model. We propose a data generation scheme to cover multiple video tasks based on instance-level video segmentation datasets. Our model is trained by incorporating a mask prediction decoder head + +and optimizing a region-aware loss to aid the encoder to preserve the original content while the generation model propagates the modified region. This novel design opens up new possibilities: In editing scenarios, GenProp allows substantial changes to an object's shape; for insertion, the inserted objects can exhibit independent motion; for removal, GenProp effectively removes effects like shadows and reflections from the whole video; for tracking, GenProp is capable of tracking objects and their associated effects together. Experiment results demonstrate the leading performance of our model in various video tasks, and we further provide in-depth analyses of the proposed framework. + +# 1. Introduction + +Recently, large-scale video generation models [7, 17, 18, 32, 35, 42, 46, 57] have shown impressive performance, generating highly realistic videos while being able to simulate the complexities of the real world. In this rapidly evolving domain, following works in video generation have extended the text-to-video (T2V) generation to image-to-video (I2V) [2, 5, 32, 53, 60], and are further exploring various video editing tasks such as video inpainting [65], appearance editing [34, 43], object insertion [31], usually focusing on that specific task. In this paper, we bring a new perspective, observing that many of such video applications can be modeled as a general video propagation problem. + +Video propagation itself is not a new concept, with traditional methods often relying on optical flow [9, 44], depth [6, 55], radiance fields [33], and atlases [20, 24] to propagate the changes in sparse intermediate frames (typically the first frame) to the rest of the video. However, such approaches can be prone to error accumulation, leading to limited robustness and generalization ability. Furthermore, they often focus on a single task [9, 33] or entail retraining for a specific task for propagation [28, 31, 34, 61]. In contrast, we extend the first-frame editing and design a more general framework for generative video propagation encompassing various editing scenarios by leveraging video generation models's power in modeling real-world scenes. + +Our model, GenProp, is able to propagate the changes in the first frame to the whole video while keeping other parts consistent to the original video, without requiring any additional motion predictions (e.g., optical flow). This general formulation enables many downstream applications such as removal, insertion, replacement (object and/or background), text-based editing, outpainting and even object tracking, some of which are shown in Fig. 1. We further demonstrate that our model is also able to expand the scope of what is usually achievable in each task, specifically: (1) substantial shape modifications in object editing tasks, (2) independent motion of inserted objects in insertion tasks, (3) removal of object effects like shadows and reflections + +![](images/1eba15b32d3d0d1b0af231a48e143520a5f09daa572e69c36e0771f2f2246f93.jpg) +Figure 2. Model Overview. During inference, our framework takes in the original video as input through a selective content encoder (SCE) to retain content in unchanged regions. Changes applied to the first frame are propagated throughout the video using an I2V model while other regions remain intact. + +in removal tasks, and (4) accurate tracking of objects along with their associated effects. Note that unlike existing video editing models that often require a dense mask labeling for all individual frames (e.g., for object removal), GenProp does not require any mask input, thanks to the propagation-based approach, greatly simplifying the editing process. + +Our model architecture consists of two main components as shown in Fig. 2: the Selective Content Encoder (SCE) that encodes the information of the original video, and the I2V generation model that takes in the edited first frame for propagation. The training objective is to allow SCE to selectively encode the features of the unchanged parts of the video, while preserving the generation capabilities of I2V models to propagate the altered parts. To effectively disentangle these two functions, we introduce a region-aware loss and penalize the gradients within the modified region for SCE, as ideally, SCE should not encode content in the edited area. For training the model, we propose using synthetic data derived from video instance segmentation datasets. As shown in the attention map visualizations in Fig 3, we observe that GenProp indeed attends to the region to be modified and the I2V model is guided to generate (propagate) the new content into those regions. To further aid the model, we incorporate an auxiliary decoder head during training to predict the modified region. + +Our contributions are summarized as follows: + +- We extend first-frame editing to a general generative video propagation framework, which propagates changes in the first frame to the entire video using the generative power of I2V models, enabling broader applications. +- We carefully design our model, GenProp, with a Selective Content Encoder (SCE), dedicated loss functions and a mask prediction head and propose a synthetic data generation pipeline for training this model. +- Our model supports various downstream applications such as removal, insertion, replacement, editing, and tracking. We observe that it supports outpainting, with + +out task-specific data during training. + +- Experiment results show that our model outperforms SOTA methods in video editing and object removal while expanding the scope of existing tasks including tracking. + +# 2. Related Work + +Video Propagation. Traditional methods are typically designed for a single task and often require retraining for new tasks [9, 21, 33]. Many approaches address propagation by first tracking instance masks, then performing inpainting [25, 26], with segmentation often as the initial step. SAM 2 [39], the current SotA tracking model, can track the masks accurately and efficiently. Some methods rely on optical flow [9, 44] or depth [6, 55] to ensure consistent motion and spatial coherence. CoDef [33] uses deformation fields from the source video to guide edits from the first frame. While these representations aid motion tracking and structural consistency, they add complexity and may limit flexibility, especially with significant shape changes or complex backgrounds. Depth, sketches, and optical flow can also be combined with diffusion models [11, 29, 48, 52, 56]. + +Diffusion-based Video Editing. Most diffusion-based video editing methods rely on text control, where the primary goal is to make edits that are coherent to text prompts while preserving the unchanged regions of the video. Some methods utilize text-to-image models for zero-shot editing through attention control [6, 14, 23, 37, 41, 47, 49]. Some other works require intermediate variables like optical flows or depth maps to stabilize motion. Others rely on per-case fine-tuning to adapt to specific motion [4, 30, 50, 62], but this approach is typically slow and prone to generate similar results from the original video due to reconstruction tuning. SORA [32] denoises the noised videos under the target description to do editing. These methods are generally limited to altering the appearance rather than making significant changes to object shapes. Additionally, because of unclear attention maps, especially in complex scenes, background changes often lack precision and coherence. InsV2V [8] and EVE [43] edit videos based on text instructions but are also limited to appearance changes. Some recent efforts have attempted to directly edit motion based on text prompts [22, 58, 63], but their resulting video output tends to strike a balance between the text-based guidance and the original video's motion, which can be hard to control. + +Image-to-Video Generation and Editing. Image-to-video (I2V) generation models take an input image along with a text prompt to generate a sequence of frames, making them a foundational application in video generation due to its familiarity and versatility. Notable open-source models include Stable Video Diffusion [5], I2VgenXL [60], and SparseCtrl [16], while high-performance commercial models, such as Gen-2, PikaLabs [2], SORA [32], and Movie + +![](images/a1c179671a6e3119e899f500848aaaa90a16eb691985fbb94b383c9f1fc5ee04.jpg) +Figure 3. Attention Map Visualization. We observe that the attention maps gradually focus on the regions to be removed and the I2V model is guided to generate new content in those regions. + +Gen [35], further push the boundaries in this field. + +Several methods propagate edits from the first frame. For example, some works [13, 40, 55, 56] rely on first-frame edits but require auxiliary inputs like optical flow or depth maps for motion continuity. VideoSwap [15] uses sparse key points to control the motion. AnyV2V [27] and VideoShop [12] can also propagate first-frame edits across a video sequence; however, as a training-free framework, its generalization ability is limited. I2VEdit [34], in contrast, necessitates learning motion LoRAs [19] for each video clip, adding computational complexity. Revideo [31], built on Stable Video Diffusion (SVD), enables control over the generation using the edited first frame and a specified motion trajectory. However, its approach involves masking parts of the input video with a black square, which removes significant information and restricts the method in handling complex background edits and large shape alterations. + +# 3. Method + +Generative video propagation has the following key challenges: (1) Realism - changes in the first frame should be naturally propagated to the following frames, (2) Consistency - all other regions should remain consistent to the original video, and (3) Generality - the model should be general enough to be applicable to multiple video tasks. In GenProp, we leverage an I2V generation model for (1); we introduce a selective content encoder and a mask prediction decoder and train the model with a region-aware loss to address (2); and we propose a data generation scheme and also benefit from the versatile I2V model for (3). + +# 3.1. Problem Formulation + +Given an input video $V = \{v_{1}, v_{2}, \ldots, v_{T}\}$ with $T$ frames, let $v_{1}'$ denote the modified first frame. The goal is to propagate this modification, producing a modified video $V' = \{v_{1}', v_{2}', \ldots, v_{T}'\}$ , where each frame $v_{t}'$ (for $t = 2, \ldots, T$ ) retains the modification applied to the key frame $v_{1}$ while maintaining consistency in both appearance and motion throughout the sequence. We employ a latent diffusion model that encodes pixel information in the latent space. With a slight abuse of notations, we continue using $v_{t}$ for this latent representation. In formal terms, during inference, + +![](images/a901667e74370e1bf21cffb9ed48c6ca5a2ea4f96ab35be3600653505c34face.jpg) +Figure 4. Training Framework of GenProp. Our framework integrates a Selective Content Encoder and a Mask Prediction Decoder on top of the I2V generation model, enforcing the model to propagate the edited region while preserving the content in the original video for all other regions. With synthetic data augmentations and task embeddings, our model is trained to propagate various changes in the first frame. + +GenProp generates each frame $v_{t}^{\prime}$ as: + +$$ +v _ {t} ^ {\prime} = \mathcal {G} (\mathcal {E} (V), v _ {1} ^ {\prime}, t), \quad \forall t \in \{2, \dots , T \}, \tag {1} +$$ + +where $\mathcal{G}$ is the I2V generation model guided by the selective content encoder (SCE), $\mathcal{E}(V)$ . + +For training, we use synthetic data constructed from existing video instance segmentation datasets to create paired samples (details given in Sec. 3.4). We define a data generation operator $\mathcal{D}$ that constructs training data pairs $(v_{i},\hat{v}_{i})$ from an original video sequence $V$ . Let $\mathcal{D}(V)$ denote the synthetic data generation operator applied to the original video sequence, where: + +$$ +\left(v _ {i}, \hat {v} _ {i}\right) \in \mathcal {D} (V), \quad \forall i \in \{1, \dots , T \}. \tag {2} +$$ + +Then $\hat{V} = \{\hat{v}_1,\hat{v}_2,\dots ,\hat{v}_T\}$ is the synthetic video sequence. GenProp is trained to satisfy the following objective across all frames $i\in \{2,\ldots ,T\}$ : + +$$ +\min _ {\mathcal {E}} \sum_ {i = 2} ^ {T} \mathcal {L} \left(\mathcal {G} \left(\mathcal {E} (\hat {V}), v _ {1}, i), v _ {i}\right) \right. \tag {3} +$$ + +where $\mathcal{L}$ is a region-aware loss designed to disentangle the modified and unmodified regions, enforcing stability in the unchanged areas while allowing for accurate propagation in the edited regions (details in Sec. 3.3). To ensure that the final output adheres to real video data distributions, synthetic data is fed exclusively to the content encoder. The I2V generation model, however, uses the original video, preventing the model from inadvertently learning synthetic artifacts. + +# 3.2. Model Design + +To preserve the unchanged parts of the original video and only propagate the modified regions, we integrate two additional components to the base I2V model: Selective Content Encoder and Mask Prediction Decoder, as shown in Fig. 4. + +Selective Content Encoder. The architecture of our SCE is a replicated version of the initial $N$ blocks of the main generation model, similar to ControlNet [59]. After each encoder block, the extracted features are added to the corresponding features in the I2V model, allowing a smooth and hierarchical flow of content information. The injection layer is one multilayer perceptron with zero initialization which will also be trained. Furthermore, for bidirectional information exchange, the features of the I2V model are fused with the SCE's input before the first block. This lets SCE be aware of the modified regions so that it can selectively encode the information in the unchanged region as intended. + +Mask Prediction Decoder. The Mask Prediction Decoder (MPD) is designed to estimate the spatial regions requiring editing, helping the encoder disentangle changes from the unchanged content. While SCE utilizes the initial $N$ blocks of the I2V model, MPD mirrors this by using the final block along with one multilayer perceptron (MLP) as the final layer. It takes the latent representation from the penultimate block, which contains rich spatial and temporal information, and processes it through the MLP layer. This restores the temporal dimension, matching it to the number of video frames. The final output is trained to match the instance mask of the video via an MSE loss [10] $\mathcal{L}_{\mathrm{MPD}}$ . This guides the model to focus on the edited regions and significantly improves the accuracy of the attention maps. + +# 3.3. Region-Aware Loss + +In our training process, we use instance segmentation data to ensure that both the edited and unedited regions receive appropriate supervision. We design a Region-Aware Loss (RA Loss), shown in Fig. 5, to balance the loss of both regions, even when the edited areas are proportionally small. + +For an input video $\hat{V} = \{\hat{v}_1,\hat{v}_2,\dots ,\hat{v}_T\}$ and instance + +![](images/c06190d4cafc466641804ced634586b5de399b9fb526f85cd243fab02fd99c0c.jpg) +Figure 5. Region-Aware Loss. This loss helps the model to disentangle the edited region from the original content. + +level masks $M = \{m_1, m_2, \ldots, m_T\}$ , where $m_t \in \{0, 1\}^{H \times W}$ indicates edited regions in frame $\hat{v}_t$ , we apply Gaussian downsampling over the spatial dimensions and repeat over the temporal dimension to obtain a mask $\tilde{m}_t$ that is aligned to the shape of the latent representation of the video. The loss is separately computed for the mask and non-mask region, giving: + +$$ +\mathcal {L} _ {\text {m a s k}} = \mathbb {E} _ {t \sim \mathcal {U} (1, T)} \left[ \mathcal {L} _ {\mathrm {d}} \left(\tilde {m} _ {t} \cdot v _ {t} ^ {\text {o u t}}, \tilde {m} _ {t} \cdot v _ {t}\right) \right] \text {a n d} \tag {4} +$$ + +$$ +\mathcal {L} _ {\text {n o n - m a s k}} = \mathbb {E} _ {t \sim \mathcal {U} (1, T)} \left[ \mathcal {L} _ {\mathrm {d}} \left(\left(1 - \tilde {m} _ {t}\right) \cdot v _ {t} ^ {\text {o u t}}, \left(1 - \tilde {m} _ {t}\right) \cdot v _ {t}\right) \right], +$$ + +where $\mathcal{L}_{\mathrm{d}}$ denotes the diffusion MSE loss that measures the pixel-wise error between the generated frame $v_{t}^{\mathrm{out}}$ and ground truth $v_{t}$ . + +To further reduce the SCE's influence on the masked regions, we add a gradient loss $\mathcal{L}_{\mathrm{grad}}$ that minimizes the effect of the masked area in the encoder's input. Instead of computing second-order gradients, we approximate using a finite difference: + +$$ +\Delta f = \frac {f (\mathcal {E} (\hat {V} + \delta)) - f (\mathcal {E} (\hat {V}))}{\delta} \tag {5} +$$ + +where $f(\mathcal{E}(\hat{V}))$ represents the encoder's feature, and $\delta$ is a small perturbation. The gradient loss is defined as: + +$$ +\mathcal {L} _ {\operatorname {g r a d}} = \mathbb {E} _ {t \sim \mathcal {U} (1, T)} [ \tilde {m} _ {t} \cdot \| \Delta f \| _ {2} ]. \tag {6} +$$ + +The RA Loss $\mathcal{L}$ is a weighted sum of all three terms to ensure sufficient supervision on both masked and unmasked areas: + +$$ +\mathcal {L} = \mathcal {L} _ {\text {n o n - m a s k}} + \lambda \cdot \mathcal {L} _ {\text {m a s k}} + \beta \cdot \mathcal {L} _ {\text {g r a d}} + \gamma \cdot \mathcal {L} _ {\text {M P D}} \tag {7} +$$ + +# 3.4. Synthetic Data Generation + +Creating a large-scale paired video dataset can be costly and challenging especially for video propagation, as it is difficult to encompass all video tasks. To address this, we propose to use synthetic data derived from video instance segmentation datasets. In our training, we use YoutubeVOS [54], SAM-V2 [39], and an internal dataset. However, this data generation pipeline can be applied to any available video instance segmentation dataset. Specifically, we adopt + +a mix of augmentation techniques to the segmentation data, tailored to various propagation sub-tasks: (1) Copy-and-Paste: Objects from one video are randomly segmented and pasted into another, simulating object insertion; (2) Mask-and-Fill: The masked region undergoes inpainting, creating realistic edits within selected regions; (3) Color Fill: The masked area is filled with specific colors, representing basic object tracking scenarios. For (3), $V$ will be sent to $\mathcal{E}$ and $\hat{v}_1$ will be sent to $\mathcal{G}$ in Eq. 3. Each synthetic data type aligns with a distinct task, enabling our model to generalize across diverse applications. Task embeddings corresponding to these augmentation methods are injected into the model, guiding the model to adapt based on the augmentation type. Note that despite the variety of data creation methods and tasks, the core function of SCE remains consistent: encode the unedited information while the I2V model maintains the generative capabilities to propagate the edited regions. More details about each augmentation technique are provided in the Supplementary Material. + +# 4. Experiments + +# 4.1. Implementation Details + +As GenProp is a general framework, we experiment with both a DiT architecture similar to Sora [32] and a U-Net architecture based on Stable Video Diffusion (SVD) [5] as the base video generation model. For the former, it is trained for I2V generation on 32, 64, and 128 frames at 12 and 24 FPS, with a base resolution of $360\mathrm{p}$ . SCE (24 blocks) and MPD are trained while the I2V model is frozen. The results can be upscaled to $720\mathrm{p}$ using a super-resolution model. The learning rate is set to 5e-5 with a cosine-decay scheduler and a linear warmup. An exponential moving average is applied for training stability. A gradient norm threshold of 0.001 prevents training instability. Classifier-free guidance (CFG) value is set to 20, and the data augmentation ratio is set to $0.5 / 0.375 / 0.125$ for copy-and-paste/mask-and-fill/color fill. In the RA loss, $\lambda$ is $2.0$ , $\beta$ is $1.0$ , and $\gamma$ is $1.0$ . All experiments were conducted on 32/64 NVIDIA A100 GPUs for different architectures. We find that the DiT backbone has a better video generation quality. Our main results are from this DiT variant while the ablation studies are conducted with the SVD-based architecture. Please refer to the Supplementary Material for the results based on SVD. + +# 4.2. Comparisons + +As generative video propagation is a new problem, we compare the SotA methods in each of the three sub-tasks of GenProp. Note that our model is able to handle these tasks within the same model and further cover additional tasks such as outpainting as well as combinations of these sub-tasks as shown in the bottom row of Fig. 1. We provide extensive results in the Supplementary Material. + +![](images/b0f7fc62e691ba683e52c84eec18a322470ce3a2bebc2ae212881d2f8df27f48.jpg) +Figure 6. Visual Comparison in Multiple Video Tasks. GenProp demonstrates versatile editing capabilities, (a) allowing seamless modification of objects into those with vastly different shapes with independent motion and (b) enabling background edits. For object removal, GenProp excels at (c) effectively removing object effects together with the object and (d) realistically reconstructing large occluded areas. It is further able to perform instance tracking of objects and their effects when solid color fills are given as the first frame (see (e)). + +Diffusion-based Video Editing In Fig. 6 (a) and (b), we compare GenProp with other diffusion-based video editing methods, including text-guided and image-guided approaches. InsV2V [8] relies on instruction text for controlling generation. However, due to its limited training + +data, it struggles with significant shape changes and does not support object insertion. Pika [2] also uses text prompts to edit within a box region, but it performs poorly when the object's shape changes substantially and cannot handle background edits or object insertion. AnyV2V [27] + +
MethodClassic Test SetChallenging Test Set
\(PSNR_m\uparrow\)CLIP-T ↑CLIP-I ↑GenProp preference % AlignmentQuality\(PSNR_m\uparrow\)CLIP-T ↑CLIP-I ↑GenProp Preference % AlignmentQuality
InsV2V [8]28.9990.30490.973760.0060.0028.8420.29060.971881.8275.00
AnyV2V [27]32.0900.30500.967695.5686.6728.3380.33020.957697.7895.56
Pika [2]32.5680.32260.992362.2255.5631.3290.30230.988688.8986.67
ReVideo [31]31.7650.31960.977775.5671.1129.9200.32260.979884.4482.22
GenProp (Ours)33.8370.32290.9825--32.1630.33360.9904--
+ +Table 1. Video editing benchmark compared to existing models. $\mathrm{PSNR}_m$ measures the consistency outside the edited region. CLIP-T and CLIP-I measure text alignment and frame consistency. User study shows the percentage of users who preferred Ours over the compared method on alignment (left) and quality (right). GenProp significantly outperforms the other methods on the Challenging Set. + +
MethodCLIP-I ↑GenProp Preference %
AlignmentQuality
SAM + Propainter0.980982.2275.56
ReVideo [31]0.972886.3677.27
GenProp (Ours)0.9879--
+ +is a training-free method that uses the first frame to guide editing. While it handles appearance changes, it fails when there are large shape or background modifications, often resulting in degradation or ghosting effects. Like InsV2V and Pika, it also cannot insert objects. We use ReVideo [31] to manage large shape changes by first removing an object and then re-inserting it, but this two-stage process has drawbacks. The box-based region can cause blurry boundaries, and object motion is affected by the original point tracking, leading to accumulated errors. Additionally, the box region limits its ability to edit complex backgrounds effectively. + +Video Object Removal For object removal, we compare GenProp with a traditional inpainting pipeline, where we cascade two SotA models to achieve a propagation-like inpainting, since traditional methods require a dense mask annotation for all frames: SAM-V2 [39] for mask tracking, then Propainter [64] for inpainting the regions in the estimated masks. As shown in Fig. 6 (c) and (d), GenProp has several advantages: (1) no need for a dense mask annotation as input; (2) removal of object effects like reflections and shadows; (3) removal of large objects and natural filling within large areas. + +Video Object Tracking We compare GenProp with SAM-V2 [39] on tracking performance in Fig. 6 (e). Since SAM-V2 is trained on the large-scale SA-V dataset, it is expected that SAM-V2 often produces more precise tracking masks than GenProp. Additionally, GenProp is slower than real-time tracking methods like SAM-V2. However, it has notable advantages. Due to its video generation pretraining, GenProp has a strong understanding of physical rules. As shown in Fig. 6, unlike SAM-V2, which struggles with ob + +Table 2. Object removal comparison to other methods. GenProp outperforms baselines on consistency, alignment, and quality. + +
MethodCLIP-T ↑CLIP-I ↑
w/o MPD0.32520.9834
w/o RA Loss0.32610.9825
GenProp (Ours)0.33160.9872
+ +Table 3. Ablation study. Both MPD and RA loss can improve the success rate of editing and the quality of the output video. + +ject effects like reflections and shadows due to limited and biased training data, GenProp can consistently track these effects. This highlights the potential of approaching classic vision tasks with generation-based models. + +Quantitative Results We conduct a quantitative evaluation on several test sets. For video editing (reported in Tab. 1), we evaluate on two types of test sets: (1) Classic Test Set, which is TGVE [51]'s DAVIS [36] part and its "Object Change Caption" as the text prompt, focusing on object replacement and appearance editing; (2) Challenging Test Set, which is 30 manually collected videos from Pexels [1] and Adobe Stock [3] including large object replacement, object insertion and background replacement. For (2), the first frame is edited using a commercial photo editing tool. For Pika [2], we use the online boxing tool, running it three times for each result. For ReVideo [31], we select a box region, then to track appearance changes, we use its code to extract the original object's motion points. For edits with significant shape changes, we first remove the original object and then insert the new object, assigning a future trajectory. For assessing the consistency in the unchanged regions, we measure the PSNR outside the edit mask, denoted as $\mathrm{PSNR}_m$ . For cases with large shape changes, we apply a rough mask over the original and edited regions, only calculating the PSNR on areas outside these masks. For text alignment, we compute the cosine similarity between the CLIP [38] embeddings of the edited frame and the text prompt (CLIP-T) [31, 34, 51]. For consistency, we calculate the distance between CLIP [38] features across frames (CLIP-I) [31, 34, 51]. As shown in Tab. 1, GenProp outperforms the other methods on most metrics, especially on the Challenging Test Set. Pika exhibits better consis + +![](images/a1b97a1c724af04e52571266733519dee29d85e3ef7b6930507b43b41071b0db.jpg) +Figure 7. Visual comparison of model variants, showing the effect of MPD training (top), RA loss (middle) and Color Fill (bottom). + +tency on the Classic Test Set, as its bounding box performs reasonably well when object shapes remain relatively unchanged. ReVideo degrades on multiple objects. + +For object removal, we collect 15 videos with complex scenes, including object effects and occlusions, as existing test sets lack coverage of these cases. For SAM, we click on the object and side effects to ensure complete coverage. As shown in Tab. 2, GenProp achieves the highest consistency, while ReVideo may produce bounding box artifacts, and ProPainter struggles with object effects. + +As quality metrics often do not correctly capture the realism of the generated results, we use Amazon MTurk [45] to conduct a user study with a total of 121 participants. Each participant views videos generated by GenProp and a random baseline, along with the original video and the text prompt. They are asked two questions: 1) Which video aligns better with the instructions? 2) Which video is visually better? Participants then select one video for each question. In Tables 1 and 2, we show the percentage of time users prefer Ours over the competing baselines (alignment/quality). GenProp outperforms all baselines by a large margin, especially on the Challenging Test Set. + +# 4.3. Ablation Study + +Mask Prediction Decoder In Tab. 3, we evaluate the effect of MPD on the Challenging Test Set, showing that it can improve both Text Alignment and Consistency. As shown in + +Fig. 7 rows 1 and 2, without MPD, the output mask is often highly degraded, leading to worse removal quality. Without explicit supervision with MPD, the model may be confused which part to propagate and which part to preserve in the original video, causing partially removed objects to reappear in the following frames. MPD helps the disentanglement and both the removal results and predicted masks become more accurate with MPD, allowing for full object removal even with heavy occlusion. + +Region-Aware Loss In Tab. 3, we further test the effectiveness of the proposed RA Loss on the Challenging Test Set. A core challenge in GenProp is that SCE can mistakenly select all regions from the original video including the edited areas, weakening the I2V generation ability due to the reconstruction loss. As shown in Fig. 7 rows 3-5, without RA Loss, the original object tends to gradually reappear, hindering the propagation of the first-frame edit (the green motor). With RA Loss, the edited areas are able to be propagated in a stable and consistent way. + +Color Fill Augmentation Color Fill augmentation is another crucial factor for addressing the propagation failure. While copy-and-paste and mask-and-fill augmentations allow the model to implicitly learn object modifications, replacements, and deletions, color filling explicitly trains it for tracking, guiding the model to maintain modifications made in the first frame throughout the sequence, with the prompt "track colored regions". As shown in Fig. 7 rows 6-8, changing the girl into a small cat is challenging due to the significant shape difference. However, with color fill augmentation, GenProp successfully propagates this large modification throughout the sequence. + +# 5. Conclusion + +In this paper, we design a novel generative video propagation framework, GenProp, that harnesses the inherent video generation power of I2V models to achieve various downstream applications including removal, insertion and tracking. We demonstrate its potential by showing that it is able to expand the range of achievable edits (e.g., remove or track objects together with their associated effects) and generate highly realistic videos, without relying on traditional intermediate representations like optical flow or depth maps. By integrating a selective content encoder and leveraging an I2V generation model, GenProp consistently preserves unchanged content while dynamically propagating the changes. Synthetic data and the region-aware loss further enhance its ability to disentangle and refine edits across frames. Experimental results demonstrate its effectiveness, establishing it as a robust, flexible solution that surpasses prior methods in scope and precision. 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CoCoCo: Improving Text-Guided Video Inpainting for Better Consistency, Controllability and Compatibility. arXiv preprint arXiv:2403.12035, 2024. 2 \ No newline at end of file diff --git a/CVPR/2025/Generative Video Propagation/images.zip b/CVPR/2025/Generative Video Propagation/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..1e00375074b5835dd1d7bcd8e0776c3f39edcff6 --- /dev/null +++ b/CVPR/2025/Generative Video Propagation/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:5ecc4cf99cdd5b65c673a8720947a3a3934551583f45e83625f4971820230eb3 +size 1043643 diff --git a/CVPR/2025/Generative Video Propagation/layout.json b/CVPR/2025/Generative Video Propagation/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..4322ab51b8e5ab50bef3840823ae9a85ce1eae3a --- /dev/null +++ b/CVPR/2025/Generative Video Propagation/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:b73cb1d853ffbf5037fa3ed22f60cd46044529811aa6bd78fe4db33e29b59a3b +size 340953 diff --git a/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_content_list.json b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..7cbbfcb1b33fb709ae616d43b9cc41b04303edd8 --- /dev/null +++ b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:64773cd431741f1e13cfe897bca0ea62fe169cf20cce192d29a72c2d119195d2 +size 81705 diff --git a/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_model.json b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_model.json new file mode 100644 index 0000000000000000000000000000000000000000..0aa0d5ec5cd9d03dd00988e88873c4dbaaa826e2 --- /dev/null +++ b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:09cfc36ae1e5e463f13bed3082d39e5aec0c911051db6fced777af3ff4c8c791 +size 99530 diff --git a/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_origin.pdf b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..80a1dafc8807feff9c66185edd2770eac35d37bd --- /dev/null +++ b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/34978457-438a-44a4-8e52-8d1c37bd09c2_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:c6848550af5a7f52e4272063da6e07a9406b372e04c49bf35eaa0c7683be0aea +size 3792702 diff --git a/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/full.md b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/full.md new file mode 100644 index 0000000000000000000000000000000000000000..957b021962d965bfc0b4871ffd5b01817a6a0ab4 --- /dev/null +++ b/CVPR/2025/Generative Zero-Shot Composed Image Retrieval/full.md @@ -0,0 +1,272 @@ +# Generative Zero-Shot Composed Image Retrieval + +Lan Wang $^{1}$ Wei Ao $^{1}$ Vishnu Naresh Boddeti $^{1}$ Ser-Nam Lim $^{2}$ + +$^{1}$ Michigan State University $^{2}$ University of Central Florida + +{wanglan3, aowei, vishnu}@msu.edu sernam@ucf.edu + +# Abstract + +Composed Image Retrieval (CIR) is a vision-language task utilizing queries comprising images and textual descriptions to achieve precise image retrieval. This task seeks to find images that are visually similar to a reference image while incorporating specific changes or features described textually (visual delta). CIR enables a more flexible and user-specific retrieval by bridging visual data with verbal instructions. This paper introduces a novel generative method that augments Composed Image Retrieval by Composed Image Generation (CIG) to provide pseudotarget images. CIG utilizes a textual inversion network to map reference images into semantic word space, which generates pseudo-target images in combination with textual descriptions. These images serve as additional visual information, significantly improving the accuracy and relevance of retrieved images when integrated into existing retrieval frameworks. Experiments conducted across multiple CIR datasets and several baseline methods demonstrate improvements in retrieval performance, which shows the potential of our approach as an effective add-on for existing composed image retrieval. Project Page: https://lanlw.github.io/CIG/ + +# 1. Introduction + +Composed Image Retrieval (CIR) takes the composed vision-language queries as input and searches for target images [3, 8, 17, 24, 30, 49]. By combining visual data and verbal instructions, CIR enables a more flexible, user-specific, and precise image retrieval. The composed query includes a reference image $I_{r}$ and a delta caption $T_{r}$ . The target image $I_{t}$ should visually be like the reference image $I_{r}$ but capture the content described by the caption $T_{r}$ [4]. Compared to image-only or text-only retrieval, it is easier for the user to find an image $(I_{r})$ that depicts the necessary visual content and then describe the desired difference in natural language [49]. + +CIR datasets, like CIRR [30] and CIRCO [4], are made up of $(I_r, T_r, I_t)$ triplets. Constructing CIR datasets, therefore, requires huge human labeling efforts, which hinders + +the widespread adoption and development of CIR algorithms. Existing methods can be categorized into two groups, namely supervised CIR and zero-shot CIR. Supervised CIR methods [2, 7, 9, 11, 19, 21, 24, 31, 32, 41, 46, 49, 52], are trained on CIR datasets. However, due to the lack of large-scale triplets datasets, supervised methods can only be trained and evaluated on small datasets, which limits their generalization capability. On the contrary, zero-shot methods [1, 4, 15, 26, 29, 38, 43, 44, 51] do not require triplets and train solely based on the reference image and delta caption. + +The mainstream solutions like SEARLE [1, 4], Pic2Word [38], Context-I2W [45], LinCIR [15] encode the reference image as a pseudo token and further train a fusion encoder, $\Phi(I_r, T_r)$ , that composes the reference image and delta caption in the language embedding space. There is a representation gap between the composed embeddings $(\Phi(I_r, T_r))$ and the target image embeddings $(\psi(I_t))$ . The former is in the language space, while the latter is in the image space. Intuitively, if we train a fusion encoder $(\Psi(I_r, T_r))$ in the image space, we would improve the image retrieval performance because now both $\Psi(I_r, T_r)$ and $\psi(I_t)$ are in the image space. However, TIRG [49] reports inferior performance when integrating the text information into image embedding space. Some LLM-based methods, such as CIREVL [20], have significantly improved performance. However, their inefficiency remains an issue for retrieval. In this paper, we therefore propose a different approach towards this by asking the question: Can a pseudo target image help composed image retrieval? + +To answer the above question, we propose a Composed Image Generation (CIG) approach to assist the CIR task from image space. Our method is straightforward, utilizing the reference image and delta caption to generate pseudotarget images, which are then used to aid image retrieval, as shown in Figure 1. Our method does not require triplet datasets for pre-training, and it can serve as an add-on to any existing CIR method to enhance its performance. First, during the training phase, we only need image-caption pairs. Using pre-trained text inversion networks, we map the image to the token embedding space. The caption is then encoded to produce a composed embedding, which we use as + +![](images/bc25054d3dfc5b8121d582d12cae7913738259cbdede1c2f60ebc0f57233730c.jpg) +Figure 1. Zero-Shot Composed Image Retrieval vs. Pseudo Target-Aided Composed Image Retrieval. Conventional ZS-CIR methods map the image latent embedding into the token embedding space by textual inversion. The proposed Pseudo Target-Aided method provides additional information for composed embeddings from pseudo-target images. + +a condition to train latent diffusion models [36] for reconstructing the same image, removing any need for triplets during training. Interestingly, we found that such a model, trained under self-supervision without even seeing a single ground truth target image, is capable of generating pseudotarget image during inference that greatly resembles the ground truth (see Figure 3 and 4 for example). During the retrieval stage, we map both the reference and pseudo target images to the token embedding space and encode them with the delta caption to generate a more informative composed textual embedding for target image retrieval. Our method can improve the performance of various approaches with only a minimal increase in time required. + +Our contribution can be summarized as follows: 1) We explore an effective generative method for zero-shot compositional image retrieval, CIG, which can be combined with any CIR methods; 2) Our training process does not require any triplets, utilizing only image-caption pairs in a self-supervised training regime; 3) We conduct multiple experiments on different baselines and obtain significant improvements over different benchmarks; 4) CIG provides a new direction for the CIR task, directly generating a new image by users' instruction while staying faithful to the reference image. + +# 2. Related Work + +# 2.1. Composed Image Retrieval (CIR) + +Composed image retrieval (CIR) enables users to input multimodal queries to search for images. CIR can be used for fashion [50] and e-commerce recommendation systems [2, 3, 27]. Compared to traditional image-only and text-only retrieval, users do not need to describe visual content and only need to provide the necessary difference caption. Existing works focus on two important problems: (1) how to fuse embeddings of a reference image and a delta caption, and (2) how to train CIR models without (reference image, delta caption, target image) triplet datasets. For (1), naive fusion shows inferior performance due to the multimodal gap between image and text. Recently, SEARLE [4], Pic2Word [38], LinCIR [15] treat the reference image as a pseudo token and plug the pseudo token into the caption sentence (referred to as pseudo caption), leading to + +SOTA performance. For (2), the motivation stems from the fact that building CIR datasets requires huge human efforts. Zero-shot approaches that do not use CIR datasets during training arise in popularity as a result. Inspired by VLMs, the supervision is the contrastive loss between embeddings of the reference image and the pseudo caption. In this paper, we explore a new direction by generating pseudo images. + +# 2.2. Vision-Language Model (VLM) + +Vision-language models (VLMs) align image and text features in the same embedding space [35]. Transformers [47] are usually employed as image and text encoders in VLMs because they can effectively extract features from images [12] and texts [10]. VLMs are pretrained on large-scale datasets of (image, text) pairs and then finetuned for downstream tasks like classification, recognition, and localization. CLIP [35] (Contrastive Language-Image Pretraining) jointly trains image and text encoders to align corresponding pairs. VLMs show increasing representation learning ability under the scaling law [5, 13], but incur high computational costs for training. In addition to the above contrastive learning, PaLI-3 [6] encodes images to visual tokens that are concatenated with queries. PaLI-3 achieves SOTA performance on vision-language benchmarks while decreasing model size by $10\times$ . To alleviate the training cost of VLMs, BLIP-2 [25] bootstraps off-the-shelf pretrained vision and language models and introduces a lightweight network to bridge the modality gap. + +# 2.3. Diffusion Models + +Diffusion models [16, 42] are a class of generative neural networks motivated by non-equilibrium thermodynamics. Diffusion models have been shown to generate high-quality images [33]. The original diffusion models operated in the pixel space, leading to prohibitively high computational costs. To address this problem, the latent diffusion model [36] was introduced that operates in the latent space by using variational autoencoder (VAE) [22]. Furthermore, to guide the image generation by the textual prompt, stable diffusion uses the cross attention [47] mechanism to integrate the text embedding of the prompt. Recent advancements in personalized text-to-image generation have focused on adapting diffusion models to synthesize images + +![](images/286d0c2e9cc88fbfd0ac24b14b73346d2546307905cd83a69727a3d5008175bb.jpg) +Figure 2. Overview of the proposed Composed Image Generation (CIG). During training, CIG model uses composed prompt embeddings as textual conditions, and learn image information from them. In inference stage, the reference image and delta caption form the composed prompt embedding, which CIG model utilizes to generate pseudo target images. These pseudo target images assist in improving ZS-CIR. Top: the training process, including textual inversion network pretraining (left) and CIG model pertaining (right); bottom: inference process for CIR. + +of specific subjects or concepts [14, 23, 37]. These approaches improve subject and concept fidelity in diffusion-based generative models, inspiring subsequent work on controllable and personalized image synthesis. In this paper, we leverage a latent diffusion model to generate pseudo target images conditioned on composed textual embeddings. This modification enables the model to effectively synthesize images that integrate information from both the original reference image and the caption. + +# 3. Methodology + +In composed image retrieval, the user is querying an image database with a reference image $I_{r}$ and delta caption $T_{r}$ pair, as shown in Figure 1. The matched image in the database is called the target image $I_{t}$ . As an example, consider that the user is querying a photo of "dog". The reference image includes the necessary visual content of a dog, while a delta caption would describe the difference between the reference and target images, e.g., "The main color of the face has changed from brown to white". + +# 3.1. Preliminaries + +Image and Text Encoders. Following recent approaches like SEARLE [4], Pic2Word [38], LinCIR [15], we apply a pretrained VLM, specifically CLIP [35], by taking advantage of the multimodal representation learning ability of CLIP encoders. The CLIP model includes an image encoder $\psi(I)$ and a text encoder $\phi(T)$ . The CLIP model was + +pretrained on 400 million (image, text) pairs, so the image and text embeddings yielded by its encoders are aligned in a common image-language feature space. In our pipeline, the visual feature of a reference image is extracted by the image encoder, which is then integrated into a delta caption text. Finally, the text encoder extracts the composed feature from the caption (see the upper left panel of Figure 2). Both image and text encoders are frozen during training due to the large number of parameters ( $>100$ million). Instead, composed image-language models learn a fusion encoder $\Phi(I_r, T_r)$ that maps the reference image and delta caption, $(I_r, T_r)$ , to a composed feature in an (image-)text embedding space, i.e. $\Phi(I_r, T_r) \mapsto x \in \mathbb{R}^d$ where $d$ is the predefined dimension of the embedding space. The features of the reference images are obtained by an image encoder, $\psi(I_t) \mapsto y \in \mathbb{R}^d$ . + +During training, the cosine similarity between $x$ and $y$ , $\frac{xy}{\|x\|\|y\|}$ , is maximized. During inference, the target image is retrieved based on $I_{t} = \operatorname{argmax}_{I\in \mathcal{D}}\frac{\Phi(I_{r},T_{r})\psi(I)}{\|\Phi(I_{r},T_{r})\|\|\psi(I)\|}$ . There are two directions to learn the fusion encoder: (1) Language $\mapsto$ Image, $\Psi(I_r,T_r)$ : inject language information into image embeddings, and (2) Image $\mapsto$ Language, $\Phi(I_r,T_r)$ : inject image information into language embeddings. (1) TIRG [49] edits the image embeddings by integrating the language information using a gated residual connection. (2) CBIR [2] directly fuses embeddings of the reference image and the delta caption and fine-tunes the text encoder. SEARLE [4] uses a CLIP image encoder to gener + +ate a pseudo token given a reference image and then plugs in the pseudo token into the delta caption. Then, a CLIP text encoder is applied to map the edited delta caption to an embedding. In addition to frozen image and text encoders, Pic2Word [38] introduces a small trainable mapping network to learn the pseudo token given the image embedding yielded by the image encoder. LinCIR [15] shares similar ideas as SEARLE and pic2Word but only trains the text encoder using self-supervised learning. + +Diffusion Models. Latent Diffusion Models (LDM) [36] works in the latent space of powerful pretrained autoencoders, which reduce the computational complexity of high-dimensional data. The model includes three components: the encoding to latent space, the diffusion process within this space, and the final decoding to reconstruct the data. Encoder $\mathcal{E}$ compresses images $x$ to latent $z = \mathcal{E}(x)$ , and Decoder $\mathcal{D}$ reconstructs it back to image $\mathcal{D}(z) \approx x$ . A time-conditional UNet $\varepsilon_{\theta}(o,t)$ is trained to remove the noise using the objective: + +$$ +L _ {L D M} := \mathbb {E} _ {\varepsilon (x), \varepsilon_ {\theta} \sim \mathcal {N} (0, 1), t} [ \| \varepsilon - \varepsilon_ {\theta} (z _ {t}, t) \| _ {2} ^ {2} ]. \tag {1} +$$ + +Similar to other generative models, LDM can be implemented with a conditional denoising autoencoder: + +$$ +L _ {L D M} := \mathbb {E} _ {\mathcal {E} (x), y, \varepsilon_ {\theta} \sim \mathcal {N} (0, 1), t} [ \| \varepsilon - \varepsilon_ {\theta} \left(z _ {t}, t, \tau_ {\theta} (y)\right) \| _ {2} ^ {2} ], \tag {2} +$$ + +where $y$ is the conditional input such as text, $\tau_{\theta}$ is a domain specific encoder that projects $y$ to an intermediate representation. + +# 3.2. Composed Image Retrieval through Composed Image Generation + +Figure 2 shows the framework of the proposed CIG. Given an image-caption dataset with image-caption pairs $S = \{(x_i, t_i)\}_{i=1}^N$ , where $x \in \mathcal{X}$ and $t \in \mathcal{T}$ are images and captions, we first map the images to text embedding space and construct composed prompt embeddings. Then, we fine-tune a latent diffusion model to reconstruct the image using composed prompt as textual condition, after which the pretrained diffusion model is used to generate pseudo-target images in the inference stage. It is noteworthy that the fine-tuning is in fact self-supervised, seeking only to reconstruct the original image and does not require any triplets, but interestingly induced an ability to generate pseudo target during inference. Finally, those generated images are utilized to boost composed image retrieval. + +Textual Inversion Network. The textual inversion network $f_{M}$ learns a projection from the image latent embedding space to the token embedding space. Instead of learning from scratch, we employed a pre-trained textual inversion network from mainstream zero-shot CIR methods [4, 15, 38] since they are either pre-trained with a large number of image-text pairs with contrastive loss or augmented with carefully designed text context. Those pre + +trained textual inversion networks have a good ability to extract information for reference images, which is important for composed image generation. Following methods [4, 15], we use the text embedding space of the CLIP text encoder as the target embedding space. The pretrained CLIP image encoder $\psi (\cdot)$ is first adopted to extract the image feature, then the pre-trained textual inversion networks project the CLIP features to word embeddings: $s = f_{M}(\psi (\pmb {x}))$ + +Composed Image Generation. To integrate the pseudo token embedding with text, we construct the template $T$ "a photo of $S^*$ that {caption}" and extract its features using the CLIP text encoder. Then, the composed prompt embedding is obtained: $p = \phi(T)$ . To make the caption a better contextual description, we apply a keyword masking strategy to mask a keyword token from each caption. The "keyword" is defined as consecutive adjectives and nouns, which follows the settings of [15]. + +We finetune Latent Diffusion Models to adopt the composed prompt embedding as a textual condition for reconstruction. Unlike pure text prompts, our composed prompt embedding contains image information, which in effect induces the model to generate target images under the instruction of the delta caption and maintain the information contained in the reference images. A time-conditional UNet is finetuned for CIG objective: + +$$ +L _ {C I G} = \mathbb {E} _ {\mathcal {E} (\boldsymbol {x}), \varepsilon_ {\theta} \sim \mathcal {N} (0, 1), t} [ \| \varepsilon - \varepsilon_ {\theta} (\boldsymbol {z} _ {t}, t, \boldsymbol {p}) \| _ {2} ^ {2} ], \tag {3} +$$ + +where $z = \mathcal{E}(\pmb{x})$ is images latent compressed by encoder $\mathcal{E}$ from LDMs and $t$ is the timestep. + +In inference stage, we construct a new template $T_{\delta}$ "a photo of $S^{*}$ that {delta caption}" for CIG task. The LDMs take the composed embedding $\pmb{p}_{\delta} = \phi (T_{\delta})$ of delta caption $T_{r}$ and reference image $I_{r}$ as input, generating pseudo target image $\tilde{\pmb{x}}$ . + +Composed Image Retrieval. To benefit CIR task, we combine pseudo target $\tilde{\pmb{x}}$ with the reference image $I_{r}$ and delta caption $T_{r}$ in text embedding space. We conduct a similar way as generating the composed prompt embedding $\pmb{p}_{\delta}$ . We construct a new template $T_{\delta}$ for pseudo target images as "a photo of $S^{*}$ that {delta caption}" using word embeddings $\tilde{s} = f_{M}(\psi (\tilde{\pmb{x}}))$ , generating the composed text embedding of the pseudo image and delta caption, $\tilde{\pmb{p}}_{\delta}$ . Finally, the retrieved target is defined as: + +$$ +I _ {t} = \underset {I} {\operatorname {a r g m a x}} \frac {\left(\boldsymbol {p} _ {\delta} + \lambda \cdot \tilde {\boldsymbol {p}} _ {\delta}\right) \psi (I)}{\| \left(\boldsymbol {p} _ {\delta} + \lambda \cdot \tilde {\boldsymbol {p}} _ {\delta}\right) \| \| \psi (I) \|}, \tag {4} +$$ + +where $\lambda$ is a trade-off hyperparameter to control the weight of the composed text embedding of the pseudo image and delta caption. + +# 4. Experiments + +# 4.1. Experimental Settings + +Implementation Details. We employ the Stable Diffusion [36] V1-5 and SDXL [34] as our text-to-image models. We + +Table 1. Quantitative results on CIRR test set. Results of Pic2Word[38], SEARLE[4], LinCIR [15] and those baselines + CIG (highlight in gray), using different CLIP backbones and diffusion models as shown. CIG significantly improves the performance of different baselines. + +
MethodBackboneRecall@KRecallSubset@K
K = 1K = 5K = 10K = 50K = 1K = 2K = 3
Image-only6.8922.9933.6859.2321.0441.0460.31
Text-only21.8145.2257.4281.0162.2481.1390.70
Image + Text11.7135.0648.9477.4932.7756.8974.96
SEARLEViT-B/3224.0053.4266.8289.7854.8976.6088.19
SEARLE + CIG25.3354.8268.0590.4357.8678.2289.25
SEARLE + CIG-XL24.7554.3667.8190.5856.2477.1889.01
SEARLE + CIG-XL turbo25.5455.0168.2490.7257.5278.3689.35
Pic2Word23.9051.7065.3087.8053.7674.4687.07
SEARLE24.2452.4866.2988.8453.7675.0188.19
LinCIR25.0453.2566.68-57.1177.3788.89
Pic2Word + CIG24.6352.7565.2886.5156.9677.0188.82
SEARLE + CIGViT-L/1425.7154.5167.2388.9456.6076.7788.99
SEARLE + CIG-XL25.0854.4167.6689.5756.0777.0888.63
SEARLE + CIG-XL turbo26.7255.5268.1089.5957.9577.8189.45
LinCIR + CIG25.6454.7767.5989.0458.1278.3489.37
LinCIR + CIG-XL25.0653.6966.9989.0155.7876.6388.41
LinCIR + CIG-XL turbo26.1754.9467.6489.2358.077.8689.34
LinCIR35.2564.7276.05-63.3582.2291.98
LinCIR + CIGViT-G/1436.0566.3176.9693.8164.9483.1891.93
LinCIR + CIG-XL34.4364.5176.1293.5462.2481.3591.28
LinCIR + CIG-XL turbo35.4766.076.8993.5765.1383.2592.24
+ +adopt the textual inversion networks from [4] for Stable Diffusion V1-5 and [15] for SDXL. In evaluation, we also use SDXL turbo [39], a real-time diffusion model. For fair comparison, in inference stage, we use the baselines' text inversion network and only provide the generated pseudo target images as additional information. To finetune the text-to-image model, we use 595K filtered image-text pairs from CC3M [40] provided by [28] as our training dataset. It contains 595K images-caption pairs that were selected to obtain a more balanced concept coverage distribution. We use their synthetic BLIP captions and re-download the original-sized images, resulting in 490K images-caption pairs. We take the first consecutive adjectives and noun as keywords and remove them from the caption. During training, we only update the key and value projection layers in the cross attention layer. Our model is trained with a learning rate of 1e-6 using a batch size of 16 on $4 \times$ A6000 GPUs. + +Datasets and Baselines. We use the CIRR [30], CIRCO [4], Fashion-IQ [50] and GeneCIS [48] datasets for CIR task. Following the original benchmarks, we use Recall@k as the metric on the CIRR, GeneCIS, and Fashion-IQ and the mean average precision (mAP@k) for the CIRCO dataset. We compare with recent ZS-CIR methods: Pic2Word [38], SEARLE [4] and LinCIR [15], with different backbones including ViT-B, ViT-L and ViT-G CLIP. In addition, we also compared with LLM based CIR method CIREVL [20]. The variants "image-only", "text-only" and + +“image+text” denote performing retrieval with CLIP using only the reference image, delta caption, as well as averaging their embeddings respectively. + +# 4.2. ZS-CIR Benchmark Comparisons + +We evaluate three different versions of CIG models: CIG, CIG-XL, CIG-XL turbo, which uses Stable Diffusion V1-5, SDXL, SDXL turbo as base models separately. + +CIRR. Table 1 reports the result for CIRR test set. As previously observed, in CIRR, the reference images are almost not related to the target images [4, 20, 38]. Therefore, our method has a significant advantage on this dataset, as generating pseudo target images helps bridge the gap with the actual target images. Experimental results also confirm this. There is an improvement in Recall and $Recall_{Subset}$ across different baselines. The proposed CIG got the most significant improvement for SEARLE, especially with ViT/L14 backbones, CIG-XL turbo increases the top 1 recall from 24.24 to 26.72. Overall, on the CIRR dataset, our method shows a stronger improvement over SEARLE compared to other baselines in terms of recall. + +Fashion-IQ. Table 2 provides the result for Fashion-IQ validation set. Compared to other benchmarks, the improvement on the Fashion IQ dataset is slightly less significant. This may be due to the more challenging nature of clothing related generation, making the benefits from generated images limited. Previous work has shown that enhancing + +Table 2. Quantitative results on Fashion-IQ validation set. Results of Pic2Word[38], SEARLE[4], LinCIR [15] and those baselines + CIG, using different CLIP backbones and diffusion models as shown. CIG improves the performance over different dress types. + +
MethodBackboneShirtDressTopteeAverage
R@10R@50R@10R@50R@10R@50R@10R@50
Image-only6.9214.234.4612.196.3213.775.9013.37
Text-only19.8734.9915.4235.0520.8140.4918.7036.84
Image + TextViT-B/3213.4426.2513.8330.8817.0831.6714.7829.60
SEARLE24.4441.6118.5439.5125.7046.4622.8942.53
SEARLE + CIG-XL24.5841.4117.7439.8625.6546.3522.9942.54
SEARLE + CIG-XL turbo24.7341.4618.9439.6625.5046.6623.0642.59
Pic2Word26.2043.6020.0040.2027.9047.4024.7043.70
SEARLE26.8945.5820.4843.1329.3249.9725.5646.23
LinCIR29.1046.8120.9242.4428.8150.1826.2846.49
Pic2Word + CIG25.7143.6220.6742.6427.4448.1924.6044.82
Pic2Word + CIG-XLViT-L/1425.8643.3820.3842.1928.4548.2924.9044.62
Pic2Word + CIG-XL turbo26.0642.7920.8742.4428.5649.3125.1644.85
SEARLE + CIG-XL26.9945.4421.1243.3829.2750.3825.7946.40
SEARLE + CIG-XL turbo26.9945.4420.6243.5829.3750.4825.6646.50
LinCIR + CIG28.7047.0621.1243.8829.7350.2326.5247.05
LinCIR + CIG-XL28.6647.2021.2743.9829.8350.2826.5947.15
LinCIR + CIG-XL turbo28.9047.2521.1243.8829.7850.5426.6047.22
LinCIR46.7665.1138.0860.8850.4871.0945.1165.69
LinCIR + CIGViT-G/1447.1566.6339.6161.2850.6971.6545.8266.52
LinCIR + CIG-XL47.3566.6839.7160.9350.6971.3945.9266.34
LinCIR + CIG-XL turbo47.3066.4439.5661.0850.5471.5545.8066.35
+ +Table 3. Quantitative results on CIRCO test set. Results of SEARLE[4] and LinCIR [15] and those baselines + CIG (highlight rows in gray), using different CLIP backbones and diffusion models as shown. CIG improves the performance. + +
MethodBackbonemAP@k
k=5k=10k=25k=50
Image-only1.341.602.122.41
Text-only2.562.672.983.18
Image + Text2.653.254.144.54
SEARLEViT-B/329.359.9411.1311.84
SEARLE + CIG10.1910.611.8312.47
SEARLE +CIG-XL10.310.7912.1212.76
SEARLE +CIG-XL turbo10.4511.0212.3413.0
Pic2Word8.729.5110.6411.29
SEARLE11.6812.7314.3315.12
LinCIR12.5913.5815.0015.86
SEARLE + CIG12.1313.0214.6315.41
SEARLE + CIG-XLViT-L/1412.9513.6215.2816.05
SEARLE + CIG-XL turbo12.8413.6415.3216.17
LinCIR + CIG -XL12.9713.6415.1416.01
LinCIR + CIG -XL turbo12.8413.7715.2516.12
LinCIR19.7121.0123.1324.18
LinCIR + CIG -XLViT-G/1420.6421.9024.0425.20
LinCIR + CIG -XL turbo20.6221.8224.025.12
+ +text context information significantly improves results on this dataset [4, 15]. Nonetheless, we still achieved further improvements across all baselines. Therefore, our method can be effectively combined with strong baselines. + +![](images/292d3b0c92448bd7e55035cea4bf6a15817f7f0f13586710603b87ab57f591c4.jpg) +Figure 3. Qualitative Evaluation on CIRR validation datasets. CIG effectively make changes according to the caption while preserving the reference image features. + +![](images/aae6f85703da7e7374540ba187b84993c8c1c89c97dfdefd7c3c5a9ed3416ee7.jpg) +Figure 4. Qualitative Evaluation on Fashion-IQ validation datasets. CIG effectively modifies clothing while retaining original clothing features. + +Table 4. Quantitative results on GeneCIS test set. * denotes our reproduced LinCIR model using their official repo. Our results are based on reproduced LinCIR model. + +
MethodBackboneFocus AttributeChange AttributeFocus ObjectChange ObjectAvg R@1
R@1R@2R@3R@1R@2R@3R@1R@2R@3R@1R@2R@3
Pic2Word15.6528.1638.6513.8724.6733.058.4218.0125.776.6815.0524.0311.16
SEARLE17.0029.6540.7016.3825.2834.147.7616.6825.317.9116.8425.0512.26
LinCIR16.9029.9541.4516.1927.9836.848.2717.4026.227.4015.7125.0012.19
LinCIR*ViT-L/1416.6029.6540.3516.1927.9836.848.2117.9125.567.9615.6125.0512.24
LinCIR + CIG16.9529.4040.4316.0528.5537.178.4217.4526.738.5715.3624.8512.50
LinCIR + CIG-XL16.7029.6540.8515.8128.8837.418.3217.3525.468.0115.4624.2312.21
LinCIR + CIG-XL turbo16.8029.7040.9015.9128.8837.458.3717.3525.107.8615.4624.2912.24
LinCIR19.0533.0042.3017.5730.1638.0710.1019.0828.067.9116.3325.7113.66
LinCIR*ViT-G/1418.9532.9542.7017.9030.1138.979.8018.8827.767.7016.3325.9713.59
LinCIR + CIG19.0532.8542.4017.830.2639.1610.6119.2327.407.9116.9425.3613.84
LinCIR + CIG-XL19.1032.5542.5017.4230.3539.029.9518.4227.607.9116.2825.4113.60
LinCIR + CIG-XL turbo19.1532.9042.5017.5730.4538.879.9518.4227.457.2416.3325.0613.48
+ +Table 5. Quantitative comparison with LLM-based methods on CIRR and CIRCO test sets. The backboone is ViT-L/14 using OpenCLIP weights [18]. The reported CIREvL results are reproduced from their official implementation. + +
MethodCIRRCIRCO +mAP@k
Recall@KRecallSubset@Kk=5k=10k=25k=50
@1@5@10@50@1@5@10
CIREVL27.1856.9469.7489.5460.7581.0891.1122.4023.0525.1426.23
CIREVL + CIG27.3557.1369.5789.6960.8980.9291.1322.4623.1025.1826.26
+ +CIRCO. Table 3 provides the results for the CIRCO test dataset. This dataset addresses the presence of false negatives in previous datasets. It is built based on real-world images and includes multiple ground truth for each reference image. Our method again shows improvements across different baselines on CIRCO. Notably, for SEARLE, our XL and XL Turbo models exhibit significant enhancements. + +GeneCIS. The tasks in GeneCIS are different from previous datasets. It's a benchmark for conditional image similarity, applicable to four different retrieval tasks: focusing on an attribute or object, which involves finding images with a similar attribute or object, and changing an attribute or object, which involves altering a specific attribute or object while preserving other characteristics. This dataset is more challenging because the captions include just 1 - 2 words, which is not sufficient for generation. Table 4 shows the results on GeneCIS dataset. Our method produced improvements across all four different tasks. In object related task, our method provides more improvements. This is may be because object changes are easier for diffusion model understand than attributes. + +# 4.3. Ablation Study and Performance Analysis + +In this section, several experiments are conducted to provide a comprehensive understanding of CIG, including ablation studies, qualitative and quantitative evaluation on generated examples, and efficiency evaluations. More discussion can be found in Appendix. + +Qualitative Evaluation on Composed Image Generation. + +We visualize the generated images across different benchmarks, using the Stable Diffusion V1-5 model. Figure 3 shows the results on the CIRR dataset, which mainly includes natural and daily scenes. From the results in the first three columns, our method effectively changes animals according to the caption while preserving the original image features. The example in the fourth column demonstrates a scenario where the reference image and target image have less in common in this dataset. Despite this, we successfully generated the target image, which features two fruity pies. In the generated images, we even retained the reference image's characteristic of having thick cream. + +Figure 4 showcases the generated images on the FashionIQ dataset. On a clothing dataset that includes dresses, tops, and shirts, our method produces excellent results. It effectively modifies the images according to the captions, including changing patterns, sleeves, colors, and styles while retaining the original clothing features. The generated images closely resemble the target images. Additionally, in the last example, our generated image surpasses the target image by preserving the collar of the reference image, whereas the target image does not even retain the original clothing style. The visualization of CIRCO and GeneCIS can be found in Appendix. + +Quantitative Evaluation Composed Image Generation. We further evaluated the quantitative performance of the generated images. Specifically, we calculated the cosine similarity between the generated images and the composed text embeddings, denoted as CLIP scores. We used text em + +Table 6. Discussion on Generation Quantitative Evaluation and Efficiency Evaluation. + +(a) Composed Image Generation Quantitative Evaluation on CIRR validation set. + +
Methodtarget imagesSEARLE + SDSEARLE+ CIG
Clip Score0.25550.27620.2810
+ +(b) Additional inference time comparison. + +
BackboneViT-L/14
MethodSD V1-5SDXLSDXL-turbo
Time(s)2.452.560.14
+ +(c) Inference time comparison on CIRR. + +
BackboneViT-L/14
MethodSEARLECIREVLCIG
Time(s)0.0261.870.17
+ +Table 7. Ablation Study on different fusion strategies. Evaluations on CIRR and CIRCO datasets show that fusing on composed textual embedding is more beneficial. +(a) CIRR validation set (Recall@K and RecallSubset@K). + +
MethodRecall@KRecallSubset@K
K=1K=5K=10K=1K=2K=3
Text embedding26.1754.7568.1458.7778.5289.45
Pseudo token25.6454.6367.5758.7979.1789.33
Image level24.3254.4867.0953.7075.1786.61
+ +(b) CIRCO validation set (mAP@K). + +
MethodmAP@k
K=5K=10K=25K=50
Text embedding10.9812.1213.6514.41
Pseudo token10.5711.6813.1213.79
Image level10.4311.5513.1413.83
+ +beddings from SEARLE [4] and ViT-L/14 as backbones. We compare the CLIP score with both target images and the images generated by original Stable Diffusion V1-5. Table 6a presents the results on the CIRR validation dataset, showing that our generated images are closer to the composed text embeddings than the target images and image generated by original Stable Diffusion model. + +Efficiency Evaluation. Time efficiency is a crucial factor in retrieval tasks. With the use of diffusion models, there are natural concerns about the efficiency of our method. Therefore, we conducted an efficiency evaluation to show the additional inference time required by our method, as shown in the Table 6b. To evaluate the additional inference time, we use a single A6000 GPU with a batchsize of 16 and use SEARLE as the baseline. In the most demanding cases, such as with Stable Diffusion v1-5 and SDXL, the extra time per image is around 2 seconds, which is acceptable for current composed image retrieval tasks. Additionally, we propose an alternative solution using SDXL Turbo as our model. In this scenario, the additional inference time is only around $100\mathrm{ms}$ and does not impact the retrieval performance. We believe that once the training code for SDXL Turbo is released, both the generation quality and retrieval performance will further improve. + +We additionally compared the average runtime per image across different methods. As shown in Table 6 (c), although CIG is slower than traditional methods, it is significantly faster than CIREVL, a popular LLM based method, balancing speed and performance. Table 5 shows that combining our method with CIREVL methods can further enhance performance, demonstrating that our approach is also effective when applied to LLM-based methods. + +Ablation Study on different fusion strategies. We demonstrated the performance of integrating generated images in different settings, as shown in Table 7. We used SEARLE as the baseline and Stable Diffusion v1-5 as our base model. "Text embedding" represents our default setting, where the composed text embedding of caption and reference image + +is combined with the composed text embedding of caption and generated images. "Pseudo token" indicates that the generated image is first mapped to a pseudo token, which is then fused with the reference image's pseudo token. "Image level" means that the CLIP features are extracted from the generated image and directly fused with the composed text embedding, it primarily integrates image features, emphasizing spatial information. However, the CIR task relies more on global semantics. Therefore, fusion at the textual embedding level is more reasonable, as it better enhances semantic information. The results show that the first two fusion methods yield better performance on both CIR and CIRCO datasets. + +# 5. Conclusion + +In this paper, we explore a new direction to integrate image features and text features in composed image retrieval. Existing zero-shot CIR algorithms treat the reference image as a single pseudo token which is then plugged into the caption, yielding a pseudo caption. It is effective to describe the reference image as a single token in some cases, e.g. a single objective. However, it cannot maintain most visual content in the reference image, leading to a multimodal gap. To bridge the multimodal gap, we propose to generate a pseudo target image to preserve the visual content by integrating the reference image and the delta caption. To our knowledge, this paper is the first to answer the question both visually and experimentally: Can the pseudo target image help composed image retrieval? Our algorithm is simple and complementary to existing methods. We apply the latent diffusion model to generate pseudo target images by integrating the reference image and the delta caption. The training process does not require CIR datasets. Adequate visualization examples over different datasets show that the pseudo images are visually similar to the target images, which increases the cosine similarity in the embedding space, leading to better retrieval performance. + +Acknowledgements. This work was supported by the Office of Naval Research (award #N00014-23-1-2417). 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The independent avatar reconstruction of each person often fails to reconstruct the geometric relationship among multiple instances, resulting in inter-penetrations among avatars. Some researchers resolve this issue via neural volumetric rendering techniques but they suffer from huge computational costs for rendering and training. In this paper, we propose a multi-person avatar reconstruction method that reconstructs a 3D avatar of each person while keeping the geometric relations among people. Our 2D Gaussian Splatting (2DGS)-based avatar representation allows us to represent geometrically-accurate surfaces of multiple instances that support sharp inside-outside tests. We utilize the monocular prior to alleviate the inter-penetration via surface ordering and to enhance the geometry in less-observed and textureless surfaces. We demonstrate the efficiency and performance of our method quantitatively and qualitatively on a multi-person dataset [49] containing close interactions. + +# 1. Introduction + +Human avatar reconstruction has been intensively studied, as the novel view synthesis achieves unprecedented advances in the past half a decade [17, 23, 24, 26, 32, 42]. Single-person avatar reconstruction combines pose tracking and novel view synthesis, where the human appearance is modeled in the canonical space articulated with the human skeleton [31]. The appearance in the target frame is then obtained by warping from the canonical to the target space based on the estimated target pose. The overall performance of single-person avatar reconstruction depends on the accuracy of pose estimation and the fidelity of appearance reconstruction. + +In contrast to single-person reconstruction, multi-person scenarios present an additional challenge: inter-penetration between body parts and inter-person occlusions. Interpenetrations occur when each avatar is processed independ- + +![](images/1e5fa2a721c162b650195992981ae5a9e66c4fdbf14b33dac5a94d9d1cea0ba2.jpg) +Figure 1. Teaser. We represent multi-person avatars using planar Gaussian splats. To overcome the view sparsity, we utilize the monocular priors during training. Our reconstruction achieves state-of-the-art performance with fast training. + +dently without the consideration of adjacent avatars. Previous approaches [7, 18, 26, 51] maintain geometric relationships by modeling the occlusion-aware image formation model, detecting penetrating regions and pushing them outward. These methods require clear surface representations such as mesh [18] or implicit surface [37] for the inner-outer test which takes a huge computational cost. They may cause the shape deviation as the skinning model does not address the soft body deformation in contact regions. + +The reconstruction becomes more challenging with sparse views, where silhouettes provide the coarse geometry bound of an avatar and triangulation-based depth priors become unreliable, particularly in less-observed and textureless areas. Recently, vision foundation models, especially a human vision foundation model Sapiens [21], achieve remarkable improvements in monocular geometric estimation. Inspired by MonoSDF [50], which shows that monocular inference improves static 3D reconstruction, we utilize the monocular prior to achieve geometrically consistent multiple avatar reconstruction. + +In this paper, we propose a method that reconstructs + +multiple avatars from sparse multi-view videos while keeping their geometric relationships. To form the discrete surface boundaries without sacrificing the rendering speed, we adopt the 2D Gaussian splatting (2DGS) representation as an avatar representation of each person. We synthesize multi-person images by warping all planar Gaussian splats onto the target space, sorting them, and blending them in the volumetric manner. To overcome inter-penetrations, we efficiently reorder surfaces of foreground and background instances without explicitly addressing the physical interactions in contact regions. We utilize monocular geometric priors to improve the geometric details while mitigating the ambiguity of sparse views and textureless regions. Our method achieves the state-of-the-art performance among multi-person avatar reconstruction methods in terms of geometry and rendering quality. + +# 2. Related Work + +Dynamic Avatar Reconstruction Early approaches to avatar reconstruction focus on simultaneous surface scanning and non-rigid tracking [4, 13, 30, 39]. Avatar geometries are captured using a commercial depth camera such as KINECT [29]. The captured surfaces are aligned and integrated in the canonical space by estimating the non-rigid motion, controlled by the embedded deformation graph [38]. + +Recent studies tackle the problem of avatar reconstruction by estimating the motion offset field and reconstructing the human appearance, utilizing the human template body model and the deep pose prior [31] to establish coarse correspondence fields between the canonical and the target frames [32]. Building on the success of neural-based novel view synthesis [27, 28, 44, 48], various neural volumetric representations have been explored in avatar reconstruction, ranging from vanilla implicit neural networks [42] to sophisticated approaches using latent features stored in meshes [32] and lattice grids [26]. To focus on reconstruction near the template surfaces, some neural volumetric representations learn the radiance field in the surface-aligned volume, associated with texture space [15, 22, 45, 54]. Learning the background scene together helps automate the reconstruction pipeline [17]. These neural representations train the density-based radiance field defined in the canonical space by warping the camera rays. However, density-based radiance fields struggle to separate the geometry and the texture, resulting in physically inconsistent surface geometry. Although implicit signed distance field representations [10, 14] improve surface quality, neural volumetric representations still suffer from a long training time. + +In another venue, the explicit scene representation, called Gaussian splatting [20], achieves the compatible performance in the novel-view synthesis with fast rendering and training thanks to the differentiable rasterization. In + +order to represent the dynamic appearance of avatars, the Gaussian splats in the canonical space are moved into the target space by using the skinning model [36]. Additional deformation fields improve the reconstruction quality by enhancing the correspondence between frames through pose-dependent deformation [33] and auxiliary deformation guided by latent bones [24]. Although these approaches achieve fast training and real-time rendering, their surfaces are not well-aligned to the actual surfaces [9]. We extend this approach to the planar Gaussian splats [12], achieving both geometric-consistent reconstruction and fast training. + +Multi-Person Avatar Reconstruction Multi-person dynamic avatar reconstruction has been studied by constructing an independent canonical space for each avatar and aggregating their appearance through volumetric rendering [37, 52]. This simple extension to multi-person utilizes the multi-view consistency to find the corresponding instance for each pixel, which works in far-person scenarios. + +In close-interaction scenarios, independent reconstruction of each avatar falls into the geometrically inconsistent results such as inter-penetrations between avatars. The inter-penetration hinders the appearance reconstruction of avatars, since a camera ray cannot reach the corresponding point. To resolve this inter-penetration problem, the major approach penalizes the simultaneous occupancy by multiple avatars [6, 7, 16, 18, 26, 49, 51]. Though this approach is physically sound, it requires the per-point inference for inner points and may cause unwanted shape deviation due to model inadequacy for elastic body deformation. The instance segmentation map helps to correct the ordering of visible surfaces along the ray [7, 16, 18, 52]. We use the surface ordering strategy to expose the penetrated parts without over-regulating unseen contact parts. + +Exploring Monocular Priors Monocular prior models for geometry estimation [1, 5, 8, 11, 19, 35] and segmentation [34] have been proposed by training networks with large image datasets of general scenes. Some researchers focus on human-centric prior models. ECON [43] estimates the geometry of the clothed human supervised by the clothed-human scanning dataset. A large human-vision foundation model, Sapiens [21], trained with a curated human image dataset demonstrates the state-of-the-art performance in human-centric vision tasks such as 2D pose estimation, body-part segmentation, and monocular geometry estimation. + +Recent works have demonstrated that monocular geometry priors enhance static scene reconstruction across various scene representations, e.g. the neural implicit functions [50] and the Gaussian-based models [3, 40]. In this paper, we exploit the monocular priors to enhance dynamic multi-person avatar reconstruction from sparse multi-view observations. + +![](images/dd2ab68509f5b3e3792c3662ad1aba9624b028b67068550d229e173b7dec2418.jpg) +Sec. 3.1 Surface-Aware Avatar Representation +Sec. 3.2 Optimization with Monocular Priors +Figure 2. Overview. We define each avatar's representation as a set of planar Gaussian splats [12] in the different canonical spaces. The avatars are transformed to the integrated target space through the deformation field. We render the property maps of the scene such as RGB color, depth, normal, and instance, in the volumetric manner and encourage the similarity between renderings and monocular predictions during optimization. + +# 3. Method + +Our goal is to reconstruct the consistent geometric relationships among avatars by resolving the inter-penetration issues while estimating the geometrically accurate appearance of avatars. Sec. 3.1 proposes a geometrically consistent avatar representation that has well-defined surfaces that enables precise inside-outside testing. Sec. 3.2 explains objective functions to train the multiple avatar representation from multi-view videos. + +# 3.1. Surface-Aware Avatar Representation + +A surface-aware appearance model enables the reconstruction of geometrically consistent 3D avatar surfaces by producing clear boundaries between the avatar's interior and exterior, allowing detection of physically-incoherent events such as inter-penetrations. To achieve this, we propose a planar Gaussian mixture appearance model articulated with the human body template model [31]. For each avatar, we sput planar Gaussian disks onto the independent canonical space aligned with the reference human pose called DApose [17]. Each Gaussian sput has a spatial density distribution $G$ parameterized by the rotation $\mathbf{R}$ , the center position $\mathbf{t}$ , and the scale matrix $\mathbf{S}$ : + +$$ +G (\mathbf {u}) = e ^ {- \frac {1}{2} \mathbf {u} ^ {T} \mathbf {S} ^ {- T} \mathbf {S} ^ {- 1} \mathbf {u}}, +$$ + +where $\mathbf{u}$ is a local 2D coordinate $(u,v)$ of the $i$ -th Gaussian splot corresponding to the 3D coordinate $\mathbf{x} = \mathbf{R}\mathbf{u} + \mathbf{t}$ . It contains surface properties such as view-dependent color $\mathbf{c}$ , opacity $\alpha$ , and surface normal $\mathbf{n}$ to represent the geometric and radiometric appearance. + +To represent the appearance at the target frame, each Gaussian splat in the canonical space is moved to the corresponding position in the target space. The spatial deformation between the canonical and target spaces is defined as linear blending of transformations of adjacent human body joints $\{\mathbf{T}_k\}$ called linear-blending skinning (LBS): + +$$ +\hat {\mathbf {T}} (\mathbf {x}) = \sum_ {k = 1} ^ {n _ {b}} w _ {k} (\mathbf {x}) \mathbf {T} _ {k}, \hat {\mathbf {x}} = \hat {\mathbf {T}} (\mathbf {x}) \mathbf {x}, \tag {1} +$$ + +where $w_{k}$ is the blending weight for the $k$ -th body joint, $\mathbf{x}$ is a canonical point, $\hat{\mathbf{x}}$ is the corresponding target point, $n_b$ is the number of adjacent human joints, and $\bar{\mathbf{T}} (\mathbf{x})$ is a deformation field from the canonical space to the target space. In addition, we add the auxiliary deformation field [24] to cope with general motions of clothes. + +The translated Gaussian splats of avatars are gathered in the target space then are sorted by depth and projected onto the image space via volumetric alpha blending in order to + +render the animated avatar appearance: + +$$ +\mathbf {p} (\mathbf {r}) = \sum_ {i = 1} \mathbf {p} _ {i} \alpha_ {i} G _ {i} \left(\mathbf {u} _ {i} (\mathbf {r})\right) \prod_ {j = 1} ^ {i - 1} \left(1 - \alpha_ {j} G _ {j} \left(\mathbf {u} _ {j} (\mathbf {r})\right)\right) \tag {2} +$$ + +where $i$ is the index of a Gaussian splat, $\mathbf{p}_i\in \{\mathbf{c}_i(\mathbf{r}),\mathbf{n}_i,d_i\}$ and $\alpha_{i}$ are a property of Gaussian splats and an opacity of the Gaussian splat, $\mathbf{r}$ is a pixel ray, and $\mathbf{u}_i(\mathbf{x})$ is the ray-splat intersection point. Thanks to the nature of planar Gaussian splats, the mixture of them estimates the well-defined surfaces and the surface-aligned texture appearance by regularizing their relative distances under multi-view supervision [12]. + +# 3.2. Optimization with Monocular Priors + +In the previous sections, we build the differentiable rendering pipeline for our multiple avatar representations. We train each person's avatar by rendering all visible avatars into video frames and penalizing the photometric differences. To address the ambiguity of sparse-view photometric reconstruction, we adopt vision foundation models [21, 34] to utilize monocular priors such as instance segmentation and monocular geometry estimation. Besides, we encourage the planar Gaussian splats to construct surface-aligned appearance and estimate the accurate human body pose by regularizing the Gaussian splats and the auxiliary motion field introduced in [24, 50]. + +Photometric Reconstruction Loss We optimize the multi-person avatar representations from multi-view RGB videos via the photometric reconstruction loss. We compute the $L1$ difference and the structure similarity image metric: + +$$ +\mathcal {L} _ {c} = \sum_ {\mathbf {r} \in \mathcal {R}} | | \mathbf {c} (\mathbf {r}) - \hat {\mathbf {c}} (\mathbf {r}) | | _ {1} + \lambda_ {S S I M} \cdot \operatorname {S S I M} \left(\mathbf {C} _ {k}, \hat {\mathbf {C}} _ {k}\right), \tag {3} +$$ + +where $\mathbf{r}$ is a pixel or its ray, $\mathcal{R}$ is a set of pixels at the iteration, $\hat{\mathbf{c}} (\cdot)$ is the pixel observation value, $n_i$ is the number of all video frames, $\lambda_{ssim}$ is a linear coefficient set to 0.1, and $\mathbf{C}_i$ and $\hat{\mathbf{C}}_k$ is the $k$ -th rendering image and the observation image, respectively. + +Surface Ordering Loss In order to encourage clear boundaries between avatars and prevent incorrect depth orders of their surfaces, we use the instance segmentation map as the surface visibility map. We compute the cross entropy loss to correct the surface ordering: + +$$ +\mathcal {L} _ {s o} = - \sum_ {\mathbf {r} \in \mathcal {R}} \sum_ {o = 1} ^ {n _ {o}} \log \frac {\exp (\mathbf {s} _ {o} (\mathbf {r}))}{\sum_ {i = 1} ^ {n _ {o}} \exp (\mathbf {s} _ {i} (\mathbf {r}))} y _ {o} (\mathbf {r}), \tag {4} +$$ + +where $y_{o}(\cdot)$ is a mask map for instance $o$ and $s_i(\cdot)$ is a probability map of the $i$ -th avatar computed as the opacity map. + +The segmentation map is inferred by SAM2 [34]. We manually prompt the segmentation map to fix the incorrectly segmented regions and refine it via guide filtering as the initial inferred map is not accurate near the instance boundaries. + +Monocular Geometry Loss To improve the reconstruction quality in under-observed and textureless areas, we aggregate the monocular geometry priors from all video frames. We use the state-of-the-art human vision foundation model Sapiens [21] as a teacher model that infers plausible and natural monocular depth and normal maps for clothed humans. Due to the scale and shift ambiguity in monocular depth $\hat{d}$ , we compute the scale-shift invariant loss for depth supervision [50]: + +$$ +\mathcal {L} _ {d} = \min _ {w, q} \sum_ {\mathbf {r} \in \mathcal {R}} \| (\omega \cdot d (\mathbf {r}) + q) - \hat {d} (\mathbf {r}) \| _ {2} ^ {2}, \tag {5} +$$ + +where scale $w$ and translation $q$ are estimated for each RGB frame. For normal supervision, we compute the cosine distance and the L1 distance with monocular normal $\hat{\mathbf{n}}$ : + +$$ +\mathcal {L} _ {n} = \sum_ {\mathbf {r} \in \mathcal {R}} \| \mathbf {n} (\mathbf {r}) - \hat {\mathbf {n}} (\mathbf {r}) \| _ {1} + \| 1 - \mathbf {n} (\mathbf {r}) \cdot \hat {\mathbf {n}} (\mathbf {r}) \| _ {1}. \tag {6} +$$ + +Total Loss Our total loss includes all losses introduced above and the regularization terms to encourage planar Gaussian splats to construct surface-aware appearance [12] and to mitigate the over-deviation in the representation and the motion field [24]: + +$$ +\begin{array}{l} \mathcal {L} = \lambda_ {c} \mathcal {L} _ {c} + \lambda_ {s o} \mathcal {L} _ {s o} + \lambda_ {d} \mathcal {L} _ {d} + \lambda_ {n} \mathcal {L} _ {n} \\ + \lambda_ {r n} \mathcal {L} _ {r n} + \lambda_ {r d} \mathcal {L} _ {r d} + \lambda_ {r e g} \mathcal {L} _ {r e g}, \\ \end{array} +$$ + +where $\lambda_{(\cdot)}$ is a loss coefficient of each term, $\mathcal{L}_{rn}$ is the normal consistency term between Gaussian's normals and the gradients of depth map, $\mathcal{L}_{rd}$ is the depth concentration term for Gaussian splats intersected with a ray, $\mathcal{L}_{reg}$ is the regularization term introduced in [24]. Please refer to [12, 24] for details. + +# 4. Implementation Details + +Pose Initialization and Refinement The accurate initial body pose and hand pose are critical for reconstructing the high-quality avatar appearance. To this end, we first train an SMPL-X [31], a human body template model with hand pose and facial expression, via the keypoint projection consistency [31, 53] for each person in multi-view video frames. We penalize the self-collision and force the naturalness and the temporal smoothness of estimated human models during training to alleviate the noticeable artifacts. Note that human keypoints of each avatar are estimated via the human vision model [21]. + +
MethodSequenceAppearanceGeometry
PSNR↑SSIM↑LPIPS↓P2S↓CD↓COS↓L2↓
EasyMocapBackhug0229.39780.96160.04990.51320.90700.03550.0701
Hug0128.38630.95080.06610.59100.99360.04770.0929
Talk2227.16940.94030.07640.70201.31250.05210.0997
Dance1524.91440.93730.08730.63291.11000.05240.1018
Football2124.28950.93370.07900.91631.57440.05430.1013
Multi-GARTBackhug0229.90260.96330.06221.24581.77100.02900.0611
Hug0129.33920.95580.07461.59442.02740.03630.0767
Talk2228.80420.94930.08141.23391.70770.03540.0765
Dance1525.92050.94640.08211.13771.67610.03550.0751
Football2125.75260.94150.08941.33941.93400.03680.0769
OursBackhug0231.81150.97050.04170.48060.58940.01130.0311
Hug0131.23310.96430.05170.50340.61360.01380.0387
Talk2230.16910.95580.05860.56400.63590.01400.0401
Dance1527.81460.95460.05630.47690.49710.01570.0419
Football2127.36340.94900.06400.55500.59150.01580.0420
+ +Table 1. Quantitative comparison on the Hi4D Dataset [49] that captures multi-person close-interaction scenarios. We compare our method against EasyMocap [37] and multi-GART [24], with the latter extended by us for multi-person reconstruction. Our method achieves state-of-the-art performance in both rendering quality and geometry accuracy. + +However, the human poses estimated above suffer from the inter-penetration among avatars. We refine the initial pose parameters via the surface ordering loss between the projected human meshes and the segmentation map defined in Eq. 4. Our refined human poses agree with the actual surfaces without modeling surface deformation and the inner-outer test. + +Training Details We initialize Gaussian splats at vertices of the human template model in the canonical space. We optimize poses and Gaussian splats for every avatar simultaneously during training. We adaptively control the number of Gaussian splats in a heuristic way [12, 20]. We observed that training poses in the earlier stage suffer from quality loss due to incorrectly estimated appearance. We first train the avatar appearance with fixed initial avatar poses. After the avatar appearance is roughly estimated, we start joint optimization of poses and avatar appearances at the half-time of the training iterations. Our method completes total 3000 training iterations which takes 10 minutes on a single NVIDIA RTX A6000 GPU. Empirically, we set the scaling factors $(\lambda_c, \lambda_{so}, \lambda_d, \lambda_n, \lambda_{rn}, \lambda_{rd}, \lambda_{reg})$ to $(1.0, 1.0, 0.05, 0.025, 0.1, 0.05, 0.01, 0.5)$ , respectively. + +Geometry Extraction To extract the mesh of each frame space, we utilize the volumetric fusion method [2] introduced in [12]. We transform Gaussian splats to the target space, render them for uniformly sampled camera views, and obtain multi-view depth maps. The truncated signed distance function (TSDF) of each depth map is then cumulated and stored in the lattice grid. The final mesh is ex + +tracted from the integrated TSDF field using the marching cube algorithm [25]. We sample 100 camera views on the bounding hemisphere positioned at distances similar to the observation views. + +# 5. Experiments + +Dataset In order to analyze the overall performance of our multi-person reconstruction including geometric accuracy, we use the Hi4D dataset [49] that captures multiple multi-person interaction scenarios through 8 synchronized static cameras and provides raw 3D scans and highly accurate estimated individual poses per frame as ground-truth. Each scenario consists of close human interaction between two individuals across 200 video frames. For our evaluation, we select video sequences that clearly exhibit close contacts: backhug02, hug01, talk22, dance15, and football21. To evaluate the general performance for novel poses, we split the frames into training and testing sets. We sample training frames every 4 frames starting from frame 0, and test frames every 8 frames starting from frame 2. + +Evaluation Metrics We evaluate the rendering quality using PSNR, SSIM, and LPIPS metrics, and the geometric quality using point-to-surface (P2S) and Chamfer distance (CD) metrics. For surface orientation assessment, we measure normal consistency by cosine distance (COS) and $L_{2}$ distance (L2). + +Comparison with Other MP Reconstruction We compare our method with two multi-person reconstruction methods as baselines, EasyMocap [37] and multi-GART, + +![](images/8a5991f9aa117f2a4710dbcf2b0481ededdb6a4552f73341fafd4179c71584a2.jpg) +Figure 3. Qualitative comparison against baselines [24, 37]. EasyMocap [37] suffers from rugged surfaces, incorrect surfacing near boundaries, and cloud artifacts. Multi-GART, the multi-person extension of GART [24], struggles with surface alignment and fails to reconstruct thin structures such as fingers. Our method achieves the geometrically consistent surface reconstruction. + +![](images/a69c55918ad7edfc84c33963923a45b838ac9603e9ec2569d6cef9ad9fb3893a.jpg) +Figure 4. Qualitative comparison of monocular normal priors [5, 8, 11, 19, 21, 40, 43]. We leverage monocular normal priors (thumbail) to reconstruct multiple avatars (large). Reconstruction with Sapiens [21], the human-centric vision model, achieves the top performance in geometric accuracy. + +the multi-person version of GART [24]. We implemented multi-GART that includes volumetric rendering with multiple avatars transformed in the target space. Multi-GART + +does not apply any monocular priors and does not use the surface ordering loss. While EasyMocap supports human pose and shape estimation, multi-GART requires pose ini + +![](images/66f2eb22b147afe4f73c38b8d4bb84b51f68be91afad0d42c75fb9fea058be73.jpg) +Figure 5. Qualitative comparison against EasyMocap [37] and Multi-GART [24]. + +tialization. We input the ground-truth poses included in the dataset into Multi-GART. + +Tab. 1 presents a quantitative comparison with other state-of-the-art methods. EasyMocap, which uses an implicit neural representation [27], exhibits the longest training time (2-3 days) yet shows the lowest performance. In contrast, multi-GART, a state-of-the-art method in single-person avatar reconstruction, achieves high rendering quality even in multi-person scenarios. However, due to its surface ambiguity [9, 12], multi-GART shows inaccurate geometry reconstruction. On the other hand, our method achieves superior results in both rendering quality and geometric accuracy. + +Fig. 3 and Fig. 5 qualitatively demonstrate the geometric and radiometric performance of our method against the baselines. Although EasyMocap builds a background color radiance field model, it fails to separate background colors from foreground instances. EasyMocap reconstructs noisy surfaces in the textureless regions and generates layered surfaces near boundaries and small clouds in the empty region. Multi-GART produces inconsistent surface geometry due to unwanted shape-texture entanglement in the volumetric radiance field [9, 12]. Multi-GART suffers from blob artifacts near the instance boundaries or thin structures like fingers during image rendering. Thanks to our surface-aware radiance field representation with the surface regularization terms, our method constructs smooth and complete surfaces that are well-aligned with the ground-truth surfaces and produces smooth detailed texture appearance. + +
ModelsPSNR↑SSIM↑LPIPS↓P2S↓CD↓COS↓L2↓
W/o mono. prior30.12190.95540.06030.66960.77200.01800.0485
Ommidata-low [5]30.16740.95530.06170.65730.80380.01860.0516
Ommidata-high [40, 50]30.17990.95530.06170.69480.88410.01900.0529
Metric3Dv2 [11]30.16180.95550.06060.59270.66480.01640.0463
Geowizard [8]30.21670.95470.06330.92131.48800.02840.0685
Marigold [19]30.18110.95560.05990.58680.67910.01560.0439
ECON [43]30.18710.95570.05980.60010.70380.01650.0470
Sapiens [21]30.16780.95580.05860.56560.64800.01420.0403
+ +Table 2. Quantitative comparison of monocular normal priors on sequence talk22. + +
ModelsPSNR↑SSIM↑LPIPS↓P2S↓CD↓COS↓L2↓
W/o mono. prior30.13250.95550.06020.67200.76910.01810.0485
ZoeDepth [1]30.15400.95550.06020.67100.76540.01810.0486
Metric3D [11]30.14780.95550.06020.66820.77210.01810.0486
Geowizard [8]30.15040.95560.06010.67270.77300.01810.0486
Marigold [19]30.16170.95560.06020.67160.76270.01800.0485
DA-v2 [47]30.13200.95550.06010.66850.76660.01810.0485
Sapiens [21]30.15000.95550.06010.66900.78200.01810.0487
+ +Table 3. Quantitative comparison of monocular depth priors on sequence talk22. + +
MethodsPSNR↑SSIM↑LPIPS↓P2S↓CD↓COS↓L2↓
W/o Lrn, Lrd29.83480.95910.05530.58560.69720.01520.0406
W/o Lr, Ln29.66190.95860.05610.58360.68460.01720.0452
Ours29.67830.95880.05450.51600.58550.01410.0388
+ +Table 4. Quantitative analysis for ablation study of geometric losses. We examine both rendering and geometric performance while excluding each objective term. Our full model achieves the best geometric reconstruction while maintaining the rendering quality. + +
mIoU Low 1%↑mIoU Low 5%↑mIoU Low 10%↑mIoU↑
Multi-GART0.69660.72630.75610.9145
W/o Lso0.61280.67870.73850.9349
Ours0.70030.74750.78820.9381
+ +Table 5. Quantitative comparison of instance segmentation maps. We compute mean Intersection over Union (mIoU) over the foreground area of every test frame. We divide the frame into 200 patches and select the lowest $1\%$ , $5\%$ , and $10\%$ IoU patches from W/o $\mathcal{L}_{so}$ and evaluate other methods at the same patch locations. + +Comparison among Monocular Geometric Priors We first examine the effect of monocular normal priors including Omnidata-low [5], Omnidata-high [40, 50], Metric3Dv2 [11], GeoWizard [8], Marigold [19], ECON [43], and Sapiens [21]. To this end, we only activate monocular normal loss during training. in Tab. 2 and Fig. 4. Omnidata-low and Omnidata-high degenerate geometry reconstruction especially in normal orientations. Geowizard fails to estimate geometrically consistent normals, resulting in inconsistent avatar reconstruction. Metric3Dv2 and ECON enhance the reconstruction quality but the reconstructions are overly smooth in faces and clothes. Marigold helps with consistent reconstruction on clothes but shows low quality on face region. Sapiens, a human centric vision foundation model, successfully detects details of clothes and faces, achieving the top performance. We use Sapiens as our teacher network. + +![](images/54c2556a0fa7e73404b6d3fae6a5e782a76f991d3e2cecb4b266fee5064cb374.jpg) +GT +W/o $\mathcal{L}_{rn}$ $\mathcal{L}_{rd}$ +W/o $\mathcal{L}_n,\mathcal{L}_d$ +Ours + +![](images/2cc45bce7a6250aa06df0eb982f4c5f2d138a05a70d6acc82543e1c1039c024d.jpg) +Figure 6. Qualitative analysis of ablation study. The Gaussian regularization terms $\mathcal{L}_{rn}$ and $\mathcal{L}_{rd}$ reconstruct the smooth surfaces. Training monocular geometric priors $\mathcal{L}_n$ and $\mathcal{L}_d$ reduce the angled surfaces. Our full model reconstructs high quality surfaces. +GT (Hi4D) +Multi-GART +Figure 7. Qualitative comparison for surface ordering. The surface-aware avatar model allows the reconstruction of clear surface boundaries and the surface ordering loss encourages the extraction of penetrating parts. + +![](images/f5bdea32b91800f179307e2ab9b03d238118a599a7719f2723bf60e8f965ab3f.jpg) +W/o $\mathcal{L}_{so}$ + +Tab. 3 shows the influence of state-of-the-art monocular depth priors. We observe that the monocular depth loss makes subtle improvement with any depth priors that are trained to be consistent with normal priors. This implies that aligning orientations of Gaussian splats effectively construct the surface-consistent appearance while translating the Gaussian splat doesn't make a significant improvement. + +Ablation Study Tab. 4 and Fig. 6 demonstrate the effectiveness of each geometric objective term in both quantitative and qualitative results. The regularization term for planar Gaussian splats [12] enhances the surface smoothness. Training monocular geometric priors enables the reconstruction of curved surfaces through their ability to predict geometric gradients from images, reducing the angled surfaces. By combining all of them, our full model achieves state-of-the-art performance with competitive rendering quality. + +To demonstrate the effectiveness of our surface ordering loss, we introduce a novel metric that measures the mean intersection-over-union (mIoU) in tightly interacting regions. We first find potentially-contacted patch regions that could suffer from poor surface ordering. We select patches with the lowest mIoUs trained without the surface ordering loss. Then, we compare them with the corresponding patches (red box in Fig. 7) computed with surface ordering. Tab. 5 and Fig. 7 illustrate that our surface ordering loss enhances depth ordering in potentially-contacted regions and the quality of avatar boundaries. Compared to Multi-GART, our full model produces more distinct object boundaries and alleviates the inter-penetration issues. + +# 6. Discussion + +Despite achieving state-of-the-art performance in multi-person reconstruction, our method has some limitations. Since we fit avatar models in the canonical space using only the deformation field, a more flexible motion field is needed to capture fine dynamic details like wrinkles. Additionally, our model reconstructs static surface colors and normals, leading to smooth surfaces when temporal variations occur. Integrating Vid2Avatar [10], which enables pose-dependent surface colors, could help preserve dynamic appearance changes. Lastly, our method relies on monocular geometric priors, inheriting any biases they introduce. Physically-based inverse rendering could mitigate this [41, 46] by leveraging shape-from-shading constraints to refine surface details. + +# 7. Conclusion + +We propose the surface-aware avatar representation that uses planar Gaussian splats with surface regularization terms, facilitating the surface-aligned appearance reconstruction. To robustly reconstruct multi-person avatars against inter-penetrations and occlusions between avatars in close-interaction scenarios, we apply the monocular geometric and instance priors by modeling the objective functions between the monocular predictions and the estimations. We compare the state-of-the-art monocular geometric priors in multi-person reconstruction to find the best associated prior. Our full model achieves state-of-the-art performance on dynamic multi-person reconstruction from multiview videos while taking around 5 minutes to train. + +# Acknowledgment + +This work was supported by the National Research Foundation of Korea (NRF) grant (No. RS-2023-00212828) and the Institute of Information & Communications Technology Planning & Evaluation (IITP) grant (No. 2018-0-00207, Immersive Media Research Laboratory), both funded by the Korea government (MSIT). + +# References + +[1] S. F. Bhat, R. Birkl, D. Wofk, P. Wonka, and M. Müller. Zoedepth: Zero-shot transfer by combining relative and metric depth. arXiv preprint arXiv:2302.12288, 2023. 2, 7 +[2] B. Curless and M. Levoy. A volumetric method for building complex models from range images. In Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pages 303-312, 1996. 5 +[3] P. Dai, J. Xu, W. Xie, X. Liu, H. Wang, and W. Xu. High-quality surface reconstruction using gaussian surfels. 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However, artifacts are often observed in the estimated depth map, e.g., depth values for points located in the same region may jump dramatically. To address this issue, we propose a novel self-supervised monocular depth estimation framework called GeoDepth, where we explore the intrinsic geometric representation in 3D scenes for producing accurate and continuous depth maps. In particular, we model the complex 3D scene as a collection of planes with varying sizes, where each plane is characterized by a unique set of parameters, namely planar normal (indicating plane orientation) and planar offset (defining the perpendicular distance from the camera center to the plane). Under this modeling, points in the same plane are enforced to share a unique representation and their depth variations related only to pixel coordinates, thus this geometric relationship can be exploited to regularize the depth variations of these points. To this end, we design a structured plane generation module that introduces spatio-temporal geometric cues and the plane uniqueness principle to recover the correct scene plane representation. In addition, we develop a depth discontinuity module to identify depth discontinuity regions and subsequently optimize them. Our experiments on the KITTI and NYUv2 datasets demonstrate that GeoDepth achieves state-of-the-art performance, with additional tests on Make3D and ScanNet validating its generalization capabilities. + +# 1. Introduction + +Monocular depth estimation is a pivotal task in computer vision, which aims to predict a pixel-wise depth map for a given image. Each value in the depth map measures the distance from the corresponding point in the 3D scene to the camera plane [44]. Given its ability to provide 3D + +scene structure information, monocular depth estimation is broadly applicable in fields such as autonomous driving [11, 33], robotics [7], and augmented reality [31]. While supervised learning can deliver high-performance depth predictions, acquiring dense depth labels is often costly. As a result, self-supervised monocular depth estimation methods, which leverage only video or stereo images for training [9, 13, 46, 60], have emerged as a practical alternative. + +Despite its advantages, self-supervised monocular depth estimation frequently encounters difficulties in achieving accurate and smooth depth estimation, particularly in regions lacking texture [27, 55, 57]. This mainly because the mainstream approaches usually adopts a point-to-depth modeling strategy (refer to Fig. 1(a)), where image pixels are treated as independent points, and the depth values are estimated from their discrete representations[28]. As a result, artifacts are often observed in the estimated depth map, e.g., depth values for points located in the same region may jump dramatically. We refer to this phenomenon as depth discontinuity. Some works [27, 36, 54, 55, 57, 59] attempt to leverage only plane cues from surface normals to facilitate smoother depth estimation by assuming neighboring pixels form a local plane. Nevertheless, relying solely on surface normals as plane indicators might be unreliable, as it contradicts the principle of plane uniqueness in Geometric Algebra [20], which necessitates both a normal vector and an offset for a definitive plane representation in 3D space. Therefore, it is appealing to develop a robust modeling strategy to capture the intrinsic geometric representation for achieving accurate and continuous depth estimation. + +In this paper, we propose a new self-supervised monocular depth estimation framework called GeoDepth, where a novel plane-to-depth modeling strategy is developed to address the depth discontinuity issues inherent in point-to-depth methods. The motivation of GeoDepth is that a 3D scene can essentially be modeled as a collection of planes of varying sizes, where all points within the same plane can be described by a unique set of parameters, namely the planar normal and planar offset [20]. As depicted in Fig. 1(b), our methodology models coplanar points as a uniform pla + +![](images/425cbf951a009844669d538d5697c71a67b8cfe39b84b7d6f785a07393b288a6.jpg) +(a) Point-to-depth modeling + +![](images/678528458a5290832fad2cd5403e759f98a641629d774630732bac434d05ce2f.jpg) +(b) Plane-to-depth modeling (Ours) + +![](images/66625a8baed450d81715a2fbf06fafc74ff0879d09f3750982f3baceca9750e0.jpg) +Figure 1. An illustration of our motivation. (a) Self-supervised monocular depth estimation has long been treated as a point-wise prediction problem, where the depth of each pixel is usually estimated independently. Consequently, artifacts are often observed in the estimated depth map, e.g., depth values for points located in the same region may jump dramatically. (b) Instead, our GeoDepth models the complex 3D scene as planes of varying size, parameterized by planar normals and planar offsets, and infers the geometric correlation from them to depth. In GeoDepth, coplanar points are modeled as a unified representation instead of discrete representation and their depth variations are solely related to continuous image coordinates (see Eq. (1)). Therefore, by recovering structured representation among pixels, we are able to obtain more continuous depth map. + +nar representation, rather than discrete points. This insight naturally leads us to estimate these two planar properties from the input image as a structured plane representation and derive the geometric correlation to depth from them. In our modeling framework, the depth variations of coplanar points are exclusively linked to pixel coordinates (see Eq. (1)), thereby eliminating depth discontinuities by restoring the structured representation among pixels. + +To accurately recover the plane representation, we propose a structured plane generation module. This module initially utilizes spatio-temporal geometric cues to guide the two planar properties to recover the approximate scene structure, and then jointly optimizes them based on the plane uniqueness principle [20] to ensure that coplanar points converge to a unified representation. Additionally, recognizing that depth discontinuities often occur in low-texture regions, we introduce a depth discontinuity awareness module that dynamically identifies pixels with lower photometric errors as potential depth discontinuity regions and subsequently optimizes them. + +We conduct extensive experiments on two outdoor datasets: KITTI [11] and Make3D [37], and two indoor datasets: NYUv2 [42] and ScanNet [6]. Results on KITTI + +and NYUv2 show that our method achieves state-of-the-art performance and that our design choices are effective. Results on Make3D and ScanNet verify the generalization ability of our method to unseen outdoor and indoor scenes. In summary, our main contributions are as follows: + +- We introduce GeoDepth, a novel self-supervised monocular depth estimation framework, which develops a plane-to-depth modeling strategy to address the depth discontinuity issues inherent in point-to-depth methods. +- We propose a structured plane generation module and a depth discontinuity awareness module to learn correct plane representations (i.e., normal and offset) in a self-supervised paradigm. +- Extensive experiments on widely-used outdoor datasets (KITTI and Make3D) and indoor datasets (NYUv2 and ScanNet) show the robustness and generalization ability. + +# 2. Related Work + +# 2.1. Supervised Monocular Depth Estimation + +As a pioneering work on supervised learning, Eigen et al. [8] first predicted a depth from a single image by stacking coarse-scale and fine-scale networks. Since then, many su + +pervised works have been proposed by modifying the model architecture [38, 50, 56], training on large datasets [5, 51], designing robust loss functions [26, 61], and transforming this task into an ordinal regression issue [2, 3, 21, 39]. However, we can only capture sparse depth data from the physical world, and collecting large-scale training data is time-consuming and expensive. Thus, high data requirements and collection costs limit the application of these methods. + +# 2.2. Self-supervised Monocular Depth Estimation + +Considering that large-scale annotated datasets are not always available, self-supervised depth estimation methods have attracted some attention. Garg et al. [10] first introduced an alternative to learn depth from stereo pairs in a self-supervised manner. To release the requirement of stereo images, Zhou et al. [66] estimated depth map and camera pose simultaneously and only used video data in the training phase. Following this, a series of works were proposed by designing robust losses [16, 41, 58], using auxiliary information during training [25, 48], dealing with moving objects [13, 24], and adding extra geometric constraints [27, 55]. However, these methods adopt point-to-depth modeling, that is, independently modeling the depth of each pixel [28], leading to depth discontinuities. In contrast, we revisit this task and propose a novel self-supervised framework, which utilizes plane-to-depth modeling to tackle the depth discontinuities. + +# 2.3. Plane Cues for Depth Estimation + +The purpose of depth estimation is to obtain depth maps with continuous structure. To this end, one type of monocular depth estimation work attempts to introduce multi-plane representations. GonzalezBello et al. [14, 15] predefined multiple depth planes and then used a deep neural network to learn the predefined plane to which each pixel belongs. However, as real 3D scenes are complex and contain slanted planes, such representation is sensitive to discretization [47]. Another type of work focuses on incorporating local plane prior. Yang et al. [55] introduced an edge-aware depth-normal consistency constraint inside the network to regularize the depth map by using the surface normal extracted from the depth map. Subsequently, some works [36, 54, 59] jointly predicted the depth map and the surface normal, and regularized the depth with a depth-normal consistency loss. In addition, StructDepth [27] adopted a Manhattan-world assumption in indoor settings, forcing major surfaces (floor, ceiling, and walls) to align with dominant directions. However, these methods adopted solely surface normals as plane guides, which is unreliable since it cannot represent the scene plane deterministically. Moreover, as non-planar region violates the local plane assumption, planar guidance in these methods is performed on all pixels, leading to incorrect depth training. + +# 3. Plane-to-Depth Modeling + +In monocular depth estimation, the objective is to produce a depth map where each value corresponds to the distance between the camera plane and its corresponding point in the 3D scene. Consequently, once the 3D scene has been reconstructed, the depth map can be readily derived using the principles of perspective geometry. + +Typically, a real-world 3D scene can be seen as an assembly of planes of varying dimensions, ranging from the entire scene down to a single pixel. According to the plane uniqueness representation principle, a plane in 3D space can be represented by a normal vector $\pmb{n}$ and an offset vector $\pmb{o}$ . Thus, a complete 3D scene can be mathematically denoted as: $\pi = \{\pmb{n}_k,\pmb{o}_k\}_{k = 1}^M$ , where $M$ is the number of planes in the 3D scene. According to the point-normal form, a 3D point $\pmb{P}$ on a plane $\pi_{i} = \{\pmb{n}_{i},\pmb{o}_{i}\}$ satisfies: $\pmb{n}_i^T\pmb {P} = \pmb {o}_i$ , In addition, the 3D point $\pmb{P}$ located in the plane $\pi_{i}$ can be projected to a 2D point $\pmb{p} = [u,v]^T$ in the image space: $\widetilde{\pmb{p}} = \pmb {P} / (\pmb {d}\pmb{K}^{-1})$ , where $\widetilde{\pmb{p}}$ denotes the homogeneous coordinate of $\pmb{p},\pmb{d}$ is the depth at $\pmb{P}$ , and $\pmb{K}$ is intrinsic to the camera. Thus, for an individual plane, the geometric correlation between the depth and planar normal as well as planar offset is defined as: + +$$ +\boldsymbol {d} = \frac {\boldsymbol {o} _ {i}}{\boldsymbol {n} _ {i} ^ {T} \boldsymbol {K} ^ {- 1} \widetilde {\boldsymbol {p}}}. \tag {1} +$$ + +It can be observed that the depth variations of coplanar points are exclusively linked to pixel coordinates $\pmb{p}$ , since their planar normal and planar offset are equal. This insight naturally leads us to estimate these two planar properties from the input image as a structured plane representation and derive the geometric correlation to depth from them. To this end, we extend Eq. (1) to formulate the plane-to-depth modeling for self-supervised monocular depth estimation: + +$$ +\boldsymbol {D} (\boldsymbol {p}) = \frac {\boldsymbol {O} (\boldsymbol {p})}{\boldsymbol {N} ^ {T} (\boldsymbol {p}) \boldsymbol {K} ^ {- 1} \widetilde {\boldsymbol {p}}}, \tag {2} +$$ + +where $N \in \mathbb{R}^{3 \times H \times W}$ , $\pmb{O} \in \mathbb{R}^{3 \times H \times W}$ and $\pmb{D} \in \mathbb{R}^{3 \times H \times W}$ are the planar normal, planar offset, and depth map of an image, respectively. Note that $H \times W$ represent the spatial resolution of the input image. + +Compared with the direct prediction of pixel-wise depth in existing self-supervised monocular depth estimation framework, our approach focuses on mining structured explicit plane representation and enjoys the following benefits. First, under our plane-to-depth modeling, coplanar points are modeled as a unified representation instead of discrete representation and their depth variations are solely related to continuous image coordinates. Thereby, we can avoid depth discontinuities by recover the correct structured scene representation. Second, estimating depth by fitting a plane effectively smooth local noise and reduce errors due to missing texture or other interference factors. + +![](images/86be60ac818fc9c91166447b76fe805669e0b93bda8b8315eb1480c607aef2fc.jpg) +Figure 2. Overview of the proposed method. Instead of estimating the depth map from the input image, we first predict the planar normal and planar offset as structured plane representation, where the discontinuous regions will be detected by our proposed depth discontinuity awareness module and corrected by our proposed structured plane generation, from which the depth map will then be inferred. + +# 4. The GeoDepth Model + +Based on our plane-to-depth modeling described in Section 3, we propose GeoDepth to address the depth discontinuity issues inherent in point-to-depth methods. The overview of our proposed GeoDepth is presented in Fig. 2. In our framework, instead of estimating the pixel-wise depth map from the input image, we first predict the planar normal and planar offset as structured plane representation, where the discontinuous regions will be detected by our proposed depth discontinuity awareness module and corrected by our proposed structured plane generation, from which the depth map will then be inferred. Benefiting from our plane-to-depth modeling and corresponding plane constraints, coplanar points are modeled as a unified representation instead of discrete representation and their depth variations are solely related to continuous image coordinates. This results in an accurate and continuous depth map. + +In the following sections, we first detail the two key components: structured plane generation module (Sec. 4.1) and depth discontinuity awareness module (Sec. 4.2). Then, we provide our self-supervised training scheme (Sec. 4.3). + +# 4.1. Structured Plane Generation + +To recover the correct plane representation, we propose a structured plane generation (SPG) module, which is depicted in Fig. 2. See supplementary materials for details. This module first uses spatio-temporal geometric cues to guide two planar properties to recover the approximate scene structure, and then jointly optimize them to ensure that coplanar points recover a unified representation. + +Planar Normal Alignment. We exploit spatial and temporal geometric cues to align the estimated normals. Specifically, we first restore the scene point cloud using the depth map by: $P = D K^{-1} \widetilde{p}$ , and select eight neighbor points to + +infer the normal of the central point, as shown in Fig. 3. Then, based on the orthogonality, the normal can be calculated by cross-product: $\widetilde{\pmb{n}}_z = \overrightarrow{P_zP_{zx}}\times \overrightarrow{P_zP_{zy}}$ , where $P_{z}$ is the central point, and $P_{zx},P_{zy}$ are the neighbor point. To improve the robustness of the final derived normals, we compute the average of the four initial normals: + +$$ +\bar {N} _ {c} = \frac {1}{4} \sum_ {z = 1} ^ {4} \left(\widetilde {\boldsymbol {n}} _ {z}\right). \tag {3} +$$ + +Using the derived normals, the normal alignment in the spatial dimension is defined as: + +$$ +\mathcal {A} _ {s n} = 1 - \cos \left(\Psi^ {1 / \sigma} \left(\bar {N} _ {c}\right), \Psi^ {1 / \sigma} \left(N _ {c}\right)\right). \tag {4} +$$ + +where $\Psi^{1 / \sigma}$ is the interpolation function with a downsampling rate of $1 / \sigma$ . We introduce downsampling to alleviate the impact of boundary pixels. + +Additionally, to ensure the temporal consistency of planar geometry, we further explore temporal normal alignment. Given the planar normal $N_{n}$ of the neighboring view, we can use the camera pose $T_{c2n} = [R_{c2n}|t_{c2n}]$ to infer its observation normal in the target view: $N_{n}^{\prime} = R_{n2c}N_{n}$ , where $R_{n2c}$ is the inverse of rotation matrix $R_{c2n}$ . Subsequently, the planar normal of the target frame can be recovered by warping the observation normal $N_{n}^{\prime}$ : + +$$ +\boldsymbol {N} _ {n 2 c} = \boldsymbol {N} _ {n} ^ {\prime} \left\langle \operatorname {p r o j} \left(\boldsymbol {D} _ {c}, \boldsymbol {T} _ {c 2 n}, \boldsymbol {K}\right) \right\rangle \tag {5} +$$ + +After obtaining the transformed planar normal, the normal alignment in the temporal dimension is defined as: + +$$ +\mathcal {A} _ {t n} = \min _ {n} (1 - \cos (\Psi^ {1 / \sigma} \left(\boldsymbol {N} _ {n 2 c}\right), \Psi^ {1 / \sigma} \left(\boldsymbol {N} _ {c}\right))). \tag {6} +$$ + +Using Eq. (6), we not only foster geometric consistency among samples within a batch but also extend this consistency across the entire video sequence. + +Combining Eq. (4) and Eq. (6), the complete normal alignment can be defined as: + +$$ +\mathcal {A} _ {n} = \mathcal {A} _ {s n} + \mathcal {A} _ {t n}. \tag {7} +$$ + +Planar Offset Alignment. We also mine the spatial and + +![](images/4da491b250825a5656c484c51befbdeb28d8cc9f5a35da492478ffaae637fa2e.jpg) +Figure 3. The illustration of Depth-to-Normal. + +temporal geometric cues to align planar offset. According to the Eq. (2), given the derived planar normal $\bar{N}_c$ and estimated depth $D_{c}$ , we can infer a pseudo planar offset: + +$$ +\bar {\boldsymbol {O}} _ {c} (\boldsymbol {p}) = \boldsymbol {D} _ {c} (\boldsymbol {p}) \bar {\boldsymbol {N}} _ {c} ^ {T} (\boldsymbol {p}) \mathbf {K} ^ {- 1} \widetilde {\boldsymbol {p}} \tag {8} +$$ + +Thus, the spatial offset alignment is defined as: + +$$ +\mathcal {A} _ {s o} = \mathcal {P} \left(\Psi^ {1 / \sigma} (\boldsymbol {O} _ {c}), \Psi^ {1 / \sigma} (\bar {\boldsymbol {O}} _ {c})\right), \tag {9} +$$ + +where $\mathcal{P}$ is the photometric error [13]. + +Then, we mine temporal cues to align the estimate planar offset. Given the depth map $D_{c}$ of captured image, we can obtain its observation depth $D_{n}^{\prime}$ in the neighboring view based on the warp operation, and then infer the observation planar offset of the neighboring view: + +$$ +\mathbf {O} _ {n} ^ {\prime} (p) = \boldsymbol {D} _ {n} ^ {\prime} \boldsymbol {N} _ {n} ^ {T} (p) \mathbf {K} ^ {- 1} \tilde {\boldsymbol {p}} \tag {10} +$$ + +Besides, the sample planar offset of source view can be calculated by interpolating estimated offset $O_{n}$ : + +$$ +\boldsymbol {O} _ {n} ^ {\prime \prime} = \boldsymbol {O} _ {n} \left\langle p r o j \left(\boldsymbol {D} _ {c}, \boldsymbol {T} _ {c 2 n}, \boldsymbol {K}\right) \right\rangle \tag {11} +$$ + +It is noted that we cannot directly use $\mathbf{O}_n$ because the warping flow does not lie on the pixel grid. Finally, the temporal planar offset alignment is defined as: + +$$ +\mathcal {A} _ {t o} = \min _ {n} \mathcal {P} \left(\Psi^ {1 / \sigma} \left(\boldsymbol {O} _ {n} ^ {\prime}\right), \Psi^ {1 / \sigma} \left(\boldsymbol {O} _ {n} ^ {\prime \prime}\right)\right). \tag {12} +$$ + +Similar to the temporal normal alignment, this constraint allows the consistency to be propagated to the entire video sequence during the training stage. + +Similar to planar normal alignment, our spatio-temporal offset alignment can be defined as: + +$$ +\mathcal {A} _ {o} = \mathcal {A} _ {s o} + \mathcal {A} _ {t o}. \tag {13} +$$ + +Planar Uniqueness Alignment. By using the planar normal alignment and the planar offset alignment respectively, we can recover the roughly planar structure of the two planar properties. However, these two planar properties do not exist in isolation. According to the plane uniqueness representation principle, all points in a same plane can be represented by sharing a unique set of planar normal and planar offset. To this end, we jointly optimize the planar normal and planar offset by penalizing their first-order gradients to ensure that coplanar points recover a unified representation: + +$$ +\mathcal {A} _ {u} = \left| \nabla \Psi^ {1 / \sigma} \left(\boldsymbol {N} _ {c}\right) \right| + \left| \nabla \Psi^ {1 / \sigma} \left(\boldsymbol {O} _ {c}\right) \right|. \tag {14} +$$ + +Eq.(14) enforces consistent gradient variations, reinforcing the geometric consistency of both attributes so that they collectively represent the same plane across coplanar points. + +The impact of SPG on scene geometry estimation is shown Fig. 4. Without SPG, the plane representation is inaccurate, while with SPG guidance, the plane represent + +![](images/7b69dc02bad202322dd8982f0f51ff7480fbe2735dce568bbecb9eb6c764b804.jpg) +Input sample +Figure 4. Visualization of scene geometric cues. (a) Without SPG, the plane representation is inaccurate. (b) With SPG guidance, the plane representations are consistent, and the depth map is accurate. + +![](images/f32d65ee66c0ae9c10def075cd66e57ecee87f9bfb0402b9e5ea4d2e119de394.jpg) +Planar normal + +![](images/43e9a309303c3ec52c688dfbc6a06583b7d234e6e9bbd05d0fc8cd23aedd1645.jpg) +Planar offset +Depth + +tations are consistent, and the depth map is accurate. + +# 4.2. Depth Discontinuity Awareness + +We know that depth discontinuity typically manifest in low-texture regions, where photometric errors are usually small and insufficient to provide effective supervision. To localize these discontinuity regions, we propose a depth discontinuity awareness module, which adaptively selects areas with lower photometric errors. This module is illustrated in Fig. 2. Using the inferred depth map $D$ , the predicted camera pose $T_{c2n}$ , and the neighboring image $I_s$ , we first synthesize the target image $I_{n2c}$ . Then, we calculate the per-pixel photometric errors $\mathcal{P}(I_c, I_{n2c})$ . Finally, discontinuous regions can be identified by a threshold $\mathcal{T}$ : + +$$ +\mathcal {R} = \left[ \mathcal {P} \left(\boldsymbol {I} _ {c}, \boldsymbol {I} _ {n 2 c}\right) < \mathcal {T} \right], \tag {15} +$$ + +where $[\cdot ]$ is the Iverson bracket. For $\mathcal{R}$ , a value of 1 corresponds to discontinuous depth, and 0 to continuous depth. + +Obviously, it is unreasonable to use a fixed threshold due to the varying degree of low-frequency components in each image. For this, we propose to use an adaptive threshold. Considering that the photometric error will gradually decrease with the improvement of depth accuracy during training, $\mathcal{T}$ is designed to be the mean of the photometric errors: + +$$ +\mathcal {T} = \frac {1}{H \times W} \sum_ {p} \mathcal {P} \left(\boldsymbol {I} _ {c}, \boldsymbol {I} _ {n 2 c}\right). \tag {16} +$$ + +Besides, pixels in high-texture areas can usually estimate accurate depth and thus exhibit lower photometric errors, but will have slightly larger errors than low-texture pixels due to their own pixel intensity and bilinear interpolation. Thus, to filter out these pixels, we reformulate Eq. (15) as: + +$$ +\mathcal {R} = \left[ \mathcal {P} \left(\boldsymbol {I} _ {c}, \boldsymbol {I} _ {n 2 c}\right) < \mu \cdot \mathcal {T} \right], \tag {17} +$$ + +where $\mu$ is a balancing coefficient used to preserve discontinuity pixels. Using Eq. 17, we are able to accurately aware discontinuous regions and then avoid depth discontinuities by incorporating the structured plane generation module. + +# 4.3. Self-Supervised Training + +Similar to general self-supervised frameworks [13, 46, 60], our proposed GeoDepth consists of a depth network $\mathcal{F}_d$ and a pose network $\mathcal{F}_p$ . Given a training instance $\{I_c, I_n\}$ , we first use the $\mathcal{F}_d$ to estimate their two planar properties $\{N_c, O_c\}$ and $\{N_n, O_n\}$ , respectively, and predict the relative pose $T_{c2n}$ between them by $\mathcal{F}_p$ . Subsequently, we infer the final depth according to Eq. (2). To learn a robust depth estimation model, in addition to the general loss $\mathcal{L}_g$ , we add + +
DatasetMethodSizeModeTrain TestRMSE↓RMSE log↓Sq Rel↓Abs Rel↓δ<1.25↑δ<1.252↑δ<1.253↑
KITTIMonodepth [12]512×256S✓✓5.9270.2471.3440.1480.8030.9220.964
3Net [35]512×256S✓✓5.8880.2081.2010.1190.8440.9410.978
Monodepth2 [13]640×192S✓✓4.9600.2080.8730.1090.8640.9480.975
BRNet [19]640×192S✓✓4.7160.1970.8760.1030.9540.978
Monodepth2 [13]640×192MS✓✓4.7500.1960.8180.1060.8740.9570.979
DepthHints [48]640×192MS✓✓4.6270.1890.7690.1050.8750.9590.982
HR-Depth [32]640×192MS✓✓4.6120.1850.7850.1070.8870.9620.982
R-MSFM6 [67]640×192MS✓✓4.6250.1890.7870.1110.8820.9610.981
Monodepth2 [13]640×192M✓✓4.8630.1930.9030.1150.8770.9590.971
HR-Depth [32]640×192M✓✓4.6320.1850.7920.1090.8840.9620.983
CADepth-Net [53]640×192M✓✓4.5350.1810.7690.1050.8920.9640.983
DIFFNet [64]640×192M✓✓4.4830.1800.7640.1020.8960.9650.983
MonoFormer [1]640×192M✓✓4.5800.1830.8460.1040.8910.9620.982
SC-DepthV3 [45]640×192M✓✓4.7090.1880.7560.1180.8640.9600.984
SRD-Depth [30]640×192M✓✓4.6190.1860.7620.1110.8770.9610.983
Swin-Depth [40]640×192M✓✓4.5100.1820.7390.1060.8900.9640.984
Lite-Mono [60]640×192M✓✓4.5610.1830.7650.1070.8860.9630.983
ShuffleMono [29]640×192M✓✓4.8210.1930.8500.1140.8720.9570.980
Liu et al. [29]640×192M✓✓4.7240.1870.7470.1140.8630.9600.984
Dynamo-Depth [46]640×192M✓✓4.5050.1830.7580.1120.8730.9590.984
GeoDepth640×192M✓✓4.3810.1760.6940.1000.8970.9660.984
+ +![](images/f7a6beb8c78c88c36ebc2fb5a0accc7fe706e99f8c6e9f42b23817b791f55119.jpg) +KITT dataset is used to assess within-dataset performance, while the Make3D dataset is used to evaluate cross-dataset generalization. $\checkmark$ in the train column or test column means training or testing in this dataset, while $"\times "$ in the train column means not training in this dataset. " -" indicates not applicable. The best results are in bold. + +![](images/a305732c42ee3831fac8c9ccce68e79a5a0f69a62e60d523a25e7379a6565834.jpg) + +![](images/2eabe546d3767e1420c95ca68322f12c3c6dcaa9e7462bee117854e129f68760.jpg) + +(a) Input +![](images/3c4dc12344006d4a0aa9ca58506751a21d1c2fadcc9dc36c1087d62180b90836.jpg) +Figure 5. Qualitative results on the KITTI dataset [11]. The depth maps predicted by MonoDepth2 and Lite-Mono exhibit inconsistencies in planar regions and noticeable errors along object edges. In contrast, our method produces smoother and more accurate depth estimations, effectively preserving both planar structures and sharp boundaries. + +![](images/0981aaef812258ab2c009b1204771c77d5cd0ff3e9a6d96c3756f8f39aa0ed24.jpg) + +![](images/cab04ddb682cc04ee842529fb97419ce24a938ffe2559232546b982d33236972.jpg) + +![](images/ecbca046fc0da37dd62f4d2e60cee09b3ed4058e772bb8ac1a6e500afd86679e.jpg) +(b) Monodepth2 + +![](images/80fec41f7b8ff9c9bc9b3ed0864361e0dc3efdbaf5ab1ec77fbeb47d10eed7dc.jpg) + +![](images/1b8fab11a47e8895a6eb526b9358a8d6ca247749367bc084302795091807283b.jpg) + +![](images/b20d99a929932dc6a40e5087426343593179eadeaa583a9060a7178f8b5daba1.jpg) +(c) Lite-Mono + +![](images/b4df1fd7118e0515d397bd46c8ff9d42327324c643ecc8b21baee941e99094de.jpg) + +![](images/06c87b1397938398d63211de17b959db837833c6ec04ba2bc326f5e46d9fded4.jpg) + +![](images/6185847fab4daab740fce8e6619fe584bab189f52aa154cc4f6e5cfb020e010f.jpg) +(d) Ours + +a structured planar generation loss $\mathcal{L}_{sp}$ during training. Our overall loss function can be formulated as: + +$$ +\mathcal {L} = \mathcal {L} _ {g} + \mathcal {L} _ {s p}. \tag {18} +$$ + +The $\mathcal{L}_g$ consists of a minimum photometric loss and an edge-ware smoothness loss: $\mathcal{L}_g = \mathcal{L}_{ph} + \lambda \mathcal{L}_{sm}$ , where + +$\mathcal{L}_{ph} = \sum_{n}\min_{n}\mathcal{P}(I_c,I_{n2c}),\mathcal{L}_{sm} = \sum |\partial_xD_c^* |e^{-|\partial_xI_c|}+$ $|\partial_yD_c^* |e^{-|\partial_yI_c|}$ and $\lambda$ is fixed to 0.001. $D_{c}^{*} = D_{c} / \bar{D}_{c}$ + +is the mean-normalized inverse depth. $\mathcal{L}_{sp}$ is defined as: $\mathcal{L}_{sp} = \sum \Psi^{1 / \sigma}(\mathcal{R})(\gamma \mathcal{A}_n + \varphi \mathcal{A}_o + \omega \mathcal{A}_u)$ , where $\gamma$ , $\varphi$ , and $\omega$ are set as 0.03, 0.01 and 0.1. + +![](images/3ce649409726d3f704525a5911e030672ebcadbcbb014f327f24fd8c309d60a6.jpg) + +![](images/3cb7136035cfb7bd831cb36285e2677ba2e3af4e22951e9019fe0ea558c612d2.jpg) + +
DatasetMethodSizeModeTrainTestRMSE↓Abs Rel↓δ<1.25↑δ<1.252↑δ<1.253↑
NYUV2MovingIndoor [65]320×256M✓✓0.7120.2080.6740.9000.968
Monodepth2 [13]320×256M✓✓0.6010.1600.7670.9490.988
P2Net [57]320×256M✓✓0.5990.1590.7720.9420.984
SC-DepthV1 [4]320×256M✓✓0.6390.1590.7340.9370.983
PLNet [22]320×256M✓✓0.5620.1510.7900.9530.989
StructDepth [27]320×256M✓✓0.5400.1420.8130.9540.988
ADPDepth [43]320×256M✓✓0.5920.1650.7530.9340.981
F2Depth [17]320×256M✓✓0.5690.1530.7870.9500.987
Guo et al. [18]320×256M✓✓0.5670.1520.7920.9500.988
Ours320×256M✓✓0.5200.1340.8330.9630.991
ScanNetMovingIndoor [65]320×256M×✓0.4830.2120.6500.9050.976
Monodepth2 [13]320×256M×✓0.4580.2000.6720.9220.981
TrainFlow [63]320×256M×✓0.4150.1790.7260.9270.980
P2Net [57]320×256M×✓0.4200.1750.7400.9320.982
PLNet [22]320×256M×✓0.4140.1760.7350.9390.985
IFMNet [49]320×256M×✓0.4020.1700.7580.9400.989
SC-Depthv1 [4]320×256M×✓0.3920.1690.7490.9380.983
StructDepth [27]320×256M×✓0.4000.1650.7540.9390.985
GeoDepth320×256M×✓0.3870.1610.7690.9460.987
+ +Table 2. Quantitative depth estimation results on the NYUv2 [42] and ScanNet [6] datasets. The NYUv2 dataset is used to assess within-dataset performance, while the ScanNet dataset is used to evaluate cross-dataset generalization. + +# 5. Experiments + +# 5.1. Datasets and Evaluation Metrics + +Outdoor Datasets. KITTI [11] is a standard outdoor benchmark. Following Monodepth2 [13], we use the data split of Eigen et al. [8], which has 39,180 monocular triplets for training, 4,424 for evaluation, and 697 for testing. Make3D [37] is often used as outdoor generalization test. It consists 134 images. The image is resized to $640 \times 192$ during both training and testing. + +Indoor Datasets. NYUv2 [42] contains 464 videos captured by a hand-held camera. Following StructDepth [22], we use 654 images for testing and the remaining 335 sequences for training and validation. ScanNet [6] provides 1513 indoor videos, captured by handheld devices. We use the test split in StructDepth [27], including 533 images, to verify generalization. The image is resized to $320 \times 256$ during both training and testing. + +Evaluation Metrics. We follow Monodepth2 [13] using absolute relative error (Abs Rel), relative squared error (Sq Rel), root mean squared error (RMSE), root mean squared logarithmic error (RMSE log), and threshold accuracy $(\sigma < 1.25, \sigma < 1.25^2$ and $\sigma < 1.25^3)$ . + +# 5.2. Implementation Details + +We implemented model in PyTorch [34] using an NVIDIA RTX 3090 GPU. Our models are trained for 20 epochs on the outdoor dataset and 40 epochs on the indoor dataset using Adam optimizer [23], with a batch size of 12 and 16, respectively. The learning rate is set to $10^{-4}$ , and de + +cays to $10^{-5}$ after 15 epoch for outdoor dataset and after 20 epoch for indoor dataset. The $\alpha$ , $\sigma$ , and $\mu$ are set to 0.85, 2, and 0.5, respectively. Our goal was to validate the core idea of plane-to-depth modeling, so we did not incorporate performance-improving techniques from recent SOTA methods (e.g., arbitrary-scale data augmentation in RA-Depth and the transformer-based feature extractor in MonoViT). Instead, we opted for a simpler architecture (only borrowing the DepthNet and PoseNet from RA-Depth) to avoid introducing excessive complexity and to focus on demonstrating the effectiveness of our method. Thus, we did not include a direct comparison with these works. However, the results of integrating our idea with SOTA methods are reported in the supplementary material. + +# 5.3. Comparison on Outdoor Scene + +KITTI. Table 1 provides quantitative results of training and testing on the outdoor dataset, i.e., KITTI dataset. Our method outperforms existing self-supervised approaches on all metrics. In particular, our method relatively outperforms the classical method Swin-Depth by $6.1\%$ and by $5.7\%$ in terms of Sq Rel and Abs Rel, respectively. Moreover, our method achieves superior performance when trained only on monocular videos, even compared to methods trained on stereo pairs or a combination of stereo pairs and monocular videos. We also compare the qualitative performance with the classic work Monodepth2 [13] and the recent work Lite-Mono [60]. As can be seen in Fig. 5, the depth maps predicted by MonoDepth2 and Lite-Mono are inconsistent in plane areas and exhibit noticeable errors at edges. In con + +![](images/0b372db24001e35c3482a9cf17c5caa8266f81bdfb701128491159c26462e971.jpg) +(a) Input +Figure 6. Qualitative results on the NYUv2 dataset [42]. + +![](images/320ea2d4da795c7adac62ed40097ab9dba39ba2fe820e39894739c4d20eda686.jpg) +(b) StructDepth + +![](images/a7af788f18751c34d7ac7464c4babb2b50d0455781951add4cde272a7efd0f36.jpg) +(c) PLNet + +![](images/af1401ddc8301c2e3b4a2ea544030051bf9af505ead3fb05becf8482670f8c84.jpg) +(d) Ours + +trast, the depth generated by our method is smooth and accurate for both plane regions and edges. + +Generalization Study on Make3D. To show the generalization capability in outdoor scenes, we test on Make3D [37]. All models were trained only on KITTI. Table 1 shows the quantitative comparison. Our method outperforms all previous work, indicating our method can be well generalized to unseen outdoor scenes. + +# 5.4. Comparison on Indoor Scene + +NYUv2. Compared to outdoor scenes, indoor scenes is challenging because it contains many low-texture planes. To verify the effectiveness in difficult scene, we trained and tested on NYUv2 [42], and the results are shown in Table 2. Our method outperforms all other self-supervised methods, which demonstrates that utilizing plane-to-depth modeling can improve the depth quality. Moreover, we provide the qualitative performance with self-supervised methods including focusing on indoor scenes, as shown in Fig. 6. It can be found that our proposed method obtain continuous depth results in region lacking texture. + +Generalization Study on Make3D. Table 2 shows the generalization comparison of our method with state-of-the-art methods on ScanNet [6]. All models are trained on NYUV2 [42]. Our method outperforms all previous approaches, which demonstrates our method can be well generalized to unseen indoor scenes. + +# 5.5. Ablation Study. + +In Table 3, we present an ablation impact of three key components in to-Depth Modeling (P2D), Depth Di (DDA), and Structured Plane Gen components are progressively added that predicts depth directly from a sin + +# Effects of Plane-to-Depth Modeli + +Plane-to-Depth modeling shows a + +over the baseline. By modeling planes explicitly and inferring the depth from plane properties, RMSE decreases from 4.471 to 4.436, and Sq Rel decreases 0.751 to 0.740, indicating our plane-to-depth modeling can efficiently leverage structured scene cues across pixels for enhancing depth accuracy. Furthermore, compared with the + +
MethodP2D SPG DDARMSE ↓ Sq Rel↓ δ<1.25↑#Params
Baseline4.4710.7510.8959.98M
+P2D✓4.4360.7400.89610.0M
+P2D+SPG✓ ✓4.4120.7220.89610.0M
GeoDepth✓ ✓ ✓4.3810.6940.89710.0M
+ +Table 3. Ablation study. Baseline: Predict depth directly from a single image. P2D: Using Plane-to-Depth modeling. DDA: Using Depth Discontinuity Awareness module SPG: Using Structured Plane Generation module. + +baseline framework, there are only few parameter increases, indicating that the performance improvement mainly comes from modeling rather than by increasing model parameters. Effects of Structured Plane Generation. When the SPG module is added to the P2D model, there is a further reduction in RMSE and Sq Rel, with values dropping to 4.412 and 0.722, respectively. Moreover, the SPG module does not add any new model parameters. This configuration demonstrates that SPG significantly enhances the structured prediction of depth planes, thereby optimizing the depth performance of the model. + +Effects of Depth Discontinuity Awareness. Finally, adding the DDA module, as seen in the full model (GeoDepth), yields the best results. The complete model achieves an RMSE of 4.381 and Sq Rel of 0.694, with $\sigma$ reaching 0.897. Moreover, the DDA module does not add any new model parameters. This improvement highlights the ability of the DDA module to accurately identify discontinuous regions and then avoid depth discontinuities by incorporating the structured plane generation module. + +# 6. Cond + +In this paper, we introduce a paradigm shift for continuous depth estimation by proposing GeoDepth, which utilizes plane-to-depth modeling to overcome the depth discontinuity of point-to-depth methods. Specifically, our GeoDepth models the complex 3D scene as planes of varying size, parameterized by planar normals and planar offsets, and infers the depth from them. Then, we propose a structured plane generation module and a depth discontinuity awareness module to learn correct plane representations (i.e., normal and offset) in a self-supervised paradigm. Extensive experiments on widely-used outdoor datasets (KITTI and Make 1D) and indoor datasets (NYUv2 and ScanNet) show the robustness and generalization ability. + +# Acknowledgements + +This work is supported by the National Natural Science Foundation of China (No. 62176047), the National Natural Science Foundation of China (No. 62476051), the Sichuan Natural Science Foundation (No. 2024NSFTD0041), and the Sichuan Science and Technology Program (No. 2021YFS0374). + +# References + +[1] Jinwoo Bae, Sungho Moon, and Sunghoon Im. Deep digging into the generalization of self-supervised monocular depth estimation. In Proceedings of the AAAI conference on artificial intelligence, pages 187-196, 2023. 6 +[2] Shariq Farooq Bhat, Ibrahim Alhashim, and Peter Wonka. Adabins: Depth estimation using adaptive bins. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition, pages 4009-4018, 2021. 3 +[3] Shariq Farooq Bhat, Ibraheem Alhashim, and Peter Wonka. 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In these scenarios, some samples may exhibit high similarity, yet they convey different semantics, making traditional distance metrics inadequate for distinguishing between positive and negative samples. This paper introduces geodesic distance as a novel distance metric in multi-modal learning for the first time, to mine correlations between samples, aiming to address the limitations of common distance metric. Our approach incorporates a comprehensive series of strategies to adapt geodesic distance for the current multimodal learning. Specifically, we construct a graph structure to represent the adjacency relationships among samples by thresholding distances between them and then apply the shortest-path algorithm to obtain geodesic distance within this graph. To facilitate efficient computation, we further propose a hierarchical graph structure through clustering and combined with incremental update strategies for dynamic status updates. Extensive experiments across various downstream tasks validate the effectiveness of our proposed method, demonstrating its capability to capture complex relationships between samples and improve the performance of multimodal learning models. + +# 1. 1 Introduction + +Recent years have witnessed remarkable progress on multimodal learning [3, 26, 28, 37, 46], driven by the rapid development of large transformer models [55]. In multimodal learning, image-text pairs are encoded into a unified representation space through carefully designed pre-training tasks [9, 29, 62]. The consistency of cross-modal representations facilitates the model with strong generalization abilities [56, 60], achieving satisfactory performance on various downstream tasks. + +A prevalent paradigm in multimodal learning includes + +![](images/713db2d67aaadc5d9a19c8c1e7623faabcc8d2b9a699917c4ed9dccf9ea0d9b4.jpg) +Figure 1. The motivation of leveraging geodesic metric. Based on the topological structures, geodesic distance can depict sample similarity more accurately. + +extracting features from different modalities, encouraging proximity between matching features and dispersity between mismatched ones by contrastive supervision [46], such as InfoNCE loss [16]. This paradigm inherently relies on distance computation between multi-modality features to mine positive and negative samples. CLIP [46] computes cosine similarity between cross-modal samples within a large batch, while ALBEF [26], maintains a momentum feature queue and calculates distances between batch features and queue features, thus avoiding large batch size. Recent works, such as TCL [58] and MAFA [4], adopt a similar paradigm but pay more attention to negatives. However, these works assume that samples are distributed in a spherical space [16], overlooking the possibility of distributions in more complex non-Euclidean spaces. For example, some sentences similar at the word level may possess close distances with trivial metrics but convey vastly different semantics, as shown in Fig.1. We propose that geodesic distance [21] can serve as an effective distance metric for multimodal learning, aiding in considering the data topology structure and thus more accurately depicting distances between samples. + +In this paper, we introduce geodesic distance to multimodal learning for the first time. Such distance metric enhances the characterization of relationships between sam + +plies in multi-modality datasets with complex data distribution. The benefits of using geodesic distance as a metric in multimodal learning are evident. Firstly, geodesic distance more accurately captures the underlying structure of complex data manifolds, especially when integrating data from diverse modalities. Therefore, we can easily distinguish samples with close cosine distances but distant geodesic distances to mine more accurate positive and negative samples. Secondly, traditional distance computations are one-to-one, meaning the distance between two points depends solely on those two points, which can lead to inaccuracy in portraying relative distances between distant points [10]. This ambiguity can adversely impact model optimization. In contrast, geodesic distance considers many-to-many (global) relationships, where data points are interconnected and the distance between two samples involves the participation of other routing points. The deterministic point-to-point path significantly reduces ambiguity and enhances interpretability in distance calculations, especially for more distant samples. + +Unlike traditional distance, the calculation of geodesic distance relies on a sample pool, which provides a reference frame for modeling distances between sample pairs. We posit that the local spaces neighboring each sample adhere to simple manifold assumption (as Def.2), allowing us to compute distances using a straightforward one-to-one metric (as Def.1). Consequently, we build a graph based on short-distance adjacency relationships within the sample pool, establishing undirected edges between locally adjacent samples. The distance between samples is represented as the shortest path between points in this graph, which can be computed using shortest-path algorithms. For simplicity, we employ the Floyd algorithm [13]. However, directly calculating geodesic distance for a large number of samples would result in huge computational complexity. To facilitate efficient computation, we model the sample pool as a hierarchical graph. Within each layer of the graph, we partition samples into disjoint clusters through sample clustering. We then construct a graph among cluster centers and use the Floyd algorithm to calculate the shortest path between these cluster centers. Distances within each cluster are recursively propagated to the next layer of the hierarchical graph. At the bottom layer, we assume that the local manifold is simple enough to employ trivial distance metrics. For the distance between any two samples, we backtrack layer by layer in the hierarchical graph from bottom to top, to assess whether they belong to the same cluster, up to the top layer, as illustrated in Fig.2. Additionally, we develop efficient incremental update strategies to accommodate sample updates and reduce computational complexity. + +We believe geodesic distance can effectively facilitate current multimodal learning, yielding improved pre-trained models with more accurate distance modeling. Our mul + +timodal pre-training experiments yield promising results across various tasks, such as image-text retrieval, visual question answering, visual entailment, natural language for visual reasoning, and visual grounding. Extensive results verify the effectiveness of this geodesic perspective. + +# 2. Related Work + +# 2.1. Multi-modal Learning + +Multimodal pre-training can be mainly categorized into single-stream networks [9, 18, 28, 29, 37, 49], dual-stream networks [19, 26, 30, 46, 53], and Xformer networks [3, 27, 60?]. Single-stream networks concatenate text tokens and visual tokens and then utilize a transformer [55] for modality fusion. This structure can be seen as treating visual modality as prompt for the text modality [25]. Depending on the way of obtaining visual tokens, single-stream networks can further be divided into region-based methods [9, 29, 62], grid-based methods [18], and patch-based methods [20]. Dual-stream networks encode images and texts separately and then align paired image-text features with contrastive loss to map features of different modalities into a unified representation space. This paradigm can be viewed as maximizing a lower bound on the mutual information between modalities [26]. Among them, CLIP [46], trained on $400\mathrm{M}$ image-text pairs, has demonstrated remarkable zero-shot ability across various downstream tasks. Subsequent improvement efforts include [6, 19, 30, 42]. ImageBind [15] aligns more modalities and has inspired numerous interesting works [50]. Xformer networks combine advantages from single-stream and dual-stream networks, performing end-to-end feature extraction, alignment, and fusion for different modalities. Benefiting from the design, Xformer exhibits strong retrieval capabilities as well as superior multimodal reasoning ability. Numerous works have also introduced novel structures such as VLMO [3] and BeiT3 [56]. Multimodal learning requires elaborate pre-training tasks, and commonly used pre-training tasks include Masked Language Modeling(MLM) [12], Image-Text Matching (ITM) [26], Image-Text Contrastive (ITC) [46], Word Patch Alignment (WPA) [9], and so on. + +# 2.2. Geodesic Distance + +Geodesic distance provides more structural information in complex manifolds. Mitchell et al. [39] proposes an MMP algorithm to get the exact computation of geodesic distance. Many approximate methods [11, 21, 52] are developed to reduce computational cost. The classic dimensionality reduction algorithm ISOMAP [54] uses geodesic distance to measure the distance between points, and then reconstructs the data in a low-dimensional Euclidean space. Recently, many arts of various fields have integrated geodesic distance into existing deep learning paradigms and achieved + +![](images/64334c6eec04696dd088b74099bc07f260c907bb70010d5606408a034866bca2.jpg) +Figure 2. An overview of our proposed hierarchical graph structure, where we display the clusters and geodesic paths. + +favorable results. GCNN [38] proposes a convolution operator that adapts to the data manifold, taking into account the manifold distribution within the patch during the feature extraction. To reduce computational complexity, GeoNet [17] is committed to learning potential sample geodesic features. Geodesic-Former [40] proposes a geometric-guided approach to enhance the few-shot capability in point cloud segmentation. GraphWalk [44] proposes a differentiable geodesic distance estimator, but suffers from low accuracy. Except for the application in 3D vision [31, 40], there are also explorations on image [2, 24, 33] to achieve appearance-based similarity estimates. In this paper, we use geodesic distance for contrastive supervision for the first time in multimodal learning seamlessly and calculate geodesic distance based on topological structures. + +# 3. Methodology + +In this section, we elaborate on employing geodesic distance as distance measurement, and utilizing multimodal learning as a point of entry. Sec.3.1 introduces basic paradigms of distance computation in multimodal learning. In Sec.3.2 delves into the algorithms of geodesic distance computation. Next, in Sec.3.3 and Sec.3.4, we develop efficient methods for geodesic metric computation and the adaption to current multimodal learning. Finally, Sec. 3.5 and Sec. 3.6 detail the algorithmic implementation and theoretical analyses. + +# 3.1. Preliminary + +In multimodal learning, a fundamental paradigm involves extracting features from numerous numbers of paired samples (e.g. image-text pairs), then pulling paired samples closer while pushing mismatched samples apart [19, 46]. Stable model optimization relies on a sufficient number of negative samples for contrastive learning [7, 16]. For instance, CLIP [46] employs a very large batch size of 32,768, while ALBEF [26], TCL [58] and MAFA [4] maintains a + +# Algorithm 1 A Step for Multimodal Model Optimization + +Require: Data of modalities $A$ , $B$ , feature queue $Q_{a}$ , $Q_{b}$ +Ensure: Model parameters $\theta$ + +1: Extract features $F_{a}$ , $F_{b}$ and moment features $F_{a}^{m}$ , $F_{b}^{m}$ for input batch. +2: Compute the distance between $F_{a}$ and $[F_b^m, Q_b]$ , and the distance between $F_{b}$ and $[F_a^m, Q_a]$ . +3: Calculate losses and update model parameters $\theta$ . +4: Update $F_{a}^{m}$ and $F_{b}^{m}$ into feature queues $Q_{a}$ and $Q_{b}$ . + +large and consistent momentum feature queue with size of 65,536, 65,536 and 480,000, respectively. All these methods provide sufficient samples for constructing topological structures, which enables precise computation of geodesic distances. Considering computational efficiency and model performance, we adopt the paradigm of ALBEF, TCL and MAFA. The feature queue generated by the momentum model ensures an adequate number of contrastive samples even with small batch sizes. As presented in Alg.1, given the momentum feature queue $Q_{a}, Q_{b} \in \mathbb{R}^{N \times c}$ , batch feature $F_{a}, F_{b} \in \mathbb{R}^{B \times c}$ of two modalities, where $N$ is the feature queue size, $B$ denotes batch size, $c$ is channel dimension, the distance between $F_{a}$ and $Q_{b}$ necessitates computing the geodesic distances from each sample in $F_{a}$ to each sample in the feature queue $Q_{b}$ , and vice versa. Additionally, we need to update the current batch into the feature queue without disrupting the topological structure used for computing geodesic distances. + +# 3.2. Geodesic View + +The computation of geodesic distance typically relies on assumptions about the manifold structure. A common assumption [1] is that data is intrinsically embedded onto a spherical surface [16]. However, this assumption could be overly simplistic, as mapping samples onto a spherical surface fails to capture more complex manifold structures, as shown in Fig.2. To better accommodate the complex manifold, we opt for data topological structures for geodesic distance computation. Previous works [40, 54] construct feature points into a graph using local proximity relationships. Inspired by this, for a sample pool $P$ of size $N$ , we define each point to possess proximity relationships with its $n$ nearest neighbors. + +For the sake of discussion, we first give some basic definitions as follows, + +Definition 1 (Trivial Distance Metric) We define the distance metric as the trivial distance metric if and only if the distance calculation relies solely on these two related points, and is independent of other routing points, such as cosine distance and Euclidean distance. + +Definition 2 (Simple Manifold Assumption) For any two points $x_{i}, x_{j}$ within a local space with flat data distribution, the difference between geodesic metric $d_{g}(x_{i}, x_{j})$ and trivial metric $d_{t}(x_{i}, x_{j})$ satisfies, + +$$ +\left| d _ {g} \left(x _ {i}, x _ {j}\right) - d _ {t} \left(x _ {i}, x _ {j}\right) \right| < \delta , \tag {1} +$$ + +where $\delta$ is a threshold. We can then define this local space satisfies simple manifold assumption. + +For two proximity points $x_{i}$ and $x_{j}$ , there exists an edge with a weight of $d(x_{i},x_{j})$ between them. We assume the local manifold surrounding each point to be a simple manifold, where we can employ a trivial distance metric. Consequently, all points are encompassed within a graph structure, and we can utilize the Floyd algorithm [13] to compute the shortest paths between each point pair. Ultimately, we obtain a geodesic distance matrix $G_{D}\in \mathbb{R}^{N\times N}$ with respect to the sample pool $P$ . + +# 3.3. Hierarchical Structure + +Despite the above geodesic perspectives, applying geodesic distance in multimodal learning remains several challenges. Firstly, to ensure stable model convergence, feature queues are often large, resulting in a considerably large sample pool. Constructing a graph and computing the shortest paths for all points in such a pool can be computationally prohibitive. Secondly, the distances from points outside the graph to every point within the graph must also be taken into account. Finally, the momentum features of each batch should be updated into the graph after each step optimization. We will elaborate on the solutions to these issues in detail below. + +# Q1: How to obtain geodesic distances between points in a large-scale sample pool? + +Based on the simple manifold assumption of local data space, we first cluster the samples in the sample pool, with the number of cluster centers denoted as $n_{\text{cluster}}$ . Subsequently, we only construct graphs for the cluster centers and compute the shortest paths by the Floyd algorithm. At this point, the distance between any two points $x_i, x_j$ in the sample pool can be expressed as the distance from each point to its respective cluster center $C(x_i), C(x_j)$ , denoted as $d(x_i, C(x_i))$ , $d(x_j, C(x_j))$ , plus the shortest path distance between the two cluster centers, denotes as $d_g(C(x_i), C(x_j))$ . The distance computation from a sample point to its corresponding cluster center occurs within a cluster. If the cluster is small enough to meet the simple manifold assumption, we can directly apply a trivial distance metric. Otherwise, we recursively apply clustering within this cluster until the clusters at the lowest level satisfy the simple manifold assumption. Consequently, the distances between any two points in the sample pool proceed by traversing the hierarchical structure of the graph from + +bottom to top, accumulating the distances between sample points and their respective cluster centers during the backtracking process, until the two cluster centers at a certain level belong to the same cluster. Then, the geodesic distance between these two cluster centers will be added to the final result, as shown in Fig. 2. We name this algorithm as hierarchical geodesic distance algorithm. For a graph with $n$ layers and the $n$ -th layer is the bottommost layer, the distance of $d(x_i, x_j)$ can be calculated as + +$$ +\begin{array}{l} d (x _ {i}, x _ {j}) = d _ {g} (C _ {s} (x _ {i}), C _ {s} (x _ {j})) + d (x _ {i}, C _ {s} (x _ {i})) + d (x _ {j}, C _ {s} (x _ {j})), \\ \text {w h e r e} \end{array} +$$ + +$$ +\begin{array}{l} d \left(x _ {i}, C _ {k} \left(x _ {i}\right)\right) = d _ {g} \left(C _ {k + 1} \left(x _ {i}\right), C _ {k + 1} \left(C _ {k} \left(x _ {i}\right)\right)\right) \\ + d \left(x _ {i}, C _ {k} \left(x _ {i}\right)\right) \\ + d \left(C _ {k} \left(x _ {i}\right), C _ {k + 1} \left(C _ {k} \left(x _ {i}\right)\right)\right), \text {w h e n} s \leq k < n \\ \end{array} +$$ + +$$ +d \left(x _ {i}, C _ {n} \left(x _ {i}\right)\right) = d _ {t} \left(x _ {i}, C _ {n} \left(x _ {i}\right)\right), \text {w h e n} k = n. +$$ + +(2) + +$s$ denotes the layer where two sub-cluster centers belong to the same cluster. $C_s, C_{s+1}, \ldots, C_n$ denote the corresponding cluster centers at layer $s, s+1, \ldots, n$ . $d_g()$ represents geodesic distance obtained by Floyd algorithm, while $d_t$ represents trivial distance metrics, such as cosine distance and Euclidean distance. + +# Q2: How to compute the distance from a point outside the graph to all points in the sample pool? + +For the constructed hierarchical graph, the distance from each point $x_{i}$ to its respective bottom-level cluster center $C_n(x_i)$ , and the distance among all bottom-level cluster centers in the graph, can be conveniently obtained. By combining these two distances, we obtain the distance from each point $x_{i}$ in the graph to all bottom-level cluster centers $C_n$ , i.e. $d(x_{i},C_{n}(x_{j})) = d(x_{i},C_{n}(x_{i})) + d(C_{n}(x_{i}),C_{n}(x_{j}))$ , where $C_n(x_j)$ is any one bottom level cluster center. Subsequently, we decompose the distance from a point outside the graph $x_{o}$ to a point in the sample pool $x_{i}$ into the distance from the point outside the graph to its nearest bottom-level cluster center $d(x_o,C_n^{near}(x_o))$ and the distance from this cluster center to the point inside the graph $d(C_n^{near}(x_o),x_i)$ , as shown in Fig.2. We have already obtained the distance from cluster centers to any points inside the graph $d(C_n,x_i)$ as described above. Hence, we ultimately obtain the distance from a point outside the graph to any point inside the graph, as Eq.3, + +$$ +d \left(x _ {o}, x _ {i}\right) = d \left(x _ {o}, C _ {n} ^ {\text {n e a r}} \left(x _ {o}\right)\right) + d \left(C _ {n} ^ {\text {n e a r}} \left(x _ {o}\right), x _ {i}\right). \tag {3} +$$ + +# Q3: How to perform graph updates? + +With our proposed hierarchical structure, graph updates become relatively straightforward. As mentioned above, we have already determined the nearest bottom-level cluster center for each point outside the graph. We simply need to attach these points to their respective nearest cluster centers. + +To ensure that the overall size of the graph remains stable, we remove the oldest samples following [16]. + +In addition to the feature queue, we maintain a circular index queue representing the bottom-level cluster centers to which each point belongs. The graph update boils down to covering the feature queue and the index queue. To avoid redundant computations, we also maintain queues for the distances from each point to its nearest bottom-level cluster center and to all bottom-level cluster centers, and we update these two queues simultaneously. To prevent the hierarchical structure from becoming outdated during training, we perform an overall update to the hierarchical graph structure every $T_0$ step. The overall training process can be summarized as follows. Firstly, in every $T_0$ step, we reconstruct the hierarchical graph structure $S$ , obtaining the bottom-level cluster center $\mathcal{K}$ for each point in the graph and the distances $\mathcal{D}_o$ from each point to all bottom-level centers. For a common step $t$ , we fix the hierarchical graph $S$ , and compute the geodesic distances from each point in batch to the points in the sample pool for the model optimization. Finally, we update the $\mathcal{K}$ and $\mathcal{D}_o$ with the current batch. + +# 3.4. Algorithm Adaptation + +In multimodal learning, we need to compute the distance from the features $F_{a}$ of modality $A$ to the features $F_{b}^{m}$ of modality $B$ as well as the feature queue $Q_{b}$ . The paired samples from $F_{a}$ and $F_{b}^{m}$ serve as positive samples, while the feature queue $Q_{b}$ serves as negative samples. This requires us to first update the feature $F_{b}^{m}$ to $Q_{b}$ , which involves treating $F_{b}^{m}$ as points outside the graph, computing the distance from each sample in $F_{b}^{m}$ to the sample pool $Q_{b}$ , and then updating the intermediate results to the corresponding queue. Next, the features of modality $A$ are treated as points outside the graph, and the distances from each sample in $F_{a}$ to each point in the updated sample pool $Q_{b}^{update}$ are computed. Since the paired features in the sample pool and modality $A$ depend on the position where $F_{b}^{m}$ is inserted into the pool, we hence construct the corresponding ground truth based on the insertion position of $F_{b}^{m}$ . + +Under the assumption of a simple manifold, we use cosine distance as the trivial metric. Then each segment of the geodesic distance path corresponds to an angular distance, with the total geodesic distance representing the accumulated angles along the shortest path. We truncate the final accumulated value, normalize it to the range $[0, \pi]$ , and then apply the cosine function to compute the loss. We refer to this procedure as angle normalization. The complete algorithm is detailed in Alg.2. + +# 3.5. Implementation Details + +We conduct our experiments with PyTorch framework on 8 NVIDIA V100 GPUs. Following [26], we extract textual features by the first 6 layers of a BERT [12] pre-trained + +Algorithm 2 Hierarchical Geodesic Distance Adaptation for Multimodal Learning +Require: Multimodal data of modalities $A, B$ , feature queue $Q_{a}$ , $Q_{b}$ , total training steps $T$ , hierarchical graph update period $T_{0}$ +Ensure: Model parameters $\theta$ +1: for $t = 1$ to $T$ do +2: if $t \% T_0 == 0$ then +3: Update the hierarchical graph $S$ . +4: Obtain the bottom-layer clusters $\mathcal{K}$ for each point. +5: Obtain the distances $\mathcal{D}_o$ from each point to all bottom-layer cluster centers. +6: end if +7: Obtaining features $F_{a}, F_{b}$ and momentum feature $F_{a}^{m}$ , $F_{b}^{m}$ respectively for current batch. +8: Calculate distances from $F_{a}^{m}$ to $Q_{a}$ and from $F_{b}^{m}$ to $Q_{b}$ +9: Update $F_{a}^{m}$ and $F_{b}^{m}$ to $Q_{a}$ and $Q_{b}$ , respectively, resulting in $Q_{a}^{update}$ and $Q_{b}^{update}$ . +10: Compute distances from $F_{a}$ to $Q_{b}^{update}$ and from $F_{b}$ to $Q_{a}^{update}$ , apply angle normalization. +11: Construct corresponding ground truth based on the insertion position of $F_{a}^{m}$ and $F_{b}^{m}$ . +12: Calculate InfoNCE loss and update model parameters $\theta$ . +13: Update $\mathcal{K}, \mathcal{D}_{o}, Q_{a} = Q_{a}^{update}, Q_{b} = Q_{b}^{update}$ +14: end for + +text encoder, while visual features are obtained from an image encoder trained with CLIP-ViT [46]. Then we compute the image-text contrastive loss $\mathcal{L}_{itc}$ on representations from the unimodal encoders. We replace the cosine distance in loss function with the proposed geodesic distance. Then we apply the last 6 layers of Bert model for multimodal fusion, where visual features interact with textual features through cross-attention. Additionally, we also employ two other pre-training tasks, i.e., masked language modeling (MLM) and image text matching (ITM), with loss functions $\mathcal{L}_{mlm}$ and $\mathcal{L}_{itm}$ . The overall loss function is defined as $\mathcal{L} = \mathcal{L}_{itc} + \mathcal{L}_{mlm} + \mathcal{L}_{itm}$ . + +We empirically set the queue size (i.e., the sample pool size) as 65536 and update the hierarchical graph every 100 iterations. During the hierarchical graph construction, we utilized the K-Means [35] for clustering with 256 cluster centers ( $n_{cluster}$ ) and 5 clustering iterations. Each cluster center has 8 neighbors for constructing the graph. To balance efficiency and effectiveness, we build a two-layer graph structure, using cosine distance as the trivial distance metric, where the parameter $\delta$ in Def.2 is set as $\sqrt{d}$ with feature dimension $d = 256$ . We truncate the final accumulated angle of the geodesic path at $4\pi$ . We conduct detailed experiments on parameter selection in Sec. 4.5. We employ the AdamW [36] optimizer with a weight decay of 0.02. For the learning rate schedule, we set the initial learning rate to $1e - 5$ , warm up to $1e - 4$ after 1000 iterations, and then follow a cosine decay to the minimum + +
Method#ImagesMSCOCO (5K test set)Flickr30K (1K test set)
Text RetrievalImage RetrievalText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
ImageBERT [45]6M44.071.280.432.359.070.270.790.294.054.379.687.5
UNITER [9]4M64.187.793.348.876.785.880.795.798.066.288.492.9
ViLT [20]4M56.582.689.640.470.081.173.293.696.555.082.589.8
CLIP [46]400M58.481.588.137.862.472.288.098.799.468.790.695.2
FILIP [59]400M61.384.390.445.970.679.389.899.299.875.093.496.3
ALBEF [26]4M68.789.594.750.176.484.590.598.899.776.893.796.7
TCL [58]4M71.490.895.453.579.087.193.099.199.679.695.197.4
MAFA* [4]4M72.691.395.653.979.687.793.599.299.780.195.697.7
Geo-ALBEF4M72.091.195.653.679.287.293.299.399.879.995.397.5
Geo-TCL4M73.992.095.854.680.688.094.099.499.880.695.997.9
Geo-MAFA4M74.792.596.155.481.488.794.699.499.881.196.398.2
ALIGN [19]1.2B58.683.089.745.669.878.688.698.799.775.793.896.8
+ +Table 1. Zero-shot image-text retrieval results on MSCOCO and Flickr30K dataset. We report the average of R@1, R@5, R@10 for evaluation. * refers to the reproduced models by the authors. + +
Method#ImagesMSCOCO (5K test set)Flickr30K (1K test set)
Text RetrievalImage RetrievalText RetrievalImage Retrieval
R@1R@5R@10R@1R@5R@10R@1R@5R@10R@1R@5R@10
ImageBERT [45]6M66.489.894.450.578.787.197.097.699.273.194.196.8
UNITER [9]4M65.788.693.852.979.988.087.398.099.275.694.196.8
OSCAR [29]4M70.091.195.554.080.888.5------
ViLT [20]4M61.586.392.742.772.983.183.596.798.664.488.793.8
VILLA [14]4M------87.997.598.876.394.296.8
VLMO-B [3]4M74.893.196.957.282.689.892.399.499.979.395.797.8
ALBEF [26]4M73.191.496.056.881.589.294.399.499.882.896.798.4
TCL [58]4M75.692.896.759.083.289.994.999.599.884.096.798.5
MAFA [4]4M78.093.496.961.283.990.296.199.799.884.997.498.6
Geo-ALBEF4M76.293.396.659.283.589.995.199.899.984.297.198.5
Geo-TCL4M78.493.796.960.984.090.596.399.999.985.197.698.6
Geo-MAFA4M79.393.997.362.584.390.896.999.9100.085.698.198.9
ALIGN [19]1.2B77.093.596.959.983.389.895.399.8100.084.997.498.6
+ +Table 2. Fine-tuned image-text retrieval results on MSCOCO and Flickr30K dataset. + +learning rate of $1e - 5$ . We conduct pre-training for 30 epochs on COCO [32], VG [22], SBU [41], and CC3M [48] datasets, with data pre-processing following [26]. We use Numba [23] with CUDA operator to implement Floyd algorithm on each layer for computation acceleration. + +More details about network structure, pre-training tasks can be found in the supplementary materials. + +# 3.6. Theoretical Analysis + +We conduct theoretical analysis of the hierarchical graph to verify graph sparsity and connectivity, which enables fast and robust geodesic distance calculation. + +Theorem 1 (The number of connected components) For a + +layer of the hierarchical graph containing $N$ cluster centers, with each point having $\sigma$ neighbors, the number of connected components $\mathcal{E}$ in this layer satisfies: + +$$ +\mathcal {E} < = \frac {N ([ 1 + \ln (1 + \sigma) ]}{1 + \sigma}. \tag {4} +$$ + +Theorem 2 (The scale of connected components) For a layer with $N$ cluster centers, the size of each connected component satisfies $b < |S_i| < a$ , if and only if the number of edges in the graph satisfies: + +$$ +b ^ {2} \left\lfloor \frac {N}{b} \right\rfloor - N < E (N) \leq (a - 1) ^ {\frac {1}{a}} N ^ {2 - \frac {1}{a}} + (a - 1) N. \tag {5} +$$ + +We can also deduce a similar upper bound with a more con + +
Method#ImagesVQANLVR2SNLI-VE
test-devtest-standarddevtest-Pvaltest
UNITER [9]4M72.7072.9177.1877.8578.5978.28
OSCAR [29]4M73.1673.4478.0778.36--
ViLT [20]4M70.94-75.2476.21--
VILLA [14]4M73.5973.6778.3979.3079.4779.03
ALBEF [26]4M74.5474.7080.2480.5080.1480.30
TCL [58]4M74.9074.9280.5481.3380.5180.29
MAFA [4]4M75.5575.7582.5282.0880.7980.96
Geo-ALBEF4M75.1375.1680.7081.0680.5680.73
Geo-TCL4M75.4675.4881.0681.9980.9980.75
Geo-MAFA4M76.0476.1983.1282.9581.4281.63
+ +Table 3. Performance on downstream visual-language tasks. + +cise form, + +$$ +E (N) \leq \left(1 - \frac {1}{a - 1}\right) \frac {N ^ {2}}{2}, \tag {6} +$$ + +where $|\mathcal{S}_i|$ represent the scale of a certain connected components $\mathcal{S}_i$ . + +The above theorems indicate that each layer of the hierarchical graph may contain multiple connected and adequately large components, implying the rationality of computing geodesic distance in our multimodal learning setting. In our implementation, we set the distance between points that are not mutually reachable in the graph to infinity. This effectively filters out some overly simple negative samples. Detailed proof can be found in the supplementary materials. + +# 4. Experiments + +# 4.1. Downstream Tasks + +We evaluate our method on five downstream tasks, including image-text retrieval, visual question answering, visual entailment, natural language for visual reasoning, and visual grounding. + +Image-Text Retrieval consists of two sub-tasks, image-to-text retrieval (TR) and text-to-image retrieval (IR). Following [26], we evaluate the pre-trained model on Flickr30K [43] and COCO [32] with both zero-shot and fine-tuning settings. For zero-shot retrieval on COCO, the pre-trained model is directly evaluated on the test data of COCO. For zero-shot retrieval on Flickr30K, we evaluate the model fine-tuned on COCO as [26]. Under fine-tuning setting, we fine-tune the pre-trained model on the training data of these datasets and evaluate on the corresponding validation and test sets. + +Visual Question Answering (VQA) aims to predict the answer to a question based on the given image. This task can be considered as a generation task following [26]. Specifically, we use a 6-layer decoder for answer generation from the 3192 candidates during inference. + +Visual Entailment (SNLI-VE) [57] predicts the relationship between the given image-text pair, which includes entailment, neutral, and contradictory. It can be treated as a three-class classification problem, and we add a multi-layer perceptron (MLP) to predict the class on the final [CLS] token. + +Natural Language for Visual Reasoning (NLVR $^2$ ) determines whether a natural language description matches a pair of images. We evaluate on the NLVR $^2$ [51] dataset following [26]. + +Visual Grounding aims to localize the region in an image that is most relevant to the given text. We adopt the weakly-supervised setting similar to image-text retrieval and evaluate on RefCOCO+ [61]. During inference, heatmaps generated by Grad-CAM [47] are used to rank the detected proposals. + +# 4.2. Image and Text Retrieval + +We evaluate the performance of our model on the COCO and Flickr30K datasets under two settings, i.e., zero-shot and fine-tuning, as reported in Tab.1 and Tab.2, respectively. We can observe that our method outperforms various arts, such as UNITER [9], OSCAR [29], VILLA [14], ViLT [20], CLIP [46], ALBEF [26], VLMO [3], TCL [58] and MAFA [4], demonstrating the effectiveness of our method. + +# 4.3. VQA, NLVR2, VE and Grounding + +We further validate our method on various downstream tasks, including VQA, NLVR², VE and visual grounding, as shown in Tab.3. Previous works like UNITER [9], OSCAR [29], VILLA [14], ALBEF [26], TCL [58], and MAFA [4] are compared. Experimental results indicate satisfactory performance on these downstream tasks. We conduct visual grounding following [26], obtaining localization regions through Grad-CAM [47]. Fig.3(right) presents our results on visual grounding, comparing with ARN [34], + +![](images/d78f5f3adf6b6262496b737161f800fade7e26ab2e4611cbb4e0c79f45de910f.jpg) +Figure 3. Visual grounding visualization (left) and performance of weakly-supervised visual grounding on RefCOCO+ (right). + +![](images/566813df1ead8752c3b4d4bd9da34ca7d90f52c768e726512ac5175ec9d565cc.jpg) + +![](images/f4f949a8cf4966f004c8a5328d16d0567f78649b56c027e2af804aaf3956a756.jpg) + +![](images/428c75f432b531f35e16f95bc10938afacd56e80ececaacec8a8c9eb268ee529.jpg) + +
MethodValTestATestB
ARN [34]32.7834.3532.13
CCL [63]34.2936.9133.56
ALBEF [26]58.4665.8946.25
Geo-ALBEF59.8267.9347.49
+ +
MethodTRIR
CLIPFT58.537.8
Geo-CLIPFT59.638.7
FLIPFT60.144.2
Geo-FLIPFT61.745.1
+ +
Method100epoch200epoch
MOCOv267.469.9
Geo-MOCOv267.870.6
SwAV66.569.1
Geo-SwAV67.169.9
+ +
MethodPCMATTI
ALBEF25.3G255s
Geo-ALBEF25.9G268s
CLIPFT24.3G213s
Geo-CLIPFT24.7G224s
+ +Table 4. Generalization on other multimodal methods. We report R@1 accuracy of text retrieval (TR) and image retrieval (IR) on COCO with zero-shot setting. +Table 5. Generalization on other selfsupervised methods. We report the Top1 accuracy of linear classification on ImageNet dataset. (ResNet50 crop $224\times 224$ +Table 6. Efficiency analysis. PCMA represents the peak CUDA memory allocations, and TTI denotes the total time cost of 100 training iterations. + +
layersTRIRTTI
175.158.5282s
276.259.2268s
376.259.1270s
+ +(a) Graph layers. + +
clustersTRIR
12874.758.1
19275.358.8
25676.259.2
38475.859.0
+ +(b) Kmeans clusters. + +
nbrsTRIR
675.958.6
876.259.2
1076.159.0
1276.259.1
+ +(c) Point neighbors. + +
itersTRIR
5075.959.1
7576.059.1
10076.259.2
12576.058.9
+ +(d) Graph updates. + +Table 7. Hyper-parameter analysis. We present the R@1 accuracy of text retrieval (TR) and image retrieval (IR) on the COCO dataset. + +CCL [63], and ALBEF [26]. + +# 4.4. Generalization + +To further validate the effectiveness of geodesic distance, we replace distance metrics in other methods, such as CLIP [46] and FLIP [30]. To avoid time-consuming pretraining, we adapt their network to momentum queue form and fine-tune our pre-training dataset with the open-source model for an epoch, denoted as $\mathrm{CLIP}_{FT}$ and $\mathrm{FLIP}_{FT}$ , where Geo represents the use of geodesic distance, as shown in Tab.4. We also verify the effectiveness of our method on self-supervised learning, such as MOCOV2 [8] and SwAV [5], as shown in the Tab.5. Under the default settings, geodesic distance achieves superior performance, showing its generalization capability. + +# 4.5. Other Analysis + +We conduct detailed analyses of the hyper-parameters. For a fair comparison, we use pre-training models without geodesic distance and only fine-tuned using different hyperparameters for the image-text retrieval, without affecting the validity of the experimental results. We analyze the number of hierarchical graph layers, the number of KMeans clusters, the number of neighbors for construct + +ing the graph, and the frequency of hierarchical graph updates, as shown in Tab. 7. We conduct experiments on ALBEF [26], and similar results can be drawn from other models. It can be observed that our performance is not sensitive to those parameters. We also investigate the algorithm efficiency regarding training time and CUDA memory consumption, as shown in Tab.6. We can observe that our method brings little extra time cost and a negligible increase in CUDA memory. + +# 5. Conclusion + +In this paper, we introduce geodesic distance for the first time to address the limitations of distance metrics in current multimodal learning frameworks. Geodesic distance, as a more accurate measurement for large-scale datasets and complex data structures, enhances the effectiveness of negative sample mining in cross-modal contrastive learning. We illustrate the methodology of employing geodesic distance within the current multimodal learning paradigms, offering detailed adaptation strategies. To enhance the efficiency and applicability, we develop the hierarchical geodesic distance algorithm for computing geodesic distance along with corresponding update strategies. Extensive experiments on downstream tasks validate the effectiveness of our method. + +Acknowledgement. This work was supported by National Science Foundation of China (U20B2072). This work was also partly supported by SJTU Medical Engineering Cross Research Grant YG2021ZD18. + +# References + +[1] E Andruchow, Gustavo Corach, and D Stojanoff. Geometry of oblique projections. arXiv preprint math/9911133, 1999. 3 +[2] Xue Bai and Guillermo Sapiro. 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Existing studies mainly focus on optimizing local updates or global aggregation, but these indirect approaches demonstrate instability when handling highly heterogeneous data distributions, especially in scenarios where label skew and domain skew coexist. To address this, we propose a geometry-guided data generation method that centers on simulating the global embedding distribution locally. We first introduce the concept of the geometric shape of an embedding distribution and then address the challenge of obtaining global geometric shapes under privacy constraints. Subsequently, we propose GGEUR, which leverages global geometric shapes to guide the generation of new samples, enabling a closer approximation to the ideal global distribution. In single-domain scenarios, we augment samples based on global geometric shapes to enhance model generalization; in multi-domain scenarios, we further employ class prototypes to simulate the global distribution across domains. Extensive experimental results demonstrate that our method significantly enhances the performance of existing approaches in handling highly heterogeneous data, including scenarios with label skew, domain skew, and their coexistence. Code published at: https://github.com/WeiDai-David/2025CVPR_GGEUR + +# 1. Introduction + +Federated Learning (FL) enables multiple clients to collaboratively train a global model without sharing raw data, ef + +![](images/1b3253c41fb0213f8b7b5e85748b0a9c6224bb591237c9ec725b324c62f4b4c1.jpg) +Figure 1. The distribution of local data on clients is imbalanced. The "bird" category has a large number of samples, allowing its local distribution to effectively represent the global distribution. In contrast, the "truck" category has insufficient samples, resulting in a significant disparity between the local and global distributions. + +fectively addressing key concerns related to data privacy and security [13, 19, 53]. However, data heterogeneity remains one of the primary challenges in FL, especially in the presence of label skew and domain skew across clients [12, 15, 17, 28, 29]. Such distributional differences lead to variations in the local optimization directions for each client, which can be particularly pronounced when data is sourced from multiple domains [5, 33, 42, 59, 66]. This cross-client distribution shift not only slows down global model convergence but also undermines the model's generalization capability across clients [5, 13, 30, 62]. + +Existing research addressing data heterogeneity in federated learning primarily focuses on two categories of methods [13]. The first is server-side optimization strategies, which aim to enhance model convergence by adjusting the global aggregation process [2, 3, 11, 32, 44, 52, 54, 57, 61, 64]. The second category includes client-side regularization [1, 7, 12, 22, 23, 42] and data augmentation methods [67, 68], which attempt to align local model optimization through guidance from the global model and loss function adjustments or directly apply data augmentation techniques + +![](images/c097e378dd5c34bd3692e9f839b6ad96c719c5aec50bee39332375da03664124.jpg) +Application of GGEUR on clients in a single-domain scenario + +![](images/2507b45e3796c06800ff84fc3a9046ba7ed202315d6c3fff031781287762956d.jpg) +Application of GGEUR on clients in a multi-domain scenario +Figure 2. Example of "bird" category: in a single-domain scenario, only the local global distribution is simulated; in a multidomain scenario, the global distribution from other data domains is also simulated on a client. + +like Mixup in the local setting [63]. However, these approaches do not directly tackle the core issue of data heterogeneity, namely, the significant misalignment between local data distributions on clients and the global data distribution. They often rely on indirect means to optimize the alignment between local and global models, which typically incurs high computational costs and depends heavily on the selection of auxiliary datasets, resulting in limited stability [13]. Motivated by these challenges, we propose a core idea: if clients can locally simulate an ideal global distribution, it may be possible to alleviate the divergence in local optimization directions, even without data sharing. In other words, through guided data augmentation, we can reduce the inconsistency between local and global distributions, fundamentally mitigating data heterogeneity issues in federated learning. + +How can we simulate a global distribution locally? Taking CIFAR-10 as an example, Figure 1 illustrates the label distribution in a random client, revealing severe imbalances. Certain categories, such as "truck," are underrepresented, making it difficult to form an effective global representation. Given privacy constraints, simulating a global distribution locally becomes a significant challenge [13]. As shown in the blue distribution in Figure 1, augmenting samples along the blue arrow direction, rather than the pink arrow, is more likely to simulate the global distribution. Thus, identifying appropriate augmentation directions and ranges becomes our key objective to overcome this challenge. + +In the single-domain scenario, some clients may possess a large number of "truck" images, while others have only a few. The aggregate set of "truck" images across all clients constitutes the global distribution for that category. We introduce the concept of geometric shapes to describe the orientation and range of data distributions (see Section 2). For instance, the global distribution of "truck" in Figure 1 spans primarily from the bottom left to the top right. If we could quantify the global geometric shape of the "truck" and disseminate it to clients, they could use it to guide new sample + +generation locally. However, privacy constraints prohibit us from aggregating all client samples to quantify this global geometric shape. To address this, we propose using local covariance matrices from multiple clients on the server side to approximate the global covariance matrix, enabling quantification of the global geometric shape (see Section 3.1). To mitigate inaccuracies in local covariance matrix estimation due to high dimensionality and sparsity in image space [36], we employ the CLIP [47] to extract embedding distributions from local client data and carry out the approximation process in the embedding space. + +After obtaining the global geometric shape for each category, we propose a method called Global Geometry-Guided Embedding Uncertainty Representation (GGEUR) to generate new samples on clients, simulating an ideal global distribution in the embedding space. Each client then only needs to train an MLP as a local classifier on the augmented data. In multi-domain scenarios, we observe that the geometric shapes of the embedding distributions for the same category across different domains exhibit similarity (see Figure 6 and Section 3.2). This makes it feasible to approximate the global geometric shape using local geometric shapes across all clients, even in multi-domain settings. In multi-domain scenarios, however, the global distribution for each category comprises distributions from all domains, necessitating that clients also simulate embeddings from other domains. Although the embedding distributions of the same category across different domains are geometrically similar, they occupy different spatial positions. Thus, unlike the single-domain scenario, we propose distributing category prototypes from other domains as shared knowledge to clients and applying GGEUR to these prototypes to generate new samples that simulate distributions from other domains (see Section 3.2). Figure 2 illustrates the difference between single-domain and multi-domain scenarios. + +Our approach, serving as a preprocessing step in FL, is easily integrated with other methods. Extensive evaluation across scenarios with label skew, domain skew, and combined skew demonstrates that our method significantly improves the performance of existing approaches, achieving state-of-the-art results in highly heterogeneous data scenarios (Section 4). This work represents a typical instance of synergy between foundational visual models and geometric knowledge within FL. + +# 2. Geometry of Embedding Distributions + +We now define the geometry of an embedding distribution and introduce a measure of similarity between these geometries. In a $P$ -dimensional space, given a dataset of a certain class $X = [x_{1}, \ldots, x_{n}] \in \mathbb{R}^{P \times n}$ , the covariance matrix of the distribution can be estimated as: + +$$ +\Sigma_ {X} = \mathbb {E} \left[ \frac {1}{n} \sum_ {i = 1} ^ {n} x _ {i} x _ {i} ^ {T} \right] = \frac {1}{n} X X ^ {T} \in \mathbb {R} ^ {P \times P}. \quad (1) +$$ + +Performing eigenvalue decomposition on $\Sigma_{X}$ yields $P$ eigenvalues $\lambda_1\geq \dots \geq \lambda_P$ and their corresponding $P$ dimensional eigenvectors $\xi_1,\ldots ,\xi_P$ . All eigenvectors are mutually orthogonal, collectively anchoring the skeleton of the data distribution, with each eigenvalue specifying the range of the distribution along the direction of its corresponding eigenvector. The combination of eigenvalues and eigenvectors defines the geometric shape of the distribution. Thus, we define the geometric shape of the data $X$ as: + +$$ +G D _ {X} = \left\{\xi_ {1}, \dots , \xi_ {P}, \lambda_ {1}, \dots , \lambda_ {P} \right\}. \tag {2} +$$ + +Given the geometries $\mathrm{GD}_{X_1}$ and $\mathrm{GD}_{X_2}$ of two distributions, their similarity is defined as: + +$$ +S \left(G D _ {X _ {1}}, G D _ {X _ {2}}\right) = \sum_ {i = 1} ^ {P} \left| \left\langle \xi_ {X _ {1}} ^ {i}, \xi_ {X _ {2}} ^ {i} \right\rangle \right|. \tag {3} +$$ + +where $S(\mathrm{GD}_{X_1}, \mathrm{GD}_{X_2})$ ranges from 0 to $P$ . A higher value indicates greater similarity in geometry. In this study, we calculate the geometric similarity using the eigenvectors corresponding to the top five eigenvalues. + +# 3. Simulating the Global Distribution Locally + +In this section, we address a critical issue: how to approximate the geometric shape of the global data distribution using local client data while preserving privacy. We then detail how to simulate the ideal global distribution locally in both single-domain and multi-domain scenarios by leveraging the geometric shape of the global distribution. + +# 3.1. Computation of Global Geometric Shapes Under Privacy Constraints + +Consider a classification task with $K$ clients and $C$ classes. Suppose each client contains $n_1^i, n_2^i, \ldots, n_K^i$ samples belonging to class $i$ , represented by the sample set $\{x_k^1, x_k^2, \ldots, x_k^{n_k^i}\}$ for client $k$ . The global distribution for class $i$ is formed by the combined distributions of these local samples across the $K$ clients. However, we cannot directly access the global distribution to derive its geometric shape. Recalling Section 2, the covariance matrix of a distribution is fundamental for obtaining its geometric shape. Thus, our goal is to approximate the global data distribution's covariance matrix without sharing data. + +We propose to approximate the global covariance matrix by leveraging the covariance matrices of all local data. Taking class $i$ as an example, we first compute the local covariance matrix $\Sigma_k^i$ and local mean $\mu_k^i (k = 1,\dots ,K)$ for class $i$ on each client as follows: + +$$ +\mu_ {k} ^ {i} = \frac {1}{n _ {k} ^ {i}} \sum_ {j = 1} ^ {n _ {k} ^ {i}} x _ {k} ^ {i, j}, \Sigma_ {k} ^ {i} = \frac {1}{n _ {k} ^ {i}} \sum_ {j = 1} ^ {n _ {k} ^ {i}} (x _ {k} ^ {i, j} - \mu_ {k} ^ {i}) (x _ {k} ^ {i, j} - \mu_ {k} ^ {i}) ^ {T}. +$$ + +The global covariance matrix is the covariance of the com + +binned data from all clients, defined as: + +$$ +\mu_ {i} = \frac {1}{N _ {i}} \sum_ {k = 1} ^ {K} \sum_ {j = 1} ^ {n _ {k} ^ {i}} x _ {k} ^ {i, j} = \frac {1}{N _ {i}} \sum_ {k = 1} ^ {K} n _ {k} ^ {i} \mu_ {k} ^ {i}, +$$ + +$$ +\Sigma_ {i} = \frac {1}{N _ {i}} \sum_ {k = 1} ^ {K} \sum_ {j = 1} ^ {n _ {k} ^ {i}} \left(x _ {k} ^ {i, j} - \mu_ {i}\right) \left(x _ {k} ^ {i, j} - \mu_ {i}\right) ^ {T}, +$$ + +where $N_{i} = \sum_{k=1}^{K} n_{k}^{i}$ represents the total number of samples in class $i$ across all clients. We can decompose $(x_{k}^{i,j} - \mu_{i})$ as $(x_{k}^{i,j} - \mu_{k}^{i}) + (\mu_{k}^{i} - \mu_{i})$ , so the global covariance matrix $\Sigma_{i}$ can be rewritten as: + +$$ +\Sigma_ {i} = \frac {1}{N _ {i}} \sum_ {k = 1} ^ {K} \sum_ {j = 1} ^ {n _ {k} ^ {i}} [ (x _ {k} ^ {i, j} - \mu_ {k} ^ {i} + \mu_ {k} ^ {i} - \mu_ {i}) (x _ {k} ^ {i, j} - \mu_ {k} ^ {i} + \mu_ {k} ^ {i} - \mu_ {i}) ^ {T} ]. +$$ + +Expanding the above equation yields: + +$$ +\begin{array}{l} \Sigma_ {i} = \frac {1}{N _ {i}} \sum_ {k = 1} ^ {K} \sum_ {j = 1} ^ {n _ {k} ^ {i}} \left[ \left(x _ {k} ^ {i, j} - \mu_ {k} ^ {i}\right) \left(x _ {k} ^ {i, j} - \mu_ {k} ^ {i}\right) ^ {T} + \left(x _ {k} ^ {i, j} - \mu_ {k} ^ {i}\right) \left(\mu_ {k} ^ {i} - \mu_ {i}\right) ^ {T} \right. \\ + \left(\mu_ {k} ^ {i} - \mu_ {i}\right) \left(x _ {k} ^ {i, j} - \mu_ {k} ^ {i}\right) ^ {T} + \left(\mu_ {k} ^ {i} - \mu_ {i}\right) \left(\mu_ {k} ^ {i} - \mu_ {i}\right) ^ {T} ]. \\ \end{array} +$$ + +By the properties of covariance matrices, the first term is the local covariance matrix $\Sigma_k^i$ , and the expected values of the second and third terms are zero. The fourth term can be computed as: + +$$ +\sum_ {j = 1} ^ {n _ {k} ^ {i}} \left(\mu_ {k} ^ {i} - \mu_ {i}\right) \left(\mu_ {k} ^ {i} - \mu_ {i}\right) ^ {T} = n _ {k} ^ {i} \left(\mu_ {k} ^ {i} - \mu_ {i}\right) \left(\mu_ {k} ^ {i} - \mu_ {i}\right) ^ {T}. +$$ + +Thus, the global covariance matrix can be obtained by combining the local covariance matrices and local means as: + +$$ +\Sigma_ {i} = \frac {1}{N _ {i}} \left(\sum_ {k = 1} ^ {K} n _ {k} ^ {i} \Sigma_ {k} ^ {i} + \sum_ {k = 1} ^ {K} n _ {k} ^ {i} \left(\mu_ {k} ^ {i} - \mu_ {i}\right) \left(\mu_ {k} ^ {i} - \mu_ {i}\right) ^ {T}\right). \tag {4} +$$ + +where each client's contribution to $\Sigma_{i}$ is determined by the coefficient $\frac{N_k^i}{N_i}$ . By performing eigenvalue decomposition on $\Sigma_{i}$ , we can derive the geometric shape of the global data distribution for class $i$ without sharing any data. For more details on privacy constraints, please refer to Appendix D. + +# 3.2. Global Geometry-Guided Embedding Uncertainty Representation (GGEUR) + +Given $K$ clients and a classification task with $C$ classes, we describe below how geometric knowledge can be used to simulate the ideal global data distribution locally in both single-domain and multi-domain scenarios. + +# 3.2.1 Single-Domain Federated Learning + +When the data originates from a single domain, we primarily address the issue of label skew. Before federated learning begins, each client uses CLIP to extract $p$ -dimensional embeddings of its local data. Each client then locally computes the per-class local covariance matrices and local sample means, which are subsequently uploaded to the server. + +![](images/afa5d04a3e47ac4030723ede9d9e4ed3339f8856443873fd1e3f22776f90d704.jpg) +Figure 3. In a single-domain scenario, each class's global geometric shape is used to guide sample augmentation on each client. The example shows how new samples are generated for Client 2. + +For each class, the server generates a global covariance matrix, $\Sigma_1, \Sigma_2, \ldots, \Sigma_C$ , using Equation (4). Next, each class's global geometric shape is quantified based on Equation (2), and these global geometric shapes (i.e., eigenvalues and eigenvectors) are sent to each client. + +We propose a Global Geometry-Guided Embedding Uncertainty Representation (GGEUR) for locally augmenting samples (i.e., embeddings) to simulate the global distribution. Specifically, for class $i$ , its global geometric shape can be represented as $\mathrm{GD}_i = \{\xi_i^1,\dots ,\xi_i^p,\lambda_i^1,\dots ,\lambda_i^p\}$ . Suppose client $k$ has only a limited number of class $i$ embeddings, denoted as $X_{k}^{i} = [X_{k}^{(i,1)},\ldots ,X_{k}^{(i,n_{k}^{i})}] \in \mathbb{R}^{p\times n_{k}^{i}}$ where $n_k^i$ represents the sample count. As shown in Figure 3, we first perform $n_k^i\times N$ random linear combinations of the eigenvectors $\xi_i^1,\dots ,\xi_i^p$ to produce $n_k^i\times N$ different vectors $\beta = \sum_{m = 1}^{p}\epsilon_{m}\lambda_{i}^{m}\xi_{i}^{m}\in \mathbb{R}^{p}$ , where $\epsilon_{j}$ follows a standard Gaussian distribution $N(0,1)$ and is scaled by the eigenvalues $\lambda_i^j$ to control the magnitude. These vectors provide the direction and range for simulating the global distribution. Next, for each existing sample $X_{k}^{(i,1)},\dots ,X_{k}^{(i,n_{k}^{i})}$ , we apply $N$ of these vectors to generate $n_k^i\times N$ new samples as follows: + +$$ +X _ {(k, h)} ^ {(i, j)} = X _ {k} ^ {(i, j)} + \beta_ {j} ^ {h}, j = 1, \dots , n _ {k} ^ {i}, h = 1, \dots , N. \tag {5} +$$ + +The total number of new samples can be set based on task requirements; in this study, for each local class, we ensure the total number of new and existing samples reaches 2000. Figure 3 and Algorithm 1 illustrate this process in detail. After embedding space augmentation, each client trains an MLP as the local model. + +Algorithm 1 GGEUR (Single-Domain Scenario) +Require: $X_{k}^{i} = [X_{k}^{(i,1)},\dots,X_{k}^{(i,n_{k}^{i})}] \in \mathbb{R}^{p\times n_{k}^{i}}$ : Sample set of class $i$ at client $k$ $GD_{i} = \{\xi_{i}^{1},\ldots ,\xi_{i}^{p},\lambda_{i}^{1},\ldots ,\lambda_{i}^{p}\}$ Global geometric shape (eigenvectors and eigenvalues) of class $i$ $N$ : Number of new samples to generate per original sample +Ensure: $X_{\mathrm{new}}^i$ Augmented sample set of class $i$ at client $k$ +1: function GGEUR(X, $GD_{i}$ $N$ 2: $X_{\mathrm{gen}}\gets \emptyset$ Initialize generated samples +3: for $h = 1$ to $N$ do +4: $\beta^h\gets \sum_{m = 1}^p\epsilon_m\lambda_i^m\xi_i^m,\epsilon_m\sim \mathcal{N}(0,1)$ +5: Generate new vector +6: $X_{\mathrm{gen}}\gets X_{\mathrm{gen}}\cup \{X + \beta^h\}$ +7: Generate and add new sample, Equation (5) +8: end for +9: return $X_{\mathrm{gen}}$ +10: end function +11: $X_{\mathrm{new}}^{i}\gets \emptyset$ Initialize augmented sample set +12: for $j = 1$ to $n_k^i$ do +13: $X_{\mathrm{new}}^{i}\gets X_{\mathrm{new}}^{i}\cup \mathrm{GGEUR}(X_{k}^{(i,j)},GD_{i},N)$ +14: end for +15: return $X_{\mathrm{new}}^{i}$ + +# 3.2.2 Multi-Domain Federated Learning + +When data originates from multiple domains, we encounter a complex scenario where both label skew and domain skew exist, as illustrated in Figure 4. In this case, different clients possess data from different domains. For clarity, we introduce two new concepts: the single-domain global distribution and the multi-domain global distribution. + +![](images/8165f8b7a37afab840a688cc1f7cf5f382a3823a99390ede414981862dd30fc7.jpg) +Figure 4. Federated scenario with both label skew and domain skew. Different textures represent data from distinct domains. + +# Definition 1 (Single-Domain Global Distribution) + +Within a particular data domain, when a category's sample count is sufficient and diverse enough to fully represent the category, this distribution of samples is termed the + +single-domain global distribution for that category. For example, in Figure 4, client 2's green samples are numerous and adequately cover the global distribution of the green category within domain 2. + +Definition 2 (Multi-Domain Global Distribution) For a given category, the combined single-domain global distributions from all data domains constitute the multi-domain global distribution of that category. As shown in Figure 4, the green distributions across all domains together form the multi-domain global distribution for the green category. + +Clearly, addressing both label skew and domain skew requires two steps: (1) Local sample augmentation to simulate the single-domain global distribution within each client's data domain. For example, in Figure 4, client 1 lacks sufficient green samples to represent the single-domain global distribution and thus requires sample augmentation. (2) Generation of new samples on each client to simulate the single-domain global distributions of other data domains. + +![](images/3abd2d5f3f6ff502a70b5617581a72af17d87ed47b30c28559d94ee8c5e4df73.jpg) +Figure 5. Example with 3 clients: Step 1 generates samples for each client from its own domain, while Step 2 simulates samples from other domains for each client. + +As depicted in Figure 5, Step 1 addresses the label skew on each client, while Step 2 addresses domain skew. In summary, our objective is to simulate the ideal multi-domain global distribution for each category locally on each client. Unlike single-domain federated learning, completing Step 1 in this context poses the challenge of obtaining the geometric shape of the single-domain global distribution. For instance, in Figure 5, client 1 has only a small number of green samples, making it difficult to access the single-domain global distribution for the green category. Fortunately, we found that when embeddings are extracted using CLIP, the geometric shapes of multiple single-domain global distributions corresponding to the same category across different domains are similar. This finding implies + +that we can identify a cross-domain shared geometric shape for each category, representing its global geometric shape. + +Specifically, we investigate this using the Digits dataset, which includes four digit-recognition datasets (i.e., MNIST [21], USPS [14], SVHN [43], and SYN [49]), each representing a different domain. First, we use CLIP (ViT-B/16) [47] to extract image embeddings for all categories across the four datasets. Then, we compute the similarity between the geometric shapes of the embedding distributions for each category in MNIST and the corresponding categories in USPS, SVHN, and SYN, as shown in Figure 6. The significantly higher values in the diagonal of each heatmap indicate that, across domains, the geometric shapes of embeddings for the same category exhibit a consistent pattern, rather than being randomly distributed. This allows us to simplify the multi-domain label skew problem in Step 1 to a label skew problem in the single-domain scenario. + +In detail, we first extract embeddings using CLIP and then locally calculate the covariance matrix and mean of local samples, which are uploaded to the server. Given CLIP's cross-domain consistency in representing the same class, we continue to use Equation (4) on the server to produce a shared global covariance matrix $\Sigma_1, \Sigma_2, \dots, \Sigma_C$ for each class. We further obtain the shared global geometric shapes, which are then sent to clients. Each client then applies GGEUR to augment samples, thereby simulating the single-domain global distribution locally. Following this, clients also need to generate new samples to simulate the single-domain global distribution from other data domains. Although the geometric shapes of embedding distributions across different domains are similar, the positions of these distributions differ. We propose transferring the class prototypes (local sample means) from other domains to the local client, and applying GGEUR to these prototypes to generate new samples, thus simulating the multi-domain global distribution. Algorithm 2 details this process. For each client, in Step 1, we ensure that the total number of new and existing samples for each class is 500. Step 2 generates 500 new samples based on each prototype separately. + +# 3.3. Comparison with Analogous Methods + +Federated data augmentation aim to bridge the gap between local data distributions and the ideal global distribution by generating more diverse data samples on clients [9, 37, 51]. For example, FedMix [63] and FEDGEN [68] use MixUp and its variants to augment client data, thus mitigating label skew. However, due to the lack of knowledge-based guidance, these methods largely rely on the diversity of local data. FedFA [67] assumes local data follows a Gaussian distribution and generates new samples centered on class prototypes. Nevertheless, the Gaussian assumption is overly idealistic [38], limiting the ability of generated samples to adequately reduce the discrepancy between local and global + +![](images/96d5eba639f6e2131543e21c7b25e6b7a9ef917cb833c77be50c4bd540d9935e.jpg) +Figure 6. Study of geometric shape similarity on the Digits dataset. + +distributions. Compared to the Gaussian assumption, the geometric shapes proposed in this work provide a more accurate description of embedding distributions. GGEUR estimates the geometric shape of the global distribution without compromising privacy and leverages it to guide data augmentation on clients. The introduction of additional geometric knowledge enables our method to effectively reduce the gap between local and global distributions. + +# 4. Experiments + +In this section, we conduct a comprehensive evaluation of our method under scenarios with label skew, domain skew, and the coexistence of both. + +# 4.1. Experiment Setup + +Label Skew Datasets. We evaluate our method on three single-domain image classification tasks. + +- Cifar-10 [20] contains 10 classes, with 50,000 images for training and 10,000 images for validation. +- Cifar-100 [20] covers 100 classes, with 50,000 training images and 10,000 validation images. +- Tiny/ImageNet [6] is the subset of ImageNet with $100K$ images of size $64 \times 64$ with 200 classes scale. + +Domain Skew Datasets. We evaluated our method on the multi-domain image classification dataset Digits and conducted analyses on Office-Caltech and PACS. + +- Digits [14, 21, 43, 49] includes four domains: MNIST, USPS, SVHN and SYN, each with 10 categories. +- Office-Caltech [8] includes four domains: Caltech, Amazon, Webcam, and DSLR, each with 10 categories. +- PACS [24] includes four domains: Photo (P) with 1,670 images, Art Painting (AP) with 2,048 images, Cartoon (Ct) with 2,344 images and Sketch (Sk) with 3,929 images. Each domain holds seven categories. + +Dataset with Coexisting Label Skew and Domain Skew. Office-Home [56] includes 4 domains: Art (A), Clipart (C), Product (P), and Real World (R), each containing 65 classes. To increase the challenge, we designed a new partitioning method for the multi-domain dataset Office-Home to create a scenario where label skew and domain skew coexist. For details, please refer to Appendix B. We name the newly constructed dataset Office-Home-LDS (Label and Domain Skew). Figure 7 shows the data distribution of + +Office-Home-LDS with $\beta = 0.1$ and $\beta = 0.5$ . + +![](images/d09cc38f7225bd0eab7072f18b93eb1a463d8fbc5f8f595f0065e4c8411d94c1.jpg) +Figure 7. Number of samples per class across four clients when $\beta$ equals 0.1 and 0.5, with each client holding data from a different domain. Additional cases are provided in Appendix B. + +Implementation Details and Comparison Methods. On the label skew dataset, we applied GGEUR to FedAvg [39] using CLIP (ViT-B/16) [47] as the backbone network and compared it with state-of-the-art federated data augmentation methods in heterogeneous federated learning, including FedMix [63], FEDGEN [68], and FedFA [67]. Additionally, we compared it with other advanced methods that use CLIP (ViT-B/16) as the backbone, such as FedTPG [45] and FedCLIP [35]. On the domain skew and Office-Home-LDS datasets, we focused on exploring the enhancement effect of GGEUR across various federated architectures. Therefore, we applied GGEUR to FedAvg, SCAFFOLD [16], MOON [25], FedDyn [1], FedOPT [48], FedProto [55], and FedNTD [22], all of which use CLIP for image feature extraction and a single-layer MLP as the local model. All experimental settings for FL methods are consistent with the latest benchmark [13]; details are provided in Appendix C. Evaluation Metrics. Following [27], we utilize the Top-1 (\%) accuracy and the standard deviation of accuracy across multi-domains as evaluation metrics. A smaller standard deviation indicates better Performance Fairness across different domains. We use the average results from the last five rounds accuracy and variance as the final performance. + +# 4.2. Evaluation Results on Label Skew Dataset + +Main Results. Tables 1, 2, and 3 show the performance improvement of GGEUR over FedAvg (CLIP+MLP) [39] under different $\beta$ values, along with comparison results with other methods. Under all label distribution skew settings, GGEUR significantly outperforms other methods, demonstrating superior classification accuracy and adaptability to imbalanced label distributions. Particularly at lower $\beta$ + +Table 1. Comparison results on CIFAR-100 and Tiny-ImageNet datasets with different degrees of label skew ( $\beta$ values). The best results are shown in underlined bold. FedAvg (CLIP+MLP) indicates that the backbone network uses CLIP and MLP, and the federated learning method employs FedAvg. + +
MethodsCIFAR-100Tiny-ImageNet
0.50.30.10.50.30.1
Zero-Shot CLIP64.8763.67
FedTPG71.4070.9568.6367.6366.7264.71
FedCLIP72.0371.2070.6470.4170.3769.50
FedMix (CLIP+MLP)81.3179.6273.8570.8968.5763.43
FEDGEN (CLIP+MLP)81.2478.9773.1572.3770.3564.16
FedFA (CLIP+MLP)81.9879.3174.6870.4170.6864.62
FedAvg (CLIP+MLP)81.4177.6868.2270.0867.6560.10
+ GGEUR83.3181.6577.7073.8972.1966.86
+ +Table 2. Evaluation results of GGEUR on CIFAR-10 and CIFAR-100 with more severe label skew (i.e., smaller $\beta$ values). + +
MethodsCIFAR-10
0.010.030.050.070.09
FedAvg (CLIP+MLP) + GGEUR90.8790.1391.9692.0591.82
94.3994.2595.0795.2195.38
MethodsCIFAR-100
0.010.030.050.070.09
FedAvg (CLIP+MLP) + GGEUR58.7160.7762.3261.6966.51
75.7275.4075.9676.7278.00
+ +Table 3. Evaluation results of GGEUR on Tiny-ImageNet with more severe label skew (i.e., smaller $\beta$ values). + +
MethodsTiny-ImageNet
0.010.030.050.070.09
FedAvg (CLIP+MLP) + GGEUR53.0354.5758.9158.7759.13
64.2765.7966.4966.3466.85
+ +values (i.e., with more severe label skew), GGEUR notably enhances the performance of FedAvg (CLIP+MLP) on CIFAR-100, validating its effectiveness in handling extreme label skew scenarios. For example, when $\beta$ is 0.01, 0.03, and 0.05, GGEUR achieves performance gains of $17.01\%$ , $14.63\%$ , and $13.64\%$ , respectively. These results indicate that GGEUR not only exhibits good generalization ability in standard settings but also maintains robust performance in cases of significant label skew. Moreover, our large-scale client experiments further confirm the scalability and consistent effectiveness of GGEUR under increased client participation, details are provided in Appendix E. + +Comparison with Peer Methods. We implemented FedMix, FEDGEN, and FedFA for comparison in Table 1, and in all cases, our method outperformed these three approaches. This demonstrates the superiority of geometric shapes as knowledge over the Gaussian assumption and traditional data augmentation methods. + +# 4.3. Evaluation Results on Domain Skew Dataset + +Ablation Study. As shown in Algorithm 2, simulating the multi-domain global distribution requires two steps. + +Table 4. Evaluation results on the Digits dataset. GGEUR by default includes both Step 1 and Step 2. + +
MethodsDigits
MNISTUSPSVHN SYNAVG ↑STD ↓
FedMix (CLIP+MLP)95.0390.2557.5072.6078.8514.89
FEDGEN (CLIP+MLP)95.8592.5258.7773.6280.1914.99
FedFA (CLIP+MLP)96.6892.9757.8775.5380.7615.44
FedAvg [39]90.4060.3034.6846.9958.0920.74
FedAvg (CLIP+MLP)95.1289.7456.3665.1776.6016.25
+ GGEUR (Step 1)96.0293.0258.5573.1380.1815.28
+ GGEUR (Step 1 & 2)97.0594.1263.5474.7382.3613.84
SCAFFOLD [16]97.7994.4526.6490.6977.3929.41
SCAFFOLD (CLIP+MLP)94.6290.0854.3368.7176.9316.31
+ GGEUR95.9192.0863.2571.5480.7013.69
MOON [25]92.7868.1133.3639.2858.3623.82
MOON (CLIP+MLP)75.6473.0938.8352.7460.0715.14
+ GGEUR (Step 1)84.6481.9643.0460.3567.5016.97
+ GGEUR (Step 1 & 2)95.1691.1355.2371.0078.1316.08
FedDyn [1]88.9160.3434.5750.7258.6519.76
FedDyn (CLIP+MLP)95.4692.1358.8970.3079.1915.19
+ GGEUR97.0794.0263.3474.8382.3113.88
FedOPT [48]92.7187.6231.3287.9274.8925.38
FedOPT (CLIP+MLP)94.5788.7958.6566.4777.1214.96
+ GGEUR96.4393.4762.3570.7580.7514.54
FedProto [55]90.5489.5434.6158.0068.1823.38
FedProto (CLIP+MLP)94.8692.6354.2965.5276.8317.40
+ GGEUR97.1994.1263.7073.8382.2113.96
FedNTD [22]52.3158.0718.0397.2956.4328.12
FedNTD (CLIP+MLP)95.8291.4358.2669.9578.8615.41
+ GGEUR97.0894.3263.5773.5382.1314.06
+ +We selected the classic FedAvg (CLIP+MLP) and MOON (CLIP+MLP) for an ablation study on the Digits dataset. The experimental results, highlighted in yellow in Table 4, show that each step incrementally improves the original methods, and their combination achieves the best results. + +Main Results. Tables 4, 5, and 6 present the experimental results on datasets with domain skews. It can be observed that simply using CLIP [47] for image representation, combined with a single-layer MLP for federated learning, already surpasses existing methods. This improvement is attributed to the advancements in the foundation model, and GGEUR can further significantly enhance the performance of the global model. For instance, on the Digits dataset, GGEUR improves the average performance of FedAvg (CLIP+MLP) [39], MOON (CLIP+MLP) [25], and FedProto (CLIP+MLP) [55] by $5.76\%$ , $18.06\%$ , and $5.38\%$ , respectively. Additionally, compared to other methods, GGEUR significantly reduces the accuracy variance across different domains. This demonstrates that GGEUR effectively adapts to features from different domains when handling cross-domain data distribution disparities, providing more robust and fair performance. We also conducted experiments to measure the computational cost of GGEUR, which demonstrated that the additional overhead introduced by our method is minimal. Further details can be found in Appendix F. + +Table 5. Evaluation results on Office-Caltech. + +
MethodsOffice-Caltech
AmCaDWAVG↑STD↓
FedAvg [39]81.9973.2179.3767.9375.626.31
FedAvg (CLIP+MLP)98.2696.7410010098.751.57
SCAFFOLD [16]39.7742.5078.0270.6957.7519.44
SCAFFOLD (CLIP+MLP)96.1892.8895.8393.2694.541.70
MOON [25]84.4275.9884.6768.9778.517.53
MOON (CLIP+MLP)98.6197.3310098.8898.701.09
FedDyn [1]84.0272.5977.3468.9775.726.50
FedDyn (CLIP+MLP)98.6196.7410010098.841.54
FedOPT [48]79.0571.9689.3474.4878.717.67
FedOPT (CLIP+MLP)98.2697.3310010098.901.33
FedProto [55]87.7975.9890.0079.3183.276.70
FedProto (CLIP+MLP)98.2696.7410010098.751.57
FedNTD [22]10.9510.8914.6710.3411.711.99
FedNTD (CLIP+MLP)97.9296.1410010098.511.86
+ +Table 6. Evaluation results on PACS. + +
MethodsPACS
PAPCtSkAVG ↑STD ↓
FedAvg [39]76.0964.1983.5089.4078.309.41
FedAvg (CLIP+MLP)99.4098.3799.0193.6497.602.32
SCAFFOLD [16]61.9545.4458.8754.6455.256.22
SCAFFOLD (CLIP+MLP)92.4281.6380.6887.2885.504.72
MOON [25]74.4464.1983.9289.1777.939.53
MOON (CLIP+MLP)99.6099.0299.4393.8997.992.37
FedDyn [1]78.1763.2982.2789.9378.669.70
FedDyn (CLIP+MLP)99.4098.3799.0193.5597.582.36
FedOPT [48]78.6667.6682.4183.6878.126.31
FedOPT (CLIP+MLP)99.4098.3799.0193.6497.602.32
FedProto [55]85.6373.6983.5791.1483.516.31
FedProto (CLIP+MLP)99.4098.2199.0194.2397.712.06
FedNTD [22]16.7718.2328.4793.1839.1631.51
FedNTD (CLIP+MLP)99.4098.5499.2992.2897.382.96
+ +On the Office-Caltech and PACS datasets, since the use of $\mathrm{CLIP + MLP}$ as the backbone network already achieves very high performance across all methods, these datasets are less challenging. However, our evaluation results can serve as a reference for other research. + +Comparison with Peer Methods. We implemented FedMix (CLIP+MLP), FEDGEN (CLIP+MLP), and FedFA (CLIP+MLP) for comparison in Table 4. When GGEUR is applied to FedAvg (CLIP+MLP), it outperforms these three methods by $3.51\%$ , $2.17\%$ , and $1.60\%$ , respectively. + +# 4.4. Evaluation Results on Office-Home-LDS + +To fully demonstrate the potential of GGEUR, we constructed a more challenging dataset, Office-Home-LDS, which incorporates both label skew and domain skew. Office-Home-LDS simulates a more realistic and complex scenario of distributional imbalance, encompassing cross-domain data distribution differences and label imbalance. In Table 7, we show the remarkable performance gains of GGEUR over existing methods on this dataset, along with significant reductions in accuracy variance across different domains, highlighting its effectiveness in handling highly heterogeneous data scenarios. Specif + +Table 7. Evaluation results on Office-Home-LDS $\left( {\beta = {0.1}}\right)$ . + +
MethodsOffice-Home-LDS
ACPRAVG ↑STD ↓
FedAvg (CLIP+MLP) [39] + GGEUR65.2958.1780.5676.5370.148.89
78.3379.0190.1788.4683.995.36
SCAFFOLD (CLIP+MLP) [16] + GGEUR68.7266.7983.6380.1274.827.20
78.6078.3289.8689.0783.965.51
MOON (CLIP+MLP) [25] + GGEUR69.2768.6386.5682.8776.837.99
72.0270.3186.1183.8778.086.98
FedDyn (CLIP+MLP) [1] + GGEUR58.3055.1977.6372.8665.999.47
78.8878.5590.4788.4684.095.42
FedOPT (CLIP+MLP) [48] + GGEUR58.4454.8976.8072.2565.599.16
79.0178.3290.8488.6184.205.59
FedProto (CLIP+MLP) [55] + GGEUR65.8456.4980.4174.8569.409.09
78.0577.7189.7987.8483.355.51
FedNTD (CLIP+MLP) [22] + GGEUR69.6866.6484.5380.9675.467.48
78.1974.6690.2486.7782.466.29
+ +ically, GGEUR improved the average performance of FedAvg (CLIP+MLP) [39], SCAFFOLD (CLIP+MLP) [16], FedDyn (CLIP+MLP) [1], FedOPT (CLIP+MLP) [48], FedProto (CLIP+MLP) [55], and FedNTD (CLIP+MLP) [22] by $13.85\%$ , $9.14\%$ , $18.1\%$ , $18.61\%$ , $13.95\%$ , and $7.0\%$ , respectively. These results demonstrate that GGEUR can achieve robust performance on complex multi-domain, multi-class datasets, making it an effective approach for addressing both label and domain skew. + +![](images/69a8df51a9d63591d06eada618d632a7ea3da87fa24767919bc7ead5923f74c3.jpg) +Figure 8. Comparison of convergence in average accuracy with and without integrating GGEUR in the selected FL methods. + +# 4.5. GGEUR Accelerates Convergence + +In Figure 8, we plot the average accuracy per epoch for various FL methods with and without using GGEUR. It can be observed that our method enhances the convergence speed of the FL methods, resulting in smoother curves. + +# 5. Conclusion + +This work captures the global geometric shape of the embedding distribution while preserving privacy and utilizes it to simulate an ideal global distribution on clients, bridging the gap between local and global distributions. We first introduce the concept of distributional geometric shapes and address the challenge of obtaining the global geometric shape under privacy constraints. Then, we propose leveraging the global geometric shape to assist clients in augmenting their samples. Extensive experiments demonstrate the effectiveness and compatibility of GGEUR. + +Acknowledgement. This research is supported by the National Natural Science Foundation of China (Grants 623B2080). + +# References + +[1] Durmus Alp Emre Acar, Yue Zhao, Ramon Matas Navarro, Matthew Mattina, Paul N Whatmough, and Venkatesh Saligram. 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We leverage the geometry field proposed in recent work for stochastic opaque surfaces, which can then be converted to volume densities. We adapt Gaussian kernels or surfels to splot the geometry field rather than the volume, enabling precise reconstruction of opaque solids. Our first contribution is to derive an efficient and almost exact differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels, while removing current approximations involving Taylor series and no self-attenuation. Next, we address the discontinuous loss landscape when surfels cluster near geometry, showing how to guarantee that the rendered color is a continuous function of the colors of the kernels, irrespective of ordering. Finally, we use latent representations with spherical harmonics encoded reflection vectors rather than spherical harmonics encoded colors to better address specular surfaces. We demonstrate significant improvement in the quality of reconstructed 3D surfaces on widely-used datasets. + +# 1. Introduction + +The reconstruction of opaque surfaces from a collection of calibrated RGB images is a classic challenge in computer vision. This problem has received broader attention in recent years due to the success of Neural Radiance Field (NeRF) [30] and other volumetric novel view synthesis algorithms. Although methods like NeRF [30] are effective for view synthesis, they fall short in geometric reconstruction applications, since they do not explicitly reconstruct an accurate surface. Follow up methods, which are specialized towards surface reconstruction, have proposed instead that an explicit geometry representation should parameterize the volume density field. + +The typical approach taken by previous methods [25, 27, 29, 31, 45, 48, 54, 55] is to parameterize signed or unsigned distance fields with a neural network, which can then be converted to a density field for volume rendering [31, 45]. Eikonal regularization [16] is often used to promote smooth- + +![](images/c8e3f36712fb0d3cacc5140972253b93e4277a40de0eb12dd5928529739d2353.jpg) +Input Images + +![](images/4ba02f914c0f81e1c81fee8cdef2d8e0c26e28a426ad9a60f8688bd38e745527.jpg) +(a) 2DGS + +![](images/ba892715d47491521821210bcdd5d4f4948774d2a239a0a88e2174da1caff476.jpg) +(b) Ours +Figure 1. We introduce a geometry reconstruction method from a set of calibrated RGB images by splating a geometry field with Gaussian surfels. We enable almost exact and efficient differentiable rendering. Compared to 2DGS, we reach better geometry quality and achieve overall smooth and detailed geometry without having cracks or holes. The reader may wish to zoom into the electronic version in the figures. (Note: object colors used are for visualization, not original object color). + +ness of the reconstructed surfaces. In particular, Miller et al. [31] provides a theoretical bridge between surface representations and volume rendering with stochastic geometry, and generalizes the use of distance fields to introduce a general stochastic geometry field, which we refer to as simply a geometry field. Chen et al. [5] shows that such geometry fields can be parameterized with a Poisson field. + +Recent advances in Gaussian splatting based methods [23] have motivated a new class of surface modeling methods (e.g., [7, 18, 20, 49, 59, 60]). These methods utilize kernels, i.e., 3D Gaussians or 2D Gaussians, to parameterize a density or opacity field and then perform volume splatting [23, 64] for rendering. Geometry is then recovered from the converged density or opacity field through varying definitions of the surface. The benefit compared to the neural methods comes from the speed and ability to generalize to complex scenes (e.g., [4, 11, 61]). Despite the success achieved by these approaches, the surface is not theoretically clearly defined for a general density field, which incurs approximation that limits the reconstruction quality. + +In this paper, we adapt a modern volumetric representation based on Gaussian kernels to splat the geometry field that provides precise geometry for reconstructing opaque solids. We show that we can utilize the kernels, i.e., 2D Gaussians or Gaussian surfels, to parameterize the geometry + +field and still use the efficient volume splatting algorithm for differentiable rendering. We carefully remove the approximations in the original volume splatting algorithm to ensure almost exact rendering, except for the use of global sorting to approximate per-ray sorting. We also observe that, to make the represented stochastic geometry gradually converge to the deterministic case, kernels need to be clustered around the surface. Such clustering leads to an unstable ordering of kernels in volume splatting and the rendered color a discontinuous function of the properties of kernels. The view synthesis loss then creates a discontinuous loss landscape that is detrimental for optimization. We propose a solution to ensure that the rendered color is a continuous function of the properties of the kernels. Finally, inspired by [14, 22, 40, 41, 44, 50], we also explore different choices of color representation other than spherical harmonics [35] to tackle specular surfaces. Through extensive experiments, we show that such a design with geometry clearly defined can significantly improve the quality of the reconstructed surface (see Figs. 1 and 8). + +Our main contributions are summarized as follows: + +- We derive an efficient and differentiable rendering algorithm for geometry fields parameterized by Gaussian surfels (Sec. 4.1). Besides, we carefully analyze and reduce the approximations in the rendering algorithm. +- We expose and remedy the discontinuity of the loss landscape, which ultimately helps our method to converge from stochastic geometry to a deterministic shape (Sec. 4.2). + +# 2. Related Work + +Multi-view Stereo Surface Reconstruction. The computer vision community has studied 3D reconstruction from multi-view images for decades using multi-view stereo [1, 13, 15, 19, 38, 39, 42]. Despite their high accuracy, these methods do not provide complete geometry. Therefore, CNN-based approaches (e.g., [2, 9, 10, 17, 24, 43, 46, 47, 51, 52, 58, 63]) were introduced to overcome this limitation, but they cannot reconstruct reflective surfaces. Neural surface reconstruction approaches are later introduced to address more general surface types. + +Neural Surface Reconstruction. Thanks to the advance of NeRF [30], some works (e.g., [14, 25, 28, 31, 44, 45, 48, 54, 55]) propose to utilize various representations, such as an MLP [30] or Hash-grid [33], to parameterize a SDF field and then convert it into a density field for rendering. The mesh is then extracted using marching cubes from the SDF field after convergence. Identifying the limitation of the SDF field for open-surface objects, some other works (e.g., [27, 29]) propose to leverage an UDF field instead of a SDF field. Inspired by multi-view stereo (MVS), another group of methods (e.g., [8, 12, 37]) add a multi-view consistency loss to further enhance the quality of reconstructed geometry. + +Gaussian Splatting based Surface Reconstruction. Kerbl et al. [23] propose to utilize 3D Gaussians to param- + +![](images/e32f2ac064262903163e759d84625a63e94a9b096a6092ae89ba2cffad1d519c.jpg) +Figure 2. Illustration of a ray intersecting with non-overlapping kernels $\mathcal{K}_1, \mathcal{K}_2, \ldots, \mathcal{K}_N$ , which are sorted based on their intersection intervals $[a_1, b_1], [a_2, b_2], \ldots, [a_N, b_N]$ . + +eterize the density field for differentiable view synthesis. Owing to its efficiency and high quality, it has become popular to extend Gaussian splatting (GS) for geometry reconstruction. SuGaR [18] constrains the 3D Gaussians to be flattened for extracting the geometry but still exhibits holes. 2DGS [20] and Dai et al. [7] then propose to directly use the 2D Gaussians to parameterize the density field and utilize depth-normal consistency loss or a monocular normal prior to ensure the smoothness of extracted geometry. In contrast, RaDe-GS [60] and GOF [59] still rely on 3D Gaussians, but propose custom surface definitions for the 3D Gaussian. Surfaces are extracted through TSDF fusion [6, 62] or tetrahedral grids [59]. Different from these methods, we parameterize the geometry field with 2D Gaussians and then convert it into the density field for rendering with refined volume splatting. We still use TSDF fusion to extract the geometry and achieve significant improvements in terms of geometry quality. Concurrently, PGSR [3] introduces a multi-view constraint into the optimization. + +# 3. Preliminaries + +We first introduce and analyze the volume splattering algorithm and volume representation of opaque solids. + +Volume Splatting. Consider a ray $\mathbf{x}(t) = \mathbf{o} + t\boldsymbol{\omega}$ , where $\mathbf{o}$ denotes the camera origin, $\boldsymbol{\omega}$ denotes the ray direction and $t > 0$ denotes the depth. Volume splatting [64] aims to evaluate the following volume rendering equation: + +$$ +\mathbf {C} = \int_ {0} ^ {\infty} \mathbf {c} (t) \sigma (t) \exp \left(- \int_ {0} ^ {t} \sigma \left(t ^ {\prime}\right) d t ^ {\prime}\right) d t, \tag {1} +$$ + +where $\mathbf{c}(t),\sigma (t)$ denote the color and density values, or the extinction coefficient of the volume, at $\mathbf{x}(t)$ . + +As shown in Fig. 2, Zwicker et al. [64] propose to decompose the density field as a set of independent kernels, each of which is chosen to have finite support range by cutoff, i.e., $\sigma(t) = \sum_{i=1}^{N} w_i \mathcal{K}_i(t)$ , where $N$ denotes the number of kernels, and $w_i$ and $\mathcal{K}_i(t)$ respectively denote the weight and evaluated value at $t$ for the $i^{\text{th}}$ kernel. The intersections between these kernels and the ray are assumed to be non-overlapping and, therefore, these kernels are sorted along the ray based on the intersection interval. The intersection interval of the $i^{\text{th}}$ kernel is denoted as $[a_i, b_i]$ , i.e., $\mathcal{K}_i(t) \neq 0$ if and only if $a_i \leq t \leq b_i$ . The color values inside the $i^{\text{th}}$ kernel are defined to be constant as $\mathbf{c}_i$ . + +By ignoring the self-occlusion and expanding the transmittance term with the Taylor Series, Eqn. (1) can be rewritten + +ten as: + +$$ +\mathbf {C} = \sum_ {i = 1} ^ {N} \mathbf {c} _ {i} \rho_ {i} \prod_ {j = 1} ^ {i - 1} (1 - \rho_ {j}), \tag {2} +$$ + +where $\rho_{i}$ is the integration of density value along the ray, when considering only the $i^{\mathrm{th}}$ kernel. Namely, $\rho_{i} = \int_{a_{i}}^{b_{i}}\sigma (t)dt = \int_{a_{i}}^{b_{i}}w_{i}\mathcal{K}_{i}(t)dt$ , and it is called the footprint of the $i^{\mathrm{th}}$ kernel with respect to the current ray. Notice that due to the expansion, $\rho_{i}\in [0,1]$ . + +Therefore, it is important that the footprint function be easy to evaluate efficiently, such that the evaluation of Eqn. (2) can be efficient. Volume splatting chooses to use the 3D Gaussian as the kernel, and analytically solve the footprint function by approximating the perspective transform. + +In summary, volume splatting makes the following assumption and approximation: + +- Assume there is no overlapping of any two intersections between kernels and the ray. +- Self-occlusion of each kernel is ignored, and transmittance terms and footprint functions are approximated. + +Even though remarkable view synthesis from a set of calibrated images is achieved by making the volume splattering differentiable [23], the non-overlapping assumption leads to a discontinuous view synthesis loss function and the constraint that the footprint function is within the range of $[0,1]$ . We will show that these problems are detrimental for the surface reconstruction and propose solutions. Besides, Kerbl et al. [23] uses a global sorting to approximate per-ray sorting. + +Stochastic Geometry Representation for Optical Solid. Miller et al. [31] propose that for an opaque solid existing in the $\mathbb{R}^3$ space, each point $\mathbf{x}\in \mathbb{R}^3$ is associated with a random variable $G(\mathbf{x})\in \mathbb{R}$ . Without loss of generality, the random variable is chosen to obey the normal distribution, i.e., $G(\mathbf{x})\sim \mathcal{N}(\mu (\mathbf{x}),1 / s(\mathbf{x}))$ , where $\mu (\mathbf{x})$ and $s(\mathbf{x})$ denote the mean and inverse of standard deviation. Each point $\mathbf{x}$ is then associated with an occupancy value $o(\mathbf{x})$ and vacancy value $v(\mathbf{x})$ , defined as: + +$$ +o (\mathbf {x}) = \Pr \{G (\mathbf {x}) \geq 0 \} = \Psi (\mu (\mathbf {x}) s (\mathbf {x})) \tag {3} +$$ + +$$ +v (\mathbf {x}) = \Pr \left\{G (\mathbf {x}) < 0 \right\} = \Psi (- \mu (\mathbf {x}) s (\mathbf {x})), +$$ + +where $\Psi (\cdot)$ denotes the cdf of the standard normal distribution. The solid is defined at $\mathbb{1}_{\{G(\mathbf{x})\geq 0\}}$ + +From [31], the density at $\mathbf{x}$ is defined as: + +$$ +\begin{array}{l} \sigma (\mathbf {x}) = \frac {| | \nabla v (\mathbf {x}) | |}{v (\mathbf {x})} \cdot \left(\alpha (\mathbf {x}) | \boldsymbol {\omega} \cdot \mathbf {n} (\mathbf {x}) | + \frac {1 - \alpha (\mathbf {x})}{2}\right) \\ = \frac {\psi (- \mu (\mathbf {x}) s (\mathbf {x}))}{\Psi (- \mu (\mathbf {x}) s (\mathbf {x}))} | | \nabla (\mu (\mathbf {x}) s (\mathbf {x})) | | \cdot \tag {4} \\ \left(\alpha (\mathbf {x}) | \boldsymbol {\omega} \cdot \mathbf {n} (\mathbf {x}) | + \frac {1 - \alpha (\mathbf {x})}{2}\right), \\ \end{array} +$$ + +where $\psi (\cdot)$ denotes the pdf of the standard normal distribution, $\mathbf{n}(\mathbf{x}) = -\nabla (\mu (\mathbf{x})s(\mathbf{x})) / ||\nabla (\mu (\mathbf{x})s(\mathbf{x}))||$ and + +$\alpha (\mathbf{x})\in [0,1]$ denotes an anisotropic parameter which is close to 1 near the surface, and close to 0 in the interior of the opaque solid. As $s(\mathbf{x})\to \infty$ , the stochastic geometry converges to the deterministic case. + +Notice that, in other works (e.g., [31, 45]), the $\mu(\mathbf{x})$ is defined to be a SDF field. Defining it as a SDF field allows the usage of Eikonal loss to promote the smoothness, but there is no constraint over the meaning of $\mu(\mathbf{x})$ . + +Since $\mu (\mathbf{x})$ and $s(\mathbf{x})$ are always together in Eqn. (4), we define that + +$$ +F (\mathbf {x}) := \mu (\mathbf {x}) s (\mathbf {x}), \tag {5} +$$ + +which is called the geometry field as it indicates the underlying geometry. When $\forall \mathbf{x} \in \mathbb{R}^3$ , $|F(\mathbf{x})| \to \infty$ , the represented geometry is assumed to be converged to the deterministic case. Eqn. (4) can be then written as: + +$$ +\sigma (\mathbf {x}) = \frac {\psi (- F (\mathbf {x}))}{\Psi (- F (\mathbf {x}))} | | \nabla F (\mathbf {x}) | | \cdot \left(\alpha (\mathbf {x}) | \boldsymbol {\omega} \cdot \mathbf {n} (\mathbf {x}) | + \frac {1 - \alpha (\mathbf {x})}{2}\right), +$$ + +where $\mathbf{n}(\mathbf{x}) = -\nabla F(\mathbf{x}) / ||\nabla F(\mathbf{x})||$ + +# 4. Method + +In Sec. 4.1, we describe how we can reduce the approximations taken by the splatting algorithm. We then derive a refined splatting method which enables differentiable rendering of the opaque solid represented by the geometry field. Next, in Sec. 4.2, we propose a novel solution to address the issue of discontinuous loss landscapes which arises as the stochastic geometry gradually becomes deterministic. Finally, Sec. 4.3 introduces an improvement in color representation to account for specular surfaces. + +# 4.1. Geometry Field Splitting + +Revisit Splatting Algorithm. As the volume splatting is an approximate rendering algorithm, we aim to reduce the approximations, and investigate the situation under which the refined volume splatting algorithm is exact. + +Specifically, we do not ignore the self-occlusion and do not expand the transmittance term with the Taylor series. Eqn. (2) is then replaced with: + +$$ +\mathbf {C} = \sum_ {i = 1} ^ {N} \mathbf {c} _ {i} \left(1 - \exp \left(- \rho_ {i}\right)\right) \prod_ {j = 1} ^ {i - 1} \exp \left(- \rho_ {j}\right). \tag {7} +$$ + +Please find the derivation in A.1 of the supplementary document. Notice that then $\rho_{i}\in \mathbb{R}_{+}$ with no further restrictions. + +We are now left with the non-overlapping assumption and footprint function approximation. We notice the following property: + +Property 1. When the intersection intervals of two and only two kernels $\mathcal{K}_i, \mathcal{K}_j$ fully overlap, i.e., $a_i = a_j \wedge b_i = b_j$ , and they have the same color, it is equivalent to having one kernel $\mathcal{K}_{ij}$ there with $\rho_{ij} = \rho_i + \rho_j$ and the same color. + +Proof. As these two kernels are the only two kernels whose intersection intervals fully overlap at $[a_i, b_i]$ , we can conclude that $j = i + 1$ without losing generality. Therefore, $(1 - \exp(-\rho_i)) + (1 - \exp(-\rho_j))\exp(-\rho_i) = 1 - \exp(-(\rho_i + \rho_j))$ . Notice that the alpha-blended value of these two kernels is equivalent to having a single kernel there. + +This property can be extended into the following form through mathematical induction: + +Lemma 1. When the intersection intervals of $m$ kernels $\mathcal{K}_{i_1}, \mathcal{K}_{i_2}, \ldots, \mathcal{K}_{i_m}$ fully overlap, i.e., $a_{i_1} = a_{i_2} = \ldots = a_{i_m} \wedge b_{i_1} = b_{i_2} = \ldots = b_{i_m}$ , and they have the same color, it is equivalent to having one kernel $\mathcal{K}$ there with $\rho = \rho_{i_1} + \rho_{i_2} + \ldots + \rho_{i_m}$ and the same color. + +Therefore, we can define an operator $\bigoplus$ , which satisfies the commutative, associative and identity properties, such that $\mathcal{K}_{ij} = w_i\mathcal{K}_i \oplus w_j\mathcal{K}_j$ where $\rho_{ij} = \rho_i + \rho_j$ . When the kernels on the ray have either non-overlapping or fully overlapped intersection intervals, the refined splating algorithm defined by Eqn. (7) is an exact rendering algorithm of density field defined as: $\sigma(\mathbf{x}) = \bigoplus_{i=1}^{N} w_i \mathcal{K}_i(\mathbf{x})$ , because we remove the approximations when evaluating Eqn. (1). + +By considering the remaining approximation, we can then reach the following theorem: + +Theorem 1. When 1) the intersection intervals of any two kernels are non-overlapping, or fully overlapped in which case these two kernels have the exact same color value, and, 2) the footprint function is accurately calculated, then the sorting of kernels is well-defined and Eqn. (7) gives an exact rendering of a density field which is defined as: $\sigma (\mathbf{x}) = \bigoplus_{i = 1}^{N}w_{i}\mathcal{K}_{i}(\mathbf{x})$ + +Parameterize and Render Geometry Field with Gaussian Surfels. Our overall idea is illustrated in Fig. 3. We propose to parameterize the geometry field in Eqn. (5) with kernels, then demonstrate how to convert it into the density field for volume splatting, and reveal under which conditions it is an exact rendering algorithm. We will also show that choosing Gaussian surfels as our kernels helps build a both efficient and almost exact rendering algorithm. + +Specifically, we decompose the $F(\mathbf{x})$ as: + +$$ +F (\mathbf {x}) = \bigoplus_ {i = 1} ^ {N} w _ {i} \mathcal {K} _ {i} (\mathbf {x}) - c, \tag {8} +$$ + +where $\bigoplus$ is the custom plus operator which we have just discussed and will elaborate on later, $\omega_{i} > 0$ , and $c$ is a manually chosen constant. Since we expect the kernels to cluster around the surface, the anistropic parameter $\alpha (\mathbf{x})$ is then set to 1 as discussed in [31]. + +We first discuss the property of such a formulation of $F(\mathbf{x})$ , when the represented geometry converges to the deterministic case. At the place where it is vacant, i.e., there are + +![](images/74596fd789f7d3711d526f4963a7b11e0829bbf438da36aaf93cf4186aaff9cb.jpg) +Figure 3. Overview of our algorithm. (a) We first use 2D Gaussians to parameterize the geometry field, $F$ . These kernels are expected to cluster around the surface. (b) We then convert the geometry field into the density field $\sigma$ and lastly, (c) we leverage our refined volume splatting algorithm for differentiable rendering. + +![](images/af121d3773be0cf466f3c9b4fcd4068399d8a59c26aae0bd4e5557378bbab806.jpg) + +![](images/60d9c349f2abd58c84bfa44a9b26a650aa03229008596ec5ce00ef255d979e14.jpg) + +no kernels, $F(\mathbf{x}) = -c$ , such that $v(\mathbf{x}) \approx 1$ . Therefore, $c$ is a manually chosen large positive value. At the place where kernels cluster, $F(\mathbf{x})$ is expected to be a large positive value, such that $o(\mathbf{x}) \approx 1$ . Therefore, when a ray travels in the space, the transmittance is expected to almost immediately fall from 1 to 0 at the place where it first intersects with kernels as shown in Fig. 3 (c). + +We still start from the assumption that there is no overlapping of any two intersections between kernels and the ray and then remove this assumption. From Eqn. (6), the corresponding density field is defined as: + +$$ +\sigma (\mathbf {x}) = \frac {\psi (- F (\mathbf {x}))}{\Psi (- F (\mathbf {x}))} | | \nabla F (\mathbf {x}) | | \cdot | \boldsymbol {\omega} \cdot \mathbf {n} (\mathbf {x}) |. \tag {9} +$$ + +As Eqn. (7) indicates, given a ray, our goal is to evaluate the footprint function for the $i^{\mathrm{th}}$ kernel: + +$$ +\rho_ {i} = \int_ {a _ {i}} ^ {b _ {i}} \sigma (\mathbf {x} (t)) d t. \tag {10} +$$ + +We now make our choice of kernels. Aiming at exact rendering, we choose to use 2D Gaussians or Gaussian surfels [7, 20, 34] as our kernels, instead of 3D Gaussians [23]. In general, the intersections between Gaussian surfels and a ray are points. Thus, any two of the intersections are either not overlapping at all or fully coincide, satisfying the conditions of Theorem 1. + +The $i^{\mathrm{th}}$ 2D Gaussian kernel $\mathcal{G}(\mathbf{x})$ is defined as: + +$$ +\mathcal {G} _ {i} (\mathbf {x}) = \exp \left(- \frac {1}{2} \left(\mathbf {x} - \mathbf {m} _ {i}\right) ^ {T} \Sigma_ {i} ^ {- 1} \left(\mathbf {x} - \mathbf {m} _ {i}\right)\right), \tag {11} +$$ + +where $\mathbf{m}_i$ denotes its center and $\Sigma_{i}$ denotes its covariance matrix. As shown in Fig. 4 (a), given a ray $\mathbf{x}(t) = \mathbf{o} + t\boldsymbol{\omega}$ , we are able to calculate the intersected depth $t_i$ and evaluate its kernel value at $\mathbf{x}(t_i)$ as $f_{i} = w_{i}\mathcal{G}_{i}(\mathbf{x}(t_{i}))$ [20]. We then have $F(\mathbf{x}(t))$ near $t_i$ : + +$$ +F (\mathbf {x} (t)) = \left\{\begin{array}{l l}f _ {i} - c&t = t _ {i}\\- c&| t - t _ {i} | < \epsilon , \text {w h e r e} \epsilon \rightarrow 0.\end{array}\right. \tag {12} +$$ + +![](images/ead6d1828e060f50f642acaca9870dfbe3f52b95e0d02f6440ebb65683b40ba6.jpg) +(a) + +![](images/7425973b72b24944af170ed0a35225ecfc195f5ba16c00d1b0a4c11c054779c6.jpg) +(c) + +![](images/f0f552c3cd68469b0a62707cbd85d13f744b13124320944496fff321ebde2dee.jpg) + +![](images/bd949dc33c25ac45f41ae8b7b303b3b29d82a97b8bf69294f6114146a9ed63f4.jpg) +(b) +Figure 4. (a) An illustration of intersecting the $i^{\mathrm{th}}$ Gaussian surfel, whose normal vector is denoted as $\mathbf{n}_i$ that is perpendicular to the plane containing the surfel, with a ray, whose direction is denoted as $\omega$ . The depth of the intersected point is denoted as $t_i$ , and the intersected point is denoted as $\mathbf{x}(t_i)$ . The value of the Gaussian surfel at $\mathbf{x}(t_i)$ is denoted as $f_i$ . (b) We analyze the intersection by creating a 2D coordinate plane which is parallel to the $\mathbf{n}_i$ and $\omega$ , and passes through $\mathbf{x}(t_i)$ . The angle between $\mathbf{n}_i$ and $\omega$ is denoted as $\theta_i$ . (c) On the 2D coordinate plane, within an infinitesimally small range, the intersected line, drawn as an orange line, between the Gaussian surfel and the plane can be seen as having constant geometry field value $F = f_i - c$ . (d) We expand the intersected line by linearly decaying it into $-c$ with length $h$ and direction $\mathbf{n}_i$ . It gives the surfel a 3D width, which does not follow the Gaussian distribution. As $h \to 0$ , it can be seen as equivalent to (c). + +Such a function is not even a continuous function. It seems that we cannot calculate Eqn. (9). However, since we are interested in the footprint function instead of the density field, we can reach a closed form solution by slightly modifying this function, which makes the splating algorithm a perfect fit. Specifically, we start analyzing the intersection by creating a plane as a 2D coordinate system in Fig. 4 (b). We look at an infinitesimally small range around $\mathbf{x}(t_i)$ as shown in Fig. 4 (c), such that the geometry field at the intersected line, drawn as an orange line, between the Gaussian surfel and the plane is constant, i.e., $f_{i} - c$ . We enable the calculation of Eqn. (9) and Eqn. (10) by extruding the intersected line with a linear decay. The geometry field value decays linearly from $f_{i} - c$ to $-c$ with the direction of $\mathbf{n}_i$ , which is perpendicular to the plane containing the surfel, and length of $h$ , as shown in Fig. 4 (d). It is equivalent to the original case as $h \to 0$ . The $F(\mathbf{x}(t))$ near $t_i$ is modified as: + +$$ +F (\mathbf {x} (t)) = f _ {i} \times \left(1 - \frac {\left| t - t _ {i} \right|}{h / \cos \theta_ {i}}\right) - c, \text {w h e n} | t - t _ {i} | < h / \cos \theta_ {i}, \tag {13} +$$ + +where $\cos \theta_{i} = |\boldsymbol {\omega}\cdot \mathbf{n}_{i}|$ . The $||\nabla F(\mathbf{x})||$ near $t_i$ is then calculated as: + +$$ +\left| \left| \nabla F (\mathbf {x} (t)) \right| \right| = f _ {i} / h, \text {w h e n} | t - t _ {i} | < h / \cos \theta_ {i} \tag {14} +$$ + +and it is parallel to $\mathbf{n}_i$ . Therefore, we can evaluate Eqn. (10) + +![](images/82b094313ecb0dd2947323501ee506e04c68d7eefe609fd8434524f3d9e41802.jpg) +Figure 5. Illustration of opacity value on different Gaussian surfels. (a) 2DGS only allows the opacity to reach 1 at the center. (b) Due to the enforced transformation from geometry field into density as in Eqn. (15), the opacity on a Gaussian surfel in our case does not follow a Gaussian distribution, thus differentiating it from Gaussian splattering. Furthermore, we also allow a larger central area to reach 1, thus making the Gaussian surfel more opaque which benefits the surface reconstruction. + +with Eqn. (9) as: + +$$ +\begin{array}{l} \rho_ {i} = \int_ {t _ {i} - h / \cos \theta_ {i}} ^ {t _ {i} + h / \cos \theta_ {i}} \frac {\psi (- F (\mathbf {x} (t)))}{\Psi (- F (\mathbf {x} (t)))} | | \nabla F (\mathbf {x} (t)) | | \cdot | \boldsymbol {\omega} \cdot \mathbf {n} (\mathbf {x} (t)) | d t \\ = - 2 \ln \Psi \left(c - f _ {i}\right). \tag {15} \\ \end{array} +$$ + +Please find the derivation in A.2 of the supplementary. We define $g(u) \coloneqq -2\ln \Psi (c - u)$ to simplify the notation. As the expansion goes to 0, i.e., without extrusion, $\lim_{h\to 0}\rho_{i} = g(f_{i})$ . Notice that the value range of $g(u)$ exceeds [0, 1], making approximated volume splating in Eqn. (2) not applicable and our refined volume splating in Eqn. (7) suitable. We can then use it for rendering in Eqn. (7) as: + +$$ +\mathbf {C} = \sum_ {i = 1} ^ {N} \mathbf {c} _ {i} (1 - \exp (- g (f _ {i}))) \prod_ {j = 1} ^ {i - 1} \exp (- g (f _ {j})). \tag {16} +$$ + +We now remove the non-overlapping assumption. We define $S(u) \coloneqq -2\ln \Psi (c - u)$ . Notice that $S(0) = 0$ , and $S(u)$ is a monotonically increasing function with respect to $u$ . Therefore, there exists a $S^{-1}(v), \forall v \geq 0$ . We then define $\bigoplus (\cdot)$ , such that $a \bigoplus b = S^{-1}(S(a) + S(b))$ . Besides, when $m$ Gaussian surfels $\mathcal{G}_{j+1}, \mathcal{G}_{j+2}, \dots, \mathcal{G}_{j+m}, j \in \mathbb{N}_+, m \in \mathbb{N}_+$ intersect the ray at the same place $\mathbf{x}(t_{j+1})$ , from Lemma 1, Eqn. (7) is equivalent to having a kernel whose footprint function equals to $\sum_{k=1}^{m} g(w_{j+k} \mathcal{G}_{j+k}(\mathbf{x}(t_{j+1})))$ . + +Given that + +$$ +g \left(\bigoplus_ {k = 1} ^ {m} w _ {j + k} \mathcal {G} _ {j + k} (\mathbf {x} (t _ {j + 1}))\right) = \sum_ {k = 1} ^ {m} g \left(w _ {j + k} \mathcal {G} _ {j + k} (\mathbf {x} (t _ {j + 1}))\right), +$$ + +it then corresponds to the geometry field value: + +$$ +\begin{array}{l} F (\mathbf {x} \left(t _ {j + 1}\right)) = \bigoplus_ {\substack {k = 1 \\ N}} ^ {m} w _ {j + k} \mathcal {G} _ {j + k} (\mathbf {x} \left(t _ {j + 1}\right)) - c \tag{17} \\ = \bigoplus_ {i = 1} ^ {N} w _ {i} \mathcal {G} _ {i} (\mathbf {x} (t _ {j + 1})) - c, \\ \end{array} +$$ + +as other kernels are 0 here. It follows our definition Eqn. (8). + +![](images/22eb33bace5e7a17ae9d23b13945b51f89c21e72803d5a4e2ba4ec43a22fbf5a.jpg) +(a) + +![](images/10e0ec9b6c4a512feb401a1b5e0ed79129307f47831beaf78beee7822de8d16f.jpg) +(b) +Figure 6. We illustrate the discontinuous change of rendered color in the splatting algorithm with respect to the positions of kernels. As shown in (a) and (b), when two kernels continuously change their positions and are eventually swapped, the ordering could be unstable and the rendered color $\mathbf{C}$ undergoes a discontinuous change when the ordering changes. The opacity is denoted on top of the kernel. + +Another benefit that comes with using Gaussian surfels is that we can have the expected depth $D$ efficiently calculated with volume splattering as: + +$$ +D = \sum_ {i = 1} ^ {N} t _ {i} (1 - \exp (- g (f _ {i}))) \prod_ {j = 1} ^ {i - 1} \exp (- g (f _ {j})). \tag {18} +$$ + +In contrast, with 3D Gaussians, the assumption for volume splatting that the property, i.e., depth in this case, which we want to render, is constant inside the kernel does not hold. + +Discussion. From Theorem 1, if Gaussian surfels have the same color when they have the same intersected point, the rendering is then exact, but we make the only approximation to use the global sorting to approximate the per-ray sorting as in [20, 23] for efficiency. We will discuss in Sec. 4.2 that this color constraint is also important for having a continuous loss landscape for optimization. + +In practice, as in Fig. 5, the distributions of opacity on the Gaussian surfels do not follow the Gaussian distribution anymore, thus differentiating our algorithm from Gaussian splatting. We also allow larger areas on the Gaussian surfels to become fully opaque. These benefit the surface reconstruction as shown in Sec. 5. + +# 4.2. Remedying Loss Landscape Defects + +With the rendering algorithm we introduced before, during training, we apply the view synthesis loss as $\mathcal{L}_{\mathrm{rgb}}$ , depth distortion loss as $\mathcal{L}_d$ and depth-normal consistency loss as $\mathcal{L}_n$ , following [20]. However, we use the expected depth defined in Eqn. (18) instead of the median depth in [20] to calculate $\mathcal{L}_n$ . The final loss is defined as: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {r g b}} + \lambda_ {1} \mathcal {L} _ {d} + \lambda_ {2} \mathcal {L} _ {n}, \tag {19} +$$ + +where $\lambda_{1}$ is set specific to the dataset, and $\lambda_{2} = 0.05$ . $\mathcal{L}_d$ helps encourage the Gaussian surfels to cluster together, such that the represented stochastic geometry becomes deterministic, $\mathcal{L}_d$ helps smooth the geometry, and $\mathcal{L}_{\mathrm{rgb}}$ is the main loss for driving the surface reconstruction. However, $\mathcal{L}_{\mathrm{rgb}}$ is not a continuous function of properties, including center and covariance, of the Gaussian surfel. As shown in Fig. 6, when two Gaussian surfels continuously change their intersected + +![](images/e22c4deb41e64bd2999e0fc3454c4a2c4dc91a29a771bbe55b42657826f19981.jpg) +Figure 7. Demonstration of continuously changing the colors of kernels when two kernels gradually swap their positions. + +points and swap their position, the rendered color undergoes a discontinuous change. In the case of surface reconstruction, Gaussian surfels are encouraged to cluster together, which makes the ordering unstable and optimization harder. + +We notice that, as shown in Fig. 7, if the color also continuously changes when the Gaussian surfel moves in such a way that whenever two Gaussian surfels intersect the ray at the exact same position, they have the same color, this discontinuity is solved. Therefore, given a ray which intersects with Gaussian surfels $\mathcal{G}_1,\mathcal{G}_2,\dots ,\mathcal{G}_N$ we propose to replace the color $c_{i}$ of $\mathcal{G}_i$ with $\widehat{c}_i$ as: + +$$ +\widehat {c} _ {i} = \frac {\sum_ {j = 1} ^ {N} \left(1 - \exp \left(- w _ {j}\right)\right) \exp \left(- \tau \left| t _ {j} - t _ {i} \right|\right) c _ {j}}{\sum_ {j = 1} ^ {N} \left(1 - \exp \left(- w _ {j}\right)\right) \exp \left(- \tau \left| t _ {j} - t _ {i} \right|\right)}, \tag {20} +$$ + +where $\tau = 100$ , and we blend the color based on the weight and distance. + +Theorem 2. With the color defined in Eqn. (20), Eqn. (16) gives a continuous function of properties of Gaussian surfels. + +Proof. $\widehat{c}_i$ is a continuous function of $t_1, t_2, \ldots, t_N$ . And when there exists an $i' \in \mathbb{N}$ , such that $t_i = t_{i'}$ , $\widehat{c}_i = \widehat{c}_{i'}$ . + +With the color defined in Eqn. (20), we also reach an almost exact rendering algorithm as discussed in Sec. 4.1. However, it is computationally inefficient to blend the color per ray. We instead propose an efficient approximation that blends the color in the $\mathbb{R}^3$ space. Specifically, we have: + +$$ +\widehat {c} _ {i} = \frac {\sum_ {j = 1} ^ {N} (1 - \exp (- w _ {j})) \exp (- \tau | | \mathbf {m} _ {i} - \mathbf {m} _ {j} | | _ {2}) c _ {j}}{\sum_ {j = 1} ^ {N} (1 - \exp (- w _ {j})) \exp (- \tau | | \mathbf {m} _ {i} - \mathbf {m} _ {j} | | _ {2})}, \tag {21} +$$ + +which can be efficiently implemented as propagating the color before rendering. + +# 4.3. Improve Color Representation + +The method described above significantly improves surface reconstruction quality using spherical harmonics as the color representation. However, we find it struggles to reconstruct the specular surfaces, as observed in [5, 22, 26, 40, 56]. + +We instead assign a latent $l_{i} \in \mathbb{R}^{32}$ to the $i^{\text{th}}$ Gaussian surfel and create a shallow MLP $\Phi$ , such that: + +$$ +\mathbf {c} _ {i} = \Phi (l _ {i}, \operatorname {S E} (\omega), \operatorname {S E} (\omega_ {o})), \tag {22} +$$ + +where $\mathrm{SE}(\cdot)$ denotes the spherical harmonics encoding [35], $\omega$ denotes the ray direction, and $\omega_{o}$ denotes the reflected ray direction with respect to the local normal vector, i.e., $\omega = (\mathbf{m}_i - \mathbf{o}) / ||\mathbf{m}_i - \mathbf{o}||_2$ , and $\omega_{o} = 2(\mathbf{n}_{i}\cdot \boldsymbol {\omega})\mathbf{n}_{i} - \boldsymbol{\omega}$ . We find it beneficial to input both $\omega$ and $\omega_{o}$ for dealing with both diffuse and specular surfaces, as in [41, 44]. + +![](images/7e95fa88c0748a335b31d59d552293aa087a596f95b0e4a6412cb7668efd8c2e.jpg) +Figure 8. Qualitative comparison on DTU and BlendedMVS datasets. Non-obvious differences are highlighted by insets and red circles. "F.D.S." denotes Chen et al. [5]. + +![](images/b407705f4bbc38bbed69c0fbc4f934bba91e4be10774e8853d30c9a23ae631ff.jpg) + +
Methods243740556365698397105106110114118122Avg. ↓Time
NeuS2 [48]0.590.790.740.400.930.740.851.371.370.820.740.860.440.600.580.794m
N.A. [25]0.390.790.380.300.820.721.911.201.940.670.381.150.340.840.950.85>12h
O.V. [31]1.531.211.060.740.721.140.750.981.470.860.690.800.560.620.730.92>6h
NeUDF [27]2.010.751.350.570.950.750.890.911.290.560.861.410.580.770.590.95>6h
F.D.S. [5]0.440.660.330.320.900.670.541.281.100.700.650.570.410.400.390.621h
SuGaR [18]1.471.331.130.612.251.711.151.631.621.070.792.450.980.880.791.3342m
2DGS [20]0.410.670.330.360.950.810.771.241.190.680.651.280.350.650.460.726m
G.S. [7]0.640.850.580.430.991.180.901.141.110.810.921.460.530.610.580.853m
GOF [59]0.460.680.390.381.150.820.701.141.210.650.681.040.480.680.490.7333m
RaDe-GS [60]0.460.660.350.410.790.730.671.141.180.610.640.870.370.690.480.6710m
Ours (SH)0.380.630.300.350.790.630.651.101.210.620.481.180.330.420.380.6310m
Ours (Latent)0.400.590.390.380.720.590.651.080.930.590.500.670.340.470.400.5811m
+ +Table 1. Quantitative evaluation on the DTU dataset based on the Chamfer Distance. Throughout the paper, the best metric is highlighted in red, the second best metric is highlighted in orange, and the third best metric is highlighted in yellow. + +
MethodsEvaUniTempleExcavaMuseumAvg. \( \downarrow \)
F.D.S. [5]N/A1.871.081.921.62
N.A. [25]1.492.200.882.071.66
2DGS [20]1.562.100.982.211.71
G.S. [7]2.182.26N/A2.882.44
GOF [59]1.551.990.812.231.65
RaDe-GS [60]1.672.010.882.191.69
Ours (SH)1.481.890.721.981.52
Ours (Latent)1.582.130.872.261.71
+ +# 5. Results + +We discuss implementation details and evaluation here. For detailed proof, further implementation details, evaluation results, and discussions, please refer to the supplementary. + +Implementation Details. We base our implementations and hyper-parameters on [20] and use [32] for implementing the MLP. We replace the original densification strategy [20, 23] with [57]. We use the TSDF fusion [62] to extract the mesh from rendered depth maps. The proposed color blending over all kernels is approximated through closest + +Table 2. Quantitative comparison on the BlendedMVS dataset for scene-level cases based on the Chamfer Distance $(\times 10^{-1})$ . "N/A" denotes that the method fails to converge. + +
MethodsBeaCloDogDurJadManScuStoAvg. ↓
F.D.S. [5]0.330.100.212.630.190.800.440.910.70
N.A. [25]0.320.120.313.110.150.800.430.770.75
2DGS [20]1.170.460.452.870.150.530.590.900.89
G.S. [7]0.570.350.276.620.160.530.761.451.34
GOF [59]0.590.260.342.720.120.530.481.030.76
RaDe-GS [60]0.510.250.242.830.120.520.430.840.72
Ours (SH)0.550.170.402.630.140.430.360.710.67
Ours (Latent)0.600.130.252.580.140.440.360.800.66
+ +Table 3. Quantitative comparison on the BlendedMVS dataset for object-centric cases based on the Chamfer Distance $(\times 10^{-2})$ + +k-points [36], where $k = 10$ . All the experiments are conducted on an NVIDIA 6000 Ada. + +# 5.1. Qualitative Evaluation + +As shown in Fig. 8, we compare with Chen et al. [5], Neuralangelo [25], RaDe-GS [60], and 2DGS [20] as representative methods on DTU [21], and BlendedMVS [53]. Our method better captures geometric details (e.g., nose of the skull, door of the house), while handling specular surfaces well (e.g., reflective cans and scissors), compared to Chen et al. [5] and RaDe-GS. Our method also ensures smooth geometry without holes (e.g., dog, sculpture and temple). + +![](images/fd8bd9a9003d4caf77d9dd917ab50fbc466144e6d3e33f77bcdb478ebb2ec4aa.jpg) +Reference + +![](images/20b94a3bb0a6a68e6e8a99345dac5d8dfa686b35e4903d2a283d9d832e436e5a.jpg) +Figure 9. We demonstrate the differences between SH and latent color representations on the "scan110" sample of the DTU dataset. When reconstructing specular surfaces (left), the SH representation (middle) leads to visible holes in the recovered mesh; these artifacts are resolved when using a latent representation (right). + +![](images/05dd5103ac7f4517b7ce52193b3f593a741e3c3698dc3a76aa4862de6c73b9c9.jpg) +SH Representation +Latent Representation + +Neuralangelo fails to properly represent open-boundary objects (e.g., card held by the bear). We further prepare a preliminary experiment on highly specular surfaces in C.2 of the supplementary. + +# 5.2.Quantitative Evaluation + +We evaluate on the datasets with ground-truth geometries and their corresponding camera parameters. We compare with methods, including NeuS2 [48], Neuralangelo [25], Miller et al. [31], NeUDF [27] as representative neural methods, SuGaR [18], 2DGS [20], Dai et al. [7], GOF [59], RaDe-GS [60] as representative splatting methods, and Chen et al. [5] on the DTU [21] dataset in Tab. 1. Besides, we compare with Chen et al. [5], Neuralangelo, 2DGS, Dai et al. [7], GOF and RaDe-GS on the BlendedMVS [53] dataset for scene-level cases in Tab. 2 and object-centric cases in Tab. 3. We unify the evaluation protocol and do not apply masking loss during training, nor iterative closest point during evaluation. + +It is noteworthy that our method has the best averaged metrics. We achieve the best or second best results across almost all diffuse scenes while using the SH representation. For specular cases (i.e., "scan97", "scan110" of DTU, and "Dog", "Clock" of BlendedMVS), our method with improved color representation significantly improves the reconstruction quality and achieves one of the top three metrics. We are also significantly faster than other competing methods, including, Neuralangelo and Chen et al. [5]. The additional computational cost compared to 2DGS comes from our color blending which relies on the closest-k-points. + +# 5.3. Ablation Study + +We evaluate our proposed components on the DTU dataset [21] with both SH representation and latent representation for colors, and report the Chamfer Distance (denoted as CD) in Tab. 4. Specifically, we replace the proposed geometry field-based splatting algorithm with the original 2DGS splatting algorithm, which leads to a severe drop of geometry quality. Besides, we also remove the proposed color propagation used for remedying loss landscape defects, which also leads to a drop in geometry quality. Furthermore, we study the effects of the only approximation we make, i.e., using global sorting to approximate the per-ray sorting. We + +
MethodsOurs (SH)Ours (Latent)
Full Model0.630.58
- Geometry Field Splitting0.700.72
- Remedy Loss Landscape Defects0.670.59
+ Per-Ray Sorting0.610.57
+ +Table 4. Ablation study for the proposed components on the DTU dataset based on the Chamfer Distance. + +implement a per-ray priority queue to sort the surfels based on the depths they intersect with the ray. Even though the per-ray sorting further improves the geometry quality, it consumes much more time $(3 - 4\times)$ and memory. We then do not use per-ray sorting by default and in other experiments. + +Moreover, we also demonstrate the benefits of using the latent representation for colors on the specular surfaces in Fig. 9. With SH representation, there are holes on the specular surface, while latent representation is free of this problem. + +# 6. Conclusion + +In this paper, we propose to first define a stochastic geometry field in the space with Gaussian surfels, then convert it into the density field, and render it with an efficient and differentiable refined splatting algorithm for accurate geometry reconstruction. We also identify the discontinuity of view synthesis loss and propose an efficient remedy to address it such that the represented stochastic geometry can converge to the deterministic geometry well through the optimization. Our method is not without limitations. For example, our method cannot handle transparent or semi-transparent objects due to the opaque assumption, or fuzzy objects well due to the smoothness constraint. + +In conclusion, we show that it is possible to use Gaussian surfels to accurately define the geometry and then perform efficient and differentiable almost exact rendering for geometry reconstruction. We achieve significant improvement over the geometry quality compared to other baselines, including both neural and splatting-based methods. + +Acknowledgements This work is supported by the Intelligence Advanced Research Projects Activity (IARPA) via Department of Interior/ Interior Business Center (DOI/IBC) contract number 140D0423C0076. The U.S. Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding any copyright annotation thereon. Disclaimer: The views and conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of IARPA, DOI/IBC, or the U.S. Government. We also acknowledge ONR grant N00014-23-1-2526, and NSF grants 2100237 and 2120019 for the Nautilus cluster, gifts from Adobe, Google, Qualcomm and Rembrand, the Ronald L. Graham Chair and the UC San Diego Center for Visual Computing. We thank Yash Belhe for discussions, proofreading and feedback. We also thank the NVIDIA for GPU gifts. + +# References + +[1] Michael Bleyer, Christoph Rhemann, and Carsten Rother. Patchmatch stereo - stereo matching with slanted support windows. In British Machine Vision Conference, 2011. 2 +[2] Changjiang Cai, Pan Ji, Qingan Yan, and Yi Xu. 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In Proceedings Visualization, 2001. VIS '01., pages 29-538, 2001. 1, 2 \ No newline at end of file diff --git a/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/images.zip b/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/images.zip new file mode 100644 index 0000000000000000000000000000000000000000..ad0ceaf09e69d18e850e631c1420f94605685ce9 --- /dev/null +++ b/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/images.zip @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:11b74f6df1632c9d3915f890200a10e958032eac8c02fbf6cd3a25ddbfe781f1 +size 649801 diff --git a/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/layout.json b/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/layout.json new file mode 100644 index 0000000000000000000000000000000000000000..075eb6da2241d3a8b929f1380a4104ab48bfe8ac --- /dev/null +++ b/CVPR/2025/Geometry Field Splatting with Gaussian Surfels/layout.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:758e56b7c0fef4ac26a69a79b86723bf54655f094ddb7cfff941988e8984f518 +size 561852 diff --git a/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_content_list.json b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..0d18f949a32fdfc0dac798710eafed6d7fcae859 --- /dev/null +++ b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_content_list.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:0a8d64177c04f4034c9821ace21742df6d03b54faf39565c8e9ac26090160561 +size 87755 diff --git a/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_model.json b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_model.json new file mode 100644 index 0000000000000000000000000000000000000000..5701aa06030c29c7b3b7a73d9fc5fbbcca475f69 --- /dev/null +++ b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_model.json @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:d5b4a9cb153327a0b1558f073e2cd69923e0ce93b95e62da95edffcc96a262f7 +size 119517 diff --git a/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_origin.pdf b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_origin.pdf new file mode 100644 index 0000000000000000000000000000000000000000..8e13736eda6b894c7de0f63580682def61dc3a0b --- /dev/null +++ b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/e5ea4625-10ae-4517-8bd1-667690326f38_origin.pdf @@ -0,0 +1,3 @@ +version https://git-lfs.github.com/spec/v1 +oid sha256:cda985662a355a4cf619e48112443d63273c2b9b1daff0ff18b2b5fb889a1032 +size 3313328 diff --git a/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/full.md b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/full.md new file mode 100644 index 0000000000000000000000000000000000000000..f6a2a0fd514ae943904cf0f78cea89111469e712 --- /dev/null +++ b/CVPR/2025/Geometry in Style_ 3D Stylization via Surface Normal Deformation/full.md @@ -0,0 +1,388 @@ +# Geometry in Style: 3D Stylization via Surface Normal Deformation + +Nam Anh Dinh +University of Chicago + +Itai Lang +University of Chicago + +Hyunwoo Kim +University of Chicago + +Oded Stein +University of Southern California + +Rana Hanocka +University of Chicago + +a 3d render of... + +![](images/04111214c91eec3a19e5fdfd78be956e1ee146496335644a40c361204562b0f9.jpg) +a pineapple-themed vase +Figure 1. Our method deforms a source shape (gray) into a text-specified semantic style (blue). While the deformations are expressive, they preserve the identity of the original shape. + +![](images/76cf9470a639ee69f16567f95ad607b27fa3ecb9f236e0e4fa2975d6a54f6836.jpg) +an A-posed knight in armor + +![](images/130d333e45f960d57b429ad65ac6135ff0a1daafd9b3fe75eed04d6b4e99e8f9.jpg) +a cute animal-themed chair + +![](images/3fb73036a33fc24a70b27a3236c556d50161703753ea4741fa9411b9cbf83874.jpg) +a lego goat + +# Abstract + +We present Geometry in Style, a new method for identity-preserving mesh stylization. Existing techniques either adhere to the original shape through overly restrictive deformations such as bump maps or significantly modify the input shape using expressive deformations that may introduce artifacts or alter the identity of the source shape. In contrast, we represent a deformation of a triangle mesh as a target normal vector for each vertex neighborhood. The deformations we recover from target normals are expressive enough to enable detailed stylizations yet restrictive enough to preserve the shape's identity. We achieve such deformations using our novel differentiable As-Rigid-As-Possible (dARAP) layer, a neural-network-ready adaptation of the classical ARAP algorithm which we use to solve for pervertex rotations and deformed vertices. As a differentiable layer, dARAP is paired with a visual loss from a text-to-image model to drive deformations toward style prompts, altogether giving us Geometry in Style. Our project page is at https://threedle.github.io/geometry-in-style. + +# 1. Introduction + +Semantically deforming triangle meshes is a basic task in 3D surface modeling. A common paradigm for shape cre + +ation is to take a base 3D object and deform it to sculpt a desired shape. For example, a human artist creates an intricate surface by starting with a simple generic version of an object (from a shape library, or quickly sketched), and successively deforms parts of the object like a sculptor modeling clay. + +Recently, machine learning pipelines have adopted deformations as a strategy for neural shape manipulation [2, 38, 77]. However, existing learning-based methods do not always fully mimic the classical approach: they either make small, surface-level changes for simple stylization [30, 60], or they generate large deformations that destroy the identity of the base object [26, 41]. Our method, Geometry in Style, uses text prompts to generate large deformations that create unique shapes while preserving the identity of the base shape (see Fig. 1) – much like a human sculptor would. + +We posit that existing learning methods' failure to generate the kinds of large, identity-preserving deformations that a human artist would is due to not employing the right representation for the space of deformations. Existing methods either (a) adhere to the original shape through overly restrictive deformations, such as bump maps [30, 60]; or they (b) significantly modify the input shape using expressive deformations based on gradient fields that may introduce artifacts or destroy the identity of the original shape [26, 41]. + +In this work, a deformation of a triangle mesh is repre + +![](images/d931d2974338a6be1e223eb92af5750bdeb4b86e009a4eb5841bc982597060f7.jpg) +Figure 2. Style diversity. Our method is capable of deforming various input meshes towards a variety of text-specified styles. The style can be manifested as fine geometric details, like in the ornate art deco column, or as low-frequency deformations, such as the joints of the cybernetic glove. Our method retains the structural features of the input shape, such as a flat arm on the antique sofa. Moreover, the resultant stylizations are in accordance with prompt semantics and part-aware semantics: the folds in the tropical chair are on the seat and backrest as opposed to the legs, the head of the penguin becomes like the top of a fire hydrant, and the racer bunny's thigh turns into the shape of a wheel. + +sented by target normals for vertex neighborhoods. We recover a deformation from this representation using our differentiable As-Rigid-As-Possible method (dARAP), whose formulation optimizing for local rigidity yields detailed and salient deformations that are nonetheless restrictive enough to preserve the identity of the base shape. dARAP locally rotates each vertex neighborhood individually to fit its normal to a desired target normal, and follows this local rotation with a global step that finds a global deformation that best fits all individual rotated neighborhoods. Crucially, dARAP is differentiable, and can be used as a layer in a neural network. This is achieved by replacing classical ARAP's iteration of local and global steps until convergence (impractical to backpropagate through) with dARAP's easily differentiable use of a single local and global step. Where classical ARAP needs many iterations to converge in deformation tasks with fixed target vertex positions, dARAP's use with target normals inside the Geometry in Style method (where dARAP is run once per iteration of a larger gradient descent optimization problem) achieves high-quality deformations from only a single iteration. + +We use dARAP together with a visual loss from a text-to-image model (T2I) which drives our deformation to arrive at Geometry in Style. Our visual loss leverages a cascaded T2I model to achieve high-fidelity deformations [21], allowing the use of a user-specified text prompt to deform any base shape into a stylized object without any dedicated 3D supervision data. As such, our method allows the application of a wide variety of styles, indicated intuitively by + +text prompts, to a wide variety of shapes (Figs. 1 and 2). Our stylization can manifest as different types of geometric manipulation, such as local surface texture, as well as global low-frequency deformations. Additionally, we show that our method offers control over the deformation result, where the user can easily change the strength of the stylization effect even after optimization. We contrast our method with recent deformation techniques and find that it can better achieve the target style with a lower surface distortion. + +In this work, we present: + +- $dARAP$ , a differentiable neural network layer that deforms a triangle mesh to specified target normals; and +- Geometry in Style, an identity-preserving shape deformation method from user text input using target normals as a representation of the space of deformations; + +We achieve high-quality stylization of shapes through deformation that is faithful to the identity of the input shape with a simple and easy-to-implement framework. + +# 2. Related work + +# 2.1. Classical Deformation Representations + +Our deformation technique builds on the extensive literature on variational surface deformation and mapping methods [8]. Methods in this family commonly compute a local differential deformation quantity, such as a per-element rotation, normal, jacobian matrix, or differential coordinates, subject to modeling constraints such as handles or cages. The vertex positions are then recovered using a global linear + +![](images/061f17c0436ff8c706fbc794613f9278f4c0e778ecc575114327f81550b318a5.jpg) +Figure 3. Overview of our stylization pipeline. Geometry in Style optimizes vertex normals to deform the mesh surface, subject to a stylization text prompt. Using the normals undergoing optimization as a target for our differentiable As-Rigid-As-Possible method (dARAP), the dARAP local step computes a rotation matrix per vertex; we then obtain the deformed surface via our dARAP global solve. Then, we utilize a differentiable renderer and a diffusion model-based semantic loss to guide the normals being optimized towards a deformation matching the desired style prompt. + +solve, usually derived from the least-squares minimization of energy that encodes the desired local properties. + +Important classical deformation approaches include Laplacian surface editing [84], gradient field mesh editing [96], or skinning-based approaches [24, 37]. A seminal work in this field is "as-rigid-as-possible" (ARAP) shape modeling which regularizes the local deformations of a surface to be rigid [83]. This approach promotes local rigidity with smooth and detail-preserving solutions, with various downstream applications including editing, parameterization, registration, shape optimization, and simulation [9, 12, 36, 52, 54, 107]. We adopt ARAP as the basis for our geometric stylization pipeline's deformation method. This is similar to recent neural methods that have also taken advantage of ARAP in other shape representations [6, 10, 35], especially the work of Yan et al. [92] who incorporate a differentiable ARAP loop into an image-to-3D face reconstruction pipeline. Yan et al. [92]'s use of ARAP serves to smoothen an assembly of 3D patches and requires multiple ARAP steps; on the other hand, our dARAP method is meant for optimizations of a deformation quantity (in our case, per-vertex normals) to achieve a desired deformation in a single local step-global step pair. + +Often related to such differential deformation methods, the manipulation of surface normals is a cornerstone useful for a variety of applications: shape abstraction [3], texture mapping [33, 87, 101], mesh parameterization [102], generative shape refinement [45], and more. Operating on surface normals has also been particularly core to cubic stylization [25, 50, 102] as well as geometric filters [46, 49, 70, 100, 105]. Some approaches use an ARAP-like optimization to achieve desired target normals (similar to our goal) for manufacturing [29, 85]. + +Normal-Driven Shape stylization. Liu and Jacobson [51] propose a normal-based stylization approach by shape analogies. Given a source object and a sphere-based normal + +template, modeled as a normal-to-normal function $S^2 \rightarrow S^2$ , the source shape's normals are locally rotated to match target normals dictated by the template; the deformation is obtained via ARAP solve using these local rotations. Similar to this work, we also use target normal vectors as the driving tool for our deformation. However, we use a text prompt to describe the desired style rather than a geometric exemplar, enabling semantic styles (e.g. "antique") that are not easily represented by a spherical normal template. Not being tied to a normal template, our deformations are part-aware, i.e. different parts with the same source normal do not have to receive the same target normal, and can be stylized differently as can be seen in Figs. 1 and 2). + +# 2.2. Neural Shape Manipulation + +Following the success of generative methods that optimize 2D representations via text-to-image guidance from diffusion models [31, 40, 74, 80-82] or CLIP-based scores [72, 73], there has been a large body of work using score distillation-based approaches [69, 90] to achieve 3D generation using 2D diffusion priors. These methods use a variety of shape representations, mostly implicit: Signed Distance Fields (SDF) [19, 64, 66], other implicit neural fields [4, 11, 16, 27, 59, 79] or variations on Neural Radiance Fields (NeRF) and Gaussian splatting [5, 14, 17, 18, 44, 47, 48, 53, 55, 56, 62, 71, 73, 76, 78, 89, 91, 93, 99, 103, 104, 106]. Some methods leverage the rapidly growing size of 3D datasets to train text-to-3D models that directly generate 3D representations [39, 63, 98]. + +More relevant to our present work, recent methods have used the strong representation power of neural networks to drive not just generation but also the editing and manipulation of shapes [2, 30, 60]. Hertz et al. [30]'s network predicts local vertex displacements to match local geometric characteristics of an exemplar shape. The follow-up Text2Mesh [60] replaced reference shapes by style text + +prompts. Similarly, our shape editing is flexibly guided by text, but rather than raw vertex displacements, we find rotations of the surface normal and recover an identity-preserving deformation via the dARAP solver. + +Other neural deformation and manipulation methods based include data-driven cage deformations [94], geometric fields for skinning [22], vector displacement maps [58], or deformation fields using neural representations [23, 28, 57, 88]. There is also a large family of 3D editing methods built on implicit shape representations such as NeRF, Gaussian splatting, occupancy fields, and signed distance fields [7, 13, 15, 43, 61, 65, 67, 75, 97]. + +Neural Jacobian Fields. Neural Jacobian Fields (NJF) [2] pioneered in connecting classical differential deformation methods such as Yu et al. [96] to neural, differentiable pipelines with geometric or semantic losses. This approach has powered compelling results for applications including UV mapping, re-positioning, handle-based deformation [95], and unsupervised shape morphing and correspondence [86]. + +In the NJF approach, given a local transformation matrix $\mathsf{M}_k$ per face $k$ , the least-squares best fit deformed vertices $\Phi^*$ to these differential transforms can be found by solving a Poisson equation with the cotangent Laplacian: + +$$ +\Phi^ {*} = \underset {\Phi} {\operatorname {a r g m i n}} \sum_ {k \in \text {a l l f a c e s}} a _ {k} \| \Phi \nabla_ {k} ^ {\top} - \mathsf {M} _ {k} \| _ {2} ^ {2} = L ^ {- 1} \mathcal {A} \nabla^ {\top} \mathsf {M} \tag {1} +$$ + +where $\mathsf{M}$ is all $\mathsf{M}_k$ stacked, $a_{k}$ is the area of face $k$ , $\nabla$ is the gradient operator, and $\mathcal{A}$ is the face mass matrix. This solve is differentiable with respect to $\mathsf{M}$ . We note that the global step to optimize ARAP energy [83] is also a Poisson equation with the cotangent Laplacian (Eq. (6)). As such, in dARAP, we can use a similar differentiable solver while taking advantage of the regularization inherent in ARAP. + +Neural methods that use NJF's differential deformation for text-based deformation include TextDeformer [26] and MeshUp [41] which optimize Jacobians to deform a source shape into a different semantic target e.g. turning a dog into a frog via a text prompt. Their deformations are not sufficiently restricted by construction and require an extra L2 loss between identity and the estimated Jacobians to prevent losing the shape identity altogether. In contrast, our deformation framework is more contained by construction (Sec. 3.1), preserving the source details and updating the geometry to the desired style (see Fig. 9 and Sec. 4.2). + +# 3. Method + +Our method takes as input a source triangle mesh $\mathcal{M} = (\mathcal{V},\mathcal{F})$ and a text prompt $\mathbf{x}$ . Our goal is to obtain a deformed mesh $\mathcal{M}^* = (\mathcal{V}^*,\mathcal{F})$ that semantically matches the style indicated by $\mathbf{x}$ . + +We find this deformation by optimizing per-vertex unit normals of $\mathcal{M}$ . For a mesh with $|\mathcal{V}|$ vertices, gradient descent directly optimizes a $|\mathcal{V}| \times 3$ array of real numbers, i.e., + +![](images/501fbcf0fca2d7ce32c0ad3a9de8ec88308dcb8b8ec414715e17189a831a49ae.jpg) +Original & target normal + +![](images/eb8b3663f1e27970ebc06811bb67deb3e56caca48c601d40b3c9bba8ac459ac2.jpg) +Local orthogonal Procrustes problem +Figure 4. Local Orthogonal Procrustes. The single-iteration local step of our dARAP energy solves for the best fit rotation given the original and and target normal. + +a 3-element vector per vertex. These per-vertex vectors $\hat{\mathcal{U}}$ are treated as target normals used to solve for per-vertex rotations $\hat{\mathcal{R}}$ , and then, the deformed positions $\hat{\mathcal{V}}$ . Specifically, from a current estimate $\hat{\mathcal{U}} = \{\hat{\mathbf{u}}_k \mid k \in \{1 \dots |\mathcal{V}|\}\}$ of target normals, we first perform a local step that obtains per-vertex rotation matrices $\hat{\mathcal{R}}_k = \{\hat{\mathsf{R}}_k \in \mathrm{SO}(3) \mid k \in \{1 \dots |\mathcal{V}|\}\}$ from the normals $\hat{\mathcal{U}}$ (Sec. 3.1), followed by a global step that obtains the deformed vertex locations $\hat{\mathcal{V}}$ from the per-vertex rotations $\hat{\mathcal{R}}$ (Sec. 3.2). + +We refer to this pair of local step and global step as dARAP. dARAP is closely inspired by the multiple alternating local-global iterations of classical ARAP optimizations (which are repeated many times until convergence) [83], but here condensed into a single local step and single global step as a differentiable module, usable in a neural optimization or deep learning pipeline. While for classical deformation applications, ARAP is run until convergence to achieve satisfactory results, in the context of our pipeline (Fig. 3), dARAP running only one iteration is sufficient and offers the benefits of efficient differentiability. + +# 3.1. Local Rotations from Normals + +For a vertex $k$ with edge neighborhood $\mathcal{N}_k$ , with current estimated target vector $\hat{\mathbf{u}}_k$ (normalized to unit length) and original normal vector $\mathfrak{u}_k$ (the area-weighted unit normal of vertex $k$ of the undeformed mesh), we compute a best fit rotation that transforms the bundle of vectors $\mathcal{N}_k \cup \{\mathfrak{u}_k\}$ to the bundle $\mathcal{N}_k \cup \{\hat{\mathbf{u}}_k\}$ (see Fig. 4). The best fit rotation $\hat{\mathbb{R}}_k$ minimizes the ARAP energy assuming fixed vertices $\hat{\mathbf{v}}_k$ , i.e. + +$$ +\begin{array}{l} \hat {\mathsf {R}} _ {k} = \underset {\mathsf {R} _ {k}} {\operatorname {a r g m i n}} \sum_ {(i, j) \in \mathcal {N} _ {k}} w _ {i j} \| \mathsf {R} _ {k} \mathbf {e} _ {i j} - \mathbf {e} _ {i j} \| _ {2} ^ {2} \tag {2} \\ + \lambda a _ {k} \| \mathsf {R} _ {k} \mathbf {u} _ {k} - \hat {\mathbf {u}} _ {k} \| \\ \end{array} +$$ + +where $a_{k}$ is the Voronoi mass of vertex $k$ ; $\lambda$ is a hyperparameter that scales the strength of the rotation matching the source to the target normal; $\mathbf{e}_{ij} \in \mathcal{N}_k$ are all the edge vectors in the neighborhood of vertex $k$ , and $w_{ij}$ are the cotangent weights [68] of these edges. Like Liu and Jacobson [51], we choose the spokes-and-rims neighbor + +![](images/fe4a9b779a4f63011d9deb6e9c73849c70f1227e7e8bc67835f95fbe2284806b.jpg) +a 3d render of a(n)... +Figure 5. Our method is capable of deforming the same mesh towards different text-specified styles. + +hood, consisting of halfedges in the vertex 1-ring, their twin halfedges, and halfedges opposite the vertex [12]. + +This minimization is the orthogonal Procrustes problem for each neighborhood, and can be solved [51] by finding + +$$ +\mathrm {X} _ {k} = \left[ \begin{array}{l l} \mathrm {E} _ {k} & \mathrm {u} _ {k} \end{array} \right] \left[ \begin{array}{l l} \mathrm {W} _ {k} & \\ & \lambda a _ {k} \end{array} \right] \left[ \begin{array}{l} \mathrm {E} _ {k} ^ {\top} \\ \hat {\mathrm {u}} _ {k} ^ {\top} \end{array} \right] \tag {3} +$$ + +where $\mathsf{E}_k$ is a $3\times |\mathcal{N}_k|$ matrix whose columns are the undeformed edge vectors in $\mathcal{N}_k$ , and $\mathsf{W}_k$ is a $|\mathcal{N}_k|\times |\mathcal{N}_k|$ diagonal matrix with the cotangent weights of the $\mathcal{N}_k$ edges as the entries. (The $|\mathcal{N}_k|$ dimensions in these matrices can be zero-padded to $\max_{k\in \{1\dots |\mathcal{V}|\}}|\mathcal{N}_k|$ for batched solutions.) Taking the SVD of $\mathsf{X}_k$ , we can find $\hat{\mathsf{R}}_k$ (up to multiplying the last column of $\mathbf{U}_k$ by $-1$ to ensure $\operatorname*{det}(\mathsf{R}_k) > 0$ ) as + +$$ +\begin{array}{r} \mathbf {U} _ {k} \boldsymbol {\Sigma} _ {k} \mathbf {V} _ {k} ^ {\top} = \mathbf {X} _ {k} \\ \hat {\mathbf {R}} _ {k} = \mathbf {V} _ {k} \mathbf {U} _ {k} ^ {\top} \end{array} \tag {4} +$$ + +Note that in classical ARAP iterative optimization, the term in (2) is normally $\sum_{\mathbf{e}_{ij} \in \mathcal{N}_k} \left(w_{ij} \| \mathsf{R}_k \mathbf{e}_{ij} - \mathbf{e}_{ij}'\|_2^2\right)$ where $\mathbf{e}_{ij}'$ is the vector of the most recent deformed edge $(i,j)$ in $\mathcal{N}_k$ output by the previous ARAP optimization iteration. Since dARAP is meant as a differentiable module in a larger optimization process or learning pipeline, we condense the typically many local-global alternating steps of classical ARAP to just one local step and one global step, hence the identification of $\mathbf{e}_{ij}'$ with $\mathbf{e}_{ij}$ . Coupled with setting $\lambda$ to an appropriately large value, which scales the strength of the rotation towards the requested normal $\hat{\mathbf{u}}_k$ , our single local step is still able to achieve the required expressiveness and strength to make detailed deformations, yet regularized by the Procrustes solve to retain shape identity without requiring an extra identity regularization loss as in Kim et al. [41] and Gao et al. [26]. + +Note also that in NJF-based methods such as [26, 41], the local step would be the identity function; a jacobian matrix per face is assumed given or predicted from upstream components. In our case, a matrix (a rotation) is not given, but computed from the target normal vector for each element. + +# 3.2. Global Solve from Local Rotations + +Having obtained a rotation per neighborhood with our local step, we minimize the energy fixing the rotation matrices and solving for deformed vertex locations, i.e., finding the deformed vertices $\hat{\mathcal{V}}$ such that + +$$ +\hat {\mathcal {V}} = \underset {\tilde {\mathcal {V}}} {\operatorname {a r g m i n}} \sum_ {k \in \{1 \dots | \mathcal {V} | \}} \sum_ {(i, j) \in \mathcal {N} _ {k}} w _ {i j} \| \mathrm {R} _ {k} \mathrm {e} _ {i j} - \tilde {\mathrm {e}} _ {i j} \| _ {2} ^ {2} \tag {5} +$$ + +where $\mathsf{e}_{ij} = (\mathsf{v}_j - \mathsf{v}_i)$ , $\tilde{\mathsf{e}}_{ij} = (\tilde{\mathsf{v}}_j - \tilde{\mathsf{v}}_i)$ , and $w_{ij}$ is the cotangent weight of edge $(i,j)$ . This is a linear least squares optimization for $\hat{\mathcal{V}}$ . As such, for the spokes-and-rims neighborhood, taking the derivative with respect to $\hat{\mathcal{V}}$ and setting it to zero yields a linear equation in $\hat{\mathcal{V}}$ + +$$ +L \hat {\mathcal {V}} = \left[ \begin{array}{c} \operatorname {r h s} (1) ^ {\top} \\ \vdots \\ \operatorname {r h s} (| \mathcal {V} |) ^ {\top} \end{array} \right] \tag {6} +$$ + +$$ +\operatorname {r h s} (k) = \sum_ {(k, m, n) \in \mathcal {N} _ {k} ^ {F}} \frac {\mathrm {R} _ {k} + \mathrm {R} _ {m} + \mathrm {R} _ {n}}{3} \left(\frac {w _ {k m}}{2} \mathrm {e} _ {k m} + \frac {w _ {k n}}{2} \mathrm {e} _ {k n}\right) \tag {7} +$$ + +where $\mathcal{N}_k^F$ are the faces adjacent to vertex $k$ , each one having vertices $(k,m,n)$ (i.e. even permutation such that $k$ is in front); $w_{km}, w_{kn}$ are the (undirected) cotangent weights of edges $(k,m),(k,n)$ ; and $L$ is the cotangent Laplacian. + +Equation (6) is a Poisson equation. As such, we can use the same solving and pre-factorization techniques as in NJF [2] to make our global solve step differentiable and efficient. + +# 3.3. Optimization Using a Semantic Visual Loss + +Differentiable renderer and semantic loss. Our optimization is guided by a powerful pretrained text-to-image (T2I) diffusion model. We render the deformed mesh from multiple views using a differentiable rasterizer [42], then feed the rendered views into a semantic visual loss, in our case Cascaded Score Distillation (CSD) [21] using stages 1 and 2 of the image diffusion model DeepFloyd IF [1]. + +# 4. Experiments + +Optimization details. Our initial guess for the target normals $\hat{\mathcal{U}}$ is $\mathcal{U}$ , the original area-weighted vertex normals of the undeformed mesh $\mathcal{M}$ . We set the local step hyperparameter $\lambda = 8$ (Sec. 3.1) for all of our optimizations. We run our optimization for 2500 epochs at a constant learning rate of 0.002 using the Adam optimizer, each epoch being a + +batch of 8 renders fed to CSD loss. A full optimization run takes about 2 hours 15 minutes using a single A40 GPU. We remesh our source meshes for better behavior with the cotangent Laplacian (see Sec. 4.3.) Further details on view sampling settings, CSD configuration, and source mesh preprocessing can be found in the supplementary material. + +# 4.1. Properties of Geometry in Style + +Generality and expressivity. Our method is highly versatile, and is able to deform meshes from varied domains towards a wide range of styles (Figs. 1 and 2). Our method handles organic and articulated surfaces, such as animals and the human body, as well as man-made objects with sharp features and complex topology such as chairs. The target style is specified by an open-vocabulary text prompt and can thus be described flexibly and intuitively. + +The stylization manifests in a part-aware manner, conforming to the shape's geometry. For the pineapple-themed vase in Fig. 1, our method adds a pineapple-like geometric texture to the vase's body, while the vase's head is deformed with a different ripple pattern to resemble a pineapple head. For a human body, our method creates geometric details to reflect a knight's armor in the appropriate locations, such as shoulder pads, a large chest plate, a crease across the waistline, and a hat on the head. In Fig. 2, the antique, gothic, and cardboard chairs' styles are reflected by both local geometric details and the silhouette of the deformed mesh. + +We can further take advantage of part awareness to stylize only select regions. In the inset, we localize the deformation to the head by setting the rotation of vertices outside the region to the identity matrix every iteration. The deformation is contained within the lo + +![](images/d680634302d545c793cdaa45ff0e3a2110962bae29f9dac7c09e2ebb9b7b1de6.jpg) + +cal region, yet detailed and appropriate for the rest of the body. We observe no boundary artifacts, showing dARAP's beneficial regularizing effects. + +Identity preservation. Our method applies the prescribed style to the input mesh expressively while preserving important characteristics. In Fig. 7, each input animal has a unique pose, e.g. the folded front leg of the horse. The deformation recognizably keeps the pose while stylizing the body towards the skeletal style. Similarly, the stylization of the person shape from Fig. 1 maintains body proportions. Additionally, our method preserves other distinct shape properties, e.g., the animal's facial features (Fig. 7) and the chairs' parts (Fig. 2), with semantic correspondences maintained (Fig. 10). + +We attribute our pronounced yet identity-preserving stylizations to our normal-based deformation representation. A pretrained vision foundation model provides strong guidance toward the style prompt but can also easily impart de + +![](images/1359e6702c012595131dac0154ce41ee3c423170b2211dca0db977ab7b37376b.jpg) +Figure 6. Our method is capable of deforming different input meshes towards the same text-specified style. Even with the same prompt in a shape class (a 3d render of a lego chair, a 3d render of a vase made of lego bricks), different starting shapes (different chairs, different vases) result in stylizations that closely align to the identity of the original shape, while still strong enough to induce more blocky components and lego-like surface textures. + +formations that significantly alter the identity of the shape, as witnessed in previous work that used jacobian-based deformations [26, 41], see Figs. 9 and 11. By contrast, our deformation is driven by rotations of normals, further regularized as a best-fit rotation over the spokes-and-rims neighborhood (Sec. 3.1.) This formulation selects for local rigid changes that are discouraged from scaling or shearing, thus preventing excessive structural changes while requiring no extra identity regularization loss on the local transforms. + +Specificity. Our method performs diverse shape stylizations that adhere to the target style prompt with high detail. In Fig. 5, we deform the source shape into different styles: the origami chair's backrest is thin and has creases as with paper folds; the church pulpit style is thicker with overhangs appropriate of church furniture. As further seen by the detailed prompts and styles in Figs. 1 and 2, our method produces distinct styles and shows granular effectiveness. + +Robustness. Our method exhibits robustness across shape categories and instances within the category. In Fig. 6, the same *lego* style is applied to chairs, animals, and vases. Each domain has unique geometry: the chairs have varying parts (e.g., the types of legs and backrests), the animals have smooth geometry, and the vases have sharp edges and rotational symmetry. Still, our method consistently conveys the style on the source shape with a *lego* brick-like surface pattern and by cubifying the geometry. + +![](images/0f5e28a9a515639aefd00ac51eccc04022c95bcfb00ec036eb8d327c4f634132.jpg) +Figure 7. Pose preservation. Geometry in Style stylize the shape according to the text prompt, while decently keeping characteristics of the source shape like the relative positioning of the limbs and the angle of the head. + +Tunable stylization strength. A specific value of $\lambda$ is used by deformations during the optimization process. However, this $\lambda$ can be changed when re-applying the saved optimized normals to the source mesh, allowing user control separate from the optimization pipeline itself, as shown in Fig. 8. Recall from Eq. (2) that the hyperparameter $\lambda$ influences the match from the original vertex normal to the target normal. As seen in Fig. 8, as the value of $\lambda$ increases, the geometry of the deformed shape is sharpened to strengthen to "robot" style effect, while a lower $\lambda$ results in deformed normals being closer to the original ones, though the desired style is still visible. Notably, we observe that using an inference $\lambda$ value larger than that used during optimization results in a more geometrically salient yet still sensible stylization, further demonstrating the robustness of our method. + +# 4.2. Evaluation + +We contrast our method to two recent text-guided mesh deformation methods, TextDeformer [26] and MeshUp [41] using public code released by the authors. + +Qualitative comparison. In Fig. 9, we show deformation results for TextDeformer [26], MeshUp [41], and our method. For comparison, all three methods use the same text prompt, source mesh, and view sampling settings. TextDeformer distorts the surface, changes the pose of the source shape, and does not achieve the target style. MeshUp does stylize following the text prompt, but in some cases, its surface texture may be weaker than ours, as seen in the lego goat example. + +In other cases, MeshUp's stylization is strong but produces notable distortion in arms and body proportions: in the examples knight in armor and Chinese terracotta warrior, the body gets a broader, stouter stature and does not preserve the identity and body proportions of the source shape as well as our method does. Moreover, our method does not encounter certain artifacts that MeshUp introduces, like the crushed head of the knight in armor example, or the Janus effect with a duplicate face and chestplate on the back for Chinese terracotta warrior. We achieve a prominent desired style with fewer artifacts and better preservation of + +![](images/d7da810f2dc0de8a6bed0e685c2468f87fb71a32f227e640267f35526a761787.jpg) +Figure 8. Changing stylization strength after optimization. Normals found by optimization using $\lambda = 8$ can be conveniently re-applied after optimization using a different $\lambda$ to tune the stylization strength on demand. Both larger and smaller $\lambda$ result in salient and clean stylizations at the required strength. + +source shape features. More qualitative examples are given in the supplementary material. + +Quantitative results. As a proxy for evaluating identity preservation, we measure the mean and standard deviation of the ratio (deformed triangle area / original triangle area) summarized over all triangles across the chosen meshes. We use 20 mesh-prompt pairs chosen from results seen throughout the paper; per-mesh triangle counts range from 10 thousand to 20 thousand. Source meshes are normalized to fit a side-length-2 cube centered at the origin; deformed meshes are normalized to have the same bounding box diagonal length as the source, as is done after the Poisson solve of MeshUp and our method. This quantity measures distortion and estimates how well the bounding box is respected: deformations that shrink the mesh lead to a larger rescale factor during the bounding-box-restoring normalization, thus inflating the face area ratio, and vice versa. Ideal identity-preserving values are ratio 1 with 0 standard deviation. + +Table 1 summarizes the quantitative comparison with the baseline methods [26, 41]. These deformations use jacobians, which are more prone to changing triangle scale and compromising the integrity of the mesh. In contrast, we represent a target deformation by surface normals, coupled with our dARAP layer that regularizes the resulting deformation and better preserves the original triangle area, improving faithfulness to the input shape. Indeed, as Tab. 1 shows, our triangle area ratio has an average closer to 1 with a lower standard deviation than MeshUp and TextDeformer. We also include a quantitative evaluation of CLIP similarity to the prompt for these three methods on the same shapes (see the supplementary material); our method achieves better CLIP similarity to the prompt. + +# 4.3. Limitations + +Our method uses the cotangent Laplacian, which works well only on manifold meshes and is sensitive to triangle aspect ratios. This is also true for other methods that use + +
MethodRatio meanRatio std. dev.
TextDeformer [26]0.8270.360
MeshUp [41]1.2880.363
Geometry in Style (ours)1.0800.233
+ +Table 1. Triangle area preservation. As a surrogate for measuring identity preservation, we compute the mean and standard deviation of the triangle area ratio between the deformed and source shapes. Our method preserves the triangle area better than the other methods, with an average ratio closer to 1 and a lower standard deviation. + +the cotangent Laplacian, such as TextDeformer [26] and MeshUp [41]. To mitigate this, we remesh input meshes with isotropic explicit remeshing [32], optionally after manifold preprocessing [34]. + +Another limitation is the possibility of self-intersection in deformed meshes (Fig. 11). The rods of the source lamp are rotated towards the center and intersect each other. This can be somewhat mitigated by adjusting the deformation strength parameter $\lambda$ after optimization, as discussed in Fig. 8, a strategy not straightforwardly available to MeshUp. + +# 5. Conclusion + +In this work, we presented Geometry in Style, a technique for deforming meshes to achieve a text-specified style. A key claim of the work is that prescribing a deformation via surface normals allows the recovery of deformed vertices that adhere well to the input geometry while still being ex + +![](images/ce126d82f20015b1e922e37082c8c9cd482ed9841c1c236d13465f5676421161.jpg) +a 3d render of a(n)... +Figure 9. Comparison with baselines. We compare our method with the alternative deformation techniques TextDeformer [26] and MeshUp [41]. While the baseline methods have a weaker stylization effect, change the poses, or create geometric artifacts on some examples, Geometry in Style cleanly achieves both the desired style and remains faithful to the shape of the source meshes. + +![](images/08a09e505b834f15836045bf6e842f1ae50d2085ea907cf4d10a74739fcfa3e6.jpg) +Figure 10. Correspondence. The meshes deformed with our method preserve semantic correspondence to the source mesh. Deformed vertices have the same color as the corresponding source vertices, colored by the source shape's wave kernel signature. + +![](images/4e802b98b5ef0fa61d97d31acfc884f900614e0eb87cf4145f1b974a3fa3f22e.jpg) + +pressive. We demonstrate high-quality, detailed geometric stylizations that respect the input shape's identity. + +As part of Geometry in Style, we introduce dARAP, a differentiable neural network layer that deforms a surface to achieve target normals. Our layer is simple yet effective: while traditional applications require iterating ARAP to convergence for a desirable solution, we find that within our neural network pipeline, good results can be achieved with only a single step. We speculate that by iteratively updating target normals through gradient descent, we can avoid (in a dARAP forward pass) the standard practice of needing to repeatedly iterate between local and global ARAP steps. Moreover, dARAP is general and may be used for other geometry tasks where ARAP is useful, such as parameterization, re-posing, collisions, editing, and more. + +In the future, we are interested in leveraging unsupervised segmentation strategies [20, 21] to perform localized geometric stylization. In addition, while our method is topology-preserving, follow-up work could explore edits and deformations that add explicit parts or change topology. + +![](images/4b5c2995b3f15d01987189b5a12839d2210e8a67e0ec5fe2de2367af3b75a1c7.jpg) +Figure 11. Limitations. Our method may produce self-intersections. Decreasing the parameter $\lambda$ after the optimization process can alleviate the self-intersection with only a mild reduction in the stylistic surface details. MeshUp warps the 3-lamp structure and the individual lamps and exhibits less geometric pineapple texture. + +# 6. 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Kim¹ Douglas Lanman² Numair Khan² + +$^{1}$ KAIST $^{2}$ Meta + +![](images/5e67b8d5dd2d6ed853a0466061d5579d04de9621aade9ccacbd41eeefc703b10.jpg) +Figure 1. Our method enables efficient rendering of high-quality, consistent 3D videos by addressing the challenges of view synthesis in both spatial and temporal dimensions. In multi-camera setups, novel-view synthesis must manage continuous changes across view and time to ensure smooth visualization. Existing methods process frames independently and often introduce flickering artifacts. We propose using aggregated depth as geometric guidance to a blending network to maintain consistent color and detail across frames. This results in view and temporally consistent 3D videos, achieving state-of-the-art quality while providing improved processing speed over prior methods. + +![](images/a3c66cc7e44be6c3d204c0ff069690a5377127020d46248d587b36e3e4463beb.jpg) + +![](images/32a2204c3d1d48c76d63922913067d4a86b38c1f7030b8b277f578cfe29b4be7.jpg) + +![](images/9e208f0b5a3f4b46d413988386a06769a51849e28d1037a001066d87dd5bbd46.jpg) + +![](images/f2dfa2c2fc3b4f7548a0963ed03ef20515ea457a88243443941b4643ffc1e258.jpg) + +![](images/5e6ce56a992902d59dc8caf7b51a0e0d4431d9ee3bf598e931129d79f4551a70.jpg) +Temporal plane slices show (in)consistency across time + +![](images/a667edfd70a46cc477af6dfb2a5244de12c147651bee3c73d895950b4383b00c.jpg) + +![](images/59e4313788cffc462c10921775bd80b96acfef5df0eaa02640cc95189e8cda28.jpg) + +# Abstract + +We introduce a novel geometry-guided online video view synthesis method with enhanced view and temporal consistency. Traditional approaches achieve high-quality synthesis from dense multi-view camera setups but require significant computational resources. In contrast, selective-input methods reduce this cost but often compromise quality, leading to multi-view and temporal inconsistencies such as flickering artifacts. Our method addresses this challenge to deliver efficient, high-quality novel-view synthesis with view and temporal consistency. The key innovation of our approach lies in using global geometry to guide an image-based rendering pipeline. To accomplish this, we progressively refine depth maps using color difference masks across time. These depth maps are then accumulated through truncated signed distance fields in the synthesized view's image space. This depth representation is view and temporally consistent, and is used to guide a pre-trained blending network that fuses multiple forward-rendered input-view images. Thus, the network is encouraged to output geometrically consis + +tent synthesis results across multiple views and time. Our approach achieves consistent, high-quality video synthesis, while running efficiently in an online manner. + +# 1. Introduction + +Recent strides in immersive 3D video are poised to revolutionize the way we experience education, video conferencing [30, 63], and entertainment [26, 39, 75] with virtual reality (VR), augmented reality (AR), and 3D videography [18, 66] becoming increasingly accessible and affordable. As these technologies continue to evolve, we can expect a future where immersive video content seamlessly integrates into our daily lives, transforming the way we learn, entertain, and connect with each other. + +Generating accurate scene-scale reconstructions for immersive 3D video introduces unique challenges due to complex occlusions, large depth ranges, and diverse object appearances. While systems using large camera arrays have demonstrated high-quality novel-view synthesis results [68, 69], processing all inputs of a dense camera rig simultaneously imposes substantial computational costs. This makes them impractical for real-time applications which require ef + +ficient processing of streaming input. This inherent trade-off between computational complexity, and camera density has spurred recent efforts to achieve high-quality view-synthesis results using sparser, more practical capture systems. + +Among these, one line of work uses a fixed set of very sparsely distributed cameras [14, 15, 30, 63]. These methods often rely on depth from additional sensors to overcome Nyquist sampling limits [7, 45], and provide a basic geometric framework to support appearance optimization. While such a global geometry approach ensures consistent reconstruction across views and time, it fails to represent fine detail and complex appearance changes in a scene. Furthermore, the low resolution of depth sensors limits the achievable quality of these methods in scene-scale settings, restricting them exclusively to the reconstruction of human subjects. + +Therefore, a second line of work selects a subset of optimal views from a relatively larger camera array to achieve broader scene coverage, and reconstruct more complex appearance details using an image-based rendering approach [38, 45, 82]. Further, these methods can use correspondence-based techniques to estimate high-resolution depth (explicitly, or implicitly), and overcome the Nyquist sampling limits for view synthesis required by traditional image-based rendering [68, 69]. Thus, recent work uses neural volumes [38], neural points [6], learned image-based rendering [65], and 3D Gaussian splats [82] to reconstruct diverse objects' appearance. However, these methods introduce new challenges including shifts in appearance with viewpoint, and temporal inconsistencies due to lack of continuity across frames. This makes it difficult to achieve smooth reconstructions for immersive 3D video in online systems. + +In this paper, we present a novel geometry-guided 3D video synthesis method that seeks to overcome these limitations by combining global geometry with an image-based rendering approach for high-quality, view and temporally consistent synthesis in dynamic scenes. + +The main contribution of our method is a geometry-guided 2D image blending workflow that suppresses inconsistencies across forward-rendered images. Our approach aggregates high-resolution depth maps into a globally coherent geometric structure via a truncated signed distance field (TSDF) in the synthesized view's image space. This is used to support stable synthesis across viewpoints and time by guiding a pre-trained image-based blending network. This process ensures view-consistent and temporally coherent synthesis across diverse scene conditions, as demonstrated by results on both indoor and outdoor multi-view datasets. + +# 2. Related Work + +Voxel-based View Synthesis. Real-time RGB-D 3D scanning methods [13, 22, 28, 32, 48, 50] utilize the truncated signed distance field (TSDF) [11] to integrate geometry and color information. These methods suppress noisy depth in + +formation but fail to handle dynamic scenes. To address this, 4D scanning methods [14, 15, 19, 21, 25, 49, 58] estimate the motion of objects and integrate information into a canonical TSDF space. However, they need to trade off between the resolution of expensive 3D voxel grids and computational complexity. Recently, Lawrence et al. [30] proposed an image-based TSDF that does not require an explicit 3D voxel grid to generate novel views, but the reconstructions are primarily focused on humans and not general dynamic scenes. The above methods have limitations, including the need for additional depth sensors, and simple appearance models, such as diffuse or specular BRDFs. Our algorithm overcomes these limitations by leveraging image-based rendering, enabling high-quality reconstruction of entire indoor environments with diverse moving objects. + +Neural-based View Synthesis. Image-based rendering [23, 24, 52] and neural-based multiplane images (MPIs) [16, 35, 45, 60, 70, 80, 83] have been widely used for novel-view synthesis in static scenes, with recent applications extending to dynamic scenes [40]. However, these methods require significant computation time to build explicit geometry or MPIs. Volume-based neural rendering algorithms can handle more free-viewpoint rendering in 3D [3, 4, 46, 47, 64, 74] and further in 4D [2, 5, 17, 34, 39, 75], but they remain unsuitable for online use due to the high computational cost of per-scene training. Various methods have been developed to handle generalized scene representations based on volumetric [73, 77], depth-based [6] or image-based rendering [65]. However, these methods fall short in handling dynamic scenes. Lin et al. [38] employ a generalized 3D CNN model to reconstruct dynamic scenes, while Xiao et al. [72] address novel-view synthesis in specific VR hardware. However, these approaches do not explicitly address temporal and view inconsistencies. Our algorithm does not require per-scene optimization and ensures globally and temporally consistent results across time and views by leveraging a global geometry representation. + +Point-based View Synthesis. To represent diverse scene appearance, neural features [1, 54, 56] are sometimes combined with 3D points. Recently, 3D Gaussians [27] have enabled real-time rendering for novel-view synthesis. This approach has been extended to reconstruct dynamic environments by considering the temporal domain [31, 33, 36, 37, 44, 61, 71, 76]. However, these methods require expensive per-scene optimization. In contrast, feedforward models [8-10, 29, 62, 79, 84] have been proposed to enable novel-view synthesis in sparse static scenes. Feedforward Gaussian models have also been extended to reconstruct dynamic humans [63, 82]. Recently, Guo et al. [20] proposed a depth-based free-viewpoint system for dynamic indoor scenes. However, all these methods fail to explicitly account for noisy input depth maps, which results in temporal and view inconsistencies. Our approach can handle + +![](images/e1800814cc48123e3db5d865994328f27e18fd3516b286c4488f7ace7a70b756.jpg) +Figure 2. Pipeline overview. Given multi-view RGB-D videos, our method forward-renders a subset of views into the target camera using 3D Gaussian splatting (Section 3.1). The per-view depth maps are fused using a truncated signed distance field (TSDF) that is regularized to be view and temporally consistent (Section 3.2). This geometric guidance enables a CNN to blend the forward-rendered images and inpaint disoccluded regions, to produce consistent novel view results (Section 3.3). + +objects with diverse appearance while maintaining consistency across view and time domains by incorporating global geometry information in 2D image-based rendering. + +# 3. Method + +At a high level, our method uses depth to forward-render a subset of input images into the novel camera, and then blends these renderings to generate the novel view result. This process is repeated for each frame of a multi-camera video sequence. The individual components of our pipeline are chosen to ensure view and temporal consistency, efficient computation and state-of-the-art reconstruction quality. + +Specifically, we use pixel-sized 3D Gaussians [27] to render the input images into the target view (Section 3.1). This allows us to handle occlusions, and avoids the aliasing artifacts of conventional point-splatting. Simultaneously, we use an image-based truncated signed distance field (TSDF) [30] to estimate a depth map for the target view using the input-view depths (Section 3.2). This TSDF depth is used to guide a blending network that generates a fused novel view from the forward-rendered images, including inpainted disoccluded regions (Section 3.3). Using a global geometric structure like a TSDF to guide the blending network ensures the fused output remains view-consistent at any single time frame. To further ensure temporal consistency as well, we fuse the depth of static regions from previous time frames into the current frame's TSDF. Thus, our insight is to use the TSDF as a view-temporal filter between the inconsistent input depths and the synthesized novel views. + +An overview of our pipeline is provided in Figure 2. At each time step $t$ , the input to our method is a set of $H\times W$ multi-view RGB images $\{I_n^t,n = 1,\dots,N\}$ from $N$ cameras. The pose of each camera remains fixed across time, and we compute it once using COLMAP [57]. Since the camera configuration is known beforehand, we use a stereo algorithm [41] to estimate depth maps $\{D_n^t,n = 1,\dots,N\}$ for + +the input views. This also allows us to evaluate our method on existing multi-view datasets. However, it is also possible to use RGB-D cameras for input [51]. The output of our method is an RGB image $\mathcal{I}^t$ at the target novel view. + +# 3.1. Forward Warping with 3D Gaussians + +We render a subset $\{I_k^t, k \in (1, \dots, N)\}$ of the $K$ closest input views into the novel camera using pixel-wise 3D Gaussians. Specifically, for each pixel of an input $I_k^t$ , we use the depth map $D_k^t$ and pose to determine the 3D position of an isotropic, fully-opaque Gaussian. The RGB color of each Gaussian is set to the underlying pixel value, and its scale is computed such that its projection in the source image $I_k^t$ covers a single pixel. This step produces a set of forward-rendered images $\{\mathcal{I}_k^t\}$ along with accumulated opacity of the Gaussians $\{\alpha_k^t\}$ , and depths $\{\mathcal{D}_k^t\}$ in the novel view. + +Our approach differs from previous methods that use feedforward networks to predict per-pixel Gaussian parameters [63, 79, 82]. We observed that the scale, opacity and rotation parameters predicted by these networks for Gaussians on a dense $H \times W$ pixel grid converge to near-constant values, and the predicted RGB color matches the input image. Therefore, it is more efficient to compute these parameters analytically than with a neural network. With the 3D position of each Gaussian coming from the depth map, our approach achieves high-quality rendering results that match the feed-forward models in most regions. Compared to conventional point splatting [1], our approach shows fewer aliasing artifacts like gaps between pixels and jagged edges. Nonetheless, disocclusions and errors in the depth maps $\{D_k^t\}$ lead to holes and flying pixels in the forward-rendered images $\{\mathcal{I}_k^t\}$ . Rendering the Gaussians from all $\{I_k^t\}$ in a single pass, as Zhang et al. [79] do, fails to address these artifacts and, in fact, further deteriorates edge quality due to Z-fighting (see Figure 4). Instead, we blend the separate images $\{\mathcal{I}_k^t\}$ guided by the novel view's depth. + +![](images/127d558331223b0cb81ba6875b1b93a546ac548c3ba943ffc4bb8f695f5e39d1.jpg) +Figure 3. View-temporal consistency in TSDF depth. The global TSDF provides view consistency. Temporal consistency is encouraged by filtering the input depth at consecutive frames using color difference masks for dynamic regions. Additionally, these masks are used to integrate the rendered depth from the previous frame into the TSDF, ensuring consistency across view and time. + +# 3.2. Multi-view Temporally Consistent Depth + +The depth $\mathcal{D}^t$ for the novel view at time $t$ is rendered by raymarching through a TSDF that fuses the depth of the $K$ closest input views. We use an image-based TSDF [30] that integrates depth along each ray on the fly and, thus, avoids creating an explicit 3D voxel grid. This allows it to efficiently generate high-resolution depth maps. Fusing all input depths into a global structure like a TSDF guarantees that, for a given time $t$ , the rendered depth remains view-consistent. + +To encourage temporal consistency in the TSDF, we suppress depth variations across the static regions in each input depth map $D_{n}^{t}$ . Specifically, given the set of $N$ input views $\{I_n^t\}$ , we exploit the fact that the camera poses remain fixed across time to compute a soft difference mask between the current and previous frame of each view via + +$$ +M _ {n} ^ {t} = \min \left(\frac {\left| I _ {n} ^ {t} - I _ {n} ^ {t - 1} \right|}{\lambda_ {\mathrm {t}}} + \beta , 1\right), \tag {1} +$$ + +where $\beta = 0.6$ and $\lambda_{\mathrm{t}} = 0.7$ are empirical hyperparameters that determine sensitivity to color changes. We compute the difference masks at quarter resolution, apply a $3\times 3$ max-pooling filter, and then upscale them back to their original size using bilinear interpolation. Given the difference masks, we compute temporally filtered depths in each view using + +$$ +\dot {D} _ {n} ^ {t} = M _ {n} ^ {t} \cdot D _ {n} ^ {t} + \left(1 - M _ {n} ^ {t}\right) \cdot \dot {D} _ {n} ^ {t - 1}. \tag {2} +$$ + +While the global nature of a TSDF guarantees that the rendered depth maps remain view-consistent, in practice, however, we only fuse the depth maps of the $K$ closest input views. Consequently, minor changes in the TSDF depth + +![](images/9ff80ccd22b15391eab896de2b120c6f1251c131f7cadd0fd78b08e44c9d1e3a.jpg) +Figure 4. (a) Rendering all input-view Gaussians into the target camera in a single pass [82] creates flying pixels, and disocclusion holes. (b) On the other hand, blending multiple forward-rendered images using distance-based weights [45] leads to ghosting artifacts. (c) A naive blending network is unable to fix the ghosting. (d) Our method uses the target view's geometry – rendered as a depth map from a TSDF – to guide the blending network. This allows it to correctly fuse unstable forward-rendered input views. + +![](images/6c5671c1019a101e243979736d66b43bfb56af2702510d9810688575b5e987c2.jpg) + +![](images/c3e2b16dd0314d82b6761d2fc16eeb535368951c59a018db1c830163320b55a0.jpg) + +![](images/901d9d126b846f7348f71023d9356af840b15f0c812dad80ae9d22a2959fc20b.jpg) + +can still occur as the novel viewpoint – and, thus, the set of $K$ closest views – changes. Increasing $K$ ameliorates these residual inconsistencies, but at increased computational cost. Instead, we propose to use the rendered output of the previous frame $\mathcal{D}^{t-1}$ as an additional depth input to the TSDF at frame $t$ . To account for dynamic regions, we forward splat the difference masks $M_{n}^{t}$ from Equation (1) into the novel view, and use the maximum mask value across the views as the TSDF blending weight for $\mathcal{D}^{t-1}$ . + +Thus, the output depth map is obtained by integrating temporally filtered input-view depths, and the depth output of the previous frame in an image-based TSDF (Figure 3): + +$$ +\mathcal {D} ^ {t} = \operatorname {R a y m a r c h} (\operatorname {T S D F} \left(\{\dot {D} _ {k} ^ {t} \}, \mathcal {D} ^ {t - 1}\right)). \tag {3} +$$ + +This depth map, pushed to be consistent in space and time, guides the blending of the forward-rendered views $\{\mathcal{I}_k^t\}$ . For further details, please refer to our supplementary document. + +# 3.3. Geometry-guided Blending Network + +The final novel-view output of our method, $\mathcal{I}^t$ , is generated by a weighted blending of the $K$ forward-rendered images $\{\mathcal{I}_k^t\}$ . We use per-pixel weights $\{w_k^t \in \mathbb{R}^{H \times W}\}$ . In addition, to deal with disoccluded regions in the novel view, we further blend the result with a background image $\mathcal{I}_{\mathrm{BG}}^t$ using blending weights $w_{\mathrm{BG}}^t \in \mathbb{R}^{H \times W}$ . Thus, + +$$ +\mathcal {I} _ {\mathrm {F G}} ^ {t} = \sum_ {k = 1} ^ {K} \frac {\mathcal {I} _ {k} ^ {t} \cdot \alpha_ {k} ^ {t} \cdot w _ {k} ^ {t}}{\alpha_ {k} ^ {t} \cdot w _ {k} ^ {t}} \quad \text {a n d} \tag {4} +$$ + +$$ +\mathcal {I} ^ {t} = \left(1 - w _ {\mathrm {B G}} ^ {t}\right) \cdot \mathcal {I} _ {\mathrm {F G}} ^ {t} + w _ {\mathrm {B G}} ^ {t} \cdot \mathcal {I} _ {\mathrm {B G}} ^ {t}. \tag {5} +$$ + +We use a neural network $\Theta (\cdot)$ to predict the blending weights $\{w_k^t\}$ and $w_{\mathrm{BG}}^t$ , and the background image $\mathcal{I}_{\mathrm{BG}}^t$ . The prediction is guided by the consistent TSDF depth $\mathcal{D}^t$ . To achieve this, we provide $\mathcal{D}^t$ , and the forward-rendered depth maps $\{\mathcal{D}_k^t\}$ as inputs to the network $\Theta (\cdot)$ . To encourage the + +Table 1. Quantitative comparison of view and temporal consistency. We highlight the $50\%$ best metrics in blue, proportional to their percentile. Our method achieves the best metrics on DyNeRF and D3DMV, and partially on the ENeRF-Outdoor dataset. Please refer to the qualitative results on view and temporal consistency in Figures 5 and 6, and to the supplementary material for video results. + +
DyNeRF [34]ENeRF-Outdoor [38]D3DMV [40]
MethodTCC↑STED↓SDT↓SDV↓TCC↑STED↓SDT↓SDV↓TCC↑STED↓SDT↓SDV↓
FWD [6]0.81427960.2145.6960.85022050.2712.5600.87311920.4330.769
IBRNet [65]0.834737.70.2087.2330.88565.760.1932.0030.901341.40.1152.340
GPSG [82]0.771693.00.2982.2540.812299.70.2592.1590.870637.41.2331.830
ENeRF [38]0.86776.140.1472.7100.88332.310.1893.9440.892137.00.1440.754
Ours0.87268.760.1391.7480.89744.490.1931.9700.91515.850.1050.449
+ +blending weights to reconstruct $\mathcal{D}^t$ , we use the loss + +$$ +\mathrm {L} _ {\text {D e p t h}} = \frac {1}{H W K} \left\| \mathcal {D} ^ {t} - \sum_ {k = 1} ^ {K} \frac {\mathcal {D} _ {k} ^ {t} \cdot \alpha_ {k} ^ {t} \cdot w _ {k} ^ {t}}{\alpha_ {k} ^ {t} \cdot w _ {k} ^ {t}} \right\| _ {1}. \tag {6} +$$ + +We use this loss in conjunction with image reconstruction losses, as described below. Thus, $\mathrm{L_{Depth}}$ provides a soft regularization that encourages the network to predict the unknown novel-view image using the known TSDF depth as a target. Therefore, by ensuring the TSDF depth map $\mathcal{D}^t$ remains view-temporally consistent, the reconstructed image $\mathcal{I}^t$ is guided to be consistent, too. + +The network $\Theta(\cdot)$ is a four-layer U-Net [55]. The input to the network consists of the forward-rendered images $\{\mathcal{I}_k^t\}$ , depth maps $\{D_k^t\}$ and alpha maps $\{\alpha_k^t\}$ , and the TSDF depth $\mathcal{D}^t$ . Additionally, we provide camera orientation information in the form of camera distances, and dot products between the viewing angles and normals. Please refer to the supplement for details about the network input and architecture. + +The total training loss function is + +$$ +\mathrm {L} = 0. 8 \cdot \mathrm {L} _ {1} + 0. 2 \cdot \mathrm {L} _ {\text {S S I M}} + 0. 1 \cdot \mathrm {L} _ {\text {D e p t h}} + 0. 1 \cdot \mathrm {L} _ {\text {M a s k}}, \tag {7} +$$ + +where $\mathrm{L}_1$ and $\mathrm{L}_{\mathrm{SSIM}}$ are the L1 and SSIM [67] losses on the reconstructed image $\mathcal{I}^t$ , and $\mathrm{L}_{\mathrm{Mask}}$ encourages the background weights $w_{\mathrm{BG}}^t$ to be higher in disoccluded regions. It is computed as the mean absolute difference between $w_{\mathrm{BG}}^t$ , and a binary mask of the empty regions in $\mathcal{I}^t$ . + +# 4. Evaluation + +We implement our blending network in PyTorch, and train on an NVIDIA Tesla V100 GPU. We use the Adam optimizer [43] (learning rate: $2 \times 10^{-4}$ , weight decay: $10^{-5}$ ) to train the network for 150K iterations in batches of size 12 on $640 \times 352$ crops of ScanNet [12], Google Spaces [16], and a training subset of the DyNeRF [34] dataset. We utilize Torch-TensorRT [53] to speed up inference. For Google Spaces and DyNeRF, which have fixed camera configurations, we compute the depth for each view using RAFT-Stereo [41] on manually selected image pairs. The ScanNet dataset provides + +depth from a sensor. Each training iteration, the rendering target, and $K = 4$ input views are randomly selected. Our image-based TSDF is implemented in CUDA, and we use the original 3D Gaussian splatting code [27] for forward rendering input views. + +# 4.1. Baselines + +We compare our results to four baseline methods for online view synthesis from multi-camera video: FWD [6], IBRNet [65], ENeRF [38], and GPSG [82]. We evaluate IBRNet, and ENeRF using the pretrained models provided by their authors. The pretrained models for GPSG and FWD, however, fail to generalize to our testing datasets. Therefore, for a fair comparison, we retrain their networks with the same training data and strategy as ours. + +# 4.2. Testing Datasets + +We evaluate all methods on three datasets: DyNeRF [34] $(1352\times 1014$ after $2\times$ downsampling), ENeRF-Outdoor [38] $(960\times 540,2\times$ downsampling), and D3DMV [40] $(640\times 360)$ . All three datasets provide multi-view sequences of dynamic actors in diverse static environments. We use the same set of $K$ closest views to test all methods. For testing, we use the Sear Steak and Flame Steak scenes from DyNeRF. We do not perform any fine-tuning on the test datasets. We observed sequences in the ENeRF dataset have incorrect synchronization, and inconsistent color calibration. To mitigate the impact of these effects we compute all metrics at half the rendered resolution $(480\times 270)$ on this dataset. + +# 4.3. Evaluation Metrics + +We evaluate the quality of novel views using the standard PSNR, SSIM [67], LPIPS [81], and L1 metrics. To evaluate temporal consistency, we use the spatio-temporal entropic difference (STED) [59], and a version of temporal change consistency (TCC) [78], adapted to color images: + +$$ +\mathrm {T C C} = \frac {1}{T - 1} \sum_ {t = 1} ^ {T - 1} \operatorname {S S I M} \left(\left| \mathcal {I} ^ {t} - \mathcal {I} ^ {t + 1} \right|, \left| I ^ {t} - I ^ {t + 1} \right|\right), \tag {8} +$$ + +![](images/9f022dde8bf8ed0fb40c8ad0e9ee690926235bfe2ff51fe977aec3ab2dc0dec2.jpg) +Figure 5. Qualitative comparison of view consistency. We compare view consistency using epipolar plane images (EPI). We generate the EPI for each method by rendering novel views along a horizontally-translating camera path (the $v$ dimension). For a fixed image row $y$ an EPI then represents a slice of the scene in the space-view dimensions $x - v$ , allowing a subset of points to be visualized across views as sloping lines. All baseline methods show sudden changes along EPI lines indicating view inconsistency. Our method generates smooth and continuous EPI lines, showing that it maintains view consistency as the camera translates. + +![](images/f7ab0a7df2d192be8048264758c886385be645d5781383498abf94ab49fb3fda.jpg) +Figure 6. Qualitative comparison of temporal consistency. We compare temporal consistency using a slice of the scene in the space-time dimensions $x - t$ . This is generated by rendering novel views at a fixed viewpoint while time moves forward. The baseline methods either suffer from noise in the temporal slices indicating temporal inconsistency (ENeRF, GPSG), or show blurred results due to low spatial reconstruction quality (IBRNet). Our method maintains temporal consistency while preserving high frequency spatial details. Please refer to the supplementary material for video results on all datasets. + +where $\mathcal{I}^{t,t + 1}$ and $I^{t,t + 1}$ are the rendered and ground truth images respectively. Finally, following Long et al. [42], we measure the standard deviation of the L1 error across all frames (SDT) to evaluate temporal consistency, and across all views (SDV) for view consistency. + +# 4.4. Results + +We evaluate view and temporal consistency in Table 1 and Figure 5. We use epipolar plane images (EPI), and temporal slices of a fixed camera to visualize change across time + +Table 2. Quantitative comparison of novel-view synthesis on the DyNeRF, ENeRF-Outdoor, and D3DMV datasets. We highlight the $50\%$ best metrics in blue, proportional to their percentile. Our method achieves the best metrics for the DyNeRF and D3DMV datasets. Please refer to the qualitative results on novel-view synthesis in Figure 7. + +
DyNeRF [34]ENeRF-Outdoor [38]D3DMV [40]
MethodPSNR↑SSIM↑LPIPS↓L1↓PSNR↑SSIM↑LPIPS↓L1↓PSNR↑SSIM↑LPIPS↓L1↓
FWD [6]16.970.6670.55425.7617.010.3950.69924.3919.800.5850.64019.39
IBRNet [65]22.490.8260.34711.8322.960.6630.22413.0620.710.7100.35811.98
GPSG [82]25.460.8660.3098.0023.100.6870.23110.9623.770.8840.1567.70
ENeRF [38]29.510.9270.1966.0625.790.7220.1679.8427.790.8790.1576.01
Ours31.170.9360.1915.0924.010.7030.15512.0232.580.9360.0983.60
+ +![](images/a4fd6ef5756c84f653fd1213c4da02f2c248194aa072be311d2fd8782d718ebb.jpg) +Ground Truth + +![](images/049969552561ae79bc4eb5f115d8044e0410db77c016e808e06f277fa060949c.jpg) +IBRNet [65] + +![](images/01ffe6fcc4fab53fe6eb5b570e1227555b62760cae1054fdfa9de510ce59c78b.jpg) +ENeRF [38] + +![](images/1eb8b488d8e6a9d9a94c044e7843bd9dce113ec813da522510d0c0f8407603e9.jpg) +GPSG [82] + +![](images/787a6a792b3d2b7542b90cf0ba6090567daf224d36c3618857d6589722a895e7.jpg) +Ours + +![](images/33f7d5ec5f90a12f66d69ec63a67b0016c07a562682fcf6161056a007e1a0105.jpg) + +![](images/398b85fd156923e18887c5789466d7aed366f3aa213dfc7e47cfede370eca53b.jpg) + +![](images/6377001da6c8e0ffdbec6d3b7072175184abe617a3aac5112164b08097e831fe.jpg) + +![](images/88840e0181cffebc174475dfdf7dcda0068f7bb231699fed03619a8fe1a2a78e.jpg) + +![](images/4c404b9fd59d82887a9011dd223a2c256c71c2ee1bd3f71841ee64c98f3f81fc.jpg) + +![](images/f0f2fb0c98085311630131ada72485cd2aabdf930b78b135964bb3afe1c7fc8b.jpg) +Figure 7. Qualitative comparison on the ENeRF-Outdoor [38], DyNeRF [34], and D3DMV [40] datasets. The baseline methods either generate blurry results (IBRNet, ENeRF), bleed foreground colors onto the background (ENeRF, GPSG), distort edges (GPSG), or fail to reconstruct distant background objects (IBRNet, ENeRF). Our method reconstructs fine details in the background while generating sharper results for the near-range objects such as the moving humans. + +![](images/2019112deae75895df5006e9218f8e90c42ac83c5c903af85b0d7d44c20d69d0.jpg) + +![](images/dac3e6309cdf16e311d158ef3deb579c65684d4319f9d06e18d53a5dfee922d4.jpg) + +![](images/0ed31bc90f7788815d65ab8c18aabfad087d80505831f3bfc7e1eacb8ae8a80b.jpg) + +![](images/b248e4b0f270534affe6add1f9807a794b6dc97c97884464ce331ca5d7631065.jpg) + +Table 3. Quantitative ablation study. We evaluate our method on three key contributions: using a network to blend forward-rendered input views, using TSDF depth to guide the blending network, and using difference masks for temporal filtering. No Blending directly renders all input-view Gaussians into the target view in a single pass [82]. Distance-based Blending uses the distance of the target view from each input to determine the blending weights [45]. + +
VariantPSNR↑LPIPS↓TCC↑STED↓
No Blending24.640.2640.743483.3
Distance-based Blending26.080.2110.858235.3
No TSDF Guidance31.160.1970.86995.42
No Temporal Filtering31.160.1950.86989.62
Ours31.170.1910.87268.76
+ +and space respectively. Our results are sharper than IBRNet, show less flickering at boundaries than ENeRF, and suffer no abrupt changes like GPSG. Please refer to the supplemental videos for additional results on dynamic scenes. + +A quantitative evaluation of the novel view rendering quality of all methods is presented in Table 2; qualitative results are shown in Figure 7. Our method reconstructs sharper edges, and finer details in both foreground and background. Even though the ENeRF-Outdoor dataset is challenging due to camera mis-synchronization, our method shows a marked improvement over the baselines, particularly at the edges of the actor and in disoccluded regions of the background. The latter are especially tough for ENeRF, which shows loss of detail at occlusion edges in all three datasets. + +# 4.5. Ablations + +We ablate the core contributions of our work in Table 3 to quantitatively evaluate their impact. These include: 1) A network to blend and inpaint the forward-rendered views, 2) the use of a TSDF to guide the blending network, and 3) temporally filtering the input-view depths using difference masks. To evaluate the effect of the TSDF depth, we retrain our network without the guidance depth $\mathcal{D}^t$ as input. We observe that our complete pipeline provides the best results, with the most significant gains in temporal consistency. + +Table 4 shows the computation time of each stage of our method on the DyNeRF dataset. We observe that even without TensorRT optimization, our total runtime $(\approx 100\mathrm{ms})$ is faster than the closest baseline GPSG, which runs in $143.4\mathrm{ms}$ (Figure 5). All runtimes exclude disk read time. + +Table 4. Computation time of each stage in DyNeRF dataset. + +
Forward-splattingTSDFBlendingBlending (w/o TensorRT)
10 ms6 ms23 ms65 ms
+ +![](images/a7394dc15ac8a7a17ceef74d605024c19caf8c5a8eab754bc99c256e891413e3.jpg) +Figure 8. Ablation study of the number of input views. Runtime increases roughly linearly with the number of input views $K$ . However, rendering quality saturates for $K \geqslant 4$ views. + +The choice to use a subset of $K$ cameras is motivated by efficiency, as each view adds to the TSDF, splatting, and blending time. We ablate the choice of $K$ in Figure 8. + +# 4.6. Limitations + +By using global geometry, our method promotes consistency in the rendered views. A limitation of this approach, however, is that it relies strongly on accurate geometry reconstruction. It fails, for instance, in specular regions where depth is usually bad (Figure 9). While the blending network still produces reasonable output for a single target in this case, the results suffer temporal and view consistency artifacts. Furthermore, our blending network requires well-synchronized and calibrated cameras for well-aligned forward projected input $\mathcal{I}_k^t$ . Errors in camera calibration can lead to blurring artifact. + +![](images/832222d6723d84681a7aa0207dc745099960a4d83b08b4a9ce692f92058bca71.jpg) +Figure 9. Limitations: Inaccurate TSDF depth (right) can lead to view inconsistency in novel views, seen as EPI discontinuities. + +![](images/aa096be9ab2384f778b971ac5e61c04e97edebae358380b5f0b429ca039270a9.jpg) + +# 5. Conclusion + +We present a novel method for consistent video synthesis in an online multi-view setting. This setting requires continuous and smoothly changing outputs in both the view and temporal domains, but it can easily suffer from inconsistency artifacts. To address these challenges, our approach first fuses temporally filtered depth maps into a global structure to acquire view-temporal depth in the novel view. Then, this global depth information is used to guide the blending of forward-projected RGB views. By using multi-view temporally consistent depth to mediate the output of the blending network, our method produces consistent novel views. We show that our method effectively reconstructs a variety of scenes while running faster than previous work. + +# References + +[1] Kara-Ali Aliev, Artem Sevastopolsky, Maria Kolos, Dmitry Ulyanov, and Victor Lempitsky. Neural point-based graphics. In ECCV, 2020. 2, 3 +[2] Benjamin Attal, Jia-Bin Huang, Christian Richardt, Michael Zollhoefer, Johannes Kopf, Matthew O'Toole, and Changil Kim. HyperReel: High-fidelity 6-DoF video with ray-conditioned sampling. In CVPR, 2023. 2 +[3] Jonathan T. Barron, Ben Mildenhall, Matthew Tancik, Peter Hedman, Ricardo Martin-Brualla, and Pratul P. Srinivasan. Mip-NeRF: A multiscale representation for anti-aliasing neural radiance fields. In ICCV, 2021. 2 +[4] Jonathan T. Barron, Ben Mildenhall, Dor Verbin, Pratul P. 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Sarma + +Massachusetts Institute of Technology, USA + +sesarma@mit.edu + +Vigneshwaran Subbaraju + +Institute of High Performance Computing A\*STAR, Singapore + +vsubbaraju@ihpc.a-star.edu.sg + +Archan Misra + +Singapore Management University, Singapore + +archanm@smu.edu.sg + +# Abstract + +3-Dimensional Embodied Reference Understanding (3D-ERU) combines a language description and an accompanying pointing gesture to identify the most relevant target object in a 3D scene. Although prior work has explored pure language-based 3D grounding, there has been limited exploration of 3D-ERU, which also incorporates human pointing gestures. To address this gap, we introduce a data augmentation framework - Imputer, and use it to curate a new benchmark dataset - ImputeRefer for 3D-ERU, by incorporating human pointing gestures into existing 3D scene datasets that only contain language instructions. We also propose Ges3ViG, a novel model for 3D-ERU that achieves $\sim 30\%$ improvement in accuracy as compared to other 3D-ERU models and $\sim 9\%$ compared to other purely language-based 3D grounding models. Our code and dataset are available at https://github.com/AtharvMane/Ges3ViG. + +# 1. Introduction + +Referring Expression Comprehension (REC) is a fundamental vision-language task that involves identifying a target object that is referred to by an instruction, as illustrated in Figure 1. Grounding such referring expressions in 3-dimensional space is a critical perceptual capability for robots and intelligent situated agents. Although several studies have explored grounding purely linguistic referring expressions in 3D scenes without accompanying pointing gestures [5, 37], pointing is an integral part of human communication and plays a vital role in situated and embodied + +![](images/b58cf8d89b26c94de8401f47791f27574544feac53e1237ec37e9a227df5cf2b.jpg) +Figure 1. 3D grounding of referring expressions with pointing. + +interactions. However, the problem of 3D Embodied Reference Understanding (3D-ERU) – which includes natural human pointing gestures along with natural language references for 3D visual grounding remains relatively underexplored. This task involves (a) determination of the human's position and the pointed direction in 3D space, and (b) identification of an object that best fits the verbal instruction and the pointed location. + +To obtain a large workable dataset for 3D-ERU, prior work such as ScanERU [25], explored an augmentation approach by inserting a human avatar into the 3D scenes found in a pre-existing 3D-REC dataset called ScanRefer [5], such that the avatar is pointing to the target object that is being referred by the language instruction. However, the following issues remain to be tackled in both data curation and model development for 3D-ERU: + +- Manual positioning of human avatar: To address the complexities of positioning the human avatar in available and appropriate vacant spaces within the 3D environment, ScanERU employed crowd-sourced human subjects to manually insert the avatar into the 3D scenes provided by ScanRefer. However, our inspection, $^{1}$ revealed + +that the human avatars are placed very close to the target object, thus making the language instruction completely redundant. This is problematic as the models developed using such a dataset will be biased towards learning the pointing gesture alone, disregarding the language references. The scalability of the manual placement approach is also questionable, and an automated method may be preferable for collecting large-scale data. + +- Unrealistic language descriptions: ScanERU retained the original language descriptions from ScanRefer even after incorporating pointing gestures. This is not realistic as prior work such as [34] has shown that the choice of words and vocabulary of the language instructions will be different when a pointing gesture is used (see Figure 1). +- Limited computational model: The baseline model provided by ScanERU assumes that the ground truth of the human's position in the scene is known and does not localize the human. However, localizing the human is an integral part of 3D-ERU, and hence, a holistic model for 3D-ERU must integrate human localization into its pipeline. We show that effective learning of human position improves the performance of 3D-ERU models. + +To address these issues, we propose a novel automated data augmentation approach along with a revamped instruction dataset for 3D-ERU. We then develop a new model that incorporates human localization into 3D grounding. The following are the main contributions of this work: + +- We introduce Imputer, an automated framework for augmenting existing 3D-REC datasets (e.g., ScanRefer) for 3D-ERU tasks by inserting human avatars into suitable spaces in the 3D scenes with precise control over their positioning, such that they point towards the target. +- We introduce the ImputeRefer dataset for the 3D-ERU task, which requires more complex reasoning to identify target objects than ScanERU due to a larger average distance between the human avatar and the target object. Also, the language instructions in ImputeRefer are regenerated by a VLM that is prompted by providing the context that there is a human pointing at the target. +- We develop Ges3ViG, a unified model for 3D-ERU that performs both human localization and reference understanding. It implements a new combined loss function to simultaneously learn human-localization and instruction grounding. It also uses a novel multi-stage fusion mechanism to effectively integrate the pointing gesture and the language text to achieve a significant $\sim 29.46\%$ increase in grounding accuracy compared to ScanERU. + +Overall, we believe that ImputeRefer and Ges3ViG help to significantly advance work on 3D-ERU. + +# 2. Related Work + +Referring Expression Comprehension (REC) on 2D images has been well studied, starting from ReferIt [23], + +and several other works that followed [26, 31, 36]. Recently, transformer-based architectures [12] and Vision-Language Models (VLMs) [32] have emerged as promising approaches for 2D-REC. The incorporation of pointing gestures into 2D-REC has also been studied by works such as M2Gestic [33], YouRefIt [8] and COSM2IC [34]. However, these 2D RGB image-based approaches are not directly applicable to 3D point cloud data, due to differences in data representation and the significant increase in the search space. For 3D-REC, pointcloud-based datasets such as ScanRefer [5] and ReferIt3D [1] were developed, with scenes obtained from the ScanNet dataset [11]. Among them, ScanRefer stands out as a large-scale 3D-REC dataset featuring human-annotated language descriptions, comprising 46,055 descriptions of 11,046 different target objects. Existing work on 3D-REC encompasses graph-based approaches [13, 20], neuro-symbolic approaches [19], techniques using multi-view images and 2D semantics [2, 21, 35], and unified models that address both dense captioning and 3D-REC [3, 6, 9]. M3DRefCLIP [37], currently, the state-of-the-art in 3D-REC, introduces a CLIP model-based approach for extracting visual features [30]. However, these works do not consider pointing gestures, which humans naturally use when referring to objects in a scene. + +The problem of 3D-ERU, which considers the incorporation of pointing gestures for comprehending referring expressions in a 3D scene remains under-explored compared to 3D-REC. ScanERU [25] proposed inserting a human avatar into an existing 3D-REC dataset. To date, this stands as the sole dataset for 3D-ERU. However, ScanERU's approach for dataset creation suffers from drawbacks such as (a) laborious manual placement of human avatar, (b) positioning the avatar too close to the target, (c) language expressions that are generated without consideration of the pointing gesture, and (d) implicitly assuming that the 3D ground truth location of the human avatar is externally available. These drawbacks hinder both the scalability of the dataset and the performance of the models. + +In contrast to ScanERU, our work adopts an automated approach to insert the human avatar in the 3D scenes. Our proposed dataset consists of more challenging and realistic instructions as the human avatar is placed further away from the target (leading to larger pointing errors) and the language instructions are re-generated using a VLM that also considers the human pointing at the target object. Furthermore, our model includes human localization into the pipeline for 3D-ERU. + +# 3. Imputer Framework + +We next describe our augmentation framework - Imputer-to automatically generate a 3D-ERU dataset. Similar to ScanERU [25], we use the 3D scenes obtained from ScanNetV2 [11] and insert a human avatar into it. Imputer con + +sists of two parts: (a) Pointing gesture augmentation, where we propose a simple automated approach to determine the possible locations to 'impute' the pointing human avatar and (b) Language description generation, where we employ a Generative model—Gemini [15], to augment the existing verbal description to incorporate the pointing gesture. We next describe each of these components. + +# 3.1. Pointing Gesture Augmentation with Imputer + +Figure 2 illustrates the intermediate steps involved in the pointing gesture augmentation with Imputer framework. Before we delve into the computational process involved in inserting a human avatar, we note the following assumptions made by Imputer about the 3D scene: (a) all the 3D scenes are oriented such that the floor's normal is aligned with the Z-axis, (b) the floor is level (there are no artifacts like stairs) for a major part of the scene, and (c) the human avatar mesh is pre-aligned with the 'floor' of the scene. If the mesh is not pre-oriented correctly, one can use software such as CloudCompare [16] to adjust it. This process only needs to be performed once per avatar, as the same mesh can be reused across all scenes. + +Acquiring realistic human avatars: Augmenting the scene with a pointing gesture requires generating a human point cloud that can be augmented into the 3D scene such that the generated human point cloud performs a pointing gesture towards the target object. We begin this step by extracting the base human meshes for male and female subjects separately from the SMPL-X dataset [27]. Next, we utilize the Blender package [10] to adjust various model parameters, such as joint poses, height, weight, and gender, to introduce diversity across the generated human point clouds. To add color textures, we use samples from SMPLite-X [4], creating a total of 12 textured human models, evenly distributed between genders with six models each (Detailed figures provided in Supplementary). + +The workflow of the Imputer framework is as follows. We first voxelize the scene and determine its boundaries. Then, we search for a set of vacant spaces for placing the human avatar so that there is a direct line of sight available for pointing at the target. The avatar is then placed in a suitable vacant space. Finally, a generative model is prompted to generate a language instruction for referring to the target object. These steps are explained in detail below. + +Voxelization of the scene: We voxelize the scene to discretize the search space, which allows for efficient querying of point occupancy. Checking occupancy in a voxel grid is substantially faster compared to meshes or point clouds, and voxel grids allow interaction with 'empty space'. These empty spaces are crucial, as they define the potential locations where the human avatar can be placed. We create voxel grid $V_{1}(\mathbb{N}^{3}\to \{0,1\})$ , which represents the origi + +![](images/beb50e6c5ecd048aad8c88feeb95fb9230c6eefa1d9aac4de37c2dedc94ef1c2.jpg) +Figure 2. Imputer pointing gesture generation + +nal scene with the target object, and voxel grid $V_{2}(\mathbb{N}^{3}\to \{0,1\})$ which represents the scene with the target object removed. Each voxel $V_{i}(x,y,z)$ in $V_{1}$ and $V_{2}$ is assigned a value of '1' if it is occupied by an object or '0' if it is unoccupied. We also voxelized the human avatar mesh separately to get a 3D grid (similar dimension as $V_{1}$ and $V_{2}$ ) given by $H(\mathbb{N}^3\to \{0,1\})$ . A voxel $H(x,y,z)$ is assigned a value of '1' only if it is occupied by the human or to '0' otherwise. The height of the human in the voxel grid is denoted by $h_{hv}$ . + +Determining scene boundaries: In this step, we calculate the scene bounds to ensure that the avatar is placed within the scene. This is done by identifying the the largest contour on the planar voxel grid created by projecting the voxel grid $V_{1}$ onto the $XY$ -plane. We then create a binary voxel grid $B(\mathbb{N}^3 \to 1,0)$ , with the same dimensions as $V_{1}$ . A voxel $B(x,y,z)$ is assigned a value of '1' if its $x$ and $y$ coordinates lie within the contour boundary, or '0' otherwise. + +Finding regions for plausible occupancy: Next, we identify all regions within the scene that can accommodate a human mesh. To ensure that the feet of the human avatar is placed appropriately, i.e., just touching the floor of the scene, we must determine the appropriate co-ordinates of the human feet $(x_{foot}, y_{foot}, z_{foot})$ and a plausible representative $z$ -coordinate for the floor level within the voxel grid. We define the 'foot' as the lowest point in the human avatar mesh after converting it into a voxel scale. Since there are multiple voxels corresponding to 'floor', we adopt the following approach to estimate the vertical displacement of the floor (denoted as $h_{flr}$ ) with respect to the origin of the scene. The 3D scenes in the ScanRefer dataset originate from ScanNetV2 [11]. Using the segmentation ground truth from ScanNetV2, we can extract a list of vertices labeled as 'floor'. We calculate $h_{flr}$ by taking the minimum of the following two values: (1) the average height of all floor vertices plus an offset $C_1 = 0.04\mathrm{m}$ , and (2) the $85^{\text{th}}$ percentile of the height distribution of 'floor' points. Here, $C_1$ and $85^{\text{th}}$ percentile are chosen empirically. Next, we convert this estimated height to a voxel scale denoted as $h_{fv}$ . The final floor height estimated is given by $\hat{h}_{fv} = \max(C_2, h_{fv})$ , + +where $C_2 = 4$ . $C_2$ is chosen to account for potential artifacts, such as floor misalignment, that could cause it to extend into voxels at heights above zero. We allow for a small tolerance by permitting the human model to be positioned up to 4 voxels ( $\sim 10$ cm in world coordinates) above the floor. In practice, this offset is generally less than 5 cm. + +We then adopt a sliding volume approach to identify sufficiently large vacant spaces that can fit the human avatar. The size of the sliding volume is chosen to be equal to the size of the human avatar voxel grid. We then use the human voxel grid as a mask to check if there is sufficient space to fit the human avatar at a given point $(i,j)$ on the floor. We consider the human avatar volume $H$ comprising of voxels whose co-ordinates range from $(i,j,\hat{h}_{fv})$ to $(i + x_{max},j + y_{max},\hat{h}_{fv} + h_{hv})$ . We see that the entire volume falls into a clear space of the scene if it satisfies, + +$$ +\begin{array}{l} \sum_ {x = 0} ^ {x _ {m a x}} \sum_ {y = 0} ^ {y _ {m a x}} \sum_ {z = 0} ^ {h _ {h v}} H (x, y, z) \\ = \sum_ {x = 0} ^ {x _ {\max }} \sum_ {y = 0} ^ {y _ {\max }} \sum_ {z = 0} ^ {h _ {h v}} H (x, y, z) \times V _ {1} (i + x, j + y, \hat {h} _ {f v} + z) \tag {1} \\ \end{array} +$$ + +In practice, we observed that there could be some cases of improper human positioning even after the above condition is satisfied (especially after rotation of the avatar). To avoid such scenarios, we increase the border widths by $25\mathrm{cm}$ (10 voxels), which is approximately half the average shoulder-to-shoulder width of a human. We store the co-ordinates $(i,j,\hat{h}_{fv} + h_{hv})$ in the set $O_{no\_collide}$ if all the voxels in the volume placed at $(i,j)$ on the floor satisfy Equation 1 after accounting for the additional allowance. + +Grid visibility search: In this step, we aim to identify all the voxels that are accessible via a direct line-of-sight (a spatially contiguous set of empty voxels) from the center of the object. These voxels would serve as plausible locations from where the human avatar could point at the object. We define the center of the 3D bounding box of the target object as the origin of the line of sight. We use the voxel grid $V_{2}$ , where the target object is removed for visibility search. This is done so that the target object's own boundary surface does not interfere with line-of-sight calculation. + +Prior studies (e.g., [14]) have used a path-counting algorithm in 2D space to calculate visibility scores for grid cells. We extend this approach to 3D environments to compute the regions with line-of-sight. Given $V_{2}$ , we compute a visibility score grid, $S(\mathbb{N}^3\to \mathbb{R})$ , where $S$ is defined as: + +$$ +\begin{array}{l} S (x, y, z) = \left(\frac {x \times S (x - 1 , y , z)}{x + y + z} + \frac {y \times S (x , y - 1 , z)}{x + y + z} \right. \\ + \frac {z \times S (x , y , z - 1)}{x + y + z}) \times V _ {2} (x, y, z) \tag {2} \\ \end{array} +$$ + +![](images/465bf84ab520c01b2e001dc4a487b252a382406b4aa2d8b3029318963fbb9c8e.jpg) +Figure 3. ImputeRefer with 'unique' and 'multiple' object scenes. The imputed human is placed at different distances from the target. + +We then obtain $S'(\mathbb{N}^3 \to \{1,0\})$ a thresholded version of $S$ , where $S'(x,y,z)$ is assigned a value of '1' if its visibility score is more than 0.33, or set to '0' otherwise. The value 0.33 was chosen using a rough rule of thumb - $\frac{1}{\text{No.ofdimensions}}$ . In [14], a threshold of 0.5 was used to calculate visibility in 2D grids. We define the set of all the coordinates where $S' = 1$ , as the region of visibility, a good approximation for all the visible regions. + +Final positioning of the human avatar: A correctly imputed human avatar, with its feet at $(x,y,z)$ and pointing at the referred object, must satisfy the following conditions: (a) the human avatar is placed within the bounds of the scene, i.e., $B(x,y,z) = 1$ , (b) the avatar does not occupy any already-occupied space in the scene, i.e., if $(x,y,z) \in O_{no_collide}$ , and (c) there is a direct unblocked line between the human avatar's gesture and the object of interest in the scene, i.e., if $S'(x,y,z) = 1$ . After identifying all such feasible points, we randomly choose 5 of these points to create diverse, feasible positions of the human avatar. For each of these points, we then use the gesturing shoulder of the human avatar as a pivot of rotation to point towards the object of interest. In natural scenarios, a human may have some directional error while pointing towards a target object. To simulate this, we introduce a rotational jitter sampled uniformly within a range of $N_{jitter} = 9^{\circ}$ to the correct pointing direction. We then calculate simple Euclidean transforms to move the human to the desired coordinate and then rotate the human in place. To choose from appropriately pointing meshes, we also store the angle $\angle A_{pointing}$ between the X-Y plane and the line joining the shoulder point to the desired pointing direction. This completes the process of augmenting the 3D scene with an appropriately-positioned human avatar as shown in Figure 2, where the avatar (green box) points towards the target object (red box). + +# 3.2. Referring Expression (Re) Generation: + +We use Gemini [15] to augment the referring expression. The input prompt to Gemini for generating the referring expression included a brief paragraph describing the scenario: a person pointing at the target object needs to generate an expression that uniquely identifies that object (details pro + +![](images/6e6f9c7d10c853c0f6fb773f41bb6d604a6e5df3368a6a971fa3f0ae102eb41e.jpg) +Figure 4. Proposed architecture of Ges3ViG + +vided in supplementary materials). To ensure diversity in the generated expressions, for each data point in the ScanRefer [5] dataset, we prompt Gemini to generate 3 different referring expressions and choose one of them randomly to generate our new dataset ImputeRefer for 3D-ERU, some samples of which are shown in Figure 3. Next, we describe the development of our Ges3ViG model using this dataset. + +# 4. Ges3ViG: Gesture-enhanced 3D Visual Grounding + +We now present Ges3ViG, a new gesture-enhanced, unified feed-forward, 3D visual grounding DNN model that integrates human localization, language understanding, and gestural reasoning to identify the 3D bounding box of the target object. To effectively combine gestural and linguistic cues, we utilize an innovative multi-stage fusion strategy that employs both early and late fusion within the same DNN. We now highlight the key components of the Ges3ViG model, visually illustrated in Figure 4. + +# 4.1. Vision Module + +We first encode the point cloud features using a PointGroup detector [22]. PointGroup, being a standard object detector for 3D point clouds $P \in \mathbb{R}^{N \times C}$ , returns both the visual features and all the objects in the scene. Here, $N$ is the number of points in the point cloud and $C$ is the number of channels per point, including the 3D coordinate, the per-point surface normal vector and the color of the point. + +We use the following outputs from the PointGroup Detector for further processing: (1) Semantic Features $(F_{s}\in$ $\mathbb{R}^{N\times 32})$ , (2) Semantic Scores $(S_{s}\in \mathbb{R}^{N\times N_{c}})$ , where $N_{c}$ is the number of classes in the dataset, (3) Proposal Features $(F_{p}^{3D}\in \mathbb{R}^{M\times 32})$ , where $M$ is the number of proposals, and (4) Proposal Scores $(S_{p}\in \mathbb{R}^{M})$ : These are essentially the instance/objectness scores for each proposal. + +We use $F_{s}$ and $S_{s}$ for Gesture Inference (details in Section 4.3), while $S_{p}$ is used to find proposals and $F_{p}^{3D}$ is passed ahead to be used as 3D visual features. For each proposal $P$ , we render the object from 3 different views as images (similar to M3DRef-CLIP [37]). The images are passed into a CLIP [29] image encoder that generates 2D features $(F_{p}^{2D} \in \mathbb{R}^{M \times 128})$ for each proposal. $F_{p}^{3D}$ and $F_{p}^{2D}$ are concatenated into joint visual features and passed through a 1D convolution to obtain $F_{v} \in \mathbb{R}^{M \times 128}$ . + +# 4.2. Language Feature Encoder + +For language features, we use CLIP to get sentence-level and token-level feature embeddings. We define our sentence features as $F_{l,s} \in \mathbb{R}^{128}$ and word features as $F_{l,t} \in \mathbb{R}^{N_{token} \times 128}$ , for an $N_{token}$ token long sequence. + +# 4.3. Gesture Feature Encoder + +To enable gestural reasoning for human segments identified from region proposals generated by the PointGroup detector, this module uses the following components. + +Joint Feature Extractor: This component computes the joint-coordinates of the pointing human and extracts joint-based features. The semantic features $(F_{s})$ computed in the vision module are used as input to this component. For a human segment $P_{hum} \subset P$ , obtained from the semantic segmentation predictions of the Vision Module and comprising $N_{hum}$ points, we extract a corresponding subset of semantic features, $F_{s,hum} \subset F_{s}$ , consisting of $N_{hum}$ vectors. Given an anticipated number of human joints, $N_{j} \in \mathbb{N}$ , the semantic feature subset $F_{s,hum}$ is processed through a point-wise MLP inspired by PointNet [28], resulting in an output $W_{hum} \in \mathbb{R}^{N_{hum} \times N_{j}}$ . Inspired from Point2Skeleton [24], the joint coordinates $J \in \mathbb{R}^{N_{j} \times 3}$ are then computed from $W_{hum}$ as $J = \text{Softmax}(W_{hum}^T) \times P_{hum}$ and the initial joint-based features $F_{j,\text{init}} \in \mathbb{R}^{N_{j},32}$ are obtained as + +$$ +F _ {j, i n i t} = \operatorname {S o f t m a x} \left(W _ {h u m} ^ {T}\right) \times F _ {s, h u m} \tag {3} +$$ + +Joint-Wise MLP: We concatenate the location of each joint with its corresponding feature to form $F_{j,init}$ . This concatenated feature is processed by Joint-wise MLP, which consists of $N_{layers}$ layers. In this configuration, the MLP processes each feature vector independently for each joint. Let $M_{i}$ represent the $i$ -th layer of the MLP, and let $P_{j,i}$ denote its output for the $j^{\text{th}}$ joint. This module's output is: + +$$ +\begin{array}{l} F _ {j, f i n a l} = P _ {j, N _ {l a y e r s}}; w h e r e P _ {j, i} = M _ {i} \left(P _ {j, i - 1}\right) \\ a n d P _ {j, 1} = M _ {1} \left(F _ {j, i n i t}\right) \tag {4} \\ \end{array} +$$ + +$$ +F _ {j, a g g r e g a t e} = \text {c o n c a t e n a t e} _ {i = 0} ^ {i = N _ {\text {l a y e r s}}} \sum_ {j = 0} ^ {N _ {j}} P _ {j, i} \tag {5} +$$ + +Here $N_{j}$ is the number of joints specified in SMPL. + +We then adopt a multi-stage fusion approach that combines early and late fusion techniques to effectively fuse the extracted gesture features with language features. We first perform an early fusion of the 'reference' modalities by concatenating gesture and language instruction features. The concatenated features are fed into the 'reference-scene' fusion module, which fuses them with the 3D scene/object features obtained from the vision module to produce prediction scores for the potential target objects. Finally, a late weighted fusion biases the scores towards objects that are within a certain angular radius of the pointing hand. + +# 4.4. Early Fusion of Referential Modalities + +In the proposed early fusion module, we utilize $F_{j,\text{final}} \in \mathbb{R}^{N_j \times 128}$ , which is passed through two self-attention layers, after which they are concatenated with $F_{l,t}$ to form $F_{\text{clue}} \in \mathbb{R}^{(N_{\text{token}} + N_j) \times 128}$ . Since both gesture and language modalities provide information about the same target object, we treat them similarly and perform a simple concatenation-based fusion for the two modalities. + +# 4.5. Fusion of Referential and Scene Features + +We employ the same transformer-based approach for the 'reference-scene' fusion module as used in M3DRef-CLIP [37] to integrate object features with the referential embeddings $F_{\text{clue}}$ , generating confidence scores ( $S_{\text{conf}} \in \mathbb{R}^{M}$ ) for each proposal. This module consists of two self-attention and two cross-attention blocks, where the object features sequentially pass through the self-attention and cross-attention blocks. In the cross-attention blocks, $F_{\text{clue}}$ is used as the key-value pairs. + +# 4.6. Late Fusion of Gesture + +The reference-scene fusion module's output provides confidence scores for each object proposal, allowing to identify the target object based on the highest score. To further refine this, we introduce an additional late fusion approach that explicitly biases confidence scores to favor objects that align with the pointed direction. This corrects some errors from the previous stages that could occur due to the presence of multiple distractor objects, especially in cases where the language instruction was given more importance. Specifically, we compute a pointing biasing score, $S_{b} \in \mathbb{R}^{M}$ , and add it to $S_{conf}$ to guide predictions toward points that are angularly closer to the pointing direction. To achieve this, we first extract the shoulder and fingertip points represented by $\vec{v_{1}} \in \mathbb{R}^{3}$ and $\vec{v_{2}} \in \mathbb{R}^{3}$ , respectively. The center coordinates of a predicted bounding box are represented by $\vec{v_{3}} \in \mathbb{R}^{3}$ . The pointer bias score $S_{b}$ is defined as follows: + +$$ +S _ {b} = \frac {\left(\vec {v _ {2}} - \vec {v _ {1}}\right) \cdot \left(\vec {v _ {3}} - \vec {v _ {1}}\right)}{| | \left(\left(\vec {v _ {2}} - \vec {v _ {1}}\right)\right) | | \cdot | | \left(\left(\vec {v _ {3}} - \vec {v _ {1}}\right)\right) | |} \tag {6} +$$ + +We calculate $S_{b,left} \in \mathbb{R}^M$ and $S_{b,right} \in \mathbb{R}^M$ using the equation 6 for both left and right hand respectively. + +Intuitively, humans may use either the left or right hand for pointing. To classify the pointing hand used, we employ a classification head that takes $F_{j,aggregate}$ as input to learn $W_{lr_{a}gg} \in \mathbb{R}^2$ as follows. + +$$ +W _ {l r \_ a g g} = S o f t m a x (M L P 1 (F _ {j, a g g r e g a t e})) \tag {7} +$$ + +With the calculated $W_{lr\_agg}$ , we compute the final biasing score $S_{b,final}$ as follows. + +$$ +S _ {b, f i n a l} = W _ {l r - a g g} ^ {0} \times S _ {b, l e f t} + W _ {l r - a g g} ^ {1} \times S _ {b, r i g h t} \tag {8} +$$ + +With $S_{b,final}$ from the pointing biasing score and $S_{conf}$ from the fusion module, we have two sets of object scores. To obtain the final object scores, we use an additional probabilistic head, denoted as $W_{score\_agg} \in \mathbb{R}^2$ , which adaptively aggregates scores from the two branches as follows: $W_{score\_agg} = SoftMax(MLP2(F_{j,aggregate}))$ . The final object scores are obtained using the following equation, and the target object is identified by the object proposal with the highest $S_{conf,final}$ . + +$$ +S _ {\text {c o n f , f i n a l}} = W _ {\text {s c o r e - a g g}} ^ {0} \times S _ {\text {c o n f}} + W _ {\text {s c o r e - a g g}} ^ {1} \times S _ {b, \text {f i n a l}} \tag {9} +$$ + +# 4.7. Loss Function: + +Our proposed loss function comprises of the following: + +# Object Detection Losses: + +1. Cross-entropy loss for supervising per-point semantic class prediction called the Semantic Loss, $L_{semantic}$ . +2. L1 loss for supervising per-point offset vector towards object centers (useful for instance segmentation), called the Offset Norm Loss, $L_{offset\_norm}$ . +3. A directional loss formed as a mean of minus cosine similarities to constrain the direction of per-point offset vectors called the Offset Direction Loss, $L_{offset\_dir}$ . +4. A binary cross-entropy loss for supervising per-point objectness confidence score called the Score Loss, $L_{score}$ . + +# Reference Understanding Losses: + +5. Reference Loss, $L_{ref}$ , is a multi-class cross-entropy loss to classify object referenced by the referring expressions. +6. A symmetric contrastive loss, $L_{\text{contrastive}}$ between sentence features and the visual features to aid training. + +# Human Localization Losses: + +7. L2 loss between the predicted and ground truth human joint locations. +8. A classification loss $L_{lr}$ over $W_{lr\_agg}$ to classify the gesture as left-handed or right-handed. + +# 4.8. Training Details: + +We utilize an iterative training approach where we first train the PointGroup detector and gesture feature encoder for 20 epochs with a learning rate of 0.00005 with cosine annealing, using the Adam optimizer. At this step, loss term + +$L_{semantic}$ , $L_{offset\_norm}$ , $L_{offset\_dir}$ , $L_{score}$ , $L_{hum}$ and $L_{lr}$ are enabled for optimization. Subsequently, we freeze the PointGroup detector and the gesture feature encoder and only enable the fusion module with the loss terms $L_{ref}$ and $L_{contrastive}$ enabled for 20 epochs. This step trains the comprehension module to comprehend verbal instruction. + +# 5. Results + +We use our new ImputeRefer dataset, to evaluate the performance of various models for the 3D-ERU task. ImputeRefer includes 707 point-cloud scenes sourced from the original ScanNetv2 dataset, augmented with human pointing gestures and modified referring expressions as described in Sections 3.1 and 3.2. Overall, our dataset encompasses 35,581 samples, with 9,391 designated as the test dataset. Similar to previous 3D grounding research, we adopt IoU@0.25 and IoU@0.5 as the evaluation metrics. IoU@0.25 and IoU@0.5 deem a prediction as correct if the Intersection over Union between the ground truth and predicted 3D bounding boxes $\geq 0.25$ and $\geq 0.5$ , respectively. + +# 5.1. Performance of Ges3ViG for 3D-ERU + +Table 1 presents a comparison of the accuracy of Ges3ViG against current state-of-the-art models for 3D visual grounding, both with and without gesture support. Notably, ScanERU is the only existing model that incorporates gesture-enhanced 3D visual grounding. From the results, it is evident that Ges3ViG surpasses ScanERU significantly, achieving a $29.87\%$ higher overall IoU@0.5 accuracy. In the presence of 'multiple' distractors, Ges3ViG demonstrates even more pronounced improvements of $32.71\%$ in IoU@0.5 over ScanERU. + +Ges3ViG achieves significant performance improvements over existing standard 3D visual grounding models that do not support pointing gestures. It surpasses M3DRefCLIP, the current state-of-the-art in 3D visual grounding, by $10.88\%$ , $8.50\%$ , and $8.93\%$ for 'unique', 'multiple', and 'overall' categories respectively. These cumulative performance gains across both standard 3D visual grounding and gesture-enhanced models highlight the effectiveness of Ges3ViG in integrating both gestural and linguistic reasoning within a unified architecture. + +# 5.2. Evaluating Imputer Augmentation for 3D-ERU + +We evaluate the impact of Imputer augmentation on Gesture-enhanced 3D visual grounding in Table 2. While all results here use the Ges3ViG model, the first row (ScanRefer) simply integrates the human pointing gestures into the scene while retaining the original pointing-unaware ScanRefer verbal instructions. We find that a ScanRefer instruction contains a substantially higher average word count per language description (19.18 words) compared to ImputeRefer (10.52 words), indicating that ScanRefer likely has + +Table 1. Performance of Ges3ViG Vs baselines on ImputeRefer + +
Modeluniquemultipleoverall
IoU @0.25IoU @0.5IoU @0.25IoU @0.5IoU @0.25IoU @0.5
without Gestures:
3DVG-Transformer [38]71.5650.6631.3521.5439.1727.20
HAM [7]67.1048.1325.4216.0433.5122.27
3DJCG [3]75.9359.1940.3430..6147.2436.16
RefMask-3D [18]72.4564.9525.4422.2434.5730.54
M3DRefCLIP [37]77.3260.1562.6247.2765.5349.78
with Gestures:
ScanERU [25]71.652.7931.9123.0639.5428.84
Ges3ViG84.6071.0367.5755.7770.8558.71
+ +Table 2. Effect of re-generated instructions in ImputeRefer + +
Text Inst. SourceAverage No. of wordsIoU@0.5 on Ges3ViG
uniquemultipleoverall
From ScanRefer19.1871.7756.7559.69
Generated10.5271.0355.7758.71
+ +Table 3. Ablation studies for Ges3ViG in ImputeRefer dataset + +
Modeluniquemultipleoverall
IoU @0.25IoU @0.5IoU @0.25IoU @0.5IoU @0.25IoU @0.5
Ges3ViG w/o Gestures69.2648.8452.5837.3255.7939.54
Ges3ViG noHumanLoss68.7648.5758.7542.3160.6843.51
Ges3ViG noEF_onlyLF69.4349.2854.8139.0257.6241.00
Ges3ViG onlyEF.noLF83.7170.0966.4754.9269.9358.05
Ges3ViG random_LF84.070.666.154.669.657.7
Ges3ViG onlyGest15.2911.8112.469.8013.010.18
Ges3ViG ConstantLang51.0543.8744.8936.7846.0838.15
Ges3ViG84.6071.0367.5755.7770.8558.71
+ +many redundant words. However, using the ScanRefer text instructions only results in a slightly better overall IoU@0.5 (59.69%) than using the referring expressions in ImputeRefer (58.71%), despite the detailed verbal description. In practice, however, humans generally use short verbal descriptions when using a pointing gesture, justifying our cur- ration of pointing-augmented ImputeRefer dataset. Furthermore, compared to the average human-to-target distance of $\sim 1.24$ meters in the shared subset of ScanERU instructions that we obtained, ImputeRefer has an average distance of $\sim 2.31$ meters. This approx. $2\times$ increase in distance inc- creases the complexity of gestural reasoning needed. + +# 5.3. Ablation Studies + +Table 3 summarizes the results of an ablation study to evaluate the effectiveness of early fusion, late fusion and human localization loss. We consider the following variants: + +- Ges3ViG w/o Gestures Ges3ViG without any gestural reasoning and only relying on language-based reasoning. +- Ges3ViG _onlyEF_noLF integrates the gesture information only once at the early fusion and disables the late fusion of gesture information by assigning a weight of 0 to the gesture branch in late fusion. +- Ges3ViG $\mathbf{{noEF}}$ _onlyLF integrates the gesture information only at the late weighted fusion stage and skips the early fusion block. To simulate this variant, we re-train this + +variant from scratch by directly feeding the language features to the fusion module (by-passing early fusion). + +- Ges3ViG_random_LF uses the full Ges3ViG pipeline but with random weights in the late fusion. +- Ges3ViG _onlyGest_ relies solely on the gesture and ignores all language information by assigning a full bias weight of 1 to the gesture branch in weighted late fusion. +- Ges3ViG noHumanLoss does not include the human localization loss component in the loss calculation. This network is also obtained by re-training from scratch. +- Ges3ViG ConstantLang All language references set to "This object", forcing the model to heavily rely on pointing. + +From Table 3, we observe that early fusion is more effective than late fusion for fusing the referential modalities as Ges3ViG _onlyEF_noLF provides significantly high performance than Ges3ViG _noEF_onlyLF. But the performance of Ges3ViG _onlyEF_noLF is still slightly lower than Ges3ViG. The performance of Ges3ViG _random LF is even lower than Ges3ViG _noEF_onlyLF, showing that the weighted late fusion is meaningful as it provides a small boost in accuracy as compared to early fusion. We further note that ignoring the human localization loss causes a significant difference of about $15\%$ in IoU@0.5 for Ges3ViG _noHumanLoss when compared to Ges3ViG. This underscores the importance of learning to localize the human accurately. Ges3ViG stands out as the first unified model that performs human localisation and reference understanding. Ges3ViG _onlyGest variant that relies solely on gestural scores achieves significantly lower IoU@0.5 of $10.18\%$ compared to Ges3ViG $(58.71\%)$ . Similarly, Ges3ViG _ConstantLang which relies heavily on pointing with the same language reference used across the dataset achieves significantly lower IoU@0.5 of $38.15\%$ . These findings are supported by prior studies [33, 34] that showed that language references are important for reference understanding when the target object is further away from the human, and in contrast to ScanERU, where the pointing was done from a much closer distance. This result also shows that Gemini's language instructions in ImputeRefer are meaningful and useful. + +Figure 5 summarizes the effect of distance between the human and the target object on the accuracy of Ges3ViG model variants and baselines. For this analysis, we divided the test set of ImputeRefer into the following four distance ranges, using Hall's interpersonal distance classification [17]—Intimate ( $x < 0.46m$ ), Personal ( $0.46m \leq x < 1.22m$ ), Social ( $1.22m \leq x < 3.70m$ ), and Public ( $x \geq 3.70m$ ). The test set of ImputeRefer contained 0 samples for the Intimate distance range, 1391 for Personal, 6909 for Social, and 1097 for Public distance ranges. Using this division, we plotted the variation in IoU@0.25 and IoU@0.5 across the distances in Figure 5. Across all models with gestural reasoning, we consistently observed a decline in accuracy metrics as distance increased, indicating + +![](images/56861fac9972770527b014d189c5a2397cd7dcd582702af5925e921fb532b32b.jpg) +Figure 5. Accuracy at different distance ranges for 3D-ERU + +that 3D-ERU becomes progressively more challenging as the human-to-object distance grows. We also find that the drop in IoU@0.5 is more pronounced for larger distances. In contrast, M3DRefCLIP, a model without gestural reasoning, does not exhibit a decreasing pattern of accuracy as distance increases. To ensure that gesture information is completely excluded from this study on M3DRefCLIP, we removed the human avatar from the scene. On the other hand, Ges3ViG ConstantLang, a model completely relying on pointing gestures, exhibits a clear decreasing pattern of accuracy with increasing human-to-object distance. + +# 6. Conclusion + +We have demonstrated the design and performance of an enhanced model for 3D-ERU tasks, where humans refer to target objects via both gesture and verbal cues. We first introduced the Imputer framework to automatically augment existing 3D-REC datasets with pointing gesture cues and used it to create a challenging benchmark dataset for 3D-ERU, named ImputeRefer. We then introduced the novel Ges3ViG model that jointly (a) localizes the human in the 3D scene, (b) comprehends the pointing gesture, and (c) fuses language and gestural cues to accurately identify the 3D location of the target object. Ges3ViG and ImputeRefer establish a new benchmark for the 3D-ERU task, by achieving $29.5\%$ higher accuracy compared to prior work. + +# 7. Acknowledgments + +This work was supported in part by: 1) National Research Foundation, Prime Minister's Office, Singapore under its Campus for Research Excellence and Technological Enterprise (CREATE) program. The Mens, Manus, and Machina (M3S) is an interdisciplinary research group (IRG) of the Singapore-MIT Alliance for Research and Technology (SMART) centre; 2) BITS Pilani's Grant No. GOA/ACG/2021-2022/Nov/05; 3) Science & Engineering Research Board's SERB-SURE project number SUR/2022/002735; 4) Agency for Science, Technology and Research, Singapore under Grant #A18A2b0046. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not reflect the views of the funding organizations. + +# References + +[1] Panos Achlioptas, Ahmed Abdelreehem, Fei Xia, Mohamed Elhoseiny, and Leonidas Guibas. Referit3d: Neural listeners for fine-grained 3d object identification in real-world scenes. 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GigaHands is a massive dataset of human bimanual activities with paired text annotations. Each column above shows an activity sequence from the dataset. The dataset covers diverse 3D hand activities, including hand-object interactions (blue) across object scales, gestures (orange), and self-interactions (red). Each clip is paired with descriptive text and 51 camera views, enabling radiance field reconstruction. The bottom row show other annotations in the dataset including hand shape, object shape and pose (left half images). The right half images show novel views from dynamic radiance field fitting. + +![](images/d2eabe72a63789ac9fe0336fe8b93de78d167f7c76489c43cd0aedac333e0439.jpg) + +# Abstract + +Understanding bimanual human hand activities is a critical problem in AI and robotics. We cannot build large models of bimanual activities because existing datasets lack the scale, coverage of diverse hand activities, and detailed annotations. We introduce GigaHands, a massive annotated dataset capturing 34 hours of bimanual hand activities from 56 subjects and 417 objects, totaling $14k$ motion clips derived from 183 million frames paired with $84k$ text annota + +tions. Our markerless capture setup and data acquisition protocol enable fully automatic 3D hand and object estimation while minimizing the effort required for text annotation. The scale and diversity of GigaHands enable broad applications, including text-driven action synthesis, hand motion captioning, and dynamic radiance field reconstruction. + +# 1. Introduction + +"The human hand is a marvel of evolution, whose intricate structures and capabilities have allowed us to manipulate + +the environment in ways no other species can." + +- F.R. Wilson [108] + +From the skillful manipulation involved in cooking a meal, to the rapid movement of fingers to type this sentence, hands are always busy shaping our environments and communicating with others. Enabling machines to understand and replicate the remarkable capabilities of human hands is one of the grand challenges of AI and robotics. One approach to achieve this goal could be to train models on massive datasets, the strategy followed by recent large models that learn from trillions of text tokens [27], billions of text-image pairs [89], tens of millions of 3D shapes [25], or millions of robot trajectories [12, 13, 46, 73]. However, datasets of this scale are currently unavailable for natural hand activities. + +Sourcing large-scale 3D hand activities data is challenging. The two most common methods for data acquisition involve using cameras to capture hand manipulations in the wild or in controlled studio settings. In-the-wild data includes monocular internet videos [91], egocentric videos captured using wearable cameras [22, 23, 32, 52, 57, 79], or multi-view videos from third-person cameras [30, 62, 91]. However, this data is sparse, hard to calibrate, and noisy, resulting in limited 3D motion reconstruction accuracy, especially for objects. Alternatively, studio settings bring subjects into camera-rich environments and could employ markers for accurate reconstruction. However, the staged setup and lack of real-world context limits data diversity, and marker-based tracking [8, 28, 29, 55, 58, 59, 101, 111, 116] inhibits natural interactions. + +We address the data sourcing problem preventing the scaling up of hand datasets by introducing GigaHands, a diverse, massive, and fully-annotated 3D bimanual hand activities dataset (see Figure 1). To our knowledge, GigaHands is the largest bimanual hand activities dataset, with over 183 million unique image frames with two hands each $(0.37 \times 10^{9}$ unique hand poses, hence GigaHands). We used a multi-camera markerless capture system to acquire accurate bimanual hand-object interaction activities, gestures, and self-contacts. We overcome the studio capturing limitation by designing procedural activity elicitation protocols to include as many actions as in the real-world in-the-wild setting. To ensure diversity that reflects the real world, we captured data from 56 subjects interacting with 417 real-world objects. All images in our dataset are fully annotated with: detailed activity text descriptions; 3D hand shape and pose; MANO [86] hand meshes; 3D object shape, pose and appearance; hand/object segmentation masks; 2D/3D hand keypoints; camera pose. We minimized manual annotation effort using a procedural instruct-to-annote strategy by guiding subjects with detailed instructions to reduce annotation effort post-capture. In total, we collected 34 hours of text-annotated bimanual hand activities, 13k 3D motion se + +quences, and over 14k post-processed 3D motion clips with 84k detailed atomic-level text description annotations. Our 3D hand motion clips exceed the combined size of all existing 3D bimanual hand activities datasets [57, 58, 116], and the range of verbs in our text annotations is larger than any other hand dataset, even those captured in the wild [32, 33]. + +GigaHands can unlock new capabilities in applications including motion generation, robotics, and dynamic 3D reconstruction [81]. To demonstrate, we show improvements enabled by our dataset on text-driven action synthesis and hand motion captioning, along with examples dynamic radiance field reconstruction. To sum up our contributions: + +- We present GigaHands, a massive, diverse and annotated 3D bimanual activities dataset. It includes 34 hours of activities, 14k hand motions clips paired with 84k text annotation, and over 183M unique hand images. +- A procedural data acquisition strategy that ensures activity diversity and detailed atomic-level text descriptions while minimizing manual effort. We also built an accurate and fully-automated pipeline for estimating 3D hand/object shape and pose, segmentation, and camera pose. +- We show applications enabled by our dataset's scale, including 3D hand motion generation, hand motion captioning, and dynamic semantic scene reconstruction. + +# 2. Related Work + +# 2.1. Hand Motion Data Sourcing + +Hand motion data has four primary sources, and each presents its own advantages and challenges concerning realism, diversity, accuracy, and practicality. + +Static poses involve motion planning [5, 7, 10, 93], policy learning [19, 60], or motion synthesis [20, 117, 118] from individual static positions. While these methods provide reliable 3D data, it lacks semantic richness, resulting in motions disconnected from real-world activities and not fully representing diverse human movement. + +Synthetic data from game engines [126], augmented reality [66], virtual reality [38], or simulations [39, 63, 105] allow for controlled and accurate 3D motion sequences. Despite their reliability, these synthetic motions often fail to capture the intricacies of genuine human movements, limiting their applicability in modeling natural hand behaviors. + +Real-world in-the-wild settings involves using wearable or portable sensors to capture hand interactions from ego-centric [22, 23, 32, 52, 57, 79], third-person [30, 62, 91] or both types of views [33, 95], yielding realistic and natural motions. However, obtaining reliable 3D motion data for both hands and objects is challenging due to occlusions resulting from limited sensor deployment and accuracy. Additionally, annotating such data is labor-intensive, and certain self-contact motions are difficult to record accurately. + +Studio environments place participants in controlled set- + +tings equipped with extensive sensors, enabling reliable capture of detailed information such as 3D hand motions [45, 54, 55, 72, 120, 122], object movements [8, 18, 29, 36, 37, 48, 58, 59, 111, 116], contact regions [28, 80, 101], audio [44, 49, 71, 113], and tactile data [14, 31, 78, 100]. However, collecting data in studios is arduous and may not reflect the diversity of real-life scenarios. Participants might find it challenging to perform natural motions in an unfamiliar environment, especially when encumbered with wearable sensors. For example, motion capture (MoCap) systems [8, 28, 29, 55, 58, 59, 101, 111, 116] require markers attached to the body, reducing visual realism and inhibiting movements like self-contact between hands, necessitating additional post-processing to restore a realistic appearance. On the other hand, markerless motion capture systems [18, 36, 37, 45, 48, 54, 72, 80, 120, 122] offer more realistic visuals and encourage natural motions, but they may trade off capture accuracy. GigaHands balances accuracy, diversity, realism, and practicality by replicating in-the-wild settings during activity elicitation and estimating accurate 3D motion from marker-less motion capture. + +# 2.2. Hand Datasets and Annotations + +Hand datasets vary in sources and scales, each constructed for specific purposes and enriched with various annotations. Hand motion is the most common type of annotation, represented as bounding boxes [30, 79, 91], segmentation masks [24, 52, 70], 2D keypoints [6, 43, 61, 90], 3D keypoints [82, 99, 102, 106], or parameters of parametric models [55, 77, 97]. Depending on the data source and desired detail, annotations are obtained through manual labeling [106], synthesis [66, 67, 92, 126], markers and sensors [29, 45, 54, 104, 115, 120, 122], cross-view bootstrapping [65, 96], iteratively trained keypoints extraction networks [72, 127], multi-view annotation [72], or audio refinement [44]. Semi-automatic and automatic labeling techniques significantly improve scalability. + +Object annotations are provided given the frequent interaction between hands and objects. These can be acquired from manual labeling [18, 57, 98], synthesis [21, 39], MoCap [8, 28, 58, 59, 111, 112, 116, 124], hand-object reconstruction or retrieval [15, 64, 109], or multi-view RGB-D data [36, 37, 48]. We demonstrate that multi-view RGB us sufficient for automatic annotation, enhancing scalability. + +Text annotations. To capture the rich semantic meanings in human hand actions, certain datasets provide text annotations. These annotations may include action types [26, 30, 32, 47, 79], atomic action descriptions [22, 23, 33, 52, 90], activity narration [22, 23, 33, 62], activity commentary [17, 32, 33, 116], object affordance [42, 58, 111, 116], or body dynamics [114, 122, 123]. Typically, annotations are manually provided, especially when data are collected in uncontrolled, unscripted environments [22, 23, 32, 33]. + +Table 1. Comparisons of 3D bimanual motion datasets. Dataset names are highlighted with different colors if it has no text annotations (gray), action type (green), sparse description (red), and dense description (blue). See the supp. document for the full table. + +
Nameminsmotionsposesviewsframessub.obj.
w/o Object Annotation
AssemblyHands [72]63062203k123.03M34/
Ego-Exo4D [33]//4.4M5-6/740/
w/ Object Annotation
HOI4D [57]1,3334k1.2M12.4M4800
ARCTIC [28]121339218k92.1M1011
TACO [58]2022.3k363k134.7M14196
OakInk2 [116]5572.8k993k44.01M975
HOT3D [8]8334.1k1.7M2-33.7M1933
GigaHands (Ours)2,03413.9k3.7M51183M56417
+ +Even in studio settings, post-processing is often required to extract meaningful action clips [52, 116]. We introduce a procedural instruct-and-announce pipeline that maximizes semantic interpretability and minimizes the annotation effort. + +Contact are derived from manual annotation [91], video grounding [69], thermal sensors [9, 11] or geometry analysis [80, 101, 125] based on captured data. Our dataset enables us to derive contact regions using geometry analysis on both surface mesh and density fields. + +# 3. The GigaHands Dataset + +Dataset Characteristics. GigaHands is a large and diverse dataset of bimanual hand activities with detailed annotations. It encompasses a wide range of scenarios, including hand-object interactions, gesturing, and self-contacts performed by 56 subjects who collectively used 417 objects (see Table 1). The dataset contains 2,034 minutes of bimanual hand activities, surpassing the length of any existing 3D hand motion dataset. Compared to other datasets that are unannotated [8, 28], contain motion type annotations [57, 58, 72], or provide sparse motion descriptions [33, 116], GigaHands offers detailed text annotations for all captured activities. With a total of 13k instructed motion sequences, 14k annotated motion clips, and 84k augmented text descriptions, it is larger than any other dataset. Furthermore, GigaHands includes 3.7 million bimanual 3D hand poses, represented by both 3D keypoints and MANO [86] hand meshes, comparable to the scale of Ego-Exo4D [33] – the current largest annotated 3D hand pose dataset. However, unlike Ego-Exo4D, which is annotated from selected, non-continuous frames, GigaHands provides continuous bimanual 3D hand poses and shapes. Each motion clip was captured using 51 camera views, resulting in 183M RGB frames (and 366M unique hand images). This multi-view setup enables new applications such as dynamic 3D radiance field reconstruction. Additionally, + +![](images/f0c0a50bb1889560305bb50cebfe4ac5fc5985036faa6a4819e5bd0e6a0f4a28.jpg) + +![](images/7375ef2429d032e1be05c2159f0e92db1ee773cafe6dfc1e4bb613b37c706d2c.jpg) + +the dataset contains annotations for hand/object segmentation masks, 3D object shape, pose and appearance, 2D/3D keypoints, and camera poses. + +Diverse Hand Pose and Motion. Figure 2 (left) compares hand pose diversity across datasets using t-SNE [107] clustering of 3D keypoints of both hands. Similarly, Figure 2 (middle) shows hand motion diversity through t-SNE clustering of the latent codes of a Variational Autoencoder trained for motion reconstruction. GigaHands exhibits significantly greater diversity than existing datasets in both bimanual hand pose and motion. Additionally, datapoints near the boundary of our dataset seem to correspond to text annotations that are unique in our datasets, demonstrating that diverse verbs contribute to diverse poses and motions. + +Diverse Text Annotation. GigaHands contains activities that are more diverse than existing datasets [32, 33, 116] as measured using verb counts in Figure 2 (right). Since each verb corresponds to an activity, a diverse set of verb indicates activity diversity. GigaHands contains the most verbs (1467) with 580 of them being unique to our dataset. The key to achieving this diversity is our instruct-to-annotate strategy (see Section 4.3) for automated labeled activity sourcing. Please refer to the supp. document for the source of verbs and detailed verb comparison. + +Diverse Objects. Figure 3 shows some of the tabletop objects included in GigaHands. We provide 3D meshes [2] with associated textures for rigid objects and multiview segmentation masks for non-rigid objects. Different from most datasets, we also include small-scale objects (e.g. pens) that are difficult to capture. We employ single-view reconstruction [3] to obtain meshes for these small objects. In total, the dataset includes 417 objects, with 310 multiview scanned meshes and 31 single-view generated meshes. + +![](images/59272a07af98eced47ca4c7eac52d1526d6188739c0153c155a5f14eaf3e185c.jpg) +Figure 2. Dataset Diversity. The left and middle figures illustrate the diversity of pose and motion variations in GigaHands, visualized using t-SNE embeddings. Some points along the convex hull are highlighted with their corresponding text instructions, showcasing unique motions captured in our dataset. The right figure compares the verb sets among different datasets using an UpSet visualization [50]. Each column represents the number of verbs exclusive to specific subsets of datasets, indicated by the connected dots below the columns. The rows indicate the total verb count in each dataset. GigaHands contains more verbs and more exclusive verbs compared to other datasets. + +![](images/202ca889af8d2fb74887137a5aa5dad67a38358d8ac346a068ed8c018452c50d.jpg) +Figure 3. Diverse Objects and Frequent Hand Contact Regions. GigaHands provide objects (left) spanning diverse scenarios, including cooking, office working, crafting, entertainment, and housework. The diverse activities result in contact regions (right) spanning both the front and back of both hands. + +Diverse Contacts. Since we have 3D meshes both hands and objects, we can use them to estimate contact maps on both hands, following the approach in [101]. Figure 3 shows the accumulated contact regions from randomly sampled frames across the dataset. The results reveal diverse contact areas, including regions between fingers and on the back of the hands (e.g. punching uses the backs of hands). The right hand interacts with objects more frequently than the left, since a majority of our subjects were right-handed. + +# 4. Dataset Acquisition + +We present our data acquisition pipeline, which balances realism, diversity, and accuracy while reducing annotation effort. Our procedural pipeline, called Instruct-to-Annotate (see Figure 4), consists of several key components: + +- Procedural instruction elicitation (Section 4.1) for generating instructions to guide participants during data capture. +- Filming (Section 4.2) using a markerless multi-camera system to record high-quality hand activity sequences. + +![](images/b28b74b0b2173d302a4f33ed575a3c66c651decdd00d7a5444f2345172920819.jpg) +Figure 4. Instruct-to-Annotate Pipeline. The instruction elicitation process (left yellow block) creates atomic action-level instruction scripts in a temporally smooth order, structured within scenes. This is achieved by parsing action datasets, grouping verbs into a pool, structuring scenarios, and generating scene scripts. During filming, subjects act according to these scripts, producing recorded motion sequences. Annotators then process these sequences (right blue block) by segmenting them into clips and annotating unscripted motions. + +- Motion annotation and text augmentation (Section 4.3) to refine sequences by breaking them into shorter clips with accurate annotations. +- Hand motion (Section 4.4) and object motion estimation (Section 4.5) for detailed 3D hand and object motions from the captured multi-view RGB videos. + +# 4.1. Instruction Elicitation + +To ensure diverse hand activities and reduce annotation effort, the Instruct-to-Annotate pipeline starts with a procedural instruction elicitation protocol. We began by sourcing atomic actions from multiple datasets [32, 33, 58, 116], extracting a pool of verbs corresponding to those actions. To elicit subjects to perform these verbs (actions), we manually associated each verb with multiple objects and, with the assistance of an LLM [4], grouped the verbs and objects into different scenarios such as cooking and eating, office work, crafting, entertainment, and housework. We then structured these scenarios into scenes where the objects could co-occur. Using LLM, we organized the scenes into lists of activities that utilized the objects and verbs in a temporally smooth order and automatically generated detailed instruction scripts. These scripts comprise 5 scenarios, 25 scenes, 191 activities, and 1370 instructions containing a total of 533 verbs. Please see the supp. document for details. + +# 4.2. Filming + +Hardware. To capture our dataset, we use a custom-designed multi-camera tabletop capture system that consists of 51 RGB cameras uniformly arranged within a cubic capture volume, with each face of the cube containing a $3 \times 3$ grid of cameras evenly illuminated by LED lights. Inside the cube, a transparent glass surface serves as a supportive platform for objects. Each camera records at 30fps with a resolution of $1280 \times 720$ . Cameras are software-synchronized, with the temporal phase misalignment being less than 3 ms. Camera intrinsics and extrinsics are obtained using COLMAP [87, 88] aided by fiducial markers. + +Filming Process. During filming, subjects perform actions according to the provided instructions, keeping both hands within the filming area. Instructions are converted to audio and played sequentially to guide the participants, while an operator controls the capture by playing each audio instruction and recording each motion sequence. If the ending state of a performance does not align with the next instruction, a corrective instruction will be given and rerecorded to ensure smooth transitions and reduce annotation efforts. This approach ensures all recorded sequences correspond to a pre-scripted or recorded instruction. + +# 4.3. Action Annotation & Augmentation + +Though each filmed motion sequence was paired with an instruction, manual annotation was still necessary for two reasons. First, the instructions generated by the LLM occasionally contained inconsistencies or hallucinations. Second, participants might misunderstand the instructions or add unintentional actions during filming. To encourage subjects to act freely and naturally, we intentionally retained these recordings. Annotators then split these sequences into individual clips and annotated any actions not included in the original instructions. This process resulted in a more accurate dataset with matched (description, clip) pairs. In total, we refined the 13k motion sequences into 14k motion clips. + +To further enhance the text descriptions, we used the LLM to rephrase each description 5 times, providing multiple textual variations for each motion clip. This expanded our $14\mathrm{k}$ motion clips into $84\mathrm{k}$ motion-text pairs containing 1,467 unique verbs. The augmentation prompts and examples are provided in the supp. document. + +# 4.4. Hand Motion Estimation + +GigaHands provides detailed hand motion data, including 2D and 3D hand keypoints and MANO [86] meshes for both hands. Since existing hand shape and pose estimation did not work well enough, we built our own hybrid + +method. We begin by obtaining bounding boxes for the hands across videos using YOLOv8 [85]. Then, 2D keypoints are extracted from the MANO meshes estimated with HaMeR [77] and handedness (left or right) is determined with ViTPose [110]. HaMeR meshes cannot directly be used since they lack accurate depth. With camera parameters, 2D keypoints are triangulated across views [97] to obtain accurate 3D positions. To ensure temporal smoothness in the sequences, the one-euro filter [16] is applied to the both 2D and 3D keypoints. With the bounding box and 2D & 3D keypoints, we fit the MANO parametric hand model [86] following the EasyMoCap pipeline [1]. This results in a fully automated pipeline for extracting coherent and accurate hand motions. Details and the evaluation of each step are provided in the supp. document. + +# 4.5. Object Motion Estimation + +GigaHands also provides 3D object motions represented as 3D shape and 6D pose. Given target meshes obtained from pre-scanning or single-view reconstruction, we track these objects with multi-view constraints. First, we segment the target objects from the background in each view. We detect salient objects across the video using DINOv2 [74] on frames subsampled at 1 fps. Using both object text descriptions and rendered template meshes from multiple views, we select the top-k bounding boxes most aligned with the template mesh throughout the video with Grounding DINO [56]. To eliminate false positives, we use OpenCLIP [41] to filter out boxes aligned with negative prompts. With the positive bounding boxes as the prompt, we use SAM2 [84] to segment object masks throughout the video. + +Since no existing method for object pose estimation worked well [75], we decided to build our own robust method that exploits our dense multi-view setting. We use a differentiable rendering approach [83] supervised by the multi-view masks. To initialize the translation and rotation, we first build a radiance field using Instant-NGP [68]. We initialize the object's translation using the center of the density field. To address potential object symmetries, we use object appearance to initialize the rotation. Following FoundPose [75], we render the template mesh with multiple initial rotations and use DINOv2 features to find the best match, aggregating cross-view information. This process yields precise object motion estimates even in complex, cluttered scenes. More details and the evaluation of each step are provided in the supp. document. + +# 5. Applications & Experiments + +We demonstrate the utility of GigaHands in several applications that require large-scale data, including text-driven hand motion synthesis (Section 5.1), motion captioning for our dataset (Section 5.2) and for in-the-wild datasets (Section 5.2), and dynamic radiance field reconstruction (Sec + +Table 2. Quantitative results for text-driven motion synthesis with models trained on different datasets. upper bound indicates performance calculated with the ground truth. We report the mean of 20 evaluations, and $\rightarrow$ means the closer to the upper bound the better. The model trained on GigaHands performs best on most metrics. + +
DatasetR Precision(%)↑MM Dist.↓FID↓Div.→MM.↑
@1@2@3
upper bound64.486.289.42.860.04514.2-
TACO [58]18.937.752.97.3911.011.16.83
upper bound50.471.281.13.670.0229.30-
OakInk2 [116]17.931.747.97.7519.66.883.45
upper bound77.488.891.32.960.00211.9-
GigaHands31.244.753.16.684.7010.59.11
+ +tion 5.3). More results can be found in the supp. document. + +# 5.1. Text-driven Hand Motion Synthesis + +Generating diverse and complex motions is crucial for training virtual agents and robotic manipulation. We use GigaHands to train models for text-driven hand motion synthesis, overcoming the limitations of approaches that rely on strict conditions [116] or generate only simple skills [17] due to constrained data. We demonstrate that the scale of GigaHands leads to better performance compared to other datasets [58, 116] and smaller subsets of GigaHands. + +Training and Evaluation Protocol. We split GigaHands into train, test, and val sets with a ratio of 16:3:1. From among our annotations, we chose 42 3D keypoints for both hands as the representation for model training (see the supp. document for an analysis of alternative representations). To evaluate the naturalness, diversity, and alignment of generated motions with textual descriptions, we use metrics from [34], including R-Precision, Multimodal Distance (MM Dist), Fréchet Inception Distance (FID), Diversity (Div.), and Multimodality (MM.). For computing FID and Div., we train a motion autoencoder to define a compressed motion space. For R-Precision, MM Dist, and MM., we employ contrastive learning to create a joint motion-text embedding space, following [34]. Feature extractors are trained independently for each dataset and subset. + +Results. We report text to hand motion synthesis performance using the T2M-GPT [119] backbone in Table 2 (see the supp. document for more results on GRU-based [35] and diffusion [103] architectures). Since the evaluation embedding spaces are trained on different test sets, we also evaluate the metrics on ground truth test data to indicate upper-bound performance for each test set. Models trained on GigaHands outperform others on all metrics except MM Dist., with higher R-Precision due to better text-motion alignment. Compared to OakInk2 (which also includes textual descriptions for hand motions), GigaHands achieves significantly better FID, Diversity, and Multimodality scores, + +![](images/46a918462a1e59c97952e6c17e75d23aef489983a420ba495f22cef45f70fef7.jpg) +Figure 5. Generated motions from models trained on different datasets. Texts highlighted in green, orange, and blue come from the OakInk2, TACO, and GigaHands datasets. In the bottom two rows, hand meshes highlighted in these colors are generated by models trained on the corresponding datasets. The model trained on GigaHands can generate diverse motions from a single text (right four columns) and accurate motion with text from other datasets (left two columns). Darker color indicates later frame in the sequence. + +![](images/864ebebfa268f3b087a4f2c1e8e0e58811dfdad1797fe169d461e9b3ebdaf023.jpg) + +![](images/3506bbf28301c2b06826bd4d3ae5e47e7fd89b26d813abea682b5390c71b528a.jpg) + +![](images/5bf8204a42c72489e5763d76ea72e5735e6940d98e51b7bbd8891daf5aa57c84.jpg) +Figure 6. Effect of dataset size on motion reconstruction and text-to-motion generation performance. The x-axis shows the percentage of training data used (10%, 20%, 50%, 80%, and 100%), and the y-axis displays performance metrics: FID, MM Dist., Top-1, and Top-3 accuracy. Larger datasets consistently improve performance across all metrics, highlighting the benefits of increased data scale. + +![](images/64d076543a6205866cb311406288b18faf85a5ab14ce56057fef33c0936014e5.jpg) + +likely due to its greater dataset diversity. Figure 5 shows hand motions generated by T2M-GPT trained with GigaHands using text inputs from the test sets of GigaHands, OakInk and TACO. Even without object geometry input, our model generates reasonable hand shapes and poses for object manipulation, benefiting from the diversity of objects in our dataset. Our model can also generate reasonable motion using text from other datasets, showing the comprehensiveness of GigaHands. + +Effect of Data Scale. Figure 6 illustrates the impact of dataset size on motion reconstruction and text-to-motion generation. Based on the T2M-GPT architecture, we train a motion VQ-VAE for reconstruction and a generative pretrained transformer model for text-to-motion generation using $10\%$ , $20\%$ , $50\%$ , $80\%$ , and $100\%$ of the training set, evaluating on the same test set. We evaluate FID, MM Dist., and Top 1 & Top 3 accuracies. Most metrics continually improve with larger datasets, demonstrating the value + +of larger-scale data. + +# 5.2. Hand Motion Captioning + +Captioning human hand motion helps interpret action intent. We train a motion captioning model on GigaHands and generate captions for its test set motions; we also show examples of captioning in-the-wild datasets. + +Training and Evaluation Protocol. We adopt TM2T [35] as the model backbone. For text-motion alignment evaluation, we utilize R-Precision and MM Dist., employing the same embedding space described in Section 5.1. To evaluate alignment with the ground-truth text annotations, we use BLEU [76], ROUGE [53], and BERTScore [121]. Since our dataset has diverse verbs, we evaluate text diversity with distinct-n [51] and Pairwise BLEU [94]. Since TACO lacks text annotations, we use its triplet labels () as scripts, transforming motion captioning in TACO into a classification task. + +Table 3. Quantitative evaluation for motion captioning with models trained on different datasets. GigaHands performs best on most metrics. + +
DatasetsRP@1(%)↑RP@2(%)↑RP@3(%)↑MM Dist↓
upper bound64.486.294.22.86
TACO [58]43.559.668.55.84
upper bound51.169.579.63.67
Oakink2 [116]40.458.868.24.55
upper bound75.389.193.92.87
GigaHands57.066.169.85.37
+ +Table 4. Pairewise-BLEU, BLEU@4, ROUGE, distinct-n, and BERTScore for motion captioning with models trained on different datasets. GigaHands performs best on most metrics. + +
DatasetsP-B↓B@4↑R↑dist. -1(%)↑dist. -2↑(%)BScore↑
TACO [58]4.5939.461.22.036.3557.1
Oakink2 [116]8.2139.956.32.766.8235.3
GigaHands0.91643.157.715.336.955.4
+ +![](images/f41592bb9ee6deef2f61bcd12d15618666238700793e66838cd1f9037360d24c.jpg) +Figure 7. Motion captioning results with different datasets. Each column shows a motion sequence, its ground truth text description, and two generated texts. Hand motions highlighted in green, orange, and blue come from OakInk2, TACO, and GigaHands, respectively. Texts highlighted in these colors are generated by models trained on the corresponding datasets. The model trained on GigaHands generates diverse captions from a single motion (right three columns) and accurately captions motions from other datasets (left two columns). + +![](images/50f770cbf1adeadedbcb9ea1f1b64e0d2fb684ea2b372f7dbc2a7543b773b4ec.jpg) +Figure 8. Synthesized test views using 2DGS for the motion 'zip up the pants,' displayed at two timesteps and from two viewpoints. The synthesized views faithfully reconstruct the scene by leveraging the ample camera views provided by GigaHands. + +Hand Motion Captioning for GigaHands Figure 7 shows examples of generated 3D motion captions. The model trained on GigaHands generates diverse and accurate captions. Though objects are not present in the input, the model still generates captions which include reasonable object descriptions. Table 3 and Table 4 report the quantitative performance of models trained on different datasets [58, 116]. The model trained on GigaHands achieves superior motion-text alignment, particularly in Pairwise BLEU and distinct-n, which reflect caption diversity. While our accuracy is marginally lower compared to the simple triplet captioning in TACO, our approach produces richer and more varied captions. + +3D Hand Motion Captioning for Unlabeled Datasets +GigaHands's large variety motions and associated annotations allows models trained on it to caption other 3D hand motion datasets. Fig. 7 shows some examples using the model trained on GigaHands to caption motions from TACO and OakInk2 datasets after aligning their motion range with GigaHands. This model trained with GigaHands generates finer-granularity captions for these other datasets. + +# 5.3. Dynamic Radiance Field Reconstruction + +Unlike existing hand activity datasets, GigaHands provides dense camera views. This enables new applications, such as + +building dynamic radiance fields. From the 51 views provided, we remove 12 camera views due to lighting issues and randomly select one view as the test view, resulting in 38 views used for training. We segment consistent object and hand masks throughout the video as described in Section 4.5. We then fit 2DGS [40] for frame-wise radiance field reconstruction, initializing each frame with the previous frame for temporal consistency. Figure 8 shows an example of synthesized test views for a motion clip. Notably, the pants are a non-rigid object that cannot be easily tracked, but GigaHands provides ample camera views for capturing non-rigid objects (more results in supp. document). + +# 6. Conclusion + +We present GigaHands, a massive annotated dataset of bi-manual hand activities. The dataset contains 14k motion clips with 3D hand and object motions from 56 subjects interacting with 417 real-world objects, all captured from 51 camera views. It provides 183 million unique image frames and 84k textual descriptions, enabling a wide range of applications. We demonstrated how the scale and diversity of the dataset benefit text-driven motion synthesis and motion captioning, both within the dataset and on other data. Additionally, we have shown that GigaHands enables dynamic radiance field reconstruction, opening possibilities for downstream tasks. + +Limitations and Future Directions. Despite its scale and diversity, GigaHands has limitations. The studio setting confines data collection to a limited space, making it challenging to accurately capture motions that require larger environments. While we can track rigid objects and object parts, fully automatic tracking of articulated and non-rigid objects remains challenging. Moreover, although we have showcased applications in motion synthesis and captioning, further research could explore how the dataset's scale and diversity can enhance robotic manipulation and human-computer interaction tasks. + +# Acknowledgement + +This research was supported by AFOSR grant FA9550-21-1-0214, NSF CAREER grant #2143576, and ONR DURIP grant N00014-23-1-2804. We would like to thank the OpenAI Research Access Program for API support and extend our gratitude to Ellie Pavlick, Tianran Zhang, Carmen Yu, Angela Xing, Chandradeep Pokhariya, Sudarshan Harithas, Hongyu Li, Chaerin Min, Xindi Qu, Xiaoquan Liu, Hao Sun, Melvin He and Brandon Woodard. + +# References + +[1] Easymocap - make human motion capture easier. Github, 2021.6 +[2] AR Code, Augmented Reality QR Codes — ar-code.com. https://ar-code.com/, 2024. [Accessed 05-11-2024]. 4 +[3] Meshy Docs — docs.texai. https://docs.texai/image-to-3d, 2024. [Accessed 13-11-2024]. 4 +[4] Josh Achiam, Steven Adler, Sandhini Agarwal, Lama Ahmad, Ilge Akkaya, Florencia Leoni Aleman, Diogo Almeida, Janko Altenschmidt, Sam Altman, Shyamal Anadkat, et al. Gpt-4 technical report. arXiv preprint arXiv:2303.08774, 2023.5 +[5] Heni Ben Amor, Oliver Kroemer, Ulrich Hillenbrand, Gerhard Neumann, and Jan Peters. Generalization of human grasping for multi-fingered robot hands. 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However, as a simplified simulation version of the brain neural pathway, their structures are locked during training, causing over-fitting and over-parameterization. Although recent models have begun using the biomimetic concept and empirical pruning, they still result in irrational pruning, potentially affecting the accuracy of the model. In this paper, we introduce the Glia unit, composed of oligodendrocytes (Oli) and astrocytes (Ast), to emulate the exact workflow of the mammalian brain, thereby enhancing the biological plausibility of neural functions. Oli selects neurons involved in signal transmission during neural communication and, together with Ast, adaptively optimizes the neural structure. Specifically, we first construct the artificial Glia-Neuron (G-N) model, which is formulated at the instance, group, and interaction levels with adaptive and collaborative mechanisms. Then, we construct GliaNet based on our G-N model, whose structure and connections can be continuously optimized during training. Experiments show that our GliaNet advances state-of-the-art on multiple tasks while significantly reducing its parameters. + +# 1. Introduction + +The expansion of learnable parameters in artificial neural networks (ANNs) has contributed to their extraordinary successes [11]. However, during training, the structures of ANNs are fixed, which can induce over-fitting [5, 39] and over-parameterization [3, 15] of the network. Although network structure learning methods, including but not limited to Network Compression, Knowledge Distillation, Neural Architecture Search (NAS), and Dynamic Neural Networks (DyNN), aim to alleviate the issues mentioned above, they still yield problems such as unstable performance and expensive computational costs [6, 41, 51, 52]. + +![](images/fee8f0aede814e21c11e502ad09ca3359a1a62573e561b29a52720a8227d62ec.jpg) +(c) G-N model (Ours) +Figure 1. Comparison of basic units of neuronal models. (a) The M-P model [33]. The connection between neurons is unidirectional propagation. (b) The Astrocyte-Neuron model [16, 17]. The connection of the pre-neuron is modulated by Ast through bidirectional communication and subsequently transmitted to the postneuron. (c) Our G-N model. Glia, consisting of Oli and Ast, as key supportive elements for neuronal function, exhibits the optimization of the neural pathway. The winning pre-neuron, participating in subsequent propagation, is selected by Oli. Then, the winning connection is modulated by Ast. $\times$ denotes the inhibitory neuron not connected to Ast and post-neuron. + +The aforementioned issues can be attributed to the M-P model [33], serving as the basis for building artificial perceptions. The M-P model is a simplified version of inter-neuronal communication that restricts neurotransmitters (formulated as connections or weights in a network) to unidirectional propagation, i.e., from the pre-neuron to the post-neuron (see Fig. 1a). Several researchers have conducted preliminary explorations by incorporating an astrocyte into the nervous system to propose an artificial Astrocyte-Neuron (A-N) model [16, 17]. In this model, astrocytes facilitate connections between pre- and post-neurons through bidirectional communication with connections released by the pre-neurons (see Fig. 1b). During training, astrocytes can adaptively modulate network connections in different tasks. + +However, the existing A-N model selects important connections by rigorously pruning those that are below a specified threshold following astrocyte modulation. This empirical pruning approach easily reduces accuracy when striving for a lightweight model, as evidenced in various pruning studies [29, 40]. + +Reflecting the mammalian brain's workflow, the brain's response to external stimuli initially manifests as the activation of neurons in a specific region, rather than engaging all neurons [1]. Thus, before the Astrocyte (Ast) modulates neurotransmitters, a set of neurons involved in neural communication—referred to as winning neurons—must first be selected [25], a task carried out by the Oligodendrocyte (Oli) [14]. Oli and Ast typically appear in pairs, forming a Glia unit. In this paper, we simulate functional interactions within the nervous system, comprising Glia and neuron, and propose a novel artificial Glia-Neuron (G-N) model. On the one hand, we redefine network structure learning by adaptively selecting winning neurons through Oli and modulating their neural connections via Ast. On the other hand, we expand the Glia unit into a group to achieve the optimal neural structure and connections by fostering the coordinated roles of Oli and Ast within the Glia units and their interaction between units. The formulation of our G-N model is followed in three aspects. + +First, at the instance level, Glia influences various aspects of neuronal function, including excitability and synaptic efficacy [48]. Specifically, Oli is stimulated by neuron states and releases neurotrophins to select winning neurons involved in subsequent propagation and recalibrate their states [32]. Then, neurotransmitters released by winning neurons stimulate Ast, prompting Ast product gliotransmitters to modulate these neurotransmitters [13] (see Fig. 1c). + +The fundamental unit in ANNs are neurons that reflect network activity through their states, while their connections signify the strength of associations between these states [50]. Consequently, we model a more exact workflow in brain mechanisms by simulating the interactions between Oli and neurons, as well as Ast and connections. + +Second, at the group level, a Glia unit typically does not exist in isolation; instead, multiple Glia units form a cooperative group, i.e., a group of Glia units, to jointly optimize neural communication [21]. This setup allows each member (i.e., Oli and Ast) within a Glia unit to focus on processing in a specific area, thereby enhancing optimization efficiency. Moreover, multiple Glia units overcome a limitation of the A-N model, where a single Ast can maintain only one state per iteration, thus increasing its capacity for dynamic regulation. + +Third, at the interaction level, we define the interactions of Glia units in two aspects: (i) interactions between a Glia unit across different iterations and (ii) interactions among multiple Glia units. i) The state of each Glia at time $t$ de + +pends on the result of its optimization of the corresponding subnetwork structure at time $t-1$ . ii) Glia units collaborate with each other during iterations. A Glia unit is stimulated not only by states from its associated partial pre-neurons but also by implicit influences from other pre-neuron states through its interactions with other Glia units [35]. + +With our proposed G-N model, we construct the GliaNet, where its structure and connections can be adaptively optimized during training. Our primary contributions include: + +- We formulate an artificial Glia-Neuron (G-N) model at instance, group and interaction levels with adaptive and collaborative mechanisms. +- We construct the GliaNet which adaptively optimizes the dynamically changing structure and neural connections during training based on our G-N model. +- We extensively evaluate GliaNet on multiple tasks with public datasets, e.g., improving accuracy by $0.08\% \sim 2.93\%$ on classification. AP improved by $0.8\% \sim 1.0\%$ on segmentation and $0.7\% \sim 1.1\%$ on object detection. + +# 2. Related Work + +M-P model-based networks. These networks fix their structures during training, and several methods aim to address challenges arising from this constraint from different perspectives. We categorize representative methods below. + +Parameter pruning contains non-structural pruning for disabling weak connections [15] and structural pruning for zeroing out groups of filters [46], which has a tedious fine-tuning process and easily leads to a decrease in accuracy. + +Knowledge distillation shows that the student model learns little from some teacher models due to the model capacity gap between them [55]. + +Dynamic neural network (DyNN) includes sample-wise by adjusting architectures based on sample [34], spatial-wise by performing inference concerning different spatial locations of images [44], and temporal-wise by allocating less computation to the inputs at minor temporal locations [19]. The structure and parameters of DyNN varied by each sample or different spatial locations of images [18]. Instead, we adaptively optimize structure and parameters to fit data. + +Neural architecture search (NAS) contains parameters and architecture optimization. NAS can be viewed as a method for searching connections from the M-P model-based search space [49]. The parameters optimization includes independent optimization [37] and sharing optimization [2]. The architecture optimization includes: 1) search space defines which architectures can be defined, including global and cell-based [56] search spaces; 2) search strategy includes: RL-based methods [57] use the performances of generated architectures as the rewards for training the controller. EA-based methods [37] search architectures with evolutionary algorithms. Gradient-based methods [9] regard network ar + +chitecture as a group of learnable parameters; 3) estimation strategy scores the searched architectures [49]. + +Biologically Plausible Neural Model. Based on the Tripartite Synapse [36], Astrocyte inserts itself into the nervous system to respond to neuron-released neurotransmitters, and then modulates them [4]. This shows that changes in neurotransmitters combine external disturbances and their state [26]. Hastings et al. focused on astrocytes communicating with distant neurons [21], and Han et al. explored modeling nervous systems with astrocytes [16, 17]. In contrast, we combine Olis with Asts to form Glia units to better mimic the optimization process of the neural pathway. + +# 3. Methodology + +This section first overviews the existing neuron model in Sec. 3.1, and introduces our Glia-Neuron model in Sec. 3.2, GliaNet in Sec. 3.3, and training scheme is in Sec. 3.4. + +# 3.1. Preliminaries + +M-P Model. The M-P model simulates simplified communication between neurons, restricting the connecting weights to unidirectional propagation. Its standard definition is + +$$ +y = \phi_ {n} \left(\sum_ {i} ^ {N} x _ {i} w _ {i}\right) = \phi_ {n} \left(\mathbf {X} ^ {\top} \mathbf {W}\right), \tag {1} +$$ + +where $N$ is the number of pre-neurons, $y$ denotes the output of the post-neuron, and $\phi_n()$ is the activation function of the neuron. Here, $\mathbf{X} = [x_1,\dots ,x_i\dots ,x_N]^{\mathrm{T}}$ be the data (or neuron state), $\mathbf{W} = [w_{1},\dots ,w_{i}\dots ,w_{N}]^{\mathrm{T}}$ be the weight and $w_{i}$ is a connecting weight from the $i^{th}$ pre-neuron with state $x_{i}$ to the post-neuron. + +Artificial Astrocyte-Neuron Model. Ast establishes bidirectional communication with neurotransmitters (weights) released by pre-neurons to modulate the conveyed information. The simplified artificial Astrocyte-Neuron (A-N) model with only one Ast can be formulated as, + +$$ +\mathbf {W} ^ {\prime} = \mathcal {P} \left(\phi_ {a} \left(f \left(w _ {i} ^ {t}\right)\right), \delta\right) = \mathcal {P} \left(\phi_ {a} \left(f \left(\mathbf {W} ^ {t}\right)\right), \delta\right), \tag {2} +$$ + +where $f(\cdot)$ and $\phi_{a}(\cdot)$ denote the modulation and activation function of Ast. Here, $\mathbf{W}'$ is the updated weight, $\mathbf{W}^t = [w_1^t,\dots ,w_i^t,\dots ,w_N^t ]^\top$ and $w_{i}^{t} = f(w^{t - 1})$ is a connecting weight concerning iterative modulation by Ast from $t - 1$ to $t$ , where $t\in [1,T]$ and $T$ is the maximum iteration number. + +However, the A-N model removes low-strength connections modulated by a single Ast through an empirical pruning function $\mathcal{P}()$ with a threshold $\delta$ . This constraint reduces model accuracy and limits the selection of optimal connection combinations. + +# 3.2. Glia-Neuron Model + +This section presents the main theoretical insights of this paper. We introduce Oli to select winning neurons adaptively, in contrast to the simplified A-N model in Eq. (2) + +![](images/8b55fa6595e271e05346e2f3173fa64c3441c35126da16481386c68af0de364d.jpg) +Figure 2. The structure of our $G-N$ model. M numbers of Olis and Asts are involved in jointly optimizing the communication between pre- and post-neurons. + +that uses empirical pruning. We propose our Glia-Neuron (G-N) model, which considers Oli and Ast as integral components of the Glia unit. This model is constructed at the instance, group, and interaction levels. + +Instance-level: The Oli establish bidirectional communication with all pre-neurons. They are stimulated by the state of pre-neurons, and their output is used as feedback to select the winning neuron [28]. Inspired by [35], we build a selection function $g(\cdot)$ of Oli. Specifically, given $N$ pre-neurons $\{\mathbf{N}_i\}_{i=1}^N$ with state $\mathbf{X} \in \mathbb{R}^{N \times 1}$ , where each neuron $\mathbf{N}_i$ with a state $x_i$ . We search for winning neurons by, + +$$ +\begin{array}{l} \widetilde {\mathbf {X}} = \mathcal {I} (g (\mathbf {X})) = \{g \left(x _ {i}\right) \in g (\mathbf {X}) \mid g \left(x _ {i}\right) \neq 0 \}, \tag {3} \\ \mathbf {e} = \phi_ {o} (g (\mathbf {X})) , \\ \end{array} +$$ + +where $g()$ and $\phi_o()$ denote the selection and activation function of Oli. Here, $\mathcal{I}()$ denotes the operation of moving zero elements from the input vector, $\widetilde{\mathbf{X}} \in \mathbb{R}^{S \times 1}$ denote the state (that participates in subsequent propagation) of $S$ winning neurons identified by Oli from $\mathbf{X}$ , and $\mathbf{e} \in \mathbb{R}^{N \times 1}$ is a binary vector with value one on winning neurons with $\mathbf{1}_N^{\top} \mathbf{e} = S$ , where $\mathbf{1}_N^{\top}$ is a 1-vector of size $N$ . + +After selecting the winning neurons, the subsequent Ast modulate their connections as described by Eq. (2), excluding the pruning function $\mathcal{P}(\cdot)$ . We formulate the Glia unit as, + +$$ +\mathbf {W} ^ {\prime} = \phi_ {a} \left(f \left(\widetilde {\mathbf {W}} ^ {t}\right)\right), \quad \widetilde {\mathbf {W}} ^ {t} = \mathcal {I} \left(\mathbf {e} \odot \mathbf {W} ^ {t}\right), \tag {4} +$$ + +where $\odot$ is the element-wise product, $\mathbf{e}$ and $\mathcal{I}()$ select the weights $\widetilde{\mathbf{W}}$ associated with $\widetilde{\mathbf{X}}$ from $\mathbf{W}$ , where $\widetilde{\mathbf{W}} \in \mathbb{R}^{S \times 1}$ . In this way, Oli simplifies the network by empowering Ast to respond solely to specific weight components, thereby enhancing Ast's modulation capacity. + +Group-level: Since Glia shares similar properties with Ast, we adopt the concepts from [17], and extend the model of the Glia unit into groups. Therefore, the model's complexity depends on the number of Glia, The Ablation study examines Glia numbers' impact on performance. + +We conduct multiple, e.g., $M$ Glia units, where $\mathbf{G}_{\{M\}} = \{\mathbf{O}_{\{M\}}, \mathbf{A}_{\{M\}}\}$ . Each Glia unit corresponding to a subset + +![](images/67da2e963b53f3bb568fefb38ab684860e951f6a7c91f635a89ad031aa49054d.jpg) +The impact of Oli and Ast on its subsequent state + +![](images/51899b1b97871355d43b0441a6d61a4c1a4a3a25066166c87a18073c201d4ec0.jpg) +(a) Interaction within a Glia unit +(b) Interaction between Glia units +Figure 3. The interaction pipeline in Glia units. (a) Olis $\mathbf{O}_{\{M\}}^t$ and Asts $\mathbf{A}_{\{M\}}^t$ at iteration $t$ is affected by history output of $\mathbf{O}_{\{M\}}^{t-1}$ and $\mathbf{A}_{\{M\}}^{t-1}$ from iteration $t-1$ . (b) A Glia unit $\{\mathbf{O}_k^t, \mathbf{A}_k^t\}$ involves interactions with the rest $M-1$ Glia $\{\mathbf{O}_{\{M-1\}}, \mathbf{A}_{\{M-1\}}^t\}$ . The red zoom in as an example of an Oli that varies temporally. + +from all $N$ pre-neurons, e.g., the $k^{th}$ Oli, $\mathbf{O}_k$ , establishes a bidirectional feedback connection with $N_{k}$ pre-neuron states to select the winning neurons. + +Then, the $k^{th}$ Ast, $\mathbf{A}_k$ , modulates the weights $\widetilde{\mathbf{W}}_k$ of these $S_{k}$ winning neurons. Note, if the $k^{th}$ Ast is not connected to any pre-neurons, it will be removed (Fig. 2). We rewrite Eq. (3) and Eq. (4) to define a group of Glia units, + +$$ +\widetilde {\mathbf {X}} = \mathcal {I} \left(g _ {k} \left(\mathbf {e} _ {k} \odot \mathbf {X}\right)\right) _ {k = 1} ^ {M}, \tag {5} +$$ + +$$ +\mathbf {W} ^ {\prime} = \phi_ {a} \left(f _ {k} \left(\widetilde {\mathbf {e}} _ {k} \odot \widetilde {\mathbf {W}} ^ {t}\right)\right) _ {k = 1} ^ {M}, +$$ + +where $g_{k}()$ and $f_{k}()$ denote the selection and modulation functions of $k^{th}$ Oli and Ast. We define $\mathbf{e}_k\in \mathbb{R}^{N\times 1}$ and $\widetilde{\mathbf{e}}_k\in \mathbb{R}^{N_k\times 1}$ to select the subset of all pre-neurons, where $\mathbf{e}_k$ and $\widetilde{\mathbf{e}}_k$ are binary vectors with value one for matching $N_{k}$ pre-neuron states with the $k^{th}$ Oli, and the weights $\widetilde{\mathbf{W}}_k$ of the associated $S_{k}$ winning neurons with the $k^{th}$ Ast. Note that $\mathbf{1}_N^{\mathrm{T}}\mathbf{e}_k = N_k$ and $\mathbf{1}_{N_k}^{\mathrm{T}}\widetilde{\mathbf{e}}_k = S_k$ + +Interaction-level: The interaction of Glia units, $\mathbf{G}_{\{M\}}$ , encompasses two aspects. i) The interaction within each Glia unit involves $\mathbf{O}_k$ collaborating with $\mathbf{A}_k$ to iteratively optimize the neural structure and connections. Moreover, $\mathbf{O}_k^t$ at the $t^{th}$ iteration is influenced by the optimization results on the network of $\mathbf{O}_k^{t - 1}$ and $\mathbf{A}_k^{t - 1}$ from the $(t - 1)^{th}$ iteration, which impacts the optimization of $\mathbf{O}_k^t$ . This enables us to improve the previous functions $g_{k}()$ and $f_{k}()\mathrm{to}g_{k}^{t}()$ and $f_{k}^{t}()\mathrm{by}$ incorporating temporal abilities (Fig. 3a). Note that the time step $t$ in $\mathbf{W}^t$ denotes the iterative modulation of weights by Ast, while $t$ in $g_k^t ()$ and $f_{k}^{t}()\mathrm{denotes~the~}t^{th}$ iteration of Oli and Ast. + +ii) The interaction between Glia units, $\mathbf{G}_{\{M\}}$ . Taking $\mathbf{G}_k = \{\mathbf{O}_k,\mathbf{A}_k\}$ as an example, $\mathbf{G}_k$ undergoes optimization by collaborating with the rest $M - 1$ Glia, $\mathbf{G}_{\{M - 1\}}$ , at each iteration (Fig. 3b). We construct the interaction function $\mathcal{U}()$ to characterize the collaboration pattern in $\mathbf{G}_{\{M\}}$ , which ensures $\mathbf{O}_k^t$ and $\mathbf{A}_k^t$ undergo continuous dynamic updates during optimization. We rewrite Eq. (5) as + +$$ +\begin{array}{l} \widetilde {\mathbf {X}} = \mathcal {U} \left(\mathcal {I} \left(g _ {k} ^ {t} \left(\mathbf {e} _ {k} \odot \mathbf {X}\right)\right)\right) _ {k = 1} ^ {M}, \\ \widetilde {\mathbf {X}} ^ {\mathsf {T}} \mathbf {W} ^ {\prime} = \mathcal {U} \left(\widetilde {\mathbf {X}} ^ {\mathsf {T}} \left(\phi_ {a} \left(f _ {k} ^ {t} \left(\widetilde {\mathbf {e}} _ {k} \odot \widetilde {\mathbf {W}} ^ {t}\right)\right)\right)\right) _ {k = 1} ^ {M}, \\ \end{array} +$$ + +where $\mathcal{U}() = \{u_1(), u_2()\}$ , $u_1()$ and $u_2()$ are applicable to the collaboration of $\mathbf{O}_{\{M\}}$ and $\mathbf{A}_{\{M\}}$ . + +Building on the concept of Glia [20], Oli receives stimulation from the pre-neuron states and provides neurotrophins as feedback to select the winning neurons. However, this becomes challenging in complex neural networks due to the potentially large number of neurons and connections. To address this, we introduce an integration function $\mathcal{H}()$ to enhance Oli's capacity to process large inputs. A similar approach is applied to Ast for integrating the connections from the winning neurons. Formally, + +$$ +\begin{array}{l} \widetilde {\mathbf {X}} = \mathcal {U} \left(\mathcal {I} \left(g _ {k} ^ {t} \left(\mathcal {H} (\mathbf {e} _ {k} \odot \mathbf {X})\right)\right)\right) _ {k = 1} ^ {M}, \\ \widetilde {\mathbf {X}} ^ {\top} \mathbf {W} ^ {\prime} = \mathcal {U} \left(\widetilde {\mathbf {X}} ^ {\top} \left(\phi_ {a} \left(f _ {k} ^ {t} \left(\mathcal {H} (\widetilde {\mathbf {e}} _ {k} \odot \widetilde {\mathbf {W}} ^ {t})\right)\right)\right)\right) _ {k = 1} ^ {M}, \tag {7} \\ \end{array} +$$ + +where $\mathcal{H}() = \{h_1(), h_2()\}$ denotes the integration function that enhances the processing ability of each $\mathbf{O}_k$ and $\mathbf{A}_k$ in $\mathbf{G}_{\{M\}}$ . We name the Eq. (7) as our G-N model. + +# 3.3. Framework of GliaNet + +With our G-N model, we can construct the GliaNet to optimize network structure and connections adaptively. Given a set of input $\mathbf{X}$ , we rearranging Eq. (1) to (7) and yields: + +$$ +\mathbf {Y} = \mathcal {N} \left(\mathcal {O} (\mathbf {X}, \Phi), \mathcal {A} (\widetilde {\mathbf {W}}, \Theta)\right), \tag {8} +$$ + +where $\mathcal{N}()$ aims to perform various downstream tasks, i.e., $\mathcal{N}()$ is an M-P model-based neural module (NM) with connecting weights $\mathbf{W}$ . We introduce the Glia module (GM) into the NM based on our G-N model. In GM, Oli identifies the winning neurons $\widetilde{\mathbf{X}}$ from $\mathbf{X}$ to participate in subsequent propagation via the function $\mathcal{O}()$ , and their weights $\widetilde{\mathbf{W}}$ are modulated by Ast via function $\mathcal{A}()$ , which defined in Eq. (2) (excluding the function $\mathcal{P}()$ ). The connecting weights of Oli $\Phi = \{\phi_{\mathcal{H}},\phi_g,\phi_{\mathcal{U}}\}$ and Ast $\Theta = \{\theta_{\mathcal{H}},\theta_f,\theta_{\mathcal{U}}\}$ are implied in $\{g_k^t ()\}_{k,t = 1}^{M,T},\{f_k^t ()\}_{k,t = 1}^{M,T},\mathcal{H}()\mathrm{and}\mathcal{U}()$ . + +Both $g_{k}^{t}()$ and $f_{k}^{t}()$ utilize a temporal-iterative approach to optimize the network structure, endowing them with the characteristics of processing time series data. Consequently, LSTM with a recursive structure is used to construct these functions, i.e., $[\mathrm{LSTM}^q]_{q=1}^Q$ , where $Q$ denotes + +the number of layers within LSTM. The input of each LSTM layer integrates the output of all previous LSTM layers, e.g., $g_{k}^{t}(x,q) = \sum_{q = 1}^{q - 1}f_{k}^{t}(x,q)$ , to enhance each Oli response to its every optimization history. + +The construction of the integration function $\mathcal{H}()$ must satisfy two requirements: 1) Compress the matrix composed of neuron states and weights in NM; 2) Ensure that the compressed matrix retains as much key information as possible. These requirements are implemented by $h_1()$ and $h_2()$ in $\mathcal{H}()$ , respectively. $h_1()$ employs average pooling, compressing each Glia input into a lower-dimensional feature. For $h_2()$ , the ViT module is utilized. Each Glia input features are treated as a patch, incorporating positional information to represent their associations across NM. Note that due to the compression operation, ViT can be designed as an extremely lightweight model. + +The collaboration between $\mathbf{G}_{\{M\}}$ is established by interaction function $\mathcal{U}(\cdot)$ , and implemented via a chain optimization strategy. As depicted in Fig. 3b, in the $k^{th}$ Glia unit $\mathbf{G}_k = \{\mathbf{O}_k,\mathbf{A}_k\}$ , $\mathbf{O}_k$ is optimized to select winning neurons, followed by the optimization of $\mathbf{A}_k$ to modulate their connections. At each iteration, training proceeds from $\mathbf{G}_1$ to $\mathbf{G}_M$ until the optimization of $\mathbf{G}_{\{M\}}$ is completed. Therefore, the realization of $\mathcal{U}(\cdot)$ involves the optimization of $\{g_k^t (\cdot)\}_{k,t = 1}^{M,T}$ and $\{f_k^t (\cdot)\}_{k,t = 1}^{M,T}$ . The chain optimization strategy, by the interaction function $\mathcal{U}(\cdot)$ , establishes the temporal correlation between different neurons, enabling the optimized neuron to have a temporal impact on other neurons. + +# 3.4. Training Scheme + +Dynamic interaction exists between the neuron and Glia [20], offering an alternative optimization strategy for GliaNet. Since neurons tend to develop preferentially in the nervous system [12], we implement optimization on the NM in the training set first and then proceed to optimize the GM in the validation set. Note that we split the original training set $(\mathbf{X})$ into training $(\mathbf{X}^{tr})$ and validation $(\mathbf{X}^{val})$ sets, and $\mathbf{X}^{tr} \gg \mathbf{X}^{val}$ . This brings two advantages: 1) $\mathbf{X}^{val}$ makes the optimized neural structure and connections have good predictive ability for unseen data via the optimization of Glia. 2) Small-scale $\mathbf{X}^{val}$ improves the training speed of GM. The optimal parameters $\mathbf{W}$ of NM are determined by minimizing the following function + +$$ +\mathbf {W} ^ {*} = \underset {\mathbf {W}} {\arg \min } \mathcal {L} ^ {\mathrm {N M}} \left(\mathcal {N} \left(\mathbf {X} ^ {t r}, \mathbf {W}\right), \mathbf {Y} _ {\mathrm {g t}}\right), \tag {9} +$$ + +where $\mathcal{L}^{\mathrm{NM}}()$ is the task specific loss function and $\mathbf{Y}_{\mathrm{gt}}$ is the ground-truth label. + +With the initialized $\mathbf{W}^*$ , we then optimize the GM with a data term $\mathcal{L}^{\mathrm{data}}()$ and regularization term $\mathcal{L}^{\mathrm{reg}}()$ , where $\widetilde{\mathbf{W}}^{*}$ is from $\mathcal{O}_k(\cdot)$ . The data term forces $k^{th}$ Glia, $\mathbf{G}_k$ , to optimize NM for high performance with its supervision as, + +$$ +\mathcal {L} _ {k} ^ {\mathrm {d a t a}} (\Phi , \Theta) = \mathcal {L} _ {k} ^ {\mathrm {N M}} \left(\mathcal {N} \left(\mathcal {O} _ {k} \left(\mathbf {X} ^ {\text {v a l}}, \Phi\right), \mathcal {A} _ {k} \left(\widetilde {\mathbf {W}} ^ {*}, \Theta\right)\right), \mathbf {Y} _ {\mathrm {g t}}\right), \tag {10} +$$ + +Algorithm 1: The GliaNet Optimization Algorithm +Input: NM parameters: W, GM parameters: $\Phi$ and $\Theta$ , training set $\mathbf{X}^{tr}$ , validation set $\mathbf{X}^{val}$ , ground-truth label: $\mathbf{Y}_{\mathrm{gt}}$ , max iterations: $R$ . Output: GliaNet output: Y +1 for $r = 1$ to $R$ : +2 if $r\% 2 == 0$ : +3 Optimize $\mathcal{L}^{\mathrm{NM}}(\mathbf{X}^{tr}, \mathbf{Y}, \mathbf{Y}_{\mathrm{gt}}) \to \mathrm{Update~W}^*$ via Eq. (9) +4 else: +5 for $k = 1$ to $M$ : +6 Optimize $\mathcal{L}_k^{\mathrm{GM}}(\mathbf{X}^{val}, \mathbf{Y}, \mathbf{Y}_{\mathrm{gt}}) \to \mathrm{Update}$ $\Phi_k^*$ and +7 $\Theta_k^*$ via Eq. (12) +8 end for +9 $\Phi^*$ and $\Theta^*$ +10 end for + +The regularization term, inspired by [54], encourages each $\mathbf{O}_k$ and $\mathbf{A}_k$ to learn similar representations for different features from GM, e.g., $z_{i}$ and $z_{N + i}$ , from the same neuron state from the NM, $\mathbf{X}$ (see supplementary material details). + +$$ +\mathcal {L} _ {k} ^ {\text {r e g}} (\Phi , \Theta) = - \sum_ {i = 1} ^ {N} \log \frac {\exp \left(z _ {i} \cdot z _ {i + N}\right) / \tau}{\sum_ {p = 1} ^ {2 N} \mathbb {1} _ {[ p \neq i ]} \exp \left(z _ {i} \cdot z _ {p}\right) / \tau}, \tag {11} +$$ + +where $\mathbb{1} \in \{0, 1\}$ is an indicator function evaluating to 1 if $p \neq i$ and $\tau$ is a temperature. Taking Eq. (10) and (11), the final learning objective of $\mathbf{G}_k$ is formulated as + +$$ +\begin{array}{l} \Phi_ {k} ^ {*}, \Theta_ {k} ^ {*} = \underset {\Phi_ {k}, \Theta_ {k}} {\arg \min } \left(\mathcal {L} _ {k} ^ {\mathrm {d a t a}} (\Phi , \Theta) + \lambda \mathcal {L} _ {k} ^ {\mathrm {r e g}} (\Phi , \Theta)\right) \\ = \underset {\Phi_ {k}, \Theta_ {k}} {\arg \min } \left(\mathcal {L} _ {k} ^ {\mathrm {G M}} (\Phi , \Theta)\right). \\ \end{array} +$$ + +(12) + +where $\lambda$ is to balance the two items. Compared with AstroNet [16] employing carefully tuned initialization, our alternative optimization strategy (see Algorithm 1) demonstrates superior effectiveness across multiple public datasets without additional manual pruning. + +# 4. Experiments + +Implementation Details. Our GliaNet is implemented in PyTorch and trained via SGD optimizer with a learning rate of $1e - 1$ . We set the number of Glia units as $M = 4$ , i.e., $\mathbf{G}_{\{4\}} = \{\mathbf{O}_{\{4\}},\mathbf{A}_{\{4\}}\}$ , each Oli and Ast contains $Q = 3$ LSTMs inside, $\lambda = 1e - 1$ in Eq. (12). Please refer to the Supplementary Material for more details. All report figures are the average of six times repeated experiments. Our code and models will be made available to facilitate reproducible research. + +Table 1. Experiments on classification with different methods on CIFAR10. With the same settings, compare networks constructed by our G-N model and other models. Our (RNT) and Our (WRN) denote that the NM in GliaNet is set to RNT or WRN. We highlight the best and the second-best numbers in bold and bold. + +
ArchitectureAcc (%)Params (M)Inference speed (ms)
RNT18 [22]94.9611.173
CDS [54]96.4911.173
AstroNet [16]96.527.312
MA-Net [17]96.816.941
Ours (RNT18)96.906.951
RNT50 [22]95.0725.605
CDS [54]96.7825.606
AstroNet [16]96.767.643
MA-Net [17]97.107.363
Ours (RNT50)97.267.342
WRN50 [53]95.0168.9010
CDS [54]96.8868.9013
AstroNet [16]96.9042.558
MA-Net [17]97.2538.897
Ours (WRN50)97.4238.266
+ +Image Classification. We validate our GliaNet performance on CIFAR10, CIFAR100 [27] and ImageNet-1k [8]), with commonly used convolutional neural networks as the NM including ResNet (RNT) [22], Wide ResNet (WRN) [53], DenseNet-BC (DNT-BC) [24], and vision transformers including ViT [10] and Swin [31]. We further compare our GliaNet with State-of-the-Art (SOTA) NAS methods [45, 47], DyNN method [52], A-N model-based AstroNet [16] and MA-Net [17], M-P model-based CDS [54] with contrastive learning to verify our adaptive ability. + +Segmentation. Our method is evaluated on the COCO [30]. The baselines include box-supervised methods [43] and fully-supervised methods [42]. + +Object Detection. Our method is evaluated on COCO with Faster RCNN [38] and Dynamic DETR [7]. Note baselines in all our experiments are re-trained following [16]. + +# 4.1. Experimental Results + +Image Classification. The experimental results of our GliaNet on CIFAR10 and ImageNet-1k are shown in Tab. 1 and Tab. 2. For CIFAR10, our GliaNet achieves SOTA accuracy on RNT18, RNT50, and WRN50 and outperforms CDS, AstroNet and MA-Net by $0.40\%$ , $0.39\%$ and $0.14\%$ in accuracy on average. Notably, our method reduces the capacity of RNT18, RNT50 and WRN50 by $37.33\%$ , $71.33\%$ and $44.47\%$ , respectively. For ImageNet-1k, on average, our GliaNet outperforms the CDS, AstroNet and MA-Net by $0.62\%$ , $0.60\%$ and $0.16\%$ in accuracy, respectively. Our method reduces the capacity of networks by $35.87\%$ and + +Table 2. Experiments on classification with different methods on ImageNet-1k. With the same settings, compare networks constructed by our $G-N$ model and other models. + +
ArchitectureAcc (%)Params (M)Inference speed (ms)
RNT18 [22]69.2111.686
CDS [54]72.8511.687
AstroNet [16]72.828.054
MA-Net [17]73.277.523
Ours (RNT18)73.397.493
RNT50 [22]75.3026.1115
CDS [54]78.2526.1118
AstroNet [16]78.318.709
MA-Net [17]78.968.169
Ours (RNT50)79.158.157
+ +Table 3. Experiments on segmentation with various backbones on COCO. RNT50, RNT50-CDS, RNT50-Ast, RNT50-MA and RNT50† pre-trained on ImageNet-1k by standard training, CDS, AstroNet, MA-Net and Our methods. + +
ModelbackboneAP\( AP_S \)\( AP_M \)\( AP_L \)
BoxInst [43]RNT5032.115.634.343.5
CDS [54]RNT50-CDS32.515.934.643.2
AstroNet [16]RNT50-Ast32.715.734.143.6
MA-Net [17]RNT50-MA34.716.434.844.6
OursRNT50†35.716.834.645.2
CondIns [42]RNT5039.121.541.750.9
CDS [54]RNT50-CDS39.821.642.251.1
AstroNet [16]RNT50-Ast40.021.841.850.8
MA-Net [17]RNT50-MA40.722.742.851.7
OursRNT50†41.522.942.852.0
+ +$68.79\%$ , respectively. By optimizing the structure and connections of the same neural module, GliaNet can adaptively find a larger network structure to fit the distribution of complex datasets. + +Segmentation. We compare with BoxInst and CondInst methods on the COCO dataset. Note that the backbone, i.e., RNT50, of the standard segmentation method is pretrained on ImageNet-1k. Keeping the same as other settings in BoxInst and CondInst, we only replace RNT50 with RNT50-CDS, RNT50-Ast, RNT50-MA and RNT50†, which are pre-trained using different methods, including CDS, AstroNet, MA-Net and our GliaNet. + +Tab. 3 reports the comparison of our method against baselines on the COCO dataset. The pre-trained G-N model based-backbone (RNT50†) with our method, compared to the second-best method (MA-Net), achieves AP improvements of $1.0\%$ and $0.8\%$ , respectively. Fig. 4 shows our qualitative segmentation comparison against previous backbones, affirming our advantages. We predict a sharper and + +![](images/0cad8a94715c712533d9aa99a423a6f744ad824d02cebb138e32f20c8bf8ad72.jpg) +(a) Input + +![](images/258dd40d006e8efbebdb74dd27aefd1a9a02e24ed7b9417f190ef2225bd4d1e1.jpg) +(b) AstroNet + +![](images/2a9559a98277174fd03d3a7874851fd36eedc868bc8f3e6d8a4fd95f79819b9a.jpg) +(c) Ours +Figure 4. We display the segmentation results on images (a) using different backbones, which are obtained by AstroNet (b) and Our (c). Our segmentation boundary is more precise compared to baselines, e.g., areas in the red rectangle. + +Table 4. Experiments on object detection with various backbones on COCO. RNT50, RNT50-CDS, RNT50-Ast, RNT50-MA and RNT50† pre-trained on ImageNet-1k by standard training, CDS, AstroNet, MA-Net and Our methods. + +
ModelbackboneAP\( AP_S \)\( AP_M \)\( AP_L \)
Faster RCNN [38]RNT5037.421.241.048.1
CDS [54]RNT50-CDS38.321.642.050.1
AstroNet [16]RNT50-Ast38.021.342.250.3
MA-Net [17]RNT50-MA39.821.942.551.6
OursRNT50†40.522.142.952.0
Dynamic DETR [7]RNT5042.924.644.954.4
CDS [54]RNT50-CDS43.225.145.454.8
AstroNet [16]RNT50-Ast43.525.045.550.0
MA-Net [17]RNT50-MA44.025.845.855.2
OursRNT50†45.126.046.054.8
+ +more complete contour compared to the AstroNet method, especially on elephant legs and horse ears. + +Object Detection. Tab. 4 shows our object detection performance on the COCO dataset. We employ the same method for acquiring backbones as in the segmentation task and then fine-tune them with identical settings for the object detection task. Experimental results indicate that utilizing the pre-trained backbone $(\mathrm{RNT50\dagger})$ from our method results in AP improvements of $0.7\%$ and $1.1\%$ compared to the second-best method, i.e., MA-Net (RNT50-MA) in Faster RCNN and Dynamic DETR, respectively. + +# 4.2. Discussions + +Comparison with Vision Transformer. We employ the visual transformer as the NM in the GliaNet for evaluating the effectiveness of our method on ImageNet-1k. The results are shown in Tab. 5. Compared with ViT and Swin, by following their settings (e.g., the input size is $384^2$ ) for training, our method achieves a notable improvement in accuracy by $1.62\%$ and $1.20\%$ . It also reduces the capacity of + +Table 5. Results of our method on the visual transformer on ImageNet-1k. Our (ViT-B) and Our (Swin-B) denote that the NM in GliaNet is set to ViT-B and Swin-B, respectively. B denotes the standard model of ViT and Swin. + +
ArchitectureAcc (%)Params (M)Inference speed (ms)
ViT-B [10]77.9086.0025
Ours (ViT-B)79.5270.2520
Swin-B [31]84.5088.0037
Ours (Swin-B)85.7078.3833
+ +Table 6. Evaluation of GliaNet in transfer learning. GliaNet and ViT are pre-trained on ImageNet-1k and then fine-tuned on CIFAR100. L denotes the large model of ViT. + +
ArchitectureAcc (%)Params (M)
ViT-B [10]87.1386.00
Ours (ViT-B)88.0572.40
ViT-L [10]86.35307.00
Ours (ViT-L)87.20252.70
+ +Table 7. Compared our method with the SOTA DyNN method on ImageNet-1k. Take RNT50, whose performance is close to that of the DyNN method as a reference. + +
ArchitectureAcc (%)Params (M)Inference speed (ms)
RNT50 [22]75.3025.6015
Boost-DyNN [52]76.0511.3811
Ours (RNT50)79.158.157
+ +ViT and Swin by $18.31\%$ and $10.93\%$ . For the popular visual transformer, our method shows the potential to alleviate the high parameter problem of transformers and provides a new perspective for obtaining efficient transformers. + +Transfer Learning Ability. We adopt ViT as our experimental benchmark. Both GliaNet (with ViT as the NM) and ViT undergo pre-training on ImageNet-1K for 40 epochs, followed by fine-tuning on CIFAR100. Tab. 6 illustrates that transfer learning, especially utilizing the pre-trained GliaNet, yields superior performance, highlighting the remarkable transferability of our method. + +Comparison with DyNN Method. We evaluate the performance of our connection-based adaptive modulation method with the sample (feature)-based adaptive inference DyNN method. Tab. 7 reveals that, in comparison with the SOTA Boost-DyNN $(76.05\%)$ , our GliaNet $(78.96\%)$ maintains competitive performance with lower parameters. + +Comparison with NAS Methods. We report the performance results of our GliaNet and SOTA NAS methods on CIFAR10 in Tab. 8. Compared with NAS-LID and HOTNAS, our method improves the accuracy by $0.30\%$ + +Table 8. Comparison with SOTA NAS methods. GliaNet and NAS architectures are searched and evaluated on CIFAR10. Time cost only denotes the search time by our method and NAS methods. Our (DNT-BC) denotes that the TNet in our GliaNet is set to DNT-BC. + +
ArchitectureAcc (%)Params (M)Time Cost (GPU days)
DNT-BC [24]96.5425.60-
NAS-LID [23]97.526.902.30
HOTNAS [51]97.544.703.40
Ours (DNT-BC)97.827.490.70
+ +Table 9. Comparison with SOTA NAS methods fortrasferability. GliaNet and NAS architectures are searched on CIFAR10 and then evaluated on ImageNet-1k. + +
ArchitectureAcc (%)Params (M)Time Cost (GPU days)
RNT50 [22]75.3026.11-
NAS-LID [23]77.106.902.30
HOTNAS [51]77.304.703.40
Ours (RNT50)78.356.890.66
+ +and $0.28\%$ with fewer time costs. The comparison results on ImageNet-1k are demonstrated in Tab. 9. We trained the best-found architectures (both our GliaNet and NAS) on CIFAR10 to evaluate their transferability on ImageNet-1k. Compared to the second-best HOTNAS method, our method leads to an improvement in accuracy by $1.05\%$ , which verifies the transferability of our method. + +# 4.3. Ablation Studies + +This section discusses the rationality of our method, where the NM in GliaNet is set to RNT18 in all experiments and evaluated on CIFAR10. + +The Number of Glia units. We investigate the GliaNet performance concerning the numbers of Glia in the GliaNet. Tab. 10 shows a positive correlation between the number and performance of Glia, i.e., increasing Glia numbers can achieve higher accuracy. However, increasing the number of Glia units significantly increases the training time of GliaNet. Therefore, considering the time cost, we set the number of Glia to 4, i.e., $\mathbf{G}_{\{4\}} = \{\mathbf{O}_{\{4\}}, \mathbf{A}_{\{4\}}\}$ . + +Ablation of GliaNet. Compared to the A-N model-based AstroNet and MA-Net, we select winning neurons by transforming from static connection removal to dynamic neuron search, adaptively searching for neurons rather than empirically pruning connections. + +We set up progressive ablation experiments with four cases to verify the effectiveness of our method. Case 1: Study the existence of a single Glia unit in GliaNet to verify the rationale behind the collaboration between Oli and Ast in optimizing the neural structure and connections. Case + +Table 10. Comparing the accuracy of GliaNet with respect to different numbers of Glia units on CIFAR10. The "Params" in the table denotes the number of parameters in the Glia units. + +
Gliaas Numbers12468
Acc (%)96.6896.7796.8696.8796.90
Params (M)0.841.683.365.046.72
Time Cost (GPU hours)1.162.444.356.107.72
+ +Table 11. Experiments on image classification methods with different model construction manners on CIFAR10. + +
CasesModel Construction MannersAcc (%)Params (M)
RNT18-94.9611.17
Case 1A single Glia unit96.687.04
Case 2Multiple Olis96.726.95
Case 3Multiple Asts96.816.94
Case 4 (Ours)Multiple Glia units96.906.95
+ +2: Study the existence of multiple Olis in GliaNet without introducing Ast to verify the necessity of Oli's adaptive selection of winning neurons. Case 3: Study the existence of multiple Ast in GliaNet without introducing Oli to verify the necessity of Ast's adaptive modulation of connections, this is consistent with the approach used in MA-Net. Case 4: Combining Case 2 and Case 3 to validate the effectiveness of our method. Tab. 11 shows the performance of four cases. Notably, the accuracy of all cases exceeds the RNT18 baseline, and our method achieves the best performance. This demonstrates that the G-N model is more generalizable than both the M-P and A-N models. + +More. Please refer to our supplementary materials for more details, e.g., source code, training, hyper-parameter, and more experimental comparisons and visualization results. + +# 4.4. Conclusions + +In this paper, we propose the Glia-Neuron (G-N) model, which consists of Oli and Ast as integral components of Glia. We study the structural properties and interactions among Glia to develop the GliaNet. The structural properties of Glia enable it to adaptively select winning neurons suitable for network decision-making and modulate their connections. Interactions enhance the Glia's capacity to optimize neural communication. This allows our GliaNet to adaptively optimize its structure and connections during training. Experiments demonstrate that our GliaNet achieves SOTA accuracy and significantly reduces the network's parameters with adaptive optimization. + +Acknowledgment. This work was supported by the National Natural Science Foundation of China (82171965, 62302045), and the Northwest A&F University Scientific Research Startup Foundation. + +# References + +[1] Ben A Barres and Yves-Alain Barde. Neuronal and glial cell biology. Current opinion in neurobiology, 10(5):642-648, 2000. 2 +[2] Gabriel Bender, Pieter-Jan Kindermans, Barret Zoph, Vijay Vasudevan, and Quoc Le. 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However, there are few studies on 3D indoor scene generation with VLMs. This paper considers this task as a planning problem subject to spatial and layout common sense constraints. To solve the problem with a VLM, we propose a new global-local tree search algorithm. Globally, the method places each object sequentially and explores multiple placements during each placement process, where the problem space is represented as a tree. To reduce the depth of the tree, we decompose the scene structure hierarchically, i.e. room level, region level, floor object level, and supported object level. The algorithm independently generates the floor objects in different regions and supported objects placed on different floor objects. Locally, we also decompose the sub-task, the placement of each object, into multiple steps. The algorithm searches the tree of problem space. To leverage the VLM model to produce positions of objects, we discretize the top-down view space as a dense grid and fill each cell with diverse emojis to make to cells distinct. We prompt the VLM with the emoji grid and the VLM produces a reasonable location for the object by describing the position with the name of emojis. The quantitative and qualitative experimental results illustrate our approach generates more plausible 3D scenes than state-of-the-art approaches. Our source code is available at https://github.com/dw-dengwei/TreeSearchGen. + +# 1. Introduction + +3D indoor scene generation [7, 8, 11, 12, 14, 21, 30, 34, 36, 37, 39] refers to the process of automatically producing realistic 3D indoor scenes with a computer program. In recent years, some studies [8, 11, 14, 30, 37] have explored on using natural language for scene generation, as the textual prompts offer a user-friendly interface. Realistic 3D indoor + +![](images/48ba4ff9c354f4d025aac268eb17fcb832ba91815d978c25a873034a834d501f.jpg) +Figure 1. Illustration of chain-like (left) and tree-like (right) reasoning in VLMs on 3D scene generation. Each node represents a token or language sequence. The red dashed nodes indicate the VLM produces an inappropriate output. The chain-like method cannot correct the prior errors and the subsequent process reasons based on the errors, leading to a non-realistic layout, such as exceeding the room. In contrast, the tree-like method can modify the output if a mistake occurs, resulting in a more realistic layout. + +scene generation is crucial in fields such as interior design, 3D gaming, virtual/augmented reality, and embodied AI. + +The primary challenge in generating high-quality scenes is modeling plausible and realistic spatial relationships (i.e., 3D layouts) between objects. To achieve this, early studies [14, 30] adopt a data-driven fashion. They train generative models on 3D scene datasets to learn the joint distribution of real indoor scenes and their textual descriptions. However, collecting 3D scene datasets is challenging and costly, resulting in limited dataset scales and less robust models. Recently, researchers have focused on using large Vision-Language Models (VLMs) [8, 11, 37, 40] to achieve this task. VLMs are trained on large-scale datasets, enabling them to understand complex user instructions and in- + +fer 3D layouts from language based on common knowledge of indoor furnishing. For example, Feng et al. [8] propose LayoutGPT to generate the dimension, location, and orientation parameters for each object within a scene from a textual prompt. However, as shown in Figure 1, the current VLMs perform a token-level, left-to-right decision-making process during inference time [38], which is not suited for 3D layout reasoning. Specifically, such an auto-regressive reasoning method cannot modify previous outputs. If a previous object is placed at an inappropriate location, this error will accumulate. Consequently, it remains a challenge to improve VLM's reasoning ability for 3D scene generation. + +3D scene generation needs to search with a tree-like approach rather than chain-like. When furnishing a room, humans usually place objects sequentially. In addition, each object has multiple candidate positions. We pick one of them for the current object and continue to put the next objects. This process is iteratively applied until we place all the objects. If an object is put in an inappropriate location, it stops the next object from being put in the room and we will adjust the previous decision. Consequently, in Figure 1, the problem space can be represented as a tree. Each layer in the tree denotes an individual object and each node in the same layer represents the candidate placement for the object. The chain from the root node to the last layer is a layout solution. Our objective is to search on the tree to find such a chain, subjected to space range, the placement common sense, non-overlapping, and non-floating constraints. + +Based on the above analysis, we propose a novel global-local tree search method to enhance VLM reasoning for 3D indoor scene generation. Complex scenes with numerous objects make searching a deep tree challenging. Our key insight is that the scene structures can be represented hierarchically. We first construct a hierarchical scene representation from user input. A scene is decomposed as room level, region level, floor object level, and supported object level. This representation serves as a proxy between the textual input and the scene output and we can place the objects region by region, which reduces the computational cost. Subsequently, we propose a global-local tree search method to generate the layout for the object within the same region. The global tree search method places objects sequentially, mimicking human behavior. Specifically, it starts from the root node (the region) and leverages the local tree search method to generate a node in the next layer. Then, the global tree search method turns to the next layer and iteratively applies such a process until it generates all objects. The local tree search method generates the position of an individual object. At each layer, it determines one position parameter by textually and visually prompting the VLM. In our approach, each layer has multiple alternatives. Thus, our method performs a tree search in the problem space. + +To summarize, our contributions are three-fold: + +(1) We propose a novel global-local tree search method to enhance VLM reasoning for generating realistic 3D indoor scenes; +(2) We design a hierarchical scene representation as a commonsense bridge between textual input and 3D indoor scenes, further reducing computational costs. +(3) Our quantitative and qualitative studies demonstrate that our method generates more realistic 3D indoor scenes than state-of-the-art approaches. User studies suggest that our approach ranks the best among the three approaches. + +# 2. Related Work + +3D Scene Generation is not as trivial as directly using a 3D object generation model to generate multiple objects. The primary challenge lies in layout generation, which requires modeling spatial and semantic relationships among objects. In the early stage, some works train generative models (e.g. GANs [18, 19], VAEs [7, 12, 39], diffusion models [14, 30, 36, 39], and auto-regressive models [21, 34]) with 3D scene datasets [9, 10, 32]. However, the 3D scene datasets are considerably small compared with 3D object datasets (3D-FRONT [9] $18\mathrm{k}+$ vs. Objaverse [6] $800\mathrm{k}+$ and Objaverse-XL [5] $10\mathrm{M}+$ ). Thus, models trained on small-scale datasets are less robust and limited in achieving satisfactory performance. Recently, some works [8, 11, 27, 37] utilize the commonsense of VLMs to understand user-provided instructions and generate layouts. For example, they use CLIP [27] to retrieve the most relevant 3D objects by measuring the similarity scores between the textual object descriptions and the image renderings of the objects from a 3D object database. LayoutGPT [8] directly outputs the scene layout formatted as Cascading Style Sheets (CSS), including size, location, and orientation for each object. However, the current pre-trained language models cannot comprehensively perceive the space, and thus usually yield unsatisfactory results, such as objects intersecting with each other. To this end, HoloDeck [37] and AnyHome [11] propose to generate scene graphs, which represent the objects as nodes and spatial relationships as edges, and propose rule-based algorithms to convert the scene graph into the room layout. However, the rules are imperfect, leading to low diversity and impractical results. In our work, we strive to utilize the VLM to perceive the space of indoor scenes and achieve reasonable object placements rather than a rule-based algorithm. + +Reasoning with Vision-Language Models is very important in problem-solving, decision-making, and critical thinking [13]. VLMs can be prompted with a standard input-output paradigm [1, 2, 4, 15, 20, 31]. However, language models are trained to generate coherent language sequences. Such a simple prompting method falls short when the task is complex and requires multi-step reasoning. To enable step-by-step reasoning Wei et al. [35] pro + +pose Chain-of-Thought (CoT), which enforces the language models output intermediate thoughts. CoT significantly improves the performance on reasoning tasks. Nevertheless, some tasks require exploring multiple alternatives at each intermediate step rather than just picking one. To this end, Yao et al. [38] propose Tree-of-Thoughts (ToT), which maintains a tree of thoughts and leverages classical tree search algorithms to find solutions for a complex task. Inspired by ToT, we treat generating layouts for 3D scenes as a tree search problem and propose the global-local tree search method to generate layouts. + +# 3. Problem Formulation + +Given a textual prompt $x$ , we aim to generate a 3D scene with $N$ objects $S = \{o_1, o_2, \dots, o_N\}$ with a VLM, where each object $o_i = (c_i, s_i, p_i, r_i)$ , $c_i$ is the category of the object, $s_i$ , $p_i$ , and $r_i$ denote size, position and orientation, respectively. The standard input-output (IO) reasoning method directly produces a 3D scene: $S \sim p^{\mathrm{IO}}(S|x)$ . During the reasoning of VLMs, the chain-of-thought (CoT) method yields a chain of intermediate thoughts $t_1, t_2, \dots, t_n$ to bridge $x$ and $S$ . Each intermediate thought $t_i \sim p^{\mathrm{CoT}}(t_i|x, t_1, t_2, \dots, t_{i-1})$ is sampled auto-regressively and produces the final output $S \sim p^{\mathrm{CoT}}(S|x, t_1, t_2, \dots, t_n)$ . However, there is a large semantic gap between the input and output, thus it is hard for the current method to directly map from $x$ to $S$ . Besides, both IO and CoT methods follow a left-to-right manner, which cannot modify previous decisions. + +In our work, we first generate a proxy $P$ for linking the user input and the 3D scene: $p^{x\rightarrow S} = p^{P\rightarrow S}(S|P)p^{x\rightarrow P}(P|x)$ . It is a hierarchical representation, which decomposes a scene into multiple regions (see more details in Section 4). We independently generate all the regions and then combine the regions into a whole room. Each region contains an object set $S^{\prime} = \{o_{1}^{\prime},o_{2}^{\prime},\dots ,o_{N}^{\prime}\}$ and an edge set $E = \{e_{ij}|o_i,o_j\in S\}$ . The object set is different from $S = \{o_1,o_2,\dots ,o_N\}$ . In $S^{\prime}$ , the category $c_{i}$ and size $s_i$ are determined while the placement attributes, i.e. $p_i$ and $r_i$ , have not been determined in $p^{x\rightarrow P}(P|x)$ . There is an anchor object in $S^{\prime}$ that represents the primary function of this region. Each edge is the spatial relationship between an object and the anchor, denoted as $e_{i,a}$ . + +In $p^{P \to S}(S|P)$ , we propose an improved reasoning method as a tree search for 3D scene generation (see more details in Section 5). We aim to determine the orientation $r_i$ and location $p_i$ for all $o_i' \in S'$ . We propose a global-local tree search method to achieve this. It searches on the problem space, a tree, aiming at finding a solution for the placements of each object, and will trace back if it fails to go deeper into the tree. The global tree search method is an object-level solver, which manages the generating process globally. It puts the objects via the local + +tree search method sequentially as the human does: $o_{i+1} \sim p(o_{i+1}|e_{ia}, o_1, o_2, \dots, o_i, o_{i+1}')$ . It suggests that the determination of the orientation and location of the $(i+1)^{\text{th}}$ object is conditioned on the objects whose orientation and location are determined, relationship with the anchor, and the category $c_{i+1}$ and size $s_{i+1}$ of the $(i+1)^{\text{th}}$ object itself. In contrast, the local tree search method is a parameter-level solver. It decomposes the generation of the orientation and location into smaller sub-tasks. Each sub-task also has multiple alternatives and the problem space spans as a tree. + +In the following sections of this paper, we first introduce the hierarchical scene representation in Section 4. Then, we propose our global-local tree search method in Section 5.1 and Section 5.2, respectively. + +# 4. Hierarchical Scene Representation + +Generating a 3D indoor scene from natural language is a complex task because there is a large semantic gap between the text and the scene. To this end, we first leverage the VLM to understand the user requirements and produce a hierarchical scene structure representation, serving as a proxy between the text and the scene. In this section, we introduce the hierarchical representation and how to generate such a representation with the VLM. + +We represent the scene structure hierarchically including room, region, floor object, and supported object levels, as shown in Figure 2. We start from the user input and prompt the VLM to generate the hierarchical scene representation from left to right. During the generation process, we explicitly prompt the VLM to follow the user's input and consider the common sense of indoor furnishing. + +Room level. In Figure 2 (1), the first level is the root node, denoting the entire room $P$ . We prompt the VLM to generate a reasonable dimension for the room, parameterized by the length and width $\dim = (l, w)$ . + +Region level. In Figure 2 (2), the second level is the region level, we divide the room into multiple functional regions. Each region is characterized by its dimensions $\dim_i = (l_i, w_i)$ . We enforce them to share the width with the room to ease the calculation of region positions and absolute object positions in the region. + +Floor object level. In Figure 2 (3), the third level is the floor object level, which represents the objects that should be placed on the floor, called floor objects. Each floor object should belong to exactly one region. As described in Section 3, we utilize the VLM to generate $S'$ and $E$ for each region. We first prompt the VLM to generate some objects with its category $c_i$ and size $s_i$ , where the object should be semantically consistent with the region function. We request the VLM to choose an anchor object from the object set. Other objects are spatially related to the anchor object, such as a coffee table placed in front of the sofa (anchor), and we also utilize the VLM to determine the spatial rela + +![](images/d674b7d690a3bd8c045bab916549db1e87615c379db7750b084f3b746b09c0fd.jpg) +Figure 2. We prompt a VLM to generate the hierarchical scene representation level by level. From left to right, we decompose the scene into room, region, floor object, and supported object levels. The final representation is shown on the right-most side in this figure. + +tionships, i.e. edge between objects and the anchor $e_{i,a}$ . The VLM can choose from the following options: place_front, place_beside, and place_around. + +To get the 3D object models in the object set, we retrieve them from the Objaverse-1.0 database [6]. We adopt the process outlined in HoloDeck [37]. We use the CLIP model [27] to measure visual similarity, Sentence-BERT for textual similarity [28], and compute dimension discrepancies for object retrieving. + +In particular, we use the VLM to generate the placement rule for the anchor object, i.e. place_along_WALL, place_in_center, and place_at-corner. The anchor always faces the free space of the region. The anchor position and orientation are important because we need to use $e_{i,a}$ to reason the placement of other objects. + +Supported object level. In Figure 2 (4), the fourth level is the supported object level, which presents the objects that should be placed on the floor objects, named supported objects. Some floor objects, like desks and nightstands, can support other objects, while others, such as wardrobes and floor lamps, cannot. Similarly, we also build an object set and an edge set and retrieve 3D models for the supported objects akin to the process at the floor object level. + +# 5. Global-Local Tree Search in VLM + +Based on the analysis in Section 3 and the proxy $P$ in Section 4, we propose a global-local tree search method to reason a 3D scene with a VLM via $p^{P\rightarrow S}(S|P)$ . + +To make the VLM reason spatially, which requires perceiving the scene, we feed textual-visual prompts to the VLM. Specifically, we discretize the top-down view of a scene layout as a grid, as shown in Figure 4. In the grid, the existing objects are represented as rectangles and the anchor object is highlighted in red. We prompt the VLM with the grid and textual instructions, guiding it to reason spatially on the grid. For example, we wish to put a nightstand, which occupies two columns, to the right side of the anchor. The cells on the right side of the anchor are filled with distinct emojis to make the VLM distinguish the cells. The VLM is asked to answer the name of the emojis of the + +columns where the nightstand should be placed. + +# 5.1. Global Tree Search + +Given the object set $S'$ and the edge set $E$ defined in the hierarchical scene representation, we aim to reason the orientation and location of each object. + +For orientations, we prompt the VLM to select a rule from the following options: face to anchor, back to anchor, face the same direction of the anchor, and face the opposite direction of the anchor. Based on the rules and the anchor's location and orientation, we can determine the orientation of the non-anchor objects. + +Based on the problem formulation in Section 3, we treat it as a tree search problem. To solve this, we propose our global tree search method to globally maintain this process. The global tree search method can be described as: (1) decompose the thoughts, (2) generate the thoughts, and (3) search the tree of thoughts to find a solution with the depth-first-search (DFS) algorithm, where thoughts stand for the nodes in the problem tree. + +Thought decomposition. As shown in Figure 3 (2), the tree is started from the region node and each layer represents an individual object. We decompose the task into the placement for each object. We initially place the anchor object in the empty region. The remaining objects are then placed in descending order of their dimensions. + +Thought generation. In Figure 3 (2), given the relationship between the $(i + 1)^{\mathrm{th}}$ object and the anchor $e_{i + 1,a}$ and a tree state $s_i = \{o_1,o_2,\dots ,o_i\}$ , we propose at most $k$ alternative thoughts for the $(i + 1)^{\mathrm{th}}$ object. That is, $o_{i + 1}^{(j)}\sim p_{\theta}(o_{i + 1}|s_i,e_{i + 1,a})(j = 1,\dots ,k)$ , where $p_{\theta}$ is a thought generator. The thought generator $p_{\theta}$ is the local tree search method, which will be introduced in Section 5.2. + +Search algorithm. We aim to explore the most promising solution first, thus we use the DFS algorithm to search for the solution. As shown in Figure 3 (2), the algorithm starts from the region node. The algorithm iteratively generates a thought in each layer with the local tree search method. If it successfully generates a thought in layer $i + 1$ , i.e. enough space to satisfy the spatial relation, the algorithm will walk + +![](images/466477ace6b7b24a78123ecb30ec922e70eff724a6e5354adb5630c0cf07fc36.jpg) +Figure 3. To generate a layout for a scene with quantities of objects, we independently generate the layout for each region. The global and local tree search method starts from the root node and goes deep by generating a thought. If the thought generator fails to produce a thought, it will trace back to the parent node and move to another thought. + +![](images/4e0fbd4929e069ceec3f01abd5886b77bceef7d3a47bb71852950f1f07f6b6f1.jpg) +Figure 4. We discretize the top-down view as a grid and fill the cells with emojis. The brick and white go emojis stand for the wall and region boundary respectively. + +to the next layer of the tree. Otherwise, the algorithm will propose thoughts via the thought generator at most $k$ times $o_{i+1}^{(1\cdots k)}$ until succeeds. If all the $k$ attempts fail, it suggests that the previous placements, $o_1, o_2, \dots, o_i$ , tend to be inappropriate. The algorithm then traces back to layer $i$ and regards it fails in the layer. Then, it will retry in layer $i$ . The algorithm performs iteratively and ends after successfully proposing a thought in the last layer of the tree. + +# 5.2. Local Tree Search + +The local tree search method plays the thought generator for the global tree search method. It takes as input the relation between the $(i + 1)^{\mathrm{th}}$ object and the anchor $e_{i + 1,a}$ and the intermediate tree state $s_i = [o_1,o_2,\dots ,o_i]$ , and outputs the position $p_{i + 1}$ of the $(i + 1)^{\mathrm{th}}$ object. We also regard location determination as a tree search problem, named local tree search. The algorithm is described as follows: + +Thought decomposition. First, we determine the object should be placed on which side of the anchor in the top-down view (i.e. left, right, top, and bottom). Second, if the side determination step chooses top or bottom, we determine the rows in the grid as shown in Figure 4 where the new object should be placed. On the contrary, if the side is left or right, we determine columns in this step. Third, we determine the axis which is different from Step 2. At each step, there are also multiple alternatives. Thus the problem space can be presented as a tree. + +Thought generation. At each step, we textually and vi- + +sually prompt the VLM, as shown in Figure 4. The VLM is prompted to consider the layout common sense to generate reasonable thoughts. For side determination, the VLM should choose one of the side options. For row and column determinations, the VLM needs to choose the emojis where the number of them is equal to the object dimension. + +Thought Evaluation. The VLM needs to evaluate intermediate thoughts. For example, in the side determination step, we prompt the VLM to evaluate if the chosen side has an appropriate position to put the new object. In particular, for the last step, we check whether the bounding box of the new object will intersect with others. The output of the evaluator means whether the current step succeeds. + +Search algorithm. The local tree search shares the same search algorithm with the global counterpart. If the local tree search fails to produce all the thoughts in the three layers although it fully searches the tree with maximum $k$ attempts, it suggests the global tree search method unable to place the current object. + +# 6. Experiments + +
TypeSizeDescription
BathroomSmallA cozy bathroom with a compact shower and sleek vanity
BathroomMediumA modern bathroom with marble countertops and a spacious shower
BedroomMediumA modern bedroom with a comfortable queen-sized bed
KitchenMediumA modern kitchen with a kitchen island and stainless-steel finishes
Living roomSmallA snug living room with a rustic coffee table and warm throw blankets
Living roomMediumA mid-century living room with retro furniture
Living roomLargeA living room featuring oversized sofas and a projector setup
+ +Table 1. Some example prompts generated by ChatGPT. + +In this section, we present our experimental results on + +3D scene generation and provide comparisons with state-of-the-art approaches. + +# 6.1. Setup + +Input Prompts. We leverage ChatGPT to produce textual prompts for four types of scenes: bathroom, bedroom, kitchen, and living room. Each prompt consists of room size (one of small, medium, or large) and a description of how to furnish the room, such as "A room with a queen-sized bed for sleeping and an office table for working". We generate 120 prompts, with 30 prompts for each scene type. All the generated samples in our experiments originate from these prompts. Table 1 illustrates some example inputs in our experiment generated by ChatGPT. + +Parameter Settings. We apply OpenAI GPT-4o API to conduct our experiments. The breadth (the maximum attempts $k$ ) of the tree is important for the global-local tree search algorithm. If $k$ is too small, it may not successfully find an optimal solution. If $k$ is too large, the search space will be large and the API cost will be extremely high. Therefore, we make a trade-off between effect and cost. In the global tree search module, we set $k = 3$ for the anchor objects. For other objects, we set $k = 1$ . In the local tree search module, we set $k = 2$ for the side determination step and set $k = 1$ for others. + +Metrics. To quantitatively measure the methods, we follow HoloDeck [37] to compute the CLIP score [27]. Specifically, we use the OpenCLIP library with the ViT-L/14 model pre-trained on the LAION-2B dataset [29]. Subsequently, we calculate the cosine similarity between the top-down rendering of scenes and a prompt template "a top-down view of [scene type]". We multiply the similarities by 100 as the CLIP score. + +To qualitatively measure the methods, we calculate the reciprocal rank. We first render the scenes from the top-down view for each scene with Blender. Subsequently, we pair the results from different methods feeding the same input and shuffle them. We invite 15 annotators to rank the generated scenes. They are asked "Which scene is more realistic and makes common sense, jointly considering the position and orientation?" If the reciprocal rank is close to 1 of a method, it indicates the generation result by the method ranked first among the annotators. + +# 6.2. Compared Approaches + +We compare our method with two state-of-the-art approaches: HoloDeck and AnyHome: + +AnyHome [11] leverages an LLM to generate the spatial relationships between objects and then uses a rule-based algorithm to generate a coarse layout. Subsequently, AnyHome utilizes a score sampling distillation process [3, 22] + +to refine the coarse result. + +HoloDeck [37] also produces spatial relationships between objects with an LLM. It iteratively adds objects to the scene. When putting each object, it first gets all valid placements without object collisions and without exceeding the room's boundaries. Then, HoloDeck chooses the optimal place that satisfies most spatial relationships. The spatial relationships are checked by pre-defined rules. + +# 6.3.Quantitative Results + +As shown in Figure 5, our proposed method outperforms HoloDeck and AnyHome in most of the scene types. HoloDeck and AnyHome rely on pre-defined rules for object placement, limiting their flexibility. In contrast, our method puts an individual object with the local tree search module. This module decomposes the task into several steps and utilizes a VLM to reason in the top-down view space. The pre-trained VLM incorporates rich common sense and we only use it to solve such small sub-tasks that the VLM can produce reliable responses. Nevertheless, our method has less 0.24 CLIP score than HoloDeck in the kitchen. This may be because the layout of kitchens is commonly place objects along walls and they do not have obvious spatial relationships between the objects. Besides, by horizontally comparing the results of our method in different scene types, our method achieves 29.93 and 30.18 in the bedroom and living room, respectively, outperforming others. This may also be because there are obvious spatial relationships in the bedroom and living room. For instance, a TV stand in front of a sofa, a nightstand beside a bed, a table in front of a sofa, etc. + +6.4. Qualitative Results + +
MethodBathroomBedroomKitchenLiving roomAverage
AnyHome0.4210.4220.5280.4010.443
±0.16±0.19±0.26±0.15±0.20
HoloDeck0.6600.5770.5850.5630.596
±0.27±0.24±0.27±0.23±0.25
Ours0.7510.8340.7190.8680.793
±0.29±0.25±0.29±0.23±0.27
+ +Table 2. Mean (↑) and STD reciprocal rank of different methods. + +Comparison. We show some samples generated by different methods of four scene types in Figure 6. From the visualizations, our method generates more realistic scenes. For example, objects in the living room generated by our method are well placed. In Figure 6 (A), a chair is placed in front of a desk for users to sit on the chair and work on the table. In Figure 6 (B), the sofa, coffee table, and TV stand are center-aligned to make users sit on the sofa and watch TV or reach objects on the coffee table. In contrast, + +![](images/a19af1aa654ec422f66fb87dc402ccd23c3d1275d2f6a91d19dbe6acb1637b39.jpg) +Figure 5. Performance comparison in terms of CLIP score by our proposed model with state-of-the-art methods. + +![](images/069a51ef78f5e8f2e517943880790b33a767c4f4e081fb85946a0a4d4cbefd02.jpg) +Figure 6. The generation results for the bathroom, living room, kitchen, and bedroom. For visualization, we manually set floor textures for the rooms. The results are rendered with the Blender's Cycles engine. + +HoloDeck [37] tends to generate objects along walls, leading to large free space in the middle of the rooms in Figure 6 (C). Besides, HoloDeck produces a semantically inconsistent result in the bathroom, as shown in Figure 6 (D). The armchair should not be present in a living room or bedroom rather than a bathroom. AnyHome's [11] results are the worst and produce semantically inconsistent results. In Figure 6 (E), the dining table and dining chairs are not commonly placed in a kitchen. These findings validate the effectiveness of our hierarchical scene representation. We do not allow a rest region present in a bathroom or a dining region present in a kitchen. Consequently, our hierarchical scene representation can reduce the possibility of providing semantic inconsistency objects. + +Intermediate results. We show visualization results of intermediate steps in Figure 7. We can clearly see our method + +first divides the room into two regions and generate graphs for each region. In Figure 7 (4), object 2 fails to be put into the rest region because of not enough space. In Figure 7 (5), we trace back to object 1 and rotate it, enabling to have enough space to put object 2. In Figure 7 (6-7), we generate the floor objects for each region and supported objects. + +Scene control. We show a visualized example of the complex prompt input and the corresponding scene in Figure 8. The generated scene reflects details in the prompt because of the powerful VLM to understand user's instruction. + +User study. We also conduct user studies to evaluate the generation quality of our method, HoloDeck, and AnyHome. We report the mean reciprocal rank of each method in Table 2. It shows our method achieved the most promising results compared with state-of-the-art approaches. The mean reciprocal rank of our method is 0.793 on average, + +![](images/773f07318f1633005c3fec4258728ab8b846298a80059483a8d01d1e6d4e59ba.jpg) +Figure 7. Visualization results of intermediate steps of generating a scene. + +![](images/aeb526a60625d4e03030ede4fe1990fc021dc46532ba493b85304ba83feccad7.jpg) +Figure 8. Visualization example of the scene control for complex prompt. + +which stands for the samples generated by our approach ranking $1 / 0.793 = 1.26$ among the annotators. In addition, our method gets $+0.360$ and $+0.197$ reciprocal rank improvements on average compared with AnyHome and HoloDeck respectively. Notably, we perform an impressive reciprocal rank score in bedroom (0.846) and living room (0.868), which denotes our method has the advantage in such scenes containing obvious spatial relationships. + +# 6.5. Ablation Study + +
MethodBathroomBedroomKitchenLiving roomAverage
IO0.4370.3500.4410.3560.396
±0.23±0.09±0.22±0.11±0.18
CoT0.6810.7020.6760.6850.686
±0.26±0.25±0.27±0.25±0.26
Ours0.7140.7800.7140.7900.750
±0.27±0.25±0.27±0.25±0.26
+ +Table 3. Mean (↑) and STD reciprocal rank of different methods. + +To validate the effectiveness of our global-local tree search approach in reasoning 3D layout, we conduct studies on the reasoning paradigms on this task. (1) First, we use a standard Input-Output (IO) method akin to LayoutGPT [8]. The IO method uses the room's type, size, and description as input to directly produce the name, location, dimension, and orientation of objects in a scene with an LLM. (2) Second, we use a Chain-of-Thought (CoT) method [35]. The CoT method places objects step by step. If an object fails to be placed in the scene, the algorithm will not adjust previous thoughts. The IO and CoT approaches are the special cases of our method. The IO method does not contain multiple intermediate thoughts and the CoT method reasons step by step but does not explore multiple candidates on intermediate thoughts. We change the maximum attempts $k = 1$ + +for both global and local tree search modules to make our approach degrade to CoT. + +We illustrate the results of user studies in Table 3. It shows our reasoning method achieves 0.75 reciprocal rank on average and outperforms IO and CoT settings with $+0.381$ and $+0.064$ respectively. In addition, we also report the CLIP scores on different ablation settings in Figure 5. From the figure, our full method outperforms the ablation variants overall. The standard IO setting performs the worst. This may be because the training set of the LLM does not contain much 3D layout samples. Our method first leverages the LLM to produce the hierarchical scene representation. It serves as a proxy between the input and layout. Based on this representation, we decompose the layout generation task as small as possible and leverage the VLM to reason in the space. Consequently, our method gets significant improvement compared with the standard IO setting. + +The CoT setting inherits our hierarchical scene representation and task decomposition and also achieves good results. However, we find a marginal CLIP score improvement in our method compared with the CoT setting (only $+0.21$ improvement on average) and it performs slightly worse than CoT for the bathroom $(-0.46)$ and bedroom $(-0.12)$ scenes. The reason may be that we set small $k$ s for our full method for effect and cost trade-off. It leads to our global-local tree search method not fully exploring the problem space. Besides, the algorithm aims to find a global optimal. It will prune the sub-tree if it fails to put an object and discards local optimal solutions. In contrast, the CoT setting will ignore the failure objects, which can lead the algorithm to a local optimal result. + +# 7. Conclusion + +In this paper, we proposed a global-local tree search method to boost the reasoning process of VLMs to generate layouts for 3D scenes. To bridge the semantic gap between natural language instructions and 3D scenes, and reduce the search cost, we represented an indoor scene structure hierarchically and incorporated it into the tree of thoughts in VLMs. The extensive experimental results demonstrated that our approach can generate realistic 3D indoor scenes compared with state-of-the-art methods. In the future, we will extend our proposed method into outdoor scenes and AR/VR applications. + +# 8. Acknowledgment + +This work is partly supported by the Funds for the NSFC Project under Grant 62202063 and U24B20176, Beijing Natural Science Foundation (L243027). + +# References + +[1] Jinze Bai, Shuai Bai, Shusheng Yang et al. 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We build a cost-effective data acquisition system for capturing multi-view polarization images, where a linear polarizer is mounted in front of the off-the-shelf RGB camera and a single image per-view with unknown angle of the polarizer is captured, which eliminates the need for precise alignment. For objects with a hybrid of ceramics (tummy) and metal (feet), we can still nicely recover the specular components and estimate the polarimetric states, directly leading to high-fidelity geometry. + +# Abstract + +The challenge of image-based 3D reconstruction for glossy objects lies in separating diffuse and specular components on glossy surfaces from captured images, a task complicated by the ambiguity in discerning lighting conditions and material properties using RGB data alone. While state-of-the-art methods rely on tailored and/or high-end equipment for data acquisition, which can be cumbersome and time-consuming, this work introduces a scalable polarization-aided approach that employs cost-effective acquisition tools. By attaching a linear polarizer to readily available RGB cameras, multi-view polarization images can be captured without the need for advance calibration or precise measurements of the polarizer angle, substantially reducing system construction costs. The proposed approach represents polarimetric BRDF, Stokes vectors, and polarization states of object surfaces as neural implicit fields. These fields, combined with the polarizer angle, are retrieved by optimizing the rendering loss of input polarized images. By leveraging fundamental physical principles for the implicit representation of polarization rendering, our method demonstrates superiority over existing techniques through experiments in public datasets and real captured images on both reconstruction and novel view synthesis. + +# 1. Introduction + +3D reconstruction has been a long-standing topic in the graphics and vision communities. State-of-the-art methods are mostly designed for opaque surfaces with the Lambertian reflectance model and may perform sub-optimally in non-Lambertian scenes [18, 26], posing a challenge for both acquisition systems and reconstruction algorithms. + +In particular, to deal with glossy or specular regions, except for painting with diffuse coats, specially-tailored devices are often required for recording the controlled environmental illumination and/or reflective lighting conditions. An alternative approach explores polarization cues, referred to as Shape-from-Polarization (SfP) [6, 8, 34], as polarization properties are closely related to surface normals. Moreover, diffuse and specular reflectances exhibit different polarimetric statuses, with the specular being more polarized than the diffuse and their polarization angles being orthogonal. These physical insights can be valuable for algorithms. + +The existing optimization-based $SfP$ methods face challenges when processing irregular triangles or non-manifold mesh, that could be largely overcome by incorporating neural implicit surfaces. Dave et al. [7] propose the first implementation that integrates polarization cues into neural radiance fields. It should be noted, however, that this approach requires an expensive polarization camera for data acquisition to obtain full polarization states, such as Stokes vectors, as supervision for network training. In contrast, we + +argue that, an off-the-shelf RGB camera equipped with a linear polarizer can already effectively acquire the required data, thereby greatly reducing the system cost. + +Our approach employs a single captured polarization image per view as input and builds upon the polarimetric BRDF (pBRDF) model [1], which explicitly models the relation between polarization states of outgoing radiance and surface properties. To represent the object's geometry, we utilize the neural implicit surface, that enables us to query the signed distance values and surface normals at any scene points. With scene coordinates, surface normals, and view directions as input, we employ separate radiance networks to represent the diffuse and specular radiances. These radiances form the basis for computing polarization states, which are depicted by the Stokes vectors and computed using the pBRDF model. Finally, the polarized images are rendered using volume rendering given the Stokes vectors at sampled scene points and the angle of polarizer. By minimizing the rendering loss between the rendered polarized images and the input polarized images, we recover neural radiance fields and surface properties. Importantly, the polarizer angle, which is typically unknown without complex calibration procedures, can be optimized along with the networks. Results tested on both public datasets and real captured data (Sec. 4) demonstrate the effectiveness and robustness of our approach (see the example in Fig. 1). The main contributions are as follows: + +- We devise an cost-effective setup for acquiring polarization images by integrating an off-the-shelf RGB camera with a linear polarizer, eliminating the need for labor-intensive calibration and reducing the overall cost. +- We are the first to leverage a single polarization image per view, in conjunction with neural radiance fields and fundamental physical principles, to enable the end-to-end polarization rendering. +- Experimental results demonstrate that our method well handles non-Lambertian components, leading to high fidelity geometry and radiance decomposition. + +# 2. Related Work + +We will next discuss only the methods of radiance decomposition and geometry recovery for glossy/specular objects using Neural Radiance Fields (NeRF) [19]. + +Glossy and specular surface reconstruction. Recent attempts such as Zhang et al. [32] and Boss et al. [2] aim to address this ill-posed problem by decomposing the specular reflectance with the estimated BRDF. Guo et al. [11] split a scene into transmitted and reflected components, that are modeled with separate neural radiance fields. Verbin et al. [25] consider spatially-varying scene properties and parameterize the outgoing radiance with the directional encod + +ing of the reflected radiance. Yan et al. [28] extend this idea to dynamic scenes with a masked guided deformation field. Xu et al. [27] leverage an image-based rendering pipeline to reconstruct depth and reflection, and then select adjacent views for plausible coherent renderings. Kopanas et al. [15] propose a neural warp field to model catacaustic trajectories of reflections, which enables efficient point splatting-based rendering for complex specular effects. Although better rendering effects can be obtained, these methods often ignore the quality of geometry [30, 36]. Reconstruction results can be refined by balancing the importance of regions with different surface properties, such as adaptive reflection-aware photometric loss [9]. Liu et al. [17] propose to utilize two individual networks to encode the radiance of direct and indirect lights, respectively, which are selected subject to an estimated occlusion probability during rendering. Such a representation efficiently accommodates accurate surface reconstruction of reflective objects. + +Shape from Polarization (SfP). Traditional SfP requires consideration of multi-view consistency, and constraints on the continuity and smoothness of the mesh surface to address the singularities in angle and phase caused by polarization, for better reconstruction [6, 8, 22, 34, 35]. Recent years have witnessed significant advancements of volume rendering based methods in resolving the shape [3, 4, 12, 14, 16, 20, 24, 29]. To be specific, Dave et al. [7] propose the pioneering work and first incorporate polarization cues into the neural radiance field and train the network using polarization states instead of original color information. This approach naturally facilitates decomposition of radiance into diffuse and specular components, leading to improved geometries. However, accurately characterizing polarization information often requires precise rotation and calibration of the polarizer mounted in front of the camera, which can be a tedious task and limits practical utilization. Although emerging snapshot polarization image sensors (e.g., Sony IMX250MZR on-chip polarizer [23]), allow for the acquisition of multi-directional polarized images in a single capture, the cost of such devices makes them impractical for personal use. To bypass the drawbacks of both approaches, we utilize only an RGB camera and a linear polarizer to establish an efficient yet low-cost acquisition scheme, eliminating the need for tedious pre-calibration. + +# 3. Method + +# 3.1. Overview of Reconstruction Pipeline + +We aim to reconstruct the geometry and appearance of a glossy object from a set of posed polarization images $\{\mathbf{I}_{\phi_{\mathrm{pol}}}^k\}$ , where the angle of the polarizer filter $\phi_{\mathrm{pol}}$ is unknown. The entire pipeline, depicted in Fig. 2, consists of three main steps. To commence, we randomly select multi + +![](images/70394fe27bc8445453a348f3a63a16ee3f0683a6f69607d4b0a446c495685ef5.jpg) +Figure 2. Overview of neural glossy object reconstruction with polarization cues. Our method consists of three main steps (1-3): data acquisition, neural radiance field-based representation, and polarization rendering. This work employs neural rendering techniques in conjunction with the fundamental principles of polarization to generate a polarized image. These coupled modules allow for acquiring only one single polarization image at each viewing angle and then recover geometry and material properties through the optimization of rendering loss. Components marked with upward diagonal strips, such as DiffuseNet and SpecularNet, are optimized during training, while those with grid checker patterns are calculated using corresponding equations. + +ple camera poses surrounding the target object and capture a single polarization image $\mathbf{I}_{\phi_{\mathrm{pol}}}$ at each view with our low-cost data acquisition system, as shown in Fig. 1. Next, in alignment with prior study [7], we employ VolSDF [31] and Ref-NeRF [25] as the fundamental blocks for modeling the neural implicit surface and decomposed radiances. Then, we harness the polarimetric BRDF model to accurately estimate Stokes vectors $\mathbf{s}^{\mathrm{out}}$ . Furthermore, we introduce an end-to-end polarization rendering layer, which first estimates the polarizer's angle $\phi_{\mathrm{pol}}$ and then incorporates physical rules to render a polarized image $\mathbf{I}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}$ , which is compared with the captured ground-truth for loss calculation. + +As in Fig. 2, our method utilizes a polarization image $\mathbf{I}_{\phi_{\mathrm{pol}}}$ as the input and initiates by sampling a collection of 3D locations along each camera ray. These locations are processed through a coordinate-based neural implicit surface module, facilitating the estimation of signed distances and surface normals. Along with view directions, separate radiance networks are employed to determine the diffuse and specular components. This separation allows us to effectively handle the non-Lambertian properties exhibited by the surface. Combined with the polarimetric BRDF model, the outgoing Stokes vectors $\mathbf{s}^{\mathrm{out}}$ can be obtained, which lay the foundation for polarization-based rendering. The details on these methods can be found in supplementary materials. + +Next, we present a differentiable processing pipeline to estimate the polarizer's angle $\phi_{\mathrm{pol}}$ , eliminating the need for precise polarization angle measurements and facilitating the implicit rendering of desired polarized images $\mathbf{I}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}$ for loss calculation. Subsequently, we provide a comprehensive analysis of the fundamental principles of polarization and its application in aiding the reconstruction and radiance decomposition in Sec. 3.2. Moreover, we illustrate the rationale behind the efficacy of using a single polarization image + +per view to achieve our goals and elucidate the distinctions between this approach and prior methodologies in Sec. 3.3. + +# 3.2. Polarization-empowered Rendering + +In this approach, we take the estimated outgoing Stokes vector $\mathbf{s}^{\mathrm{out}}$ as input, which characterizes the polarization state of light and is represented by a four-dimensional vector $[s_0,s_1,s_2,s_3]$ . From this, we calculate the fundamental polarization information as follows: + +$$ +\mathbf {I} _ {\mathrm {u n}} = \frac {1}{2} s _ {0}, \rho = \frac {\sqrt {s _ {1} ^ {2} + s _ {2} ^ {2}}}{s _ {0}}, \phi = \frac {1}{2} \arctan 2 (s _ {2}, s _ {1}), \tag {1} +$$ + +where $\rho$ is the degree of polarization (DoP), $\phi$ is the angle of polarization (AoP), and $\mathbf{I}_{\mathrm{un}}$ is the unpolarized intensity. + +On the one hand, the polarized intensity $\mathbf{I}_{\phi_{\mathrm{pol}}}$ (i.e., the captured image) exhibits sinusoidal variation with the rotation angle of the polarizer $\phi_{\mathrm{pol}}$ , as shown below: + +$$ +\mathbf {I} _ {\phi_ {\mathrm {p o l}}} = \mathbf {I} _ {\mathrm {u n}} \left(1 + \rho \cos \left(2 \phi - 2 \phi_ {\mathrm {p o l}}\right)\right). \tag {2} +$$ + +Using Eq. 1, the only unknown variable $\phi_{\mathrm{pol}}$ can be easily solved given $\mathbf{s}^{\mathrm{out}}$ and $\mathbf{I}_{\phi_{\mathrm{pol}}}$ . + +Moreover, Mueller matrices are only valid in the aligned reference coordinate system when considering the light passing through a polarizer. Therefore, for a linear polarizer with a rotation angle of $\phi_{\mathrm{pol}}$ , its Mueller matrix must be deduced according to [5]: + +$$ +\mathbf {M} _ {\phi_ {\mathrm {p o l}}} = \mathbf {R} _ {\phi_ {\mathrm {p o l}}} ^ {\mathbf {T}} \mathbf {M} _ {\mathbf {L P}} \mathbf {R} _ {\phi_ {\mathrm {p o l}}}, \tag {3} +$$ + +where $\mathbf{R}_{\phi_{\mathrm{pol}}}$ is the rotation matrix and $\mathbf{M}_{\mathbf{LP}}$ is the Mueller matrix of an ideal linear polarizer with the horizontal trans + +mission. Both are defined as follows: + +$$ +\mathbf {R} _ {\phi_ {\mathrm {p o l}}} = \left[ \begin{array}{c c c c} 1 & 0 & 0 & 0 \\ 0 & \cos (2 \phi_ {\mathrm {p o l}}) & \sin (2 \phi_ {\mathrm {p o l}}) & 0 \\ 0 & - \sin (2 \phi_ {\mathrm {p o l}}) & \cos (2 \phi_ {\mathrm {p o l}}) & 0 \\ 0 & 0 & 0 & 1 \end{array} \right], \mathbf {M} _ {\mathbf {L P}} = \left[ \begin{array}{c c c c} 0. 5 & 0. 5 & 0 & 0 \\ 0. 5 & 0. 5 & 0 & 0 \\ 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 \end{array} \right]. \tag {4} +$$ + +Accordingly, passing/modulating through a linear polarizer, the outgoing Stokes vector $\mathbf{s}^{\mathrm{out}}$ can be transformed by: + +$$ +\mathbf {s} _ {\phi_ {\mathrm {p o l}}} ^ {\text {o u t}} = \mathbf {M} _ {\phi_ {\mathrm {p o l}}} \mathbf {s} ^ {\text {o u t}} = \mathbf {R} _ {\phi_ {\mathrm {p o l}}} ^ {\mathbf {T}} \mathbf {M} _ {\mathbf {L P}} \mathbf {R} _ {\phi_ {\mathrm {p o l}}} \mathbf {s} ^ {\text {o u t}}. \tag {5} +$$ + +Then, the final rendered polarized image is denoted by: + +$$ +\mathbf {I} _ {\phi_ {\mathrm {p o l}}} ^ {\text {o u t}} = \frac {1}{2} \mathbf {s} _ {\phi_ {\mathrm {p o l}}} ^ {\text {o u t}} [ 0 ], \tag {6} +$$ + +where $\mathbf{s}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}[0]$ is the first element of Stokes vector. + +Loss function. In order to describe the polarization status in the region of interest (RoI) and reduce the background noise, we apply a coordinate-based network to predict the soft mask $m(\mathbf{x})$ of each sampled point $\mathbf{x}$ on the camera ray. Therefore, the complete loss function consists of three components with balancing weights denoted as follows: + +$$ +\mathcal {L} = \mathcal {L} _ {\mathrm {r g b}} + \mathcal {L} _ {\text {m a s k}} + 0. 1 \mathcal {L} _ {\text {e i k o n a l}}. \tag {7} +$$ + +The RGB loss $\mathcal{L}_{\mathrm{rgb}}$ describes the discrepancies between the rendered polarized image $\mathbf{I}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}$ and the captured image $\mathbf{I}_{\phi_{\mathrm{pol}}}$ using $\ell_1$ loss. The loss is masked with the ground-truth mask to reduce the noise from surrounding environment. The predicted mask is supervised by the ground-truth mask with the binary cross entropy loss $\mathcal{L}_{\mathrm{mask}}$ . In addition, we introduce the eikonal loss $\mathcal{L}_{\mathrm{eikonal}}$ [10] to regularize the network to learn a valid signed distance field (SDF). + +# 3.3. Theoretical Analysis + +Our method aims to retrieve not only geometric and polarization information but also the polarizer's angle from multi-view images, requiring only one polarization image per view, which presents us with more unknown variables to address within a reduced set of limitations. + +As aforementioned, we utilize the polarimetric BRDF model to express the Stokes vector $\mathbf{s}^{\mathrm{out}}$ as a linear combination of polarized diffuse and specular counterparts, respectively. Here, we focus solely on the radiance component: + +$$ +\mathbf {I} ^ {\text {o u t}} = (\mathbf {n} \cdot \mathbf {i}) \left(f _ {d} (\mathbf {i}, \mathbf {n}, \mathbf {v}) + f _ {s} (\mathbf {i}, \mathbf {n}, \mathbf {v}, \eta)\right) L _ {i}, \tag {8} +$$ + +where $\mathbf{i}$ , $\mathbf{n}$ , $\mathbf{v}$ and $\eta$ denote the incident lighting direction, normal, viewing direction, and roughness. $L_{i}$ is incident illumination and is usually defined as white light ( $L_{i} = 1.0$ ). + +The diffuse reflectance $f_{d}$ pertains to light that enters the subsurface, scatters, and subsequently transmits back in the + +direction of observation. The specular reflectance $f_{s}$ models both specular lobe and spike, which are defined below: + +$$ +\begin{array}{l} f _ {d} = k _ {d} T (\mathbf {v}, \mathbf {n}) T (\mathbf {i}, \mathbf {n}), \\ \int_ {\mathcal {C}} h _ {1} W (\mathbf {i}) \mathrm {D} (\mathbf {j}), \end{array} \tag {9} +$$ + +$$ +f _ {s} = k _ {s} W (\mathbf {i}, \mathbf {n}, \mathbf {v}, \eta) R (\mathbf {h}, \mathbf {v}), +$$ + +where $W = \frac{DG}{4(\mathbf{n} \cdot \mathbf{o})}$ , and all other parameters are defined in the same manner as outlined in [1]. + +The Fresnel coefficients $T$ and $R$ at polarization filter angle $\phi_{\mathrm{pol}}$ are represented by: + +$$ +T _ {\phi_ {\mathrm {p o l}}} = \frac {T _ {p} + T _ {s}}{2} + \rho_ {t} \frac {T _ {p} - T _ {s}}{2} \cos \left(2 \phi_ {t} - 2 \phi_ {\mathrm {p o l}}\right), \tag {10} +$$ + +$$ +R _ {\phi_ {\mathrm {p o l}}} = \frac {R _ {s} + R _ {p}}{2} + \rho_ {r} \frac {R _ {s} - R _ {p}}{2} \cos \left(2 \phi_ {r} - 2 \phi_ {\mathrm {p o l}}\right), \tag {11} +$$ + +where the subscriptions $p$ and $s$ indicate the components parallel and perpendicular to the reflection plane, while $\rho_{t}$ and $\rho_{r}$ represent the degree of linear polarization for transmittance and reflection respectively, $\phi_t$ and $\phi_r$ correspond to the angle of polarization of transmission and reflection. + +Ultimately, the output estimated radiance $\mathbf{I}^{\mathrm{out}}$ (Eq. 8) at the polarization filter angle $\phi_{\mathrm{pol}}$ can be expressed as follows: + +$$ +\mathbf {I} _ {\phi_ {\mathrm {p o l}}} ^ {\text {o u t}} = (\mathbf {n} \cdot \mathbf {i}) \left(k _ {d} T (\mathbf {v}, \mathbf {n}, \phi_ {\mathrm {p o l}}) T (\mathbf {i}, \mathbf {n}) + \right. \tag {12} +$$ + +$$ +k _ {s} W (\mathbf {i}, \mathbf {n}, \mathbf {v}, \eta) R (\mathbf {h}, \mathbf {v}, \phi_ {\mathrm {p o l}})) L _ {i}. +$$ + +In our implementation, the incident direction $\mathbf{i}$ of the light is approximated as the reflected direction of $\mathbf{v}$ , thereby aligning the half vector $\mathbf{h}$ with the normal direction. Consequently, the unknown variables in Eq. 12 are limited to $\mathbf{n}$ (2 unknowns, parameterized in spherical coordinates), $k_{d}$ (3 unknowns), $k_{s}$ (3 unknowns), $\eta$ (1 unknown), and $\phi_{\mathrm{pol}}$ (1 unknown), totaling 10 unknowns. It is worth noting that, except for $\phi_{\mathrm{pol}}$ , the remaining variables represent intrinsic material properties of the object and are fully disentangled within this material model. These variables remain consistent for the same spatial point, irrespective of the viewing angle. The view dependency of color provides 3 separate constraints (R, G and B) for each view, implying that only four views are sufficient to render the problem overdetermined, eventually forming 12 independent equations. + +Distinction to prior works. In contrast to the well-established polarization method, i.e., PANDORA [7], our method necessitates the acquisition of one single polarization image at each viewing angle. We employ the proposed end-to-end rendering framework and enhance geometric and material reconstruction through optimization of the rendering loss function. Comparing with conventional non-polarization solutions, such as VolSDF [31], our + +![](images/87e3843667b90eb7a21c43371a03cbefc40401edb96c3c1d10e91049fc49001b.jpg) +Figure 3. Qualitative results of captured datasets. For each scenario, the top row shows the input reference image, ground-truth mesh (obtained by painting and scanning), and corresponding normals; the bottom row demonstrates our resolved results, including the rendered image and extracted mesh. + +method stands out in rendering out the higher-quality surface reconstruction. While multi-view consistency assumptions tend to break down when dealing with glossy surfaces in certain scenes, our polarization setup allows for the effective modeling of RGB information from various perspectives through polarization rendering, as denoted by $\mathbf{I}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}$ earlier. This unique representation seamlessly integrates both the object's normal vector and material properties, facilitating the deduction of geometric characteristics and material properties within a unified framework. By progressively enhancing the accuracy of $\mathbf{I}_{\phi_{\mathrm{pol}}}^{\mathrm{out}}$ through the minimization of rendering loss, we implicitly refine the accuracy of normal vector and subsequently elevate the quality of geometry. + +# 4. Experiment + +# 4.1. Datasets and Results + +To meet our requirements, we build a simple data acquisition system using off-the-shelf products, which includes an RGB camera (SONY A6400 with 4K resolution) and a linear polarizer, as shown in Fig. 1. We select several complex + +![](images/a107f56eefe593ecc3366c37c83c74f4ce72bd1a999552923642d91c0145dd9a.jpg) +Figure 4. Qualitative comparison with SOTA methods. Our approach excels in reconstructing intricate features such as beard and tail segments, due to the advantage of the polarization information. + +objects with varying materials, such as ceramics, metal, and plastic, see examples in Figs. 1 (RedOx) and 3 (GreenOx, Cat, Horse and Lays). In practice, we fix the orientation of polarizer across all the captured views and hold the device to collect images approximately evenly around the object, see example camera poses in Fig. 2. The multi-view images are captured under uncontrolled indoor lighting environments, and about 40 images are enough for each object. In all cases, we first downsample the image by a factor of 4 and apply COLMAP [21] to obtain the initial poses. + +Results tested on RedOx model and others are shown in Figs. 1 and 3. Note that, for a variety of different materials (ceramics, metal, etc.), with varying lighting conditions, our method still recovers the surface geometry reasonably well. Moreover, the fact that polarization cues behave differently for the diffuse and specular components greatly aid in understanding material properties and facilitating radiance decomposition, which is an inherently ill-posed problem. As depicted in presented examples, our results reasonably separate the diffuse and specular components. Additionally, the estimated polarimetric cues align with our intuition, i.e., the AoP is orthogonal for the diffuse and specular components, while the DoP is higher for the specular regions. + +# 4.2. Assessments against Counterparts + +Comparisons with non-polarization methods. We have conducted a comparison of our approach with several state-of-the-art radiance decomposition and surface reconstruction methods. For instance, as depicted in Fig. 4, NeuralPIL [2] and PhySG [32] are the baseline methods of PANDORA [7], InvRender [33] accounts for indirect lighting in the BRDF estimation and employs the Spherical Gaussian to represent direct or indirect lighting. NVDiffRec [13] utilizes differentiable Monte-Carlo sampling sampling with a denoiser. Ref-NeuS [9] aims to reduce ambiguity by attenuating the effect of reflective surfaces, while NeRO [17] proposes to reconstruct the geometry and BRDF + +Table 1. Quantitative assessment of rendering and reconstruction quality. To ensure a fair comparison in the 3D reconstruction quality, all models are normalized to the unit sphere. Note that, we do not directly compare with NeuralPIL and Ref-NeuS, as they fail to produce valid geometry in several cases, as evident in Fig. 4. Nevertheless, with the incorporation of polarization cues, our method consistently achieves the best results. + +
RedOxGreenOxCatHorseLays
PSNR ↑SSIM ↑CD ↓PSNRSSIMCDPSNRSSIMCDPSNRSSIMCDPSNRSSIMCD
NeuralPIL22.470.9378-23.510.9301-22.360.8626-21.270.9049-20.930.8657-
PhySG16.420.97372.36e-218.390.98221.43e-216.320.95131.48e-316.590.95181.31e-317.410.95692.66e-3
NVDiffRec30.860.96390.300530.660.98620.263823.610.96140.593627.150.95900.131529.310.96930.1152
InvRender22.470.96312.28e-227.320.97581.78e-222.320.95101.82e-324.920.94641.13e-325.610.96731.21e-3
Ref-NeuS27.210.8562-27.350.8528-23.270.8464-23.450.8562-27.280.91753-
NeRO19.880.85032.04e-316.980.59721.08e-324.510.80399.31e-322.220.82941.20e-326.680.92561.04e-3
Ours (diffuse)25.030.96831.06e-328.240.98607.99e-424.390.94655.91e-322.430.89967.88e-428.520.94573.50e-3
Ours (w/o pol)26.290.96623.01e-330.770.97387.14e-423.840.93431.39e-325.840.95666.76e-424.040.95202.76e-3
Ours30.880.97742.23e-431.020.98831.17e-424.830.96969.88e-527.970.96062.07e-430.820.97801.01e-3
+ +of objects with strong reflective appearances. + +These methods typically rely on RGB data, which can struggle with accurate geometry reconstruction and radiance decomposition due to the limitations of using only intensity measurements. This often results in artifacts and inconsistencies, particularly in areas with strong specular reflections. We propose that incorporating polarization information is essential as it connects surface normals with lighting and material properties, improving the accuracy of these processes. Our evaluations, using open-source code from the original authors, indicate that our approach still delivers superior quality as shown in Tab. 1. However, due to the inherent limitations in various methods, such as, PhySG's overly smooth geometry and inaccurate radiance decomposition, InvRender's superior performance only in synthetic scenarios, Ref-NeuS's effectiveness in view-dependent weighting scheme, and NeRO's proficiency in handling strong reflective objects, conventional objects in real-world settings often exhibit sub-optimal performance. + +In Tab. 1, we further conduct a thorough evaluation concerning the quantitative accuracy on the aforementioned test set. Firstly, we assess the rendering quality of our method and compare it to state-of-the-art algorithms. Hereby, we report the average PSNR and SSIM in comparison to the ground-truth test images. Next, we employ an invasive method to reconstruct the ground-truth shapes for these highly specular objects, so as to facilitate numerical assessment on the geometry recovery. Specifically, we apply a diffuse developer to objects and scan them using a high-end industrial-level 3D scanner. However, due to the potential inconsistency between the scanning and reconstruction coordinate systems, we manually scale and translate the scanned model to align with the reconstruction coordinate system. Subsequently, we utilize the non-rigid ICP algorithm to achieve the complete alignment between the scanned model and the reconstructed model under the shared coordinate system. Once aligned, the sum of the bi-directional chamfer distance (CD) between the reconstructed and scanned models is computed. + +![](images/8b5e34b2968afa464065080478a0a76a667ddda96870db53028a290253599f01.jpg) +Figure 5. Comparison of reflectance separation and surface normals with baselines on rendered Bust model. Note that, although PANDORA outputs sharp results, our method is also able to produce comparable results, because overall we use fewer constraints and need to solve for more unknowns. + +Table 2. Quantitative evaluation on rendered Bust model. We evaluate our method and PANDORA on $10\%$ held-out testsets of 45 images, and report the average peak signal-to-noise ratio (PSNR) and structured similarity (SSIM) of diffuse, specular and mixed radiance, mean angular error (MAE). + +
MethodDiffuseSpecularMixedNormals
PSNR ↑SSIM ↑PSNRSSIMPSNRSSIMMAE ↓
PANDORA23.970.90726.020.86426.860.8954.096°
Ours23.290.88725.970.86026.530.8884.227°
+ +As depicted in Fig. 4, the outcomes indicate that NVDiffRec encounters challenges in effectively disentangling the diffuse and specular components and yields fundamentally erroneous geometric estimations. Surprisingly, this deficiency appears to exert minimal influence on the ultimate rendering quality, as evidenced by the high PSNR and SSIM metrics. We hypothesize that this arises from the method's inability to effectively resolve the inherent ambiguity between these two components, yet it still manages to yield exceptional rendering results grounded primarily in RGB loss. Conversely, NeRO exhibits improved geometric reconstruction capabilities, but its performance in radiance decomposition is lackluster. This arises from its rigid design tailored for entirely specular objects. + +![](images/3ae339da6c3e49bcdcfe0046c72657cc7da7ef82e9c9f58d5f7cdefb1d0c2d69.jpg) +Figure 6. Results of Owl and Gnome models. (a) Comparison of the estimated AoP and DoP. (b) Comparison of the estimated geometry and radiance decomposition. For Owl model, the average PSNR/SSIM on $10\%$ held-out test set between the estimated results of $s_0$ and the corresponding ground-truth are 24.46/0.8756 (ours) and 25.07/0.8972 (PANDORA). The PSNR/SSIM of which on Gnome model are 28.13/0.9274 and 28.43/0.9378. + +Comparisons with polarization methods. Tested on the synthetic data, both visualized results (Fig. 5) and quantitative comparison (Tab. 2) reveal that our method achieves comparable performance with SOTAs. Using Bust model as an example, we present the ground-truth diffuse and specular components, as well as normals and environment map. + +Next, we study the raw data collected by PANDORA [7] (Owl and Gnome), as shown in the leftmost column of Fig. 6(a). These datasets are obtained by acquiring raw images with a dedicated polarization camera equipped with SONY IMX250MZR sensor [23]. After demosaicing, the raw image could be decomposed into four polarization images with different polarizing angles of $0^{\circ}$ , $45^{\circ}$ , $90^{\circ}$ , and $135^{\circ}$ . In the following experiments, we use the image with the polarizer's angle of $135^{\circ}$ as input and leverage our approach to implicitly reconstruct the Stokes vectors and other information. For each case, we randomly select $90\%$ of the images for training. The results are shown in Fig. 6. + +It is noteworthy that, in PANDORA, the AoP and DoP are directly calculated from the captured data and are used as ground truths. In contrast, our approach generates intermediate outputs from the network, and our results can also nicely interpret the polarization states. Furthermore, since polarization is closely related to surface geometry and material properties, better estimated polarization cues result in high-quality decomposed diffuse and specular components, + +![](images/8c0c5a5a5e33dbc44791326b27cda7df4331ce761ce2c56d8cbd4a5fba0e13fb.jpg) +Figure 7. Ablation study. For each example, the top row depicts the results obtained by excluding polarization cues during rendering. Additionally, we exclusively focus on the diffuse components, and the corresponding outcomes are presented in the middle row. The bottom row showcases our outputs. + +such as the tummy of the Owl and the beard of the Gnome. + +# 4.3. Analysis + +Ablation study. As shown in Fig. 7, we conduct two ablation studies for validation, such as, the effectiveness of polarization cues and the consideration of specular components. We first replace the polarized rendering as described in Sec. 3.2 with the normal volume rendering. This design choice is actually an enhanced variant of Ref-NeRF [25]. Secondly, we compute the RGB loss between the rendered diffuse radiances, by removing the specular component during rendering, and the ground truth, this is actually VolSDF [31] with mask supervision used as a baseline. + +Based on the reconstruction results, such as the top case of Fig. 7, where the surface exhibits distinct specular regions, without polarization cues, the network faces challenges in accurately learning distinctive features, leading to less precise surface geometry. Despite this, our method still demonstrates robustness in capturing surface details, even in regions with prominent specular components. + +On the other hand, the final radiance decomposition results demonstrate that polarization cues can aid the network in better approximating true diffuse and specular components. In general, to ensure the consistency across multiple views, the network tends to focus on learning the diffuse + +![](images/05e53ab5c33b999b343b3ed8d6288e5ac81d549bbc6667139984dc34596e3d85.jpg) +Figure 8. Novel view synthesis results of real-world captured objects. Remarkably, despite never encountering this particular perspective during training, the network is still capable of producing reasonably accurate rendering results. + +![](images/39bec9e876ca8702c377c5c31ede83c4a63507e36c9f2f94ef1c27376ba7f4cb.jpg) +Figure 9. Robustness analysis. Despite minor color variations occur in specular regions across different polarization angles, particularly those highlights indicated by red boxes, our algorithm effectively restores a coherent geometry, while accurately recovers the corresponding specular map. + +components. As depicted, in the absence of polarization information, the network lacks substantial physical constraints, making it challenging to learn results that adhere to physics principles. In contrast, our method faithfully follows the polarization theorem during the rendering process, enabling more intuitive and reasonable decomposition. + +Novel view synthesis. We conduct experiments on a held-out test set of the captured objects. These images are carefully chosen to be distinct from the existing viewing angles in the training set. During the testing phase, the network automatically generates essential information, including surface normals, polarization states, and decomposed + +radiances, using only the provided camera poses. The rendered visualizations of our results are illustrated in Fig. 8. + +Robustness to different angles of the polarizer. As previously mentioned, our approach does not require the polarization angle of the input image to be calibrated in advance, as this information can be implicitly solved by the network. From another perspective, the network itself is ignorant of the polarization angle of the input image, and we can theoretically obtain the same reconstruction results. To verify this, we synthesize images with different polarization angles, such as $0^{\circ}$ , $45^{\circ}$ , and $90^{\circ}$ , using Eq. 2, as shown in Fig. 9. Our algorithm produces consistent and high-quality reconstruction results for different inputs. In addition, we output the estimated angle of the polarizer from the network, with an error less than $5^{\circ}$ . + +# 5. Discussion and Conclusion + +This work presents advancements in polarization-based 3D reconstruction of glossy objects, by tackling the highly challenging yet novel task of estimating geometry and appearance from multi-view images with one single polarization angle per-view without pre-calibration. We introduce a fully differentiable polarization rendering pipeline that streamlines data acquisition to a single image per view and automatically determines the polarizer angle, eliminating manual calibration requirements and reducing costs. + +Despite challenges such as color bleeding, our approach accurately reconstructs object geometry and material properties, predicting diffuse and specular maps essential for polarization cues. By implicitly estimating the polarization angle to render a polarized image and comparing it to the captured image to compute loss, our integration of polarization information reinforces the relationship between surface normals and radiances, facilitating precise estimation of components for accurate geometry reconstructions. This work paves the way for high-fidelity reconstruction using accessible tools, with potential applications on devices like smartphones or IoTs. + +# Acknowledgments + +This work was partially supported by NSFC (U24B20154, 62322217, 62322207), Ant Group, Information Technology Center and State Key Lab of CAD&CG, Zhejiang University, and the Research Grants Council of Hong Kong (ECS 27212822, GRF 17208023). + +# References + +[1] Seung-Hwan Baek, Daniel S Jeon, Xin Tong, and Min H Kim. Simultaneous acquisition of polarimetric svbrdf and normals. 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Nerf: Representing scenes as neural radiance fields for view synthesis. In Proc. Euro. Conf. on Computer Vision, pages 405-421, 2020. 2 +[20] Henry Peters, Yunhao Ba, and Achuta Kadambi. pcon: Polarimetric coordinate networks for neural scene representations. In Proc. IEEE Conf. on Computer Vision & Pattern Recognition, pages 16579-16589, 2023. 2 +[21] Johannes Lutz Schonberger and Jan-Michael Frahm. Structure-from-motion revisited. In Proc. IEEE Conf. on Computer Vision & Pattern Recognition, 2016. 5 +[22] Mingqi Shao, Chongkun Xia, Dongxu Duan, and Xueqian Wang. Polarimetric inverse rendering for transparent shapes reconstruction. IEEE Transactions on Multimedia, 2024. 2 +[23] SONY. Polarization image sensor. https://www.sony-semicon.com/en/products/is/industry/polarization.html, 2018. Online. 2, 7 +[24] Ashish Tiwari and Shanmuganathan Raman. Ss-sfp: Neural inverse rendering for self supervised shape from (mixed) polarization. arXiv preprint arXiv:2407.09294, 2024. 2 +[25] Dor Verbin, Peter Hedman, Ben Mildenhall, Todd Zickler, Jonathan T Barron, and Pratul P Srinivasan. Ref-nerf: Structured view-dependent appearance for neural radiance fields. In Proc. IEEE Conf. on Computer Vision & Pattern Recognition, pages 5481-5490. IEEE, 2022. 2, 3, 7 +[26] Bojian Wu, Yang Zhou, Yiming Qian, Minglun Gong, and Hui Huang. Full 3d reconstruction of transparent objects. ACM Trans. on Graphics (Proc. of SIGGRAPH), 37(4): 103:1-103:11, 2018. 1 + +[27] Jiamin Xu, Xiuchao Wu, Zihan Zhu, Qixing Huang, Yin Yang, Hujun Bao, and Weiwei Xu. Scalable image-based indoor scene rendering with reflections. ACM Trans. on Graphics (Proc. of SIGGRAPH), 40(4):1-14, 2021. 2 +[28] Zhiwen Yan, Chen Li, and Gim Hee Lee. Nerf-ds: Neural radiance fields for dynamic specular objects. arXiv preprint arXiv:2303.14435, 2023. 2 +[29] LI Yang, WU Ruizheng, LI Jiyong, and CHEN Ying-cong. Gnerp: Gaussian-guided neural reconstruction of reflective objects with noisy polarization priors. arXiv preprint arXiv:2403.11899, 2024. 2 +[30] Wenqi Yang, Guanying Chen, Chaofeng Chen, Zhenfang Chen, and Kwan-Yee K Wong. Ps-nerf: Neural inverse rendering for multi-view photometric stereo. In Proc. Euro. Conf. on Computer Vision, pages 266–284. Springer, 2022. 2 +[31] Lior Yariv, Jiatao Gu, Yoni Kasten, and Yaron Lipman. Volume rendering of neural implicit surfaces. Proc. Neural Information Processing Systems, 34:4805-4815, 2021. 3, 4, 7 +[32] Kai Zhang, Fujun Luan, Qianqian Wang, Kavita Bala, and Noah Snavely. Physg: Inverse rendering with spherical gaussians for physics-based material editing and relighting. In Proc. 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While diffusion-based methods have shown promise in text generation, they still struggle to produce high-quality results. These methods often generate distorted or unrecognizable characters, particularly when dealing with complex characters like Chinese. In such systems, characters are composed of intricate stroke patterns and spatial relationships that must be precisely maintained. We present GlyphMastero, a specialized glyph encoder designed to guide the latent diffusion model for generating texts with stroke-level precision. Our key insight is that existing methods, despite using pretrained OCR models for feature extraction, fail to capture the hierarchical nature of text structures - from individual strokes to stroke-level interactions to overall character-level structure. To address this, our glyph encoder explicitly models and captures the cross-level interactions between local-level individual characters and global-level text lines through our novel glyph attention module. Meanwhile, our model implements a feature pyramid network to fuse the multi-scale OCR backbone features at the global-level. Through these cross-level and multiscale fusions, we obtain more detailed glyph-aware guidance, enabling precise control over the scene text generation process. Our method achieves an $18.02\%$ improvement in sentence accuracy over the state-of-the-art multi-lingual scene text editing baseline, while simultaneously reducing the text-region Fréchet inception distance by $53.28\%$ . + +# 1. Introduction + +Text editing is a task that, given a selected text region, replaces existing text content with new user inputs. The most + +![](images/389e4260b2e3a1227ecc36dd2430f534da5c030ee3ac550b85537e3358dc9966.jpg) +Figure 1. Example results of our scene text editing method on random images collected from the internet. The original images (left column) show source text regions marked with red boxes, with target texts displayed at the bottom left. The edited results (right column) demonstrate our method's ability to preserve both structural accuracy and style consistency through stroke-level guidance across different visual styles and writing systems. + +straightforward approach involves a two-stage process: text removal followed by font-matched text insertion. While this approach may suffice for images with printed texts, it + +requires substantial expertise in font recognition to maintain style consistency. Moreover, for text in natural scenes (i.e. scene texts), this approach faces great challenges: even with perfect font identification, achieving visual coherence between the inserted text and the scene remains infeasible due to complex environmental factors such as perspective distortions, lighting conditions, and surface properties. + +This challenge motivates the task of scene text editing, a special task within image editing domain that aims to modify texts in images while preserving the original style and maintaining visual coherence with the surrounding environment. Advances in this field benefits both everyday users and professional designers, particularly when they deal with typefaces that are either difficult to identify or impossible to replicate through conventional means. + +Toward this end, diffusion-based [4] scene text editing methodologies [1, 2, 6, 25] have demonstrated significant potential to meet these demanding requirements. DiffUTE [1], a specialized scene text editing framework built upon diffusion models, exemplifies this approach. In contrast to text-to-image generation approaches that utilize text encoders such as CLIP [14] for extracting text embeddings from descriptive languages to enable language-driven generation, the framework employs features extracted by a pretrained OCR model from rendered text lines as the glyph guidance for scene text editing. While DiffUTE achieves robust style preservation through its conditional inpainting formulation and demonstrates effective text editing capabilities for scenes with simple printed text, it shows significant limitations in text legibility when handling complex glyph structures such as Chinese characters (Figure 5). These limitations stem from the insufficient representational capacity of its OCR feature utilization in encoding intricate glyph structures. + +To address the challenge of creating robust glyph representations for achieving precise scene text editing results, we propose GlyphMastero, a novel trainable glyph encoder that generates fine-grained glyph guidance for scene text editing. Our glyph encoder distinguishes itself through its explicit modeling of hierarchical relationships between local character-level glyph features and global text-line structures. By capturing these hierarchical relationships and using them for glyph feature generation, our approach enables more nuanced glyph representation learning. Additionally, we incorporate multi-scale OCR features through a feature pyramid network (FPN) [10] to enhance the representation of global text structures. + +We adopt the inpainting-based formulation similar to DiffUTE as our generation backbone and train it with the glyph guidance from our GlyphMastero, achieving substantial performance improvements across writing systems ranging from Latin scripts to complex logographic systems such as Chinese characters. Both quantitative and qualita + +tive evaluations validate the effectiveness of our approach. In Figure 1, we present editing results on various images collected from the internet. + +# 2. Related Work + +Existing approaches for scene text editing can be broadly categorized into two paradigms: GAN-based methods and diffusion-based methods, each employing different strategies for conditioning the generative models. + +# 2.1. GAN-Based Methods + +Early approaches in the domain of scene text editing were predominantly based on Generative Adversarial Networks (GANs) [3]. Among these early works, STEFANN [18] introduced a dual-model architecture that combined a font-adaptive model for maintaining structural integrity with a dedicated style transfer network. In a different approach, MOSTEL [13] advanced the field by incorporating explicit stroke guidance maps to precisely delineate editing regions, while implementing a semi-supervised learning strategy that leveraged both synthetic and real-world data to enhance the model's generalization capabilities. In parallel, several other GAN-based methodologies [5, 8, 26, 27] explored various architectural modifications to improve the quality of text generation. Nevertheless, these GAN-based approaches consistently encountered significant challenges when dealing with complex text structures and diverse style variations, frequently resulting in generated text that exhibited unrealistic characteristics and compromised visual quality. + +# 2.2. Diffusion-Based Methods + +Diffusion models have recently shown superior capabilities in modeling complex data distributions, making them well-suited for scene text editing tasks. These methods primarily differ in their conditioning strategies, which can be categorized into two types: cross-attention guidance and latent space guidance. + +Cross-attention mechanisms have proven effective for conditioning diffusion models with additional information in scene text editing. DiffSTE [6] employs a character encoder for glyph information alongside CLIP [14] encoded instructions. AnyText [24] integrates OCR-extracted neck features from glyph images with CLIP-encoded descriptions. DiffUTE [25] utilizes fixed-length features from TrOCR's [9] final hidden state. Building on DiffUTE, we replace text embeddings with glyph guidance through our novel trainable glyph encoder for comprehensive glyph representations. + +Latent space guidance, popularized by ControlNet [30], introduces conditioning signals into diffusion models by encoding input conditions through convolutional layers and incorporating them into latent representations. Several + +![](images/20697b6bf2a80d9be3fdeea444f6fc49bae3790e2d4eb3b99f57e709faf1ffac.jpg) +Figure 2. General pipeline for conditioning latent diffusion models with additional guidance signals. An extra condition $y$ is processed through a condition encoder $\tau_{\theta}$ to produce a condition embedding $c$ . This embedding guides the denoising UNet via crossattention during the iterative denoising process, which transforms the noisy latent $z_{T}$ into a clean latent representation $z_{0}$ over $T$ steps. Finally, an image decoder $\mathcal{D}$ converts the latent representation $z_{0}$ into the final predicted conditioned image $\hat{x}$ . + +works in text generation [2, 11, 24, 28] have explored adapting this approach for scene text editing. TextDiffuser [2] implements character-level segmentation masks for fine-grained control, while GlyphControl [28] and AnyText [24] introduce indirect latent conditioning through feature concatenation. While these methods demonstrate success in text generation, their reported results suggest limitations in achieving style coherency in scene text editing. Specifically, the generated text style is typically constrained by the typeface used to render the glyph images provided as latent guidance. Based on these observations, we opt for a cross-attention-based approach paired with an inpainting formulation for scene text editing, which enables more precise control over glyph-level features while maintaining style coherence. + +# 3. Method + +# 3.1. Preliminaries + +Diffusion models work by gradually adding noise to data and then learning to reverse this process. The DDPM model [4] was among the first to demonstrate the effectiveness of diffusion models for image generation, establishing foundational principles that subsequent models have built upon. Latent diffusion models [16] (LDMs) improved upon DDPM by operating in a compressed latent space rather than directly on pixels. They first encode images into a more compact representation, apply the diffusion process, then decode back to full images. This approach is more computationally efficient than denoising in the pixel space, making it practical for real-world applications. The training objective of LDMs is to minimize: + +$$ +L _ {\mathrm {L D M}} := \mathbb {E} _ {\mathcal {E} (x), c, \epsilon \sim \mathcal {N} (0, 1), t} \left[ \| \epsilon - \epsilon_ {\theta} \left(z _ {t}, c, t\right) \| _ {2} ^ {2} \right] \tag {1} +$$ + +where $\mathcal{E}$ is the encoder that compresses $x$ to get latents $z$ , $\epsilon$ represents the ground truth noise that is added to $z$ in the forward pass, $\epsilon_{\theta}$ is the time-dependent model that predicts + +the noise added given time step $t$ , realized by a UNet [17], and $c$ represents the conditioning embeddings that guide the denoising process with the cross-attention mechanism. The extra conditioning embeddings $c$ is usually acquired by encoding the extra condition $y$ through a condition encoder $\tau_{\theta}$ that transforms it into an embedding space, such that $c = \tau_{\theta}(y)$ (Figure 2). Once the denoising process is finished, the clean latent feature $z_0$ is decoded through a decoder $\mathcal{D}$ to get the image $\hat{x} = \mathcal{D}(z_0)$ . + +The conditioning mechanism illustrated in Figure 2 can be exemplified through the case of text-guided image generation. In this context, the condition $y$ comprises natural language descriptions (or text prompts) which are processed through a $\tau_{\theta}$ that encodes texts. This encoder is typically implemented using language models, such as CLIP's [9] text encoder or T5 [15]. The resulting text embedding $c = \tau_{\theta}(y)$ serves as a guidance signal for the UNet through the cross-attention mechanism. Upon completion of the denoising process, the model yields a refined latent representation $z_0$ that is conditioned on descriptive languages, and is subsequently transformed into the final image through the image decoder, often realized by a VAE [7] decoder, to get the generated image $\hat{x} = \mathcal{D}(z_0)$ . This cross-attention guided architecture enables the text-to-image diffusion model to learn mappings between arbitrary textual descriptions and their corresponding visual representations during the iterative denoising procedure. + +Many practical applications require modifying specific parts of an image rather than generating entirely new ones. While text-to-image diffusion models excel at global image generation, they need to be extended to support such granular control over specific image regions. For text-guided inpainting, Rombach et al. [16] followed LaMa [23] by introducing additional channels to process a binary mask $m$ that indicates regions to be modified. Specifically, given a binary mask $m$ , they first calculate: + +$$ +x _ {m} = x \odot (1 - m) \tag {2} +$$ + +where $x$ denotes the input image, and $\odot$ denotes the Hadamard (element-wise) product. This operation effectively masks out (sets to zero) the regions marked for inpainting. The latent representation at timestep $t$ , denoted as $z_{t}$ , is then augmented by concatenating it with the mask $m$ and the encoded masked image $\mathcal{E}(x_m)$ , resulting in: + +$$ +\hat {z} _ {t} = \left[ z _ {t}; m; \mathcal {E} \left(x _ {m}\right) \right] \tag {3} +$$ + +where $\mathcal{E}(\cdot)$ is the image encoder function and $[\cdot]$ denotes channel-wise concatenation. The inpainting formulation generalizes text-to-image models by incorporating the binary mask $m$ as an explicit spatial control signal in conjunction with the text condition $c$ , enabling the model to preserve contextual fidelity in unmasked regions while performing targeted generation within masked areas. + +![](images/67a7bf8c466a4b0abd4813acdc69c134868aa6f49f7e0d36f93b7da6637020b4.jpg) +Figure 3. Complete model architecture of GlyphMastero. A specialized glyph encoder that introduces stroke-level precise control to the latent diffusion model for scene text editing. + +# 3.2. Overall Architecture + +We propose GlyphMastero, a novel glyph encoder that produces fine-grained glyph guidance for diffusion models in scene text editing. Relating to the general conditioning pipeline in Figure 2, our approach can be conceptualized as introducing a glyph encoder $\tau_{\theta}$ to transform text conditions $y$ into fine-grained glyph representations $c$ to guide the denoising UNet to generate scene texts. + +In contrast to prior works that directly utilize OCR features for diffusion model guidance - either as an augmentation [6, 24] to or a replacement [25] for natural language conditioning - without additional feature processing, our glyph encoder is a learnable and dedicated module that enhances feature representation through hierarchical processing. Our approach generates more fine-grained representations, significantly improving both text accuracy and style preservation in scene text generation. + +Following [2], our work builds upon inpainting formulation as described in Eq.3 to operate at a region-specific granularity, as scene text editing naturally reduces to an inpainting problem where only the masked text regions require generation. + +Our GlyphMasterso is trained jointly with the latent diffusion model using the objective described in Eq.1, optimizing the glyph encoder directly through generation-based supervision. + +# 3.3. Dual-Stream Glyph Integration + +Figure 3 illustrates the overall architecture of our glyph encoder. Following [24], we incorporate the pretrained PaddleOCR-v4 [12] recognition model - which comprises a backbone, neck, and head - as our feature extractor for glyph images rendered from input texts. We extract two streams of glyph features with the OCR model: a local-level stream (depicted in green arrows) and a global-level stream (depicted in blue arrows), which we systematically integrate through cross-level and multi-scale fusion to derive fine-grained glyph guidance $c$ . + +In the local-level stream, given a text input $y$ , we render a series of single-character glyph images, $x_{l}\in \mathbb{R}^{N\times H_{l}\times W_{l}}$ , serving as the local-level representation of the text input. Here, $N$ is the number of characters, and $H_{l}$ and $W_{l}$ are the height and width of each single character glyph image, respectively. The OCR model's last-layer backbone output, $l_{b}$ , and the neck output, $l_{n}$ , form the local-level stream feature representations. + +In the global-level stream, the input text $y$ is rendered as a unified glyph image $x_{g} \in \mathbb{R}^{H_{g} \times W_{g}}$ , where $H_{g}$ and $W_{g}$ denote the height and width dimensions, respectively. Similar to the local stream, the neck output feature, $g_{n}$ , is extracted for subsequent processing. Unlike the local stream, we integrate $M$ hierarchical backbone features ( $M = 5$ in PaddleOCR-v4) for the global stream through a FPN [10], which we fuses high-resolution, fine-grained features in shallow layers with semantic-rich features at lower resolutions in deeper layers, yielding the enhanced backbone features $g_{b}$ . + +Having extracted four features: $l_{n}$ and $l_{b}$ for the local-level stream, and $g_{n}$ and $g_{b}$ for the global-level stream, we then employ two glyph attention modules (Section 3.4) to capture interactions between local and global features for both the backbone and neck features. The cross-level interaction-enhanced features $o_{n}, o_{b} \in \mathbb{R}^{N \times d_{o}}$ are then obtained through two glyph attention modules $T_{n}$ and $T_{b}$ as follows: + +$$ +o _ {n} = T _ {n} \left(l _ {n}, g _ {n}\right), \quad o _ {b} = T _ {b} \left(l _ {b}, g _ {b}\right) \tag {4} +$$ + +where $d_{o}$ represents the output dimension of glyph attention modules. We note that $T_{n}$ and $T_{b}$ share identical architectural designs; they are independently instantiated to process neck and backbone features respectively. + +Finally, an aggregator $A$ concatenates and projects the two features as follows: + +$$ +c = A \left(o _ {b}, o _ {n}\right). \tag {5} +$$ + +The resulting condition embedding $c \in \mathbb{R}^{N \times D}$ , where + +![](images/d5c30d58e1947baa85106702c7207658bf30d678bd071d712c9294538be1ca20.jpg) +Figure 4. Glyph Attention Module + +$D = d_{o}$ , guides the UNet during both training and inference phases of scene text editing through cross-attention. + +# 3.4. Glyph Attention Module + +The intention of designing the glyph attention module is to use cross-attention to capture the interaction between character-level local features and line-level global features to get a better representation of text glyphs. + +Figure 4 illustrates the details of our glyph attention module. Given the local features $l$ and global features $g$ extracted by the OCR model (where this notation applies to both backbone and neck levels, hence omitting the subscripts for notational simplicity). We first repeat the global feature $g \in \mathbb{R}^{1 \times d_g}$ by $N$ times to obtain $\hat{g} \in \mathbb{R}^{N \times d_g}$ to match the local features $l \in \mathbb{R}^{N \times d_l}$ with respect to sequence length. Here $N$ is the number of characters in the text input. The features $l$ and $\hat{g}$ are then projected to attention space dimension $\tilde{d}$ through learnable linear transformations $\psi_l$ and $\psi_g$ , resulting in projected local and global features $l^p = \psi_l(l)$ and $g^p = \psi_g(\hat{g})$ , both in $\mathbb{R}^{N \times \tilde{d}}$ . + +We add positional embeddings to the two streams of features with rotary positional embedding (RoPE) [22] by computing: + +$$ +\bar {l} ^ {p}, \bar {g} ^ {p} = \operatorname {R o P E} \left(l ^ {p}, g ^ {p}\right) \tag {6} +$$ + +To capture interactions between local and global representations, we perform multi-head cross-attention where positionally encoded $\bar{l}^p$ serves as queries and $\bar{g}^p$ as keys and values, followed by a layer normalization (LN) to produce the attention map $z\in \mathbb{R}^{N\times \tilde{d}}$ . Finally, a linear projection $\psi_{o}$ is applied to map $z$ from attention dimension $\tilde{d}$ to the output size $d_o$ with $o = \psi_o(z)\in \mathbb{R}^{N\times d_o}$ . + +# 4. Experiments + +# 4.1. Dataset + +For both training and experimental evaluation, we utilize AnyWord-3M [25], a comprehensive dataset designed for scene text generation and editing. We utilize the dataset specifically for scene text editing scenario: each sample is + +an image containing multiple line-level annotations, which consists of text content, and its corresponding polygonal position as target area to generate new text. Since each image can have multiple text regions, we randomly sample one text-position pair in training. Our dataset formulation can be written as: + +$$ +\mathcal {D} = \left\{\left(I _ {i}, \left\{\left(T _ {i j}, P _ {i j}\right) \right\} _ {j = 1} ^ {M _ {i}}\right) \right\} _ {i = 1} ^ {N} \tag {7} +$$ + +where $N$ is the total number of images, approximately 3.5 million in case of AnyWord dataset. $M_{i}$ is number of text-position pairs in the $i$ th image. Hence $(T_{ij},P_{ij})$ is a single data sample, where $T_{ij}$ represents the target text string and $P_{ij}$ denotes its spatial location encoded as a quadrilateral polygon with four vertices. During training and evaluation, a binary mask is generated based on $T_{ij}$ to delineate the text region for inpainting. + +We evaluate our model using AnyText-Eval [25] for quantitative analysis (2000 images, 4181 English and 2092 Chinese text-position pairs) and a curated dataset of 80 challenging stylistic images (120 text-position pairs) for qualitative assessment. While AnyText-Eval provides statistical coverage, its target texts match the original, not fully reflecting real-world editing tasks. Our curated dataset focuses on challenging stylistic variations and incorporates new text contents. + +# 4.2. Baseline Methods + +For multi-lingual editing comparisons, we benchmark against state-of-the-art models DiffUTE [1] and AnyText [24]. For AnyText, we use the public AnyWord-3M checkpoint. We trained DiffUTE on AnyWord-3M for 15 epochs with a batch size of 256 and null condition probability of 0.1, matching our model's hyperparameters. + +Many existing methods primarily focused on English text, numbers, and punctuation editing. For English-only comparisons, we evaluated SRNet [26], MOSTEL [13], DiffSTE [6], TextDiffuser [2], and TextCtrl [29] using their publicly available checkpoints. + +![](images/aab93849d1b8cfaca288d73859ed57f20d66455af26c576c5fc1433a934cf61e.jpg) +Figure 5. Qualitative comparison of scene text editing methods. Our GlyphMastero framework demonstrates superior text style preservation and content replacement accuracy. For Chinese cases (with English translations in brackets), our method achieves more precise text generation than DiffUTE and better style preservation than AnyText. + +
ModelText AccuracyStyle Similarity
Sen.Acc ↑ EnglishChineseCER ↓ EnglishChineseFID ↓ EnglishChineseLPIPS ↓ EnglishChinese
DiffUTE0.33190.25230.31860.404814.317624.92950.13130.2056
AnyText0.60670.58010.17300.208810.425724.90040.10980.1978
Ours0.81700.73010.07410.13414.610111.89150.05450.1007
+ +# 4.3. Implementation Details + +We initialize the UNet with Stable-Diffusion 2.1 inpainting weights [16]. And the pretrained OCR recognition model is initialized with PaddleOCR-v4 [12]. + +Each glyph attention module has one multi-head attention layer with 4 heads, with model size $\tilde{d} = 512$ and $d_{o} = 1024$ . Their weights are initialized by Xavier initialization [20]. + +We implemented the FPN specifically suited for the PaddleOCR-V4's backbone module. The module processes a hierarchical feature pyramid $x_{1}, x_{2}, x_{3}, x_{4}, x_{5}$ , where each feature map $x_{i} \in \mathbb{R}^{C_{i} \times H_{i} \times W_{i}}$ represents different levels of glyph features. Lateral connections first project all input features to a common hidden dimension $D$ through $1 \times 1$ convolutions: $f_{i}: \mathbb{R}^{C_{i} \times H_{i} \times W_{i}} \to \mathbb{R}^{D \times H_{i} \times W_{i}}$ . Starting from $p_{5} = c_{5}$ , for each level $i = 4, 3, 2, 1$ , features are then fused as: + +$$ +p _ {i} = g _ {i} \left(u \left(p _ {i + 1}\right) + c _ {i}\right) \tag {8} +$$ + +where $u(\cdot)$ denotes bilinear upsampling, $g_{i}$ is a $3 \times 3$ convolution, and $c_{i}$ represents lateral features. The final feature map undergoes channel projection, downsampling, and pooling to produce the enhanced global feature $g_{b}$ with dimensions matching $x_{5}$ . + +The guidance aggregator consists of two parallel linear projection branches that reduce the dimensionality of input embeddings from 1024 to 512 dimensions, then concatenating them back to 1024 dimensions. + +Our model is trained for 15 epochs with a global batch size of 256 on 8 V100S-32G GPUs. We also use a null condition probability of 0.1 to allow classifier-free guidance (CFG) in inference. See Supplementary Materials for our analysis on effects of CFG in scene text editing task. + +In inference, all methods use DDIM [21] sampler with 20 steps denoising steps, with CFG scale 9 for AnyText and 3 for ours and DiffUTE. + +# 4.4. Quantitative Comparison + +We measure four metrics for different methods: sentence accuracy (Sen.Acc) and character error rate (CER) for text content fidelity; Fréchet Inception Distance (FID) [19] and LPIPS [31] for style similarity. Sen.Acc measures line-level + +Table 1. Comparison with state-of-the-art multi-lingual (English and Chines) methods. $\uparrow/\downarrow$ indicates higher/lower is better. Our method outperforms previous works across all metrics. + +
MethodsAccuracySimilarity
Sen.Acc↑CER↓FID↓LPIPS↓
SRNet0.39940.380227.000.1073
MOSTEL0.57810.198450.240.4883
DiffSTE0.51200.199314.060.1543
TextDiffuser0.52600.235033.150.2406
DiffUTE0.33190.318614.320.1313
AnyText0.60670.173010.430.1098
TextCtrl0.76540.09404.150.0425
Ours0.81700.07414.610.0545
+ +Table 2. English only quantitative comparison results. + +accuracy, while CER is for character-level accuracy. FID measures distribution-level style similarity, while LPIPS focuses on sample-level similarity. We average LPIPS distances over all samples for the final measurement. FID and LPIPS are measured between cropped ground truth image and generated text regions. + +Table 1 shows our comparisons with prior arts that has multi-lingual scene text editing capability. It is seen that our method significantly outperforms prior arts in both text generation accuracy and style similarity. Our overall sentence accuracy (averaging English and Chinese results) is $48.14\%$ and $18.02\%$ higher than DiffUTE and AnyText, respectively; CER is $25.76\%$ and $8.68\%$ lower. For style similarity, we also achieved with substantially lower FID and LPIPS distances compared to DiffUTE and AnyText. For FID evaluations, our method's distance is $57.95\%$ lower than DiffUTE, and $53.28\%$ lower than AnyText, on average. Our LPIPS distance is $53.93\%$ lower than DiffUTE, and $49.54\%$ lower than AnyText. + +Table 2 presents English-only comparison results. Our method achieved the highest accuracy metrics while outperforming all other methods in similarity measures except TextCtrl, which showed marginally better FID and LPIPS. We also evaluated our approach on TextCtrl's ScenePair dataset (1,285 test cases), using their GitHub-published results and evaluation scripts, also achieving favorable outcomes. Full comparison results are available in Supplementary Materials. + +# 4.5. Qualitative Comparison + +Figure 5 presents comparative results among our method, AnyText, and DiffUTE. Our approach demonstrates sub + +
ComponentText AccuracyStyle Similarity
Sen.Acc ↑ EnglishChineseCER ↓ EnglishChineseFID ↓ EnglishChineseLPIPS ↓ EnglishChinese
Full model0.54940.51200.17660.236730.909551.37620.11900.2134
-FPN0.45360.36980.24700.331432.455053.01270.12470.2208
-Tb0.50650.42710.21280.298730.586649.65880.11960.2110
-Tn w/ln0.32630.27350.31370.391630.627151.62880.12110.2121
w/gn0.10030.07190.57270.657934.766151.57880.14120.2334
+ +Table 3. Ablation study results. When removing ${T}_{n}$ ,we experiment with two scenarios: using local features $\left( {l}_{n}\right)$ and global features $\left( {g}_{n}\right)$ . + +stantial improvements over prior arts in both text accuracy and style preservation. We specifically include Chinese characters in our evaluation as they present a more rigorous test case, featuring complex glyph structures with multiple strokes. The superior performance in accurately generating these intricate characters demonstrates our GlyphMastero's effectiveness in capturing stroke-level precision features. More extensive qualitative results are available in the Supplementary Materials. + +# 4.6. Ablation Studies + +To evaluate the effectiveness of individual components, we conducted a systematic ablation study on GlyphMasters. The experiments are performed using a subset of 375K images from the Anyword-3M dataset, with training conducted for 15 epochs using a batch size of 256 on four NVIDIA A100-40GB GPUs. Ablation study results are recorded in Table 3. + +First, we removed the FPN that fuses multi-scale backbone feature maps, and replaced it with the final backbone layer output in global-level stream. The model trained with this modification led to a $22.42\%$ drop in average sentence accuracy for English and Chinese texts and a $28.54\%$ increase in CER (Table 3). These results demonstrate that fusing high-resolution features from shallow layers with semantic-rich features from deeper layers significantly impacts the generated text quality. + +Next, we removed the backbone glyph attention module $T_{b}$ , retaining only the neck glyph attention module $T_{n}$ for cross-level feature capture. This resulted in a $13.68\%$ drop in average sentence accuracy and a $19.20\%$ increase in CER (Table 3) compare to the full model. Notably, removing both FPN and $T_{b}$ yielded better performance than removing FPN alone. We attribute this to the FPN's role in adaptively refining features for $T_{b}$ 's cross-level feature capture. Without FPN, $T_{b}$ struggles to effectively process directly extracted backbone features. + +Finally, we removed $T_{n}$ and used only neck features as guidance, testing two scenarios. First, with position-embedded local neck features $l_{n}$ ( $w / l_{n}$ ), we observed a 43.49% drop in average sentence accuracy and 41.40% + +increase in CER. These significant degradations highlight the crucial role of our glyph attention module in capturing local-global feature relationships. Second, using global neck features $g_{n}$ as prior guidance $(w / g_{n})$ - equivalent to AnyText's OCR feature utilization - yielded the poorest results. We attribute this to $g_{n}$ prior reducing embedding length from $N$ to 1, while local neck features $l_{n}$ maintained length $N$ . + +The style similarity metrics (FID and LPIPS) remain consistent throughout ablation experiments, with only slight variations. This stability aligns with GlyphMastero's core function as a glyph encoder, where its components focus on providing fine-grained glyph guidance, while style preservation is primarily handled by the latent diffusion inpainting model's inherent capacity for maintaining local visual consistency. + +# 5. Conclusion & Limitations + +We present GlyphMastero, a novel trainable glyph encoder that advances scene text editing through effective modeling of hierarchical relationships between local character-level features and global text-line structures. Our approach addresses the challenge of encoding complex glyph structures through multi-scale feature incorporation and explicit modeling of hierarchical glyph relationships. The effectiveness of our approach is demonstrated by an $18.02\%$ improvement in sentence accuracy compare to the previous state-of-the-art method and significant enhancement in style preservation, with text-region FID reduced by $53.28\%$ . + +One limitation of our approach is that accuracy for generating long text, though improved over prior work, still lags behind shorter text. We attribute this to training data limited to $512 \times 512$ resolution and constraints of the base latent diffusion model. Future work will explore higher-resolution training and more robust base models to address this limitation. + +# 6. Acknowledgement + +Xiaolin Hu was supported by the National Natural Science Foundation of China (No. U2341228). + +# References + +[1] Haoxing Chen, Zhuoer Xu, Zhangxuan Gu, Jun Lan, Xing Zheng, Yaohui Li, Changhua Meng, Huijia Zhu, and Weiqiang Wang. Diffuse: Universal text editing diffusion model. 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In this work, we enhance video diffusion models by allowing motion control via structured latent noise sampling. This is achieved by just a change in data: we pre-process training videos to yield structured noise. Consequently, our method is agnostic to diffusion model design, requiring no changes to model architectures or training pipelines. Specifically, we propose a novel noise warping algorithm, fast enough to run in real time, that replaces random temporal Gaussianity with correlated warped noise derived from optical flow fields, while preserving the spatial Gaussianity. The efficiency of our algorithm enables us to fine-tune modern video diffusion base models using warped noise with minimal overhead, and provide a one-stop solution for a wide range of user-friendly motion control: local object motion control, global camera movement control, and motion transfer. The harmonization between temporal coherence and spatial Gaussianity in our warped noise leads to effective motion control while maintaining per-frame pixel quality. Extensive experiments and user studies demonstrate the advantages of our method, making it a robust and scalable approach for controlling motion in video diffusion models. Please see our project webpage; source code and checkpoints are available on GitHub. + +# 1. Introduction + +"We adore chaos because we love to produce order." — M. C. Escher, Dutch artist + +![](images/387aa93a08df1c9a9bf35f99d9e6ede58b342dd769ec3bfc9ab35a5e570f39d0.jpg) +Figure 1. Go-with-the-Flow presents a simple yet effective method for motion-controllable video diffusion models based on optical flow and noise warping. It only requires fine-tuning video diffusion models as a black box using warped noise patterns. Leveraging our models, we can (1) control the motion of individual objects or parts of those objects, (2) direct the camera movement by providing global flow fields corresponding to the desired movements, and (3) transfer the motion from input videos to target contexts. + +The essence of generative modeling lies in producing order from chaos, learning to transform random noise from latent space into structured outputs that align with the distribution of training data. In this paper, we propose a novel approach to enhance generative model learning by proactively introducing partial order into latent space sampling. + +Our work is motivated by the remarkable progress in video diffusion generative models [3, 4, 6, 14, 15, 60] and the equally significant challenges they face in terms of controllability beyond text and image guidance. Fine-grained interactive control over motion dynamics remains an under-explored area due to the intricate spatiotemporal correlations among video frames. The complexity of modern video diffusion architectures [6, 60], which leverage 3D autoencoders [64] and spatiotemporal tokenizers [33], further complicates efforts to adapt models for effective motion + +control. An ideal format for defining and disentangling motion control from other guidance remains an open question. + +Motion-controllable video diffusion model applications typically fall into three categories: (1) local object motion control, represented by object bounding boxes or masks with motion trajectories [12, 24, 36, 42, 45, 54, 56, 59]; (2) global camera movement control, parameterized by camera poses and trajectories [16, 28, 54, 55, 58, 59] or categorized by common directional patterns such as panning and tilting [15, 59]; and (3) motion transfer from reference videos to target contexts specified by prompts or initial frames [1, 13, 27, 32, 35, 53, 61, 62]. However, these approaches share three key limitations: (1) they often necessitate complex modifications to the base model design such as guidance attention [42], limiting compatibility with modern full-attention architectures involving spatiotemporal tokens [60]; (2) they are constrained to specific applications, requiring detailed parameterized motion signals, such as camera parameters, which are challenging to acquire or estimate accurately [67], thus restricting generalizability across diverse scenarios; and (3) they are over-rigid to motion control at the cost of spatiotemporal visual quality. + +To address these limitations, we propose a novel and straightforward method to incorporate motion control as a structured component within the chaos of video diffusion's latent space. We achieve this by correlating the temporal distribution of latent noise. Specifically, starting with a 2D Gaussian noise slice, we temporally concatenate it with warped noise slices, given the optical flow field [49] extracted from a training video sample. Fig. 2 illustrates the diagram of our method. Our approach requires only a change in data: we pre-process training videos to yield warped noise and then fine-tune a video diffusion model. As it occurs solely during noise sampling, our method is agnostic to diffusion model design, requiring no modifications to model architectures or training pipelines. Surprisingly, removing temporal Gaussianity from the noise distribution does not deteriorate model fine-tuning. Instead, it can be quickly adapted after fine-tuning because temporal structure in the chaos of latent space facilitates generative learning and enables motion correspondence. Temporal coherence occurring in the latent space also harmonizes motion control with per-frame pixel quality by inheriting the high-quality prior from the base model. + +It is worth noting that video diffusion fine-tuning relies on efficient noise warping algorithms that introduce minimal overhead during data pre-processing and noise sampling. The existing noise warping algorithm, How I Warped Your Noise (HIWYN) [7], that maintains spatial Gaussianity and enables temporal flow warping, however, suffers from the quadratic computation costs w.r.t. frame count, making it much slower than in real time and therefore impractical for large-scale video diffusion model training. To + +address this, we propose a novel noise warping algorithm that runs fast enough in real time. Rather than warping each frame through a chain of operations from the initial frame, our algorithm iteratively warps noise between consecutive frames. This is achieved by carefully tracking the noise and the flow density along a forward and a backward flow at the pixel level, accounting for both expansion and contraction dynamics, supplemented with conditional white noise sampling from HIWYN Chang et al. [7] to preserve Gaussianity. Algorithm 1 provides further details. We validate the spatial Gaussianity and time complexity of our noise-warping algorithm and apply it to training-free image diffusion models for quantitative and qualitative assessments of controllability and temporal consistency. + +During video diffusion inference, our method offers a one-stop solution for diverse motion control applications by adapting noise warping based on motion type. (1) For local object motion, we interactively transform noise elements within object masks given users' dragging signals. (2) For global camera movement control, we reuse the optical flows from reference videos to warp input noise, and regenerate videos conditioned on different texts or initial frames. (3) For arbitrary motion transfer, the motion representations are not limited to optical flows [49], but also include flows from 3D rendering engines [51], depth warping [63], etc. We validate the effectiveness of our solution across various video generation tasks, demonstrating its ability to preserve motion across different contexts or render distinct motions for the same context. Experiments and user studies indicate the advantages of our solution in pixel quality, motion control, text alignment, temporal consistency, and user preference. + +In summary, our contributions include: + +(1) A novel and simple one-stop solution for motion-controllable video diffusion models, integrating motion control as a flow field for noise warping in latent space sampling, plug-and-play for any video diffusion base models as a black box, and compatible with other types of controls. +(2) An efficient noise warping algorithm that maintains spatial Gaussianity and follows temporal motion flows across frames, facilitating motion-controllable video diffusion model fine-tuning with minimal overhead. +(3) Comprehensive experiments and user studies demonstrating the overall advantageous pixel quality, controllability, temporal consistency, and subjective preference of our method on diverse motion control applications including local object motion control, motion transfer to new contexts, and reference-based global camera movement control. + +# 2. Related work + +# 2.1. Image and video diffusion models + +A natural extension of image generation [18, 19, 26, 37, 39, 44, 46-48] use cases is to cover the temporal dimension for + +video generation. A common approach is frame-by-frame generation using fixed weights, often resulting in flicker or drift. HIWYN [7] addresses this via noise warping, introducing temporally-correlated latent noise based on optical flow, though at the cost of spatial Gaussianity and speed. We propose a novel warped noise sampling algorithm that preserves spatial Gaussianity and runs in real time. Applied to training-free models like DiffRelight [17] and DeepFloyd IF [48], our method improves temporal consistency in relighting and super-resolution. + +Training full video diffusion models offers higher quality [3, 4, 6, 8, 15, 41, 57, 60]. *AnimateDiff* [15] fine-tunes temporal attention layers atop image models. *CogVideoX* [60], a leading open-source model, combines spatial-temporal encoding via 3D causal VAEs [64] and diffusion transformers [38]. We incorporate our warped noise sampling into both *CogVideoX* and *AnimateDiff* to enable motion-controllable fine-tuning, showcasing model-agnostic applicability. + +# 2.2. Motion controllable video generation + +Motion control enhances video diffusion beyond text [15, 60] and image conditioning [14, 57, 69], enabling fine-grained spatiotemporal guidance. Existing work follows three main directions: + +First, local object motion control uses masks or boxes with trajectories [12, 24, 36, 42, 45, 54, 56, 59]. DragAnything [56] manipulates object motion in images without retraining; SG-I2V [36] synthesizes motion from single images. Our method is plug-and-play, treating models as black boxes while using synthetic flows to densify motion at the pixel level. + +Second, global camera control involves camera trajectories [16, 28, 54, 55, 58, 59] or learned directional priors [15, 21, 59, 65, 66]. Unlike supervised camera modules, our method generalizes new camera movements from reference videos without collecting pose annotations. + +Lastly, motion transfer adapts motion from reference videos [1, 13, 27, 32, 35, 53, 61, 62]. DiffusionMotionTransfer [61] preserves layout and motion fidelity; MotionClone [32] encodes motion with temporal attention. Using them as motion transfer baselines, we demonstrate our model's flexibility in combining reference geometries with target text guidance. + +# 3. Method + +Go-with-the-Flow is comprised of two separate parts: our noise warping algorithm and video diffusion fine-tuning. The noise warping algorithm operates independently from the diffusion model training process: we use the noise patterns it produces to train the diffusion model. Our motion control is based entirely on noise initializations, introducing no extra parameters to the video diffusion model. + +![](images/cbaabd366d71bd8880319069b226e0b4378b9a3950af921313db311152fae863.jpg) +Figure 2. Our method consists of three components: flow field extraction, real-time noise warping, and diffusion model finetuning/inference. During fine-tuning, we use the original captions of video samples. At inference, our method enables adaptation of reference motion to various prompts and/or initial frames. + +Inspired by the existing noise warping algorithm HIWYN [7], which introduced noise warping for image diffusion models, we introduce a new use case for the warped noise: we use it as a form of motion conditioning for video generation models. After fine-tuning a video diffusion model on a large corpus of videos paired with warped noise, we can control the motion of videos at inference time. + +# 3.1. Go-with-the-Flow noise warping + +# 3.1.1 Algorithm + +To facilitate the large-scale noise warping required by this new use case, we introduce a fast noise warping algorithm (Algorithm 1) that warps noise frame-by-frame, storing just the previous frame's noise (with dimensions $H \times W \times C$ , where $H$ is height, $W$ is width, and $C$ is the number of channels) and a matrix of per-pixel flow density values (with dimensions $H \times W$ ). The density values indicate how much noise has been compressed into a given region. Unlike HIWYN [7] which requires time-consuming polygon rasterization and upsampling of each pixel, our algorithm directly tracks the necessary expansion and contraction between frames according to the optical flow and uses only pixel-level operations that are easily parallelizable. We show that our algorithm retains the same Gaussianity guarantee as HIWYN [7] (Proposition 1). + +Next-frame noise warping. Our noise warping algorithm calculates noise iteratively, where the noise for a given frame depends only on the state of the previous frame. + +Let $H \times W$ be the dimensions of each video frame. Let $D = [H] \times [W]$ denote a 2D matrix with height $H$ and width $W$ , where we use the notation $[n] := 1, \ldots, n$ . Given the previous frame's noise $q \in \mathbb{R}^D$ and the flow density $p \in \mathbb{R}^D$ together with forward and backward flows $f, f' : D \to \mathbb{N}^2$ , our algorithm computes the next-frame noise and density $q', p' \in \mathbb{R}^D$ such that $q'$ (resp. $p'$ ) is temporally correlated with $q$ (resp. $p$ ) via the flows. + +At a high level, our algorithm (in Algorithm 1) combines two types of dynamics: expansion and contraction. In the case of expansion, such as when a region of the video zooms in or an object moves towards the camera, one noise pixel + +is mapped to one or more noise pixels in the next frame (hence it "expands"). In the case of contraction, we adopt the Lagrangian fluid dynamics viewpoint of treating noise pixels as particles moving along the forward flow $f$ . This often leaves gaps that need to be filled. Hence, for regions not reached when flowing along $f$ , we use the backward flow $f'$ to pull back a noise pixel. That gap is filled with noise calculated with the expansion case. + +Additionally, to preserve the distribution correctly over long time periods, we use density values to keep track of how many noise pixels were aggregated into a given region, so that when mixed with other nearby particles in the contraction case, these higher density particles have a larger weight. This is illustrated in Fig. 8. + +We unify both expansion and contraction cases by building a bipartite graph $G$ where edges represent how noise and density should be transferred from the previous frame to the next. When aggregating the influence from graph edges to form the next-frame noise $q'$ , we scale the noise in accordance with the flow density to ensure the preservation of the original frame's distribution, as detailed in Algorithm 1. The expansion and contraction cases are calculated in tandem to prevent any cross-correlation, guaranteeing the output will be perfectly Gaussian. + +# 3.1.2 Theoretical analysis + +Proposition 1 (Preservation of Gaussian white noise). If the pixels of the previous-frame noise $q$ in Algorithm 1 are i.i.d. standard Gaussians, then the output next-frame noise $q'$ also has i.i.d. standard Gaussian pixels. Please check the appendix for a formal mathematical proof. + +Proposition 2 (Time Complexity). For a given frame, the time complexity of this algorithm is $O(D)$ , linear time with respect to the number of noise pixels processed. Proof: There are only two cases - contraction and expansion. Because each previous-frame pixel can only be contracted to one current-frame pixel, and during expansion each current-frame pixel can only be mapped to one previous-frame pixel, the total number of edges $E$ will never exceed $2D$ . + +# 3.2. Training-free image diffusion models with warped noise + +As shown by Chang et al. [7] and Deng et al. [10], noise warping can be combined with image diffusion models to yield temporally consistent video edits without training. To do this, we first take an input video and calculate its optical flows using RAFT [49]. Then, with Algorithm 1, we use the flow fields to create sequences of Gaussian noise for each frame in the input video, ensuring that the noise moves along the flow fields. These noises are used during the per-frame diffusion processes in place of what would normally + +be temporally independently sampled Gaussian noise. This enables temporally consistent inference for video tasks, such as relighting [17] and super-resolution [48], using image-based diffusion models. + +# 3.3. Fine-tuning video diffusion models with warped noise + +We use warped noise to condition a video diffusion model on optical flow. In particular, we fine-tune two variants of a latent video diffusion model CogVideoX [60], both the text-to-video (T2V) and image-to-video (I2V) variants. We regard CogVideoX as a black box without changing its architecture. + +We use the same training objective as in normal fin-tuning, i.e., the mean squared loss between denoised samples and samples with noise added. In fact, we use the exact same training pipeline as the original CogVideoX repository, with exactly one difference: during training, we use warped noise instead of regular Gaussian noise. For each training video, we calculate its optical flow for each frame, and create a warped noise tensor $\mathbf{Q} \in \mathbb{R}^{F \times C \times H \times W}$ , where $F, C, H, W$ are the number of frames, the number of channels, the height and width of encoded video samples respectively by applying our algorithm iteratively. + +We also introduce the concept of noise degradation, which lets us control the strength of our motion conditioning at inference time. After calculating the clean warped noise, we then degrade it by a random degradation level $\gamma \in [0,1]$ , by first sampling uncorrelated gaussian noise $\zeta \sim \mathcal{N}(0,1)$ and modifying the warped noise $\mathbf{Q} \leftarrow \frac{(1 - \gamma)\mathbf{Q} + \zeta\gamma}{\sqrt{(1 - \gamma)^2 + \gamma^2}}$ . As degradation level $\gamma \rightarrow 1$ , $\mathbf{Q}$ approaches an uncorrelated Gaussian, and as $\gamma \rightarrow 0$ , $\mathbf{Q}$ approaches clean warped noise. At inference, the user can control how strictly the resulting video should adhere to the input flow. Please see Fig. 10 for a qualitative depiction of $\gamma$ . + +In practice, because the diffusion model works on latent embeddings, we calculate the optical flow and warped noise in image space and then downsample that noise into latent space, which in the case of CogVideoX means downscaling by a factor of $8 \times 8$ spatially and 4 temporally. We use nearest-neighbor interpolation along the temporal axis and mean-pooling along the two spatial axes, which are then multiplied by 8 to preserve unit variance. + +# 3.4. Video diffusion inference with warped noise + +At inference, we generate warped noise from an input video to guide the motion of the output video. Then, using a deterministic sampling process such as DDIM [46], we use that warped noise to initialize the diffusion process of our fine-tuned video diffusion model. This method of control is much simpler than other motion control methods, as it does not require any changes to the diffusion pipeline or ar + +chitecture - using exactly the same amount of memory and runtime as the base model. + +In the case of local object motion control, we allow the user to specify object movements through a simple user interface as shown in Fig. 3. It is used to generate synthetic optical flows, where multiple layers of polygons are overlaid on an image. Then, these polygons are translated, rotated and scaled with paths defined by the user. We warp the noise accordingly, and use that noise to initialize the diffusion process, along with a text prompt, and in the case of the image-to-video model, a given first frame image. By controlling the extent to which the output video follows these polygons, users can simulate camera movement by shifting the background, or even 3D motion effects by overlaying two polygons in parallax and moving them at different speeds. We find that this motion control representation is quite robust to user error, where even if the polygon only roughly matches the object or area of interest it will still produce high quality results. For local object motion, we typically use a degradation value $\gamma$ between 0.5 and 0.7, depending on the level of motion precision the user desires, which is a higher level than we would normally use for motion transfer. + +The case of motion transfer and camera motion control are very similar – the only difference is the source of the flows used to generate the warped noise. In the case of motion transfer, we calculate the optical flow of a driving video, get warped noises that match the motion. Like in local object motion control, we use that warped noise to initialize a diffusion process. In the case of motion transfer, we typically use a lower degradation value $\gamma$ between 0.2 and 0.5, as we usually want the output video's motion to match the driving video's motion as closely as possible. + +# 4. Experiments + +# 4.1. Gaussianity + +Evaluation metrics. Validating the preservation of spatial i.i.d. Gaussianity, we follow the evaluation protocol outlined by InfRes [10]. Specifically, we use Moran's $I$ to measure the spatial correlation of warped noise and the Kolmogorov-Smirnov (K-S) test to assess normality. + +Baselines. Following HIWYN [7], we choose fixed per frame and independently sampled noise as oracle baselines for perfect spatial Gaussianity but zero temporal correlation. We choose bilinear, bicubic, and nearest neighbor temporal interpolation as oracle baselines for sufficient temporal correlation but no spatial Gaussianity. We also compare with recent noise warping algorithms including HIWYN [7] and InfRes [10]. In line with these papers, we also include baselines Preserve Your Own Correlation (PYoCo) [11] and Control-A-Video (CaV) [9], which have perfect Gaussianity but zero and poor temporal correlation, respectively. + +Table 1. Noise warping algorithm benchmarking in terms of Gaussianity, efficiency, and spatial quality and temporal consistency for two image diffusion based applications. $\uparrow/\downarrow$ indicates a higher/ lower value is better. + +
Noise w/o warpingNoise warping method
FixedRandomBilinearBicubicNearestPlyCoCaVHIWYNInfResOurs
Gaussianity
Moran's I (index) ↓-0.000270.000190.300.240.260.00023-0.000790.00110.000360.00014
Moran's I (p-value) ↑0.290.360.00.00.00.730.250.110.600.84
K-S Test (index) ↓0.0890.0750.340.370.170.130.0730.0620.0550.060
K-S Test (p-value) ↑0.120.190.00050.00040.040.080.270.420.500.44
Efficiency at 1024×1024 resolution
GPU time (ms) ↓< 1< 14.414.336.823.542.3155.22.612.14
Super-resolution - DeepFloyd IF
LPIPS ↓0.290.290.600.620.550.280.280.290.280.29
SSIM ↑0.880.880.720.700.650.880.880.870.880.88
PSNR ↑29.3629.4128.6828.5528.5929.4029.3929.3129.3829.39
Warping error ↓163.84233.65165.90167.95244.72186.63220.28164.35190.82152.04
Relighting - DifFReight
LPIPS ↓0.330.310.400.410.730.350.350.360.350.33
SSIM ↑0.690.770.730.700.380.580.670.640.600.70
PSNR ↑28.9129.0228.8728.8228.2128.8328.8728.8228.8128.92
Warping error ↓86.65128.1147.5343.57164.4295.24106.7787.7287.9785.82
+ +# Results. According to Tab. 1 1st section, we observe: + +(1) For Moran's I, a value close to 0 indicates no spatial cross-correlation, which is desirable for i.i.d. noise. Our method achieves a Moran's I index of 0.00014 and a high p-value of 0.84, indicating strong evidence for no spatial autocorrelation. Similarly low Moran's I values and high p-values are observed for PYoCo, CaV, HIWYN and InfRes, because they also aim to generate spatially gaussian outputs. + +(2) The K-S test compares the empirical distribution of the warped noise to a standard normal distribution. A small K-S statistic and a high p-value indicate the two distributions are similar. Our method obtains a K-S statistic of 0.060 and p-value of 0.44, suggesting the warped noise follows a normal distribution. Comparable results are seen for the other Gaussianity-preserving methods. + +(3) In contrast, the bilinear, bicubic, and nearest neighbor warping methods fail to maintain Gaussianity, exhibiting Moran's I values an order of magnitude higher (0.24 to 0.30) with p-values of 0.0, and K-S statistics 3-6 times larger (0.17 to 0.37) with very low p-values (< 0.05). These results provide strong evidence for the presence of spatial autocorrelation and deviation from normality in the warped noise from these interpolation-based methods. + +# 4.2. Efficiency + +Noise generation efficiency is measured by wall time profiling on an NVIDIA A100 40GB GPU, generating noise at a resolution of $1024 \times 1024$ pixels. We compare with the same baselines as above. According to Tab. 1 2nd section, our method runs faster than the concurrent InfRes and significantly outperforms the most recent published baseline HIWYN by $26 \times$ , due to our algorithm's linear time complexity. The efficiency is one order of magnitude faster than real time, validating our feasibility to apply noise warping on the fly during video diffusion model fine-tuning. + +# 4.3. Video editing via image diffusion + +To further validate the effectiveness of our noise warping algorithm, we repurpose off-the-shelf image-to-image dif + +fusion models to perform video-to-video editing tasks in a frame-by-frame manner, without training. Noise is warped using our algorithm and the above baselines based on the RAFT optical flow [49] from input video and fed to two image pre-trained diffusion models: DeepFloyd IF [48] for super-resolution and DifFRelight [17] for portrait relighting. By measuring the quality and temporal consistency of the output video, we can effectively evaluate the spatial Gaussianity and temporal consistency of different noise warping algorithms. + +Evaluation metrics. We use LPIPS [68], SSIM [20], and PSNR [20] to measure the quality of the output frames w.r.t. ground truth frames. We use warping error [29] to measure temporal consistency (mean square error) between two adjacent generated frames after flow warping. + +# 4.3.1 DeepFloyd IF video super-resolution + +We evaluate noise warping on DeepFloyd IF [48] superresolution using 43 videos from the DAVIS dataset [40]. The videos were downsampled to the $64 \times 64$ and superresolved to $256 \times 256$ . + +Results. According to Tab. 1 3rd section, our algorithm outperforms all the baselines in terms of temporal consistency (warping error). Our supplementary video also shows that our algorithm is more stable for the foreground, background, and edges, in contrast to InfRes which is often unstable in the background and HIWNY which is much less stable around moving edges. Our algorithm is comparable to other methods in PSNR, SSIM, and LPIPS image quality metrics, apart from the bilinear, bicubic, and nearest methods which result in low quality generation due to spatial non-Gaussianity. See Fig. 12 in the supplementary material for more details. + +# 4.3.2 DiffRelight video relighting + +We evaluate noise warping on DifFRelight [17] portrait video relighting using their own dataset, which includes 4 subjects in 4 scenarios: a 180-degree view animation, a 720-degree view animation, a zigzag camera movement sequence, and an interpolating camera path through several fixed stage capture positions, all with fixed lighting conditions. During inference, we center crop a $1024 \times 1024$ region out of a $1080 \times 1920$ Gaussian splat rendering and infer with various noises using conditioned lighting. + +Results. According to Tab. 1 4th section, throughout all baseline comparisons, our algorithm shows consistently advantageous scores in both image and temporal metrics, validating its fundamental benefits to the image diffusion model. Although our visual results at first glance are comparable to HIWYN and InfRes in the supplementary Fig. 13 and our webpage, its visual improvements can be seen in the beard regions and skin reflections. We also notice quite + +![](images/87eafaf2b1ddc4ff03de57a99a24083748a56d2abb1784b46dda03a4fe70a63d.jpg) +Figure 3. Qualitative comparisons of local object motion control. Zoom in for details. The user selects any number of polygons, then scales, rotates, or translates them along arbitrary paths, which are then used to create the warped noise flow. + +low warping error values on the bilinear and bicubic noise inferences, likely coming from the long blurry streaks generated along the flow, while at the same time image quality deteriorates significantly. + +# 4.4. Video diffusion with motion control + +# 4.4.1 Local object motion control + +We introduce a novel method for controlling object motion, by leveraging the flows of input templates. These templates include user-defined local region masks and cut-and-drag trajectories allowing users to specify motion of one or more objects built with an intuitive UI (Fig. 3), and synthetic flows of a camera rotating around 3D objects (Fig. 9). + +During inference, we use the precise flow computed from the input template frames to guide noise warping for video generation. This enables our I2V model to apply accurate, localized movements and adjustments to the input image while preserving object structure and faithfully following the intended motion trajectory. We also provide quantitative benchmarks. Following [36], we use the VIPSeg [34] to benchmark our method on local object motion control, as well as the 40 videos from our user study. + +Baselines. We evaluate our video generation model against five state-of-the-art baselines, SG-I2V [36], MotionClone [32], DragAnything [56], to benchmark its ability to accurately control object and camera movements derived from a given input template. One of the most recent works, SG-I2V, is an I2V model for object motion transfer guided by bounding box trajectories. We adapt our user-defined polygons to bounding boxes as its input. + +Results. From Fig. 3, Fig. 9, Tab. 2, and our webpage, we observe: (1) Existing methods struggle to handle complex, localized object motions. Specifically, when specifying local adjustments, such as rotating a dog's head while keeping the rest of the body static, these methods often fail, applying unnatural translational or global transformations to the entire object. (2) We find that SG-I2V frequently misinterprets object-specific movements as global camera shifts, resulting in scene-wide translations rather than accurate object ma + +nipulations. (3) DragAnything, which employs single-line trajectory control, lacks temporal and 3D consistency, leading to significant distortions and reduced fidelity in complex motion scenarios. (4) MotionClone also fails to capture subtle object dynamics, as it relies on sparse temporal attention for motion guidance and is likely limited by the low spatial resolution of its diffusion features. (5) Qualitatively, our model outperforms these baselines by maintaining high object fidelity and 3D consistency, even in scenarios with intricate or overlapping motions. Notably, our approach preserves object integrity and introduces plausible physical interactions, such as generating realistic splashes when moving a duck within a tub. Extensive user studies and quantitative evaluations validate our superior performance in motion consistency, visual fidelity, and overall realism. + +(6) Our quantitative evaluation matches our qualitative observations. On both VIPSeg and the 40 videos from our user-study, our method outperforms all the training-based and training-free baselines. + +User study. We conducted a comprehensive user study with 40 participants, asking them to evaluate and rate different methods based on their effectiveness in object motion control and maintaining 3D and temporal consistency. Our method stands out significantly, achieving a win percentage of $82\%$ for cut-and-draglocal object motion control like Fig. 3 and $90\%$ for the turnable camera movement control like Fig. 9. The three baselines have substantially lower performance levels. More user study details are included in the supplementary material Sec. 6.3 and Fig. 15. + +# 4.4.2 Motion transfer and camera movement control + +Our method also supports motion transfer and camera movement control, working with both T2V and I2V video diffusion models. By using reference videos and applying noise warping based on their optical flows, it can effectively capture and transfer complex motions. + +Datasets. We choose the DAVIS video dataset [40] containing 43 videos of general object motion with ground truth object segmentation annotations, a random subset of 100 videos from the DL3DV dataset [31], and 19 videos generated with WonderJourney [63] that mostly feature camera movements (Fig. 5), which itself uses depth-warping. + +Evaluation metrics. For pixel quality, we calculate Fréchet Inception Distance (FID) between a set of real and generated frames. For motion controllability, we calculate (1) the mean Interaction over Union (mIoU) of CoTracker's tracking bounding boxes [25] between ground-truth and generated videos, and (2) the pixel MSE between ground-truth and generated videos, considering an I2V diffusion model is conditioned on ground-truth prompts, ground-truth initial frames, and ground-truth motion trajectories/flows. For text controllability, we calculate the cosine similarity be + +tween the prompt's CLIP [43] text embedding and the generated frames' CLIP image embeddings, and average over frames of a generated video. For temporal consistency, we calculate (1) the cosine similarity of the CLIP image embeddings between two consecutive generated frames and average over all pairs in a generated video, and (2) the Fréchet Video Distance (FVD) [50] between a set of real and generate videos. In addition, we also benchmark on four metrics of VBenchmark [23], specifically for the temporal consistency/smoothness dimension. + +Baselines. For the motion transfer T2V scenario, we compare with the recent state-of-the-art methods Diffusion Motion Transfer (DMT) [61], MotionClone [32], and MotionCtrl [54]. For the motion transfer I2V, we compare MotionClone and ImageConductor [30]) as DMT does not take an image as input. + +In addition, we demonstrate video first-frame editing, a challenge where a user starts with an original video and an edited version of its initial frame. The goal is to seamlessly propagate the edits made to the first frame throughout the entire video while preserving the original motion. We qualitatively compare with MotionClone [32] and the state-of-the-art video editing method AnyV2V [27] on real videos with photoshopped first frames. + +We also source a few images for image-based depth warping, where we take an image, use a monocular depth estimator, DepthPro [5], to get a depth map, and crudely warp it to simulate a desired camera trajectory. + +Results. We present qualitative and quantitative comparisons with baselines in Tab. 2, Fig. 4, Fig. 5, Fig. 6, Fig. 7, and our webpage. We observe: + +(1) Our superior object motion transfer: On the DAVIS dataset, which includes object motion along with some degree of camera movement, our method demonstrates improved motion fidelity and overall video quality, as measured by Vbench. In particular, in the I2V setting, where both the initial frame and the source video are provided, our method achieves significantly better scores in FID, FVD, and motion metrics, indicating much closer reconstructions of the ground truth videos. +(2) Our superior camera movement control: On the DL3DV and WonderJourney datasets, which involve substantial camera movement, our method notably outperforms MotionClone in both motion fidelity and general video quality. This highlights our method's ability to effectively replicate intricate camera movements while maintaining visual coherence. For our depth-warping example Fig. 6, our results are far better than simply warping an image from its depth map, resulting in a smooth, realistic camera trajectory. See our webpage for videos. +(3) Our superior video first-frame editing: In Fig. 7, our method seamlessly integrates the added object into the scene while accurately preserving the camera movement + +![](images/e677b2cca257ac14606dce0f50b795c1c51f5b14460a65f1984c72e89033135d.jpg) +Figure 4. Qualitative comparisons of motion transfer T2V on the DAVIS dataset. + +![](images/58e0ca40c153cf99266d3ec318fd6f00f2cd5b67ae71773ef79e055e32a4acfa.jpg) +Figure 5. We apply our method to depth-warped frames, enabling 3D scene generation from a single image, using WonderJourney results. + +![](images/d0559bc4169540198be64daef127a569290317c7412d36741aefc82febacd2df.jpg) + +![](images/ef6870e855a8eb97dd740753e9ddfb745d75ba5506e488dc2481fb1c7f1aa994.jpg) +Figure 6. 3D scene exploration using DepthPro for depth estimation, creating warped video and noise, which feeds into our motion-conditioned I2V model. +Figure 7. Comparison of initial frame video editing results across different methods. All methods start with the same edited initial frame derived from the original video. + +from the original video. In contrast, both baselines exhibit significant identity loss: MotionClone generates additional, unintended objects, and in AnyV2V, the foreground object gradually disappears. This demonstrates the superiority of our method in maintaining the original video's motion while preserving the identity of the object added to the first frame. + +# 4.4.3 Ablation studies + +In Tab. 2 for the DAVIS I2V task, we compare our method with a variant that excludes motion conditioning using + +Table 2. Quantitative comparisons of motion transfer. $\uparrow / \downarrow$ indicates a higher/ lower value is better. Bold indicates the best results. Gray background rows indicate our final model. Dashed lines separate ablation study from baseline benchmarking. + +
Train free?FID ↓CoTrck. mIoU ↑Opt. flow err. ↓Pixel MSE ↓CLIP text ↓CLIP img. ↓FVD ×103↓Subj. cons. ↓VBench ↑ Bg. cons. ↓Motion smooth ↓Temp. flicker
Local object motion control on VIPSeg
MotionClone✓85.20.710.480.0860.310.951.260.880.850.940.90
SG-12V✓61.40.630.840.0650.310.971.060.930.950.960.94
Ours×41.10.750.360.0390.320.980.470.910.920.970.95
Local object motion control on our 40 samples in the user study
MotionClone✓96.6-0.800.0480.330.981.380.860.930.970.95
SG-12V✓79.9-0.640.0420.320.981.270.950.950.980.94
DragAnything×82.8-0.620.0470.310.971.300.930.950.980.95
Ours×74.3-0.560.0280.320.980.940.960.950.980.96
Motion transfer 12V on DAVIS
DMT✓-0.850.28-0.310.95-0.860.920.940.91
MotionClone✓-0.750.38-0.320.93-0.780.890.860.81
MotionCtrl×-0.470.85-0.320.97-0.970.930.980.92
Ours×-0.700.41-0.330.98-0.880.930.970.89
Ours-Cog VX-2B×-0.640.48-0.320.95-0.890.910.970.90
Motion transfer 12V on DAVIS
MotionClone✓99.40.720.420.0680.310.941.840.750.850.920.87
ImageConductor×104.60.660.640.0720.310.931.580.770.880.930.90
Orig.Cog VX-5B✓76.620.520.670.0880.310.961.360.850.910.960.92
Ours (γ=0.5)×78.60.740.360.0530.310.971.210.880.920.980.93
Our (γ=0.9)×92.50.500.650.0720.310.951.590.800.890.940.91
Our (γ=0.8)×80.60.680.470.0670.310.961.500.850.910.960.92
Our (γ=0.4)×77.70.740.360.0560.310.971.270.870.910.970.93
Our (γ=0.2)×77.10.740.370.0580.320.971.290.860.910.970.93
Our (33% data)×100.10.730.400.0660.310.971.460.850.900.970.92
Our (12.5% data)×105.20.710.390.0720.310.961.930.840.890.970.91
Camera movement transfer 12V on DL3DV
MotionClone✓82.70.710.440.1040.330.941.110.740.850.910.86
ImageConductor×89.20.610.780.0680.310.950.910.850.900.950.93
Ours×48.40.830.200.0460.320.970.340.880.920.970.93
Camera movement transfer 12V on WonderJourney
MotionClone✓177.90.810.170.1030.320.961.930.750.870.930.87
ImageConductor×166.10.790.390.0850.320.941.630.790.880.930.90
Ours×128.30.850.150.0720.310.981.550.820.910.980.94
+ +warped noise ("Original CogVideoX-5B"), relying solely on textual prompts describing the objects. We observe: (1) Better video reconstruction: Our method, which incorporates motion conditioning, achieves superior FID, FVD, and CoTracker mIoU scores, indicating more accurate reconstruction of the source video. This is because textual prompts and the initial frame alone are insufficient to capture a video's future dynamics, whereas incorporating real video-derived motion guidance enables the generation of more realistic sequences. (2) Improved video quality: By utilizing warped noise for motion conditioning, our approach not only maintains but also enhances overall video quality, as measured by Vbench, demonstrating that integrating realistic motion cues improves the plausibility of the generated videos without compromising quality. + +Further exploring the effects of degradation, we find that as the degradation values $\gamma$ increase, the motion control becomes tighter - resulting in higher optical flow and CoTracker-mIoU scores, along with a closer per-frame similarity to target videos on the I2V DAVIS task. We find that, in general, $\gamma \approx 0.5$ is a good value for most tasks. + +We also perform ablations on dataset size, comparing models trained on different fractions of our dataset: training with a fraction of dataset yields worse performance. + +In addition, we perform an ablation where we use the weaker base model CogVideoX-2B, and find its performance is weaker than our main T2V model, based on CogVideoX-5B. + +# Acknowledgments + +We would like to express our gratitude to Stephan Trojansky and Jeffrey Shapiro for their initial and ongoing executive support; Sebastian Sylwan, Daniel Heckenberg, Jitendra Agarwal, Matheus Leao, and Sungmin Lee for their IT support; Xueming Yu and David George for their hardware support; Jennifer Lao and Lianette Alnaber for their operational support; and Winnie Lin, Ahmet Tasel, Yiqun Mei, Lukas Lepicovsky, Rahul Garg, Ashish Rastogi, Ritwik Kumar, Cornelia Carapcea, and Girish Balakrishnan for their insightful technical discussions. + +# References + +[1] Luca Savant Aira, Antonio Montanaro, Emanuele Aiello, Diego Valsesia, and Enrico Magli. 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While generalizable NeRF models can generate novel views across unknown scenes by learning latent ray representations, their performance heavily depends on a large number of multi-view observations. However, with limited input views, these methods experience significant degradation in rendering quality. To address this limitation, we propose GoLF-NRT: a Global and Local feature Fusion-based Neural Rendering Transformer. GoLF-NRT enhances generalizable neural rendering from few input views by leveraging a 3D transformer with efficient sparse attention to capture global scene context. In parallel, it integrates local geometric features extracted along the epipolar line, enabling high-quality scene reconstruction from as few as 1 to 3 input views. Furthermore, we introduce an adaptive sampling strategy based on attention weights and kernel regression, improving the accuracy of transformer-based neural rendering. Extensive experiments on public datasets show that GoLF-NRT achieves state-of-the-art performance across varying numbers of input views, highlighting the effectiveness and superiority of our approach. Code is available at https://github.com/KLMAV-CUC/GoLF-NRT. + +# 1. Introduction + +Neural Radiance Fields (NeRF) [31] and its subsequent refinements [2-4, 42, 64] have achieved remarkable success in generating realistic, high-resolution, and view-consistent scenes for novel view synthesis. Despite these advancements, conventional NeRF approaches require expensive + +![](images/8219b276a958dbe9b31f0b4a9181351039c5f0528f66c668fe040cafc4be8285.jpg) +Target View + +![](images/c51dd6b2228ef50670c014b44a9d95a82d7edbb56617dd6b59a4d07821077882.jpg) +Source View 1 + +![](images/3b0c8a533a5d3e3cb1e3dcabe54784285e16d6503354316d455d0bbc2042ba45.jpg) +Source View 2 + +![](images/18512405f91b71f65c600792ef90f53f7b1ca592fd55cf51bdd2d41fd505d236.jpg) + +![](images/4de73e425b07f322bd713aa93e1c630813d3bad3765b9836821d18eebe31d357.jpg) +Only Local Geometry + +![](images/69d354ca2cecba1b326ac63817ec91a68383aebdf288e317d4e5645e74820ba0.jpg) + +![](images/408520165e4c03669f073c9e0dc2509ccc6a43bd0c5feecd21167af5b2a6e3d0.jpg) +Only Global Context + +![](images/ce8a91adfd9a85e90d02e01781a3ca7c13ab59a628047628ad251ae9d05e11be.jpg) + +![](images/d465f3b1ec5f8adc6c4e415d81eb80303838de5e55fdae8a4a13988e956d5980.jpg) +Figure 1. The integration of global context and local geometry in GoLF-NRT significantly enhances reconstruction accuracy. (a) Local geometric features (red) are extracted along the epipolar line of the target pixel, effectively capturing local geometric constraints, while surrounding features (yellow) provide the global context. (b) Relying solely on local features can introduce depth ambiguities and artifacts, while using only global features often fails to capture fine details. By combining both, GoLF-NRT achieves more precise and detailed reconstructions. + +![](images/366c609f7e974f77e6e7b09bf448a20cf21b22fe1e89197e559bfffa261d1854.jpg) +GoLF-NRT + +optimization with a large number captured images for each scene, hindering their widespread adoption in real-world applications. These constraints underscore the necessity of few-shot generalizable neural rendering, which aims to render unseen scenes from novel viewpoints using a limited number of input views. + +To address the generalization issue, existing methods mainly introduce explicit or implicit priors to extract local geometrical features, such as the depth maps [12, 36], cost volumes [6, 55, 65], geometric consistency across views [1, 24, 33], and epipolar features encoded in attention maps [38, 39, 49]. However, these methods often require many input views to accurately capture geometry. With fewer views, they tend to produce over-smoothed textures or ar- + +tifacts, particularly in occluded or reflective regions. + +To address the few-shot issue, various types of auxiliary information have been incorporated with local geometrical features, including the normalization flow [66], semantic label constraints [15, 19] and frequency content [63]. However, these human-designed auxiliary features can only be reliably extracted with at least 3 views. When the number of input views further decreases, the inherent ambiguities in auxiliary information, such as large motion, incomplete semantic labels and restricted spectral bandwidth, exacerbate the over-smooth textures or artifacts in occlusion boundaries. + +In this paper, we present GoLF-NRT (Global Local feature Fusion based Neural Rendering Transformer), a coarse-to-fine model that integrates global context features with enhanced local geometric features. Our model comprises two key modules: the global context feature extraction module and the local geometric feature extraction module. The global context feature extraction module employs a cross-view transformer-based encoder with multi-axis sparse attention to effectively learn the scene representation. This representation is then decoded into a global context feature for each ray, enabling the model to develop a comprehensive understanding of the scene from a limited set of viewpoints. The local geometric feature extraction module further refines this understanding by aggregating features along epipolar lines in each input view, alternating between a view transformer and a ray transformer. Unlike previous methods [51, 70] that directly fuse geometric and auxiliary features, our model uses the global context feature as a coarse prediction to better evaluate the contributions of different views. This approach ensures consistent scene understanding across views, improving the model's ability to handle depth ambiguity and occlusions. Additionally, we introduce an adaptive sampling strategy that transforms attention weights [50] into a smooth, regularized probability density function (PDF) using kernel regression [44-46], thereby improving the model's geometric perception and overall rendering quality. + +Compared to prevailing methods such as [32, 38, 49, 70], our GoLF-NRT framework stands out by synthesizing target rays through the integration of global context understanding and local geometric perception. This distinctive combination enables our approach to perform exceptionally well in both many-shot and few-shot scenarios, offering a robust and versatile solution to the challenges of neural rendering across varying input conditions. Our main contributions are summarized as follows: + +- We propose GoLF-NRT, a generalizable neural rendering technique that integrates global context with local geometry, ensuring consistent scene understanding across views and enhances the handling of depth ambiguity and occlusions. + +- We introduce an adaptive sampling strategy using attention mechanisms and kernel regression to extract precise local geometric features, improving the model's ability to accurately perceive geometry. +- Through extensive experiments and comparisons with state-of-the-art methods, we demonstrate that our framework consistently outperforms current generalizable neural rendering methods across various datasets, particularly in scenarios with limited input data. + +# 2. Related Works + +NeRF and Generalizable NeRF. NeRF [31] reconstructs images by predicting point density and color within a radiance field based on spatial coordinates and viewing directions. Follow-up works have improved rendering quality [2-4, 17], increased speed [7, 9, 16, 34, 40, 64], and enabled editing [27, 41, 52, 58, 61]. However, NeRF's scene-specific implicit functions limit generalization. Generalizable NeRFs address this by encoding features at each 3D point and decoding them into volume density and radiance, allowing cross-scene generalization without retraining [6, 8, 29, 47, 60, 65]. Recently, attention mechanisms and transformers have further advanced novel view synthesis and generalization [10, 18, 21, 25, 35, 53, 62]. IBRNet [55] uses transformers for volumetric density prediction, while other methods [11, 23, 37, 38, 49] employ fully attention-based models for scene representation and ray color estimation. EVE-NeRF [32] enhances representation quality by integrating view and epipolar information, though it may struggle in few-shot scenarios due to data limitations and boundary artifacts. + +Few-shot Generalizable NeRF. Various NeRF approaches address the few-shot problem. WaH-NeRF [1] tackles sample-position confusion with a deformable sampling strategy and mutual information loss. RegNeRF [33] regularizes color predictions for unseen viewpoints using a pre-trained flow model, integrating prior information for improved results. Other methods [12, 24, 36, 54, 59, 63, 66] enhance reconstruction by combining different modalities like geometry, depth, and frequency content. CaesarNeRF [70] utilize global average pooling to encode semantic information. However, it applies the same semantics to all rays, which can lead to conflicts, requiring additional calibration. LVSM [20] introduces a scalable, transformer-based model for view synthesis from sparse inputs that relies entirely on data-driven methods, bypassing traditional 3D biases. + +Generalizable 3D Gaussian Splatting. Recent developments in generalizable Gaussian splatting methods have markedly improved the efficiency of novel view synthe + +![](images/2f845ca0467a5429df943ad5a412858f5626b48f2cd3c1c458947635355c5032.jpg) +Figure 2. Overview of GoLF-NRT: 1) A FPN extracts multi-scale features from input views. 2) Coarse features are encoded to create scene representations, from which global context features are decoded for each target ray. 3) These global context features query local geometric features along the epipolar lines of all source views. The global and local features are concatenated and processed to predict the final target ray representation. 4) Pixel colors are directly predicted using a MLP. + +sis. These methods bypass the need for per-scene optimization by directly regressing Gaussian parameters via a feedforward architecture. For instance, PixelSplat [5] utilizes an epipolar transformer to resolve scale ambiguity and encode features, though its design is limited to image pair inputs. GPS-Gaussian [68] extends this approach to stereo matching, incorporating epipolar rectification, disparity estimation, and feature encoding. However, its reliance on ground-truth depth maps restricts its applicability. Splatter Image [43] proposes a single-view reconstruction approach based on Gaussian splatting, though its focus on object-centric reconstruction constrains its generalization to unseen scenes. MVSGaussian [28] combines multi-view stereo with a generalizable 3D Gaussian representation for real-time novel view synthesis. However, its single-sample-per-ray strategy necessitates highly accurate depth estimations, hindering its performance in complex scenes. + +# 3. Methodology + +Given a set of posed source views of an unknown scene, our goal is to synthesize novel views from arbitrary positions and directions. The proposed GoLF-NRT framework consists of two main stages: 1) constructing a coarse scene representation using global context, and 2) refining this representation by incorporating local geometry through epipolar feature aggregation. As shown in Fig. 2, we begin by extracting multi-scale features from source views. Coarse features, with larger receptive fields, are aggregated to capture global context, forming a preliminary target ray representation. This initial representation is then refined by aggregating fine features with smaller receptive fields along epipolar lines from all source views, resulting in a geometry-aware target ray representation. Finally, a multi-layer perceptron + +(MLP) decoder predicts the target ray's color. + +# 3.1. Multi-Scale Feature Extraction + +Given $N$ source views $\{I_i\}_{i=1}^N$ with camera parameters $\{P_i\}_{i=1}^N$ , we employ a feature pyramid network (FPN) [26] with shared weights to extract multi-scale features at 1/4, 1/8 and 1/16 resolutions. Unlike previous methods that operate on a single scale [32, 49, 70], our approach leverages features across multiple scales, thereby improving the representational capability of the model. Specifically, we use the 1/8-resolution features for global context extraction, while the 1/4-resolution features for capturing local geometric information. + +# 3.2. Global Context Feature Extraction + +Both cost volume-based [21] and attention mechanism-based [32, 38] novel view synthesis methods focus heavily on local geometric reasoning for scene generalization but often lack a global perceptual framework, limiting their performance, particularly with a limited number of input views. This limitation arises from their reliance on features along epipolar lines, overlooking rich contextual information from other areas of the source views. + +To address this, we propose incorporating features from all source views to create a global context feature for each ray. As described in Sec. 3.1, the encoder aggregates $1/8$ resolution features from all source views, generating an implicit scene representation [37], denoted as $Z_{g}$ . However, this approach is computationally intensive and impractical for high-resolution rendering. To address this, we propose a 3D transformer incorporating sparse attention, as illustrated in Fig. 3. + +![](images/b8f1b52b91d0de6ea038ff41ee8137e6d96c8c9bd2e11d72bafa47aabf7777e1.jpg) +Figure 3. Network architecture of Global Context Feature Extraction Module. The 3D transformer, with near-linear complexity, encodes the scene into a scene representation, while the decoder generates the global context feature for each target ray. + +Near-Linear Complexity 3D Transformer. Directly applying transformers to multi-view, high-resolution images is computationally expensive. To mitigate this, we adopt the sparse attention mechanism from MaxViT [48] and design a 3D transformer with near-linear computational complexity. Full-scale attention is decomposed into three sparse forms: intra-view block attention, intra-view grid attention, and inter-view attention. Intra-view block attention partitions each feature map of shape $H \times W \times C$ into non-overlapping windows of size $P \times P$ , reshaping it into a tensor of shape $\left( \frac{H}{P} \times \frac{W}{P}, P \times P, C \right)$ , and applies self-attention within each window. Similarly, intra-view grid attention divides the tensor into a shape $(G \times G, \frac{H}{G} \times \frac{W}{G}, C)$ using a fixed $G \times G$ uniform grid, resulting in windows with an adaptive size $\frac{H}{G} \times \frac{W}{G}$ , and applies self-attention along the grid axis $G \times G$ . Finally, inter-view attention gathers feature maps from the $N$ source views into a tensor of shape $(N, H \times W, C)$ , and applies self-attention along the view axis $N$ . By stacking these attention mechanisms sequentially, we capture both local and global interactions within each block. Notably, both intra-view block attention and intra-view grid attention operate with linear complexity relative to the input size, and the number of views $N$ is typically small. As a result, this design achieves efficient global interaction without incurring the quadratic computational + +costs of full-scale attention. + +To generate the global context feature $F_{g}$ for each target ray, we use a standard decoder transformer [50]. This decoder selectively attends to relevant features within the scene representation, providing a preliminary representation of the target ray. For a target ray $r$ with specified origin and direction, the global context feature is computed by querying the decoder transformer $\mathcal{D}$ as follows: + +$$ +\boldsymbol {F} _ {g} = \mathcal {D} \left(\boldsymbol {r} \mid \boldsymbol {Z} _ {g}\right). \tag {1} +$$ + +In this mechanism, the target ray serves as the query for multi-head attention, while the keys and values are computed from the scene representation $Z_{g}$ . + +Through this interaction, the model selectively extracts the most relevant global context features for the target ray. This offers a comprehensive understanding of the entire scene, allowing the model to more effectively identify crucial changes in scene attributes, even when faced with diverse scenes or few input views. + +# 3.3. Local Geometric Feature Extraction + +This module constructs a coordinate-aligned feature volume from the 1/4-resolution features $\{F_i\}_{i=1}^N$ for the target ray, aiming to capture local geometry. We utilize GNT [49], a fully attention-based generalizable NeRF method, as our backbone. GNT aggregates features along epipolar lines in source views through two transformer-based stages. In the first stage, the view transformer predicts coordinate-aligned features for each point by aggregating information from the epipolar lines in the source views. This stage is designed to establish correspondences between queried points and the source views, providing a likelihood score that indicates the correlation of a pixel on the source view to the same point in 3D space without occlusion. Consequently, the output of the view transformer yields local geometric features of the pixels. In the second stage, the ray transformer aggregates these point-wise features along the ray to compute the ray color. However, while GNT performs well with a larger number of input views, it may encounter challenges when fewer views are available, primarily due to inconsistencies introduced by occlusion or reflections, which can compromise feature aggregation by the view transformer. To address these limitations, we propose two key improvements: global context-guided aggregation and adaptive sampling. + +Global Context-Guided Aggregation. We enhance the view transformer by incorporating the global context feature $\pmb{F}_{g}$ as the initial query, replacing the element-wise max pooling used in previous methods [49]: + +$$ +\boldsymbol {F} _ {l} = \text {V i e w - T r a n s f o r m e r} (\boldsymbol {F} _ {g} | \{\boldsymbol {F} _ {i}, \boldsymbol {P} _ {i} \} _ {i = 1} ^ {N}), \qquad (2) +$$ + +where $\pmb{F}_l$ denotes the local geometric feature. By leveraging the global context feature, which containing the most + +![](images/3478560be6f3bfbcba957e1cca2ed6472c4b6a082a8e2c8270be49b644ff32a8.jpg) +Figure 4. Illustration of how adaptive sampling with kernel regression enhances local geometric perception. (a) Uniform sampling, lacking surface depth constraints, distributes points broadly and randomly. (b) Adaptive sampling based solely on attention weights can lead to disorderly sampling due to the fundamental differences between feature similarity and the PDF used in volume rendering. (c) Our adaptive sampling with kernel regression bridges this gap, focusing samples within the most likely surface depth range, thereby improving subsequent image synthesis. + +![](images/90eb486621a81c6104d012769319d7cb4521d4fd04b066ee76cd0f95983a4c3e.jpg) + +![](images/72abafb6c6d8df493cc22251292cf09ff14d18e47675a3b26f8725cec056f7dc.jpg) + +![](images/8998cf542dc31d85194a6d2d4b852df2438a38c48524061aa8a4466f19010981.jpg) + +relevant information about the target ray in the scene representation $Z_{g}$ , the view transformer can more accurately assess contributions from various source views, resulting in more precise local geometric features $F_{l}$ . These local features are subsequently concatenated with the global context feature to create a global-local embedding: + +$$ +\boldsymbol {F} _ {g - l} = \boldsymbol {F} _ {g} \oplus \boldsymbol {F} _ {l}, \tag {3} +$$ + +which is then aggregated by the ray transformer: + +$$ +\boldsymbol {F} _ {r} = \text {R a y - T r a n s f o r m e r} \left(\boldsymbol {F} _ {g - l}\right). \tag {4} +$$ + +After iterating through 8 view and ray transformer blocks, we obtain the target ray representation $\hat{F}_r$ . These improvements enhance the robustness of our model in handling challenging scenarios with limited input views, significantly advancing the accuracy of local geometric feature extraction. + +Adaptive Sampling. After the view transformer obtains point-wise features along the ray, the ray transformer aggregates them to form the ray color. The weighted aggregation can be regarded as an approximation of volume rendering [22], where the weights are learned through the attention mechanism. This insight inspires us to explore incorporating established volume rendering techniques to enhance modeling efficiency, such as hierarchical volume sampling, which prioritizes regions with significant contributions to the final rendering. We propose using the attention weights in the ray transformer as accumulation weights for volume rendering, similar to a probability density function (PDF). However, attention weights, derived from feature similarity, differ fundamentally from traditional PDFs used in volume rendering. As shown in Fig. 4(b), while attention weights + +provide valuable cues, the estimated PDF can lead to disorderly sampling. + +To bridge the gap between attention weights and the PDF, we introduce a kernel regression method [44-46] that transforms attention weights into a smooth, regularized PDF. Given $N_{c}$ uniformly sampled depths $\{d_i\}_{i = 1}^{N_c}$ along the ray with corresponding attention weights $\{w_i\}_{i = 1}^{N_c}$ , the PDF at depth $d$ is calculated as follows: + +$$ +p (d) = \sum_ {i = 1} ^ {N _ {c}} w _ {i} * \frac {K (d , d _ {i})}{\sum_ {i = 1} ^ {N _ {c}} K (d , d _ {i})}, \tag {5} +$$ + +where $K(d,d_{i})$ is the Gaussian kernel: + +$$ +K (d, d _ {i}) = \frac {1}{h \sqrt {2 \pi}} e ^ {- 0. 5 \left(\frac {d - d _ {i}}{h}\right) ^ {2}}, \tag {6} +$$ + +and $h$ is the bandwidth parameter. This method not only smooths the noise but also ensures that the resulting sampling distributions aligns with realistic, physically plausible shapes—either unimodal for opaque objects or multimodal for translucent materials, as depicted in Fig. 4(C). + +In the uniform sampling stage, $N_{c}$ features are uniformly sampled to estimate the PDF using Eq. (5). Subsequently, $N_{f}$ refined feature locations are sampled from the PDF using inverse transform sampling, biasing the samples towards the object's surface. In the adaptive sampling stage, all $N_{c} + N_{f}$ samples are used. Both stages employ the same transformer. + +# 3.4. MLP Decoder + +Given the final feature of the target ray $\hat{\pmb{F}}_r$ , the ray color is then obtained through a multi-layer perceptron (MLP) decoder: + +$$ +\hat {\boldsymbol {c}} = \operatorname {M L P} (\hat {\boldsymbol {F}}). \tag {7} +$$ + +
InputMethodsLLFFBlenderShiny
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
3-viewIBRNet [55]23.000.7520.26222.440.8740.19521.960.7100.281
MVSNeRF [6]19.840.7290.31423.620.8970.17618.550.6450.343
MatchNeRF [8]22.300.7310.23423.200.8970.16420.770.6720.249
MVSGaussian [28]24.070.8570.16425.540.9440.07320.490.6610.254
GNT [49]23.280.7680.23025.800.9050.10422.470.7200.247
EVE-NeRF [32]22.790.7540.22623.430.9030.13224.110.7810.204
CaesarNeRF [70]23.450.7940.17623.560.9080.13122.740.7230.241
GoLF-NRT24.200.8210.14824.300.9160.09725.060.7650.207
2-viewMVSNeRF [6]19.150.7040.33620.560.8560.24317.250.5770.416
MatchNeRF [8]21.080.6890.27220.570.8640.20020.280.6360.278
pixelSplat [5]22.990.8100.19015.770.7550.314---
GNT [49]20.940.6870.30123.470.8770.15120.420.6170.327
EVE-NeRF [32]19.950.6070.34021.620.8670.18020.890.6670.321
CaesarNeRF [70]21.940.7360.22422.070.8790.17621.470.6520.293
GoLF-NRT22.480.7650.19322.340.8860.14323.030.6920.261
1-viewGNT [49]16.600.4910.51415.530.6340.37115.990.4000.548
CaesarNeRF [70]18.310.5210.43515.760.6980.36617.570.4720.467
GoLF-NRT18.310.5270.41016.340.7060.30918.960.5130.393
+ +Table 1. Quantitative comparison of state-of-the-art view synthesis methods on LLFF, Blender, and Shiny datasets with 1-3 input views. Best results are in bold, second-best are underlined. + +# 4. Experiments + +# 4.1. Settings + +Dataset. Following [49, 55], we constructed our training data from both synthetic and real sources, including 1023 models from Google Scanned Object [13], RealEstate10K [69], Spaces scenes [14], and 102 real scenes captured with handheld cellphones [30, 55]. For evaluation, we used the LLFF [30], Blender [31], and Shiny [57] datasets. Notably, LLFF validation scenes were excluded from training, and Blender and Shiny datasets introduce significant variations in view distribution and scene content compared to the training dataset. The quality of the synthesized novel views is measured using the PSNR, SSIM [56], and LPIPS [67] metrics. + +Implementation Details. GoLF-NRT is trained using the Mean Square Error (MSE) loss commonly used in NeRF [31]. We optimized the model end-to-end using the Adam optimizer, setting an initial learning rate of $10^{-3}$ for the multi-scale feature extraction module and $5 \times 10^{-4}$ for other modules, with exponential decay. Training ran for 250k iterations with 682 rays sampled per iteration. During uniform sampling, we used 128 samples per ray, with an additional 64 samples during adaptive sampling. Following [49], we construct source-target view pairs by selecting a target view and forming a pool of $k \times N$ proximate views, where $k \in (1,3)$ and $N \in (8,12)$ . During training, $k$ and $N$ are uniformly sampled from these intervals, while $N$ is fixed at 10 for evaluation to ensure consistency. + +# 4.2. Comparative Studies + +We compare GoLF-NRT with several state-of-the-art generalizable NeRF methods, including PixelNeRF [65], IBRNet [55], MVSNeRF [6], MatchNeRF [8], NeuRay [29], GPNR [38], GNT [49], CaesarNeRF [70], and EVE-NeRF [32]. We conducted experiments under both few-shot and many-shot configurations to provide a comprehensive comparison with existing methods, showcasing the broad applicability and superiority of GoLF-NRT. + +As shown in Tab. 1, GoLF-NRT outperforms other methods across most metrics with 1 to 3 input views on LLFF, Blender, and Shiny. While all methods degrade with fewer views, our approach maintains high-quality results with minimal loss. Notably, with 3 input views on the LLFF dataset, GoLF-NRT surpasses CaesarNeRF [70] by $0.75\mathrm{dB}$ in PSNR, 0.027 in SSIM, and reduces LPIPS by 0.028. It's also important to note that multi-view matching becomes irrelevant when only a single image is available, explaining why our results significantly outperform GNT [49]. While CaesarNeRF also leverages semantic information for few-shot novel view synthesis, it applies identical semantics to all rays, which can lead to conflicts, even with additional calibration. In contrast, our approach selectively extracts relevant global information for each ray, using it to guide local information extraction, thereby supporting accurate ray synthesis even on complex datasets such as Shiny dataset. With 1 input view on the Shiny dataset, GoLF-NRT improves over CaesarNeRF by 1.39 dB in PSNR, 0.041 in SSIM, and reduces LPIPS by 0.074. + +![](images/e1158cc3e2d51801645ddb283c09c06a609ae8965005a2fe180b6361e74b2d83.jpg) +(a) 3 input views + +![](images/80be56b4145cca61235285cd9a31b010b0f8d7d3d39aaa820003fbc1224f621c.jpg) +Figure 5. Qualitative comparison of GoLF-NRT with GNT, EVE-NeRF, and CaesarNeRF using 3 and 2 input views: (a) Trex scene (LLFF), Ficus scene (Blender), and Lab scene (Shiny); (b) Horns scene (LLFF), Hotdog scene (Blender), and Crest scene (Shiny). Each triplet shows the reconstructed image (left), a zoomed-in view (upper right), and its corresponding error map (lower right). + +Fig. 5 presents qualitative results for configurations with 3 and 2 input views. It is evident that previous methods relying solely on local features for multi-view matching encounter difficulties in regions with edges, depth discontinuities, or reflections, often resulting in mismatches. By incorporating global features within the view transformer, our approach achieves a more holistic scene understanding, leading to enhanced consistency in matching across views. + +We also demonstrate generalizable results under many-shot conditions (10-views), as shown in Tab. 2. Our method achieved the best or second-best results across all metrics. Fig. 6 provides a qualitative comparison, confirming its effectiveness in both few-shot and many-shot scenarios. + +# 4.3. Ablations and Analysis + +We conduct a series of ablation studies to evaluate the effectiveness of our design. Tab. 3 shows that our method, which integrates both global and local features, improves PSNR by $0.44\mathrm{dB}$ , underscoring the importance of global + +context in achieving accurate novel view synthesis. Fig. 8 illustrates that our design effectively focuses on important regions. Adaptive sampling using kernel regression on attention weights reduces noise from local similarities and produces a more targeted sampling distribution, resulting in a $0.32\mathrm{dB}$ increase in PSNR. Fig. 7 shows that this significantly enhances depth recovery at object boundaries. Additionally, Tab. 4 shows that full-scale attention is computationally impractical, while our 3D transformer reduces costs, enabling high-resolution processing. + +# 5. Conclusion + +In this paper, we introduced GoLF-NRT, a novel neural rendering transformer that integrates global and local features to enhance view synthesis from few input views. Our approach utilizes a 3D transformer with efficient sparse attention for global context understanding and an adaptive sampling strategy for accurate local geometry perception, significantly improving rendering quality. Ex + +
MethodsLLFFBlenderShiny
PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓PSNR ↑SSIM ↑LPIPS ↓
PixelNeRF [65]18.660.5880.46322.650.8080.202---
IBRNet [55]25.170.8130.20026.730.9080.10123.600.7850.180
NeuRay [29]25.350.8180.19826.480.9440.09125.720.8800.175
GPNR [38]25.720.8800.17528.290.9270.08024.120.8600.170
GNT [49]25.530.8360.17826.010.9250.08826.560.8520.132
CaesarNeRF [70]25.160.8510.13826.750.9150.08326.660.8490.146
EVE-NeRF [32]27.160.8690.14127.030.9520.07227.410.8830.113
GoLF-NRT26.420.8790.10929.740.9630.06028.010.8850.112
+ +![](images/d98300c4e05b9364b24b6ae1fb751b5cd1e64299334fd9fb70c751aae5b9768c.jpg) +Figure 6. Qualitative comparison of GoLF-NRT with GNT, EVE-NeRF, and CaesarNeRF using 10 input views. Rows correspond to the Leaves scene (LLFF), Lego scene (Blender), and Food scene (Shiny). Each triplet includes a reconstructed image (left), a zoomed-in view (upper right), and its error map (lower right). + +Table 2. Quantitative comparison with state-of-the-art view synthesis methods on LLFF, Blender and Shiny datasets with 10 input views. Best results are in bold, second-best are underlined. + +
ModelPSNR↑SSIM↑LPIPS↓
only local geometry23.280.7680.230
+ global context23.550.7910.170
+ global context as query23.720.8040.159
+ adaptive sampling23.880.8060.157
+ kernel regression24.200.8210.148
+ +![](images/5022f683a48e78acb4f9946676ac52e7186bb6ce9754c93e1dc704f3fb0fc8f0.jpg) +No Adaptive Sampling + Adaptive Sampling +Figure 7. The depth maps from three sampling strategies show that adaptive sampling with kernel regression significantly improves accuracy, especially at boundaries with depth discontinuities. + +![](images/7b25953a23bc63698aebe4ce1df301dc560736d8ed9199d21e439d4dd229d8a0.jpg) + +![](images/8fc277f66dd24d126a08246a761731c3c175f5ec9cb20bfa27c5b90fb6bff972.jpg) + +![](images/c3c06a4c7cb9e1ff6937f4cf60640e80505705f86ffdf10fde4dc4459bf54ae5.jpg) +GT + +![](images/b0da8a223619bf995efdbaf72b1e79b1d850626d39671590dbacae4db4784706.jpg) +Target +Figure 8. Visualization of global and local attentions. + +![](images/0b6fbcda7deb772703579ccfd02673b154ea6249623c4f5f829339bb543f5e7f.jpg) +Global Attention + +![](images/37d62b23f8c6b4d7d7f120f16ff230383b8c8ed2c81a978723ee165f592ad7af.jpg) +Local Attention + +Table 3. Ablations. We trained model variants using the previously described setup and evaluated them on the LLFF dataset with 3 input views. + +
FLOPs (G)Parameters (M)
Full Attention11.670.37
Our 3D Transformer1.880.33
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In autonomous driving scenarios, there is rarely a single suitable trajectory. Recent methods have increasingly focused on modeling multimodal trajectory distributions. However, they suffer from trajectory selection complexity and reduced trajectory quality due to high trajectory divergence and inconsistencies between guidance and scene information. To address these issues, we introduce GoalFlow, a novel method that effectively constrains the generative process to produce high-quality, multimodal trajectories. To resolve the trajectory divergence problem inherent in diffusion-based methods, GoalFlow constrains the generated trajectories by introducing a goal point. GoalFlow establishes a novel scoring mechanism that selects the most appropriate goal point from the candidate points based on scene information. Furthermore, GoalFlow employs an efficient generative method, Flow Matching, to generate multimodal trajectories, and incorporates a refined scoring mechanism to select the optimal trajectory from the candidates. Our experimental results, validated on the Navsim[7], demonstrate that GoalFlow achieves state-of-the-art performance, delivering robust multimodal trajectories for autonomous driving. GoalFlow achieved PDMS of 90.3, significantly surpassing other methods. Compared with other diffusion-policy-based methods, our approach requires only a single denoising step to obtain excellent performance. The code is available at https: + +//github.com/YvanYin/GoalFlow. + +# 1. Introduction + +Since UniAD[15], autonomous driving has increasingly favored end-to-end systems, where tasks like mapping and + +![](images/6c49ca2a8008d8e7c8d8ce36973f6dfdb13fe749510079689cf45a7bd8758022.jpg) + +![](images/c1025cd925d7d87455acb7f039f6df105b3c00327b59dbebb1ae4deb3e669954.jpg) +Goal-Driven Generation Model +Figure 1. The comparison of different multimodal trajectory generation paradigms recently. A standalone generative model often produces highly diverse trajectories with no clear boundaries between different modalities. In contrast, the Goal-Driven Generation Model leverages the strong guidance of goal points, effectively distinguishing multiple modalities by utilizing different goal points. + +detection ultimately serve the planning task. To enhance system reliability, some end-to-end algorithms[16, 17, 27] have begun exploring ways to generate multimodal trajectories as trajectory candidates for the algorithms. In autonomous driving, command typically includes indicators for left, right, and straight actions. VAD[17] uses this command information to generate multimodal trajectories. Goal points, which provide the vehicle's location information for the next few seconds, are commonly used as guiding information in other approaches, such as SparseDrive[27]. These methods pre-define a set of goal points to generate different trajectory modes. Both approaches have succeeded in autonomous driving, offering candidate trajectories that significantly reduce collision rates. However, since these methods' guiding information does not pursue accuracy but instead provides a set of candidate values for the trajec + +tory, when the gap between the guiding information and the ground truth is large, it is prone to generating low-quality trajectories. + +In recent trajectory prediction works, some methods[18, 28, 32] aim to generate multimodal trajectories through diffusion, using scene or motion information as a condition to produce multimodal trajectories. Other methods [12] utilize diffusion to construct a world model. Without constraints, approaches like Diffusion-ES[32] tend to generate divergent trajectories, which is depicted in the second row of Fig.1, requiring a scoring mechanism based on HD maps to align with the real-world road network, which is difficult to obtain in end-to-end environments. MotionDiffuser[18] addresses trajectory divergence by using the ground truth endpoint as a constraint, which introduces overly strong prior information. GoalGAN[8] first predicts the goal point and then uses it to guide the GAN network to generate trajectories. However, GoalGAN employs grid-cell to sample goal points, which does not consider the distribution of the goal points. + +Reviewing previous work, we identified some overlooked issues:(1) Existing end-to-end autonomous driving systems tend to focus heavily on collision and L2 metrics, often adding specific losses or applying post-processing to reduce collision, while overlooking whether the vehicle remains within the drivable area. (2) Most end-to-end methods are based on regression models and aim to achieve multimodality by using different guiding information. However, when the guiding information deviates significantly from the ground truth, it can lead to the generation of low-quality trajectories. + +GoalFlow can be divided into three parts: Perception Module, Goal Point Construction Module, and Trajectory Planning Module. In the first module, following transfuser[3], images and LiDAR are fed into two separate backbones and fused into BEV feature finally. In the second module, GoalFlow establishes a dense vocabulary of goal points, and a novel scoring mechanism is used to select the optimal goal point that is closest to the ground truth goal point and within a drivable area. In the third module, GoalFlow uses flow matching to model multimodal trajectories efficiently. It conditions scene information and incorporates stronger guidance from the selected goal point. Finally, GoalFlow employs a scoring mechanism to select the optimal trajectory. Compared to directly generating trajectories with diffusion, as in the first row of Fig. 1, our approach provides strong constraints on the trajectory, leading to more reliable results. + +We conducted experimental validation in Navsim and found that our method outperformed other approaches in overall scoring. Notably, due to our goal point selection mechanism, we achieved a significant improvement in DAC scores. Additionally, we observed that this flow-matching- + +based approach is robust to the number of denoising steps during inference. Even with only a single denoising step, the score dropped by only $1.6\%$ compared to the optimal case, enhancing the potential for real-world deployment of generative models in autonomous driving. + +Our contributions can be summarized as follows: + +- We designed a novel approach to establishing goal points, demonstrating its effectiveness in guiding generative models for trajectory generation. +- We introduced flow matching to end-to-end autonomous driving and seamlessly integrated it with goal point guidance. +- We developed an innovative trajectory selection mechanism, using shadow trajectories to further address potential goal point errors. +- Our method achieved state-of-the-art results in Navsim. + +# 2. Related Work + +# 2.1. End-to-End Autonomous Driving + +Earlier end-to-end autonomous driving approaches[5][4] used imitation learning methods, directly extracting features from input images to generate trajectories. Later, Transfuser[3] advanced by fusing lidar and image information during perception, using auxiliary tasks such as mapping and detection to provide supervision for the perception. FusionAD[33] took Transfuser a step further by propagating fused perception features directly to the prediction and planning modules. Other methods [19, 20] align the traffic scene with natural language. UniAD[15] introduced a unified query design that made the framework ultimately planning-oriented. Similarly, VAD[17] focused on a planning-oriented approach by simplifying perception tasks and transforming scene representation into a vectorized format, significantly enhancing both planning capability and efficiency. Building on this, some methods[1, 22] discretized the trajectory space and constructed a trajectory vocabulary, transforming the regression task into a classification task. PARA-Drive[30] performs mapping, planning, motion prediction, and occupancy prediction tasks in parallel. GenAD[35] employed VAE and GRU for temporal trajectory reconstruction, while SparseDrive[27] progressed further in the vectorized scene representation, omitting denser BEV representations. Compared to previous methods that focus on better fitting ground truth trajectories using a regression model, we concentrate on generating high-quality multimodal trajectories in an end-to-end setting. + +# 2.2. Diffusion Model and Flow Matching + +Early generative models always used VAE[21] and GAN[10] in image generation. Recently, diffusion models that generate images by iteratively adding and remov + +![](images/a975c29e4cd8935fa543c6ed6e7cd4530d67f9043dee2bf14f158f1617d755fc.jpg) +Figure 2. Overview of the GoalFlow architecture. GoalFlow consists of three modules. The Perception Module is responsible for integrating scene information into a BEV feature $F_{bev}$ , the Goal Point Construction Module selects the optimal goal point from Goal Point Vocabulary V as guidance information, and the Trajectory Planning Module generates the trajectories by denoising from the Gaussian distribution to the target distribution. Finally, the Trajectory Scorer selects the optimal trajectory from the candidates. + +ing noise have become mainstream. DDPM[14] applies noise to images during training, converting states over time steps, and subsequently denoises them during testing to reconstruct the image. More recent methods[26] have further optimized sampling efficiency. Additionally, CFG[13] has enhanced the robustness of generated outputs. Flow Matching[23] establishes a vector field for transitioning from one distribution to another. Rectified flow[24], a specific form of flow matching, enables a direct, linear transition path between distributions. Compared to diffusion models, rectified flow often requires only a single inference step to achieve good results. + +# 2.3. MultiModal Trajectories Generation + +In planning tasks, such as manipulation and autonomous driving, a given scenario often offers multiple action options, requiring effective multimodal modeling. Recent works[2, 31] in manipulation have explored this by applying diffusion models with notable success. Autonomous driving has adopted two main multimodal strategies: the first uses discrete commands to guide trajectory generation, such as in VAD[17], which produces three distinct trajectory modes, and SparseDrive[27] and [16], which cluster fixed navigation points from datasets for trajectory guidance. The second approach introduces diffusion models directly to generate multimodal trajectories[18, 29, 32], achieving success in trajectory prediction but facing challenges in end-to-end applications. Building on diffusion models, we address limitations in accuracy and efficiency by incorporating flow matching, using goal points to guide trajectories with precision rather than focusing solely on multimodal diversity. + +# 3. Method + +# 3.1. Preliminary + +Compared to diffusion, which focuses on learning to reverse the gradual addition of noise over time to recover data, flow matching[23] focuses on learning invertible transformations that map between data distributions. Let $\pi_0$ denote a simple distribution, typically the standard normal distribution $p(x) = \mathcal{N}(x|0,I)$ , and let $\pi_1$ denote the target distribution. Under this framework, rectified flow[24] uses a simple and effective method to construct the path through optimal transport[25] displacement, which we choose as our Flow Matching method. + +Given $x_0$ sampled from $\pi_0$ , $x_1$ sampled from $\pi_1$ , and $t \in [0, 1]$ , the path from $x_0$ to $x_1$ is defined as a straight line, meaning the intermediate status $x_t$ is given by $(1 - t)x_0 + tx_1$ , with the direction of intermediate status consistently following $x_1 - x_0$ . By constructing a neural network $v_\theta$ to predict the direction $x_1 - x_0$ based on the current state $x_t$ and time step $t$ , we can obtain a path from the initial distribution $\pi_0$ to target distribution $\pi_1$ by optimizing the loss between $v_\theta(x_t, t)$ and $x_1 - x_0$ . This can be formalized as: + +$$ +v _ {\theta} \left(x _ {t}, t\right) \approx \mathbf {E} _ {x _ {0} \sim \pi_ {0}, x _ {1} \sim \pi_ {1}} \left[ v _ {t} \mid x _ {t} \right] \tag {1} +$$ + +$$ +\mathcal {L} (\theta) = \mathbf {E} _ {x _ {0} \sim \pi_ {0}, x _ {1} \sim \pi_ {1}} [ \| v _ {\theta} (x _ {t}, t) - (x _ {1} - x _ {0}) \| _ {2} ] \tag {2} +$$ + +# 3.2. GoalFlow + +# 3.2.1. Overview + +GoalFlow is a goal-driven end-to-end autonomous driving method that can generate high-quality multimodal trajectories. The overall architecture of GoalFlow is illustrated in + +Figure 2. It comprises three main components. In the Perception Module, we obtain a BEV feature $F_{\mathrm{bev}}$ that encapsulates environmental information by fusing camera images $I$ , and LiDAR data $L$ . The Goal Point Construction Module focuses on generating precise guidance information for trajectory generation. It accomplishes this by constructing a goal point vocabulary $\mathbb{V} = \{g_i\}^N$ , and employing a scoring mechanism to select the most appropriate goal point $g$ . In the Trajectory Planning Module, we produce a set of multimodal trajectories, $\mathbb{T} = \{\hat{\tau}_i\}^M$ , and then identify the optimal trajectory $\tau$ , through a trajectory scoring mechanism. + +# 3.2.2. Perception Module + +In the first step, we fuse image and LiDAR data to create a BEV feature, $F_{\mathrm{bev}}$ , that captures rich road condition information. A single modality often lacks crucial details; for example, LiDAR does not capture traffic light information, while images cannot precisely locate objects. By fusing different sensor modalities, we can achieve a more complete and accurate representation of the road conditions. + +We adopt the Transfuser architecture [3] for modality fusion. The forward, left, and right camera views are concatenated into a single image $I \in \mathbb{R}^{3 \times H_1 \times W_1}$ , while Li-DAR data is formed as a tensor $L \in \mathbb{R}^{K \times 3}$ . These inputs are passed through separate backbones, and their features are fused at different layers using multiple transformer blocks. The result is a BEV feature, $F_{\mathrm{bev}}$ , which comprehensively represents the scene. To ensure effective interaction between the ego vehicle and surrounding objects, as well as map information, we apply auxiliary supervision to the BEV feature through losses derived from HD maps and bounding boxes. + +# 3.2.3. Goal Point Construction Module. + +In this module, we construct a precise goal point to guide the trajectory generation process. Diffusion-based approach[18, 32] without constraints often leads to excessive trajectory divergence, which complicates trajectory selection. Our key observation is that a goal point contains a precise description of the short-term future position, which imposes a strong constraint on the generation model. As a result, we divide the traditional Planning Module into two steps: first, constructing a precise goal point, and second, generating the trajectory through planning. + +Goal Point Vocabulary. We aim to construct a goal point set that provides candidates for the optimal goal point. Traditional goal-based methods[11, 34], rely on lane-level information from HD map to generate goal point sets for trajectory prediction. However, HD maps are expensive, making lane information often unavailable in end-to-end driving. Inspired by VADv2[1], we discretize the endpoint space of trajectories to generate candidate goal points, enabling a solution without relying on HD maps. We clustered trajectory endpoints $\mathbf{p}_i = (x_i, y_i, \theta_i)$ in the training data + +to create $N$ cluster centers, which form our goal point vocabulary $\mathbb{V}$ . Each endpoint $p_i$ represents a position $(x_i, y_i)$ and heading $\theta_i$ . To ensure that the vocabulary represents finer-grained locations, we typically set $N$ to a large value, generally 4096 or 8192. + +Goal Point Scorer. High-quality trajectories typically exhibit the following characteristics: A small distance to the ground truth and within the drivable area. To achieve this, we evaluate each goal point $g_{i}$ in the vocabulary $\mathbb{V}$ using two distinct scores: the Distance Score $\hat{\delta}^{\mathrm{dis}}$ and the Drivable Area Compliance Score $\hat{\delta}^{\mathrm{dac}}$ . The Distance Score measures the proximity between the goal point $g_{i}$ and the endpoint of ground truth trajectory $g^{\mathrm{gt}}$ , with a continuous value in the range $\hat{\delta}^{\mathrm{dis}} \in [0,1]$ , where a higher value indicates a closer match to $g^{\mathrm{gt}}$ . The Drivable Area Compliance Score ensures that the goal point lies within the drivable area, using a binary value $\hat{\delta}^{\mathrm{dac}} \in \{0,1\}$ , where 1 indicates that the goal point is valid within the drivable area, and 0 indicates it is not. + +To construct the target distance score $\delta_i^{\mathrm{dis}}$ , we utilize the softmax function to map the Euclidean distance between the goal point $g_{i}$ and the ground truth goal point $g^{\mathrm{gt}}$ to the interval [0, 1]. This is defined as: + +$$ +\delta_ {i} ^ {\mathrm {d i s}} = \frac {\exp \left(- \| g _ {i} - g ^ {\mathrm {g t}} \| _ {2}\right)}{\sum_ {j} \exp \left(- \| g _ {j} - g ^ {\mathrm {g t}} \| _ {2}\right)} \tag {3} +$$ + +For the target drivable area compliance score $\delta_i^{\mathrm{dac}}$ , we introduce a shadow vehicle, whose bounding box is determined based on the position and heading $(x_i, y_i, \theta_i)$ in $g_i$ and the shape of the ego vehicle. Let $\{p^j\}^4$ represent the set of four corner positions of the shadow vehicle, and let $\mathbb{D}$ denote the polygon representing the drivable area. The drivable area compliance score $\delta_i^{\mathrm{dac}}$ is defined as: + +$$ +\delta_ {i} ^ {\mathrm {d a c}} = \left\{ \begin{array}{l l} 1, & \text {i f \forall j , p ^ {j} \in \mathbb {D} ^ {\circ}} \\ 0, & \text {o t h e r w i s e} \end{array} \right. +$$ + +We compute the final score $\hat{\delta}_i^{\mathrm{final}}$ by aggregating $\hat{\delta}_i^{\mathrm{dis}}$ and $\hat{\delta}_i^{\mathrm{dac}}$ . The goal point with the highest final score is selected for trajectory generation. + +$$ +\hat {\delta} _ {i} ^ {\mathrm {f i n a l}} = w _ {1} \log \hat {\delta} _ {i} ^ {\mathrm {d i s}} + w _ {2} \log \hat {\delta} _ {i} ^ {\mathrm {d a c}} +$$ + +As shown in Fig.3(a), the Transformer-based Scorer Decoder uses the result of adding $F_{v}$ and $F_{\mathrm{ego}}$ as the query, with $F_{\mathrm{bev}}$ as the key and value. The output is passed through two separate MLPs to produce the scores $\hat{\delta}^{dis}$ and $\hat{\delta}^{dac}$ for each point in the V. Fig.3(b) shows the distribution of these two scores. With the points in warmer colors representing higher scores, we observe that score $\hat{\delta}^{dis}$ effectively indicates the desired future position, while $\hat{\delta}^{dac}$ identifies if the goal point is within the drivable area. + +![](images/d0338f5ded4ef523bb51eb3c9e1d7707db182d7b66f3e16e856c27d65d923c84.jpg) +(a) + +![](images/5bae47877e195ee1b729745cab053f55712bc2c1606e7570ad264fe60833dd82.jpg) +(b) + +![](images/62f0f677a50badfd58b13e683e099cdaa42a8f4dfee63500b4d92096c4b71f38.jpg) +Figure 3. Goal Point Scorer. (a) shows the detailed structure of the Goal Point Construction Module, and (b) presents the score distributions of $\{\hat{\delta}_i^{dis}\}^N$ , $\{\hat{\delta}_i^{dac}\}^N$ , and $\{\hat{\delta}_i^{final}\}^N$ , where points with higher scores are highlighted with warmer color. +Figure 4. The network architecture used in Rectified Flow. + +# 3.2.4. Trajectory Planning Module + +In this module, we generate constrained, high-quality trajectory candidates using a generative model and then select the optimal trajectory through a scoring mechanism. Generative models based on diffusion methods like DDPM[14] and DDIM[26] typically require complex denoising paths, leading to significant time overhead during inference, which makes them unsuitable for real-time systems like autonomous driving. In contrast, Rectified Flow[24], which is based on the optimal transport path in flow matching, requires much fewer inference steps to achieve good results. We adopt Rectified Flow as the generative model, using the BEV feature and goal point as conditions to generate multimodal trajectories. + +Multimodal Trajectories Generating. We generate multimodal trajectories by modeling the shift from the noise distribution to the target trajectory distribution. During this distribution transfer process, given the current state $x_{t}$ and + +time step $t$ , we predict the shift $\mathbf{v_t}$ . + +$$ +\mathbf {v} _ {\mathbf {t}} = \tau^ {n o r m} - x _ {0} \tag {4} +$$ + +$$ +x _ {t} = (1 - t) x _ {0} + t \tau^ {\text {n o r m}} \tag {5} +$$ + +$$ +\tau^ {\text {n o r m}} = \mathcal {H} \left(\tau^ {g t}\right) \tag {6} +$$ + +Where $\tau^{gt}$ is the ground truth trajectory and $\tau^{norm}$ is its normalized form. We define $\mathcal{H}(\cdot)$ as the normalization operation applied to the trajectory. The variable $x_0$ represents the noise distribution, which follows $x_0\sim \mathcal{N}(0,\sigma^2 I)$ . The variable $x_{t}$ is obtained by linearly interpolating between $x_0$ and $\tau^{norm}$ . + +As illustrated in Fig.4, we extract different features through a series of encoders. Specifically, we encode $x_{t}$ using a linear layer, while $t$ and the goal point are transformed into feature vectors via sinusoidal encoding. The feature $F_{\mathrm{env}}$ is obtained by passing the information from $F_{\mathrm{bev}}$ and $F_{\mathrm{ego}}$ through the environment encoder. + +$$ +F _ {\text {e n v}} = E _ {\text {e n v}} \left(Q, \left(F _ {\text {B E V}} + F _ {\text {e g o}}\right), \left(F _ {\text {B E V}} + F _ {\text {e g o}}\right)\right) \tag {7} +$$ + +Here, $E_{\mathrm{env}}$ refers to a Transformer-based encoder, $Q$ denotes a learnable embedding, and $F_{\mathrm{ego}}$ represents the ego status feature, which encodes the kinematic information of the ego vehicle. + +We concatenate the features $F_{\mathrm{env}}$ , $F_{\mathrm{goal}}$ , $F_{\mathrm{trail}}$ , and $F_{\mathrm{t}}$ to form the overall feature $F_{\mathrm{all}}$ , which encapsulates the current state, time step, and scene information. This combined feature is then passed through several attention layers to predict the distribution shift $\mathbf{v}_{\mathrm{t}}$ . + +$$ +\hat {\mathbf {v}} _ {\mathbf {t}} = \mathcal {G} \left(F _ {\text {a l l}}, F _ {\text {a l l}}, F _ {\text {a l l}}\right) \tag {8} +$$ + +$$ +F _ {\text {a l l}} = \operatorname {C o n c a t} \left(F _ {\text {e n v}}, F _ {\text {g o a l}}, F _ {\text {t r a j}}, F _ {t}\right) \tag {9} +$$ + +Where $\mathcal{G}$ is the network that consists of N attention layers. + +We reconstruct the trajectory distribution using $x_0$ and $\hat{\mathbf{v}}_{\mathbf{t}}$ . Typically, we achieve this by performing multiple inference steps through the Rectified Flow, gradually transforming the noise distribution $x_0$ to the target distribution $\tau^{\mathrm{norm}}$ . Finally, we apply denormalization to $\tau^{\mathrm{norm}}$ to obtain the final trajectory $\hat{\tau}$ . + +$$ +\hat {\tau} = \mathcal {H} ^ {- 1} \left(\hat {\tau} ^ {n o r m}\right) \tag {10} +$$ + +$$ +\hat {\tau} ^ {n o r m} = x _ {0} + \frac {1}{n} \sum_ {i} ^ {n} \hat {v} _ {t _ {i}} \tag {11} +$$ + +Where $n$ is the total inference steps, and $t_i$ is the time step sampled in the $i$ -th step, which satisfies $t_i \in [0,1]$ . $\mathcal{H}^{-1}(\cdot)$ is the denormalization operation. + +Trajectory Selecting In trajectory selection, methods like SparseDrive[27] and Diffusion-ES[32] rely on kinematic simulation of the generated trajectories to predict potential collisions with surrounding agents, thus selecting the optimal trajectory. This process significantly increases the inference time. We simplify this procedure by using the goal point as a reference for selecting the trajectory. Specifically, we trade off the trajectory distance to the goal point and ego progress, selecting the optimal trajectory through a trajectory scorer. + +$$ +f \left(\hat {\tau} _ {i}\right) = - \lambda_ {1} \Phi \left(f _ {d i s} \left(\hat {\tau} _ {i}\right)\right) + \lambda_ {2} \Phi \left(f _ {p g} \left(\hat {\tau} _ {i}\right)\right) \tag {12} +$$ + +where $\Phi (\cdot)$ is the minimax operation. $f_{dis}(\hat{\tau}_i)$ presents the $\mathcal{L}_2$ distance of $\hat{\tau}_i$ and $g$ , and $f_{pg}(\hat{\tau}_i)$ presents the $\mathcal{L}_2$ distance of progress of $\hat{\tau}_i$ make. + +Furthermore, predicted goal point may contain an error that can misguide the trajectory. To mitigate this, we mask the goal point during generation to create a shadow trajectory. If the shadow trajectory deviates significantly from the main trajectory, we treat the goal point as unreliable and use the shadow as the output. + +# 3.2.5. Training Losses + +Firstly, we optimize the perception extractor exclusively, and enforce multiple perception losses for supervision, including the cross-entropy loss for HD map $(L_{HD})$ and 3D bounding box classification $(L_{bbox})$ and $L_{1}$ loss for 3D bounding box locations $(L_{loc})$ . This stage aims to enrich the BEV feature with information on various perceptions. Losses are as follows. + +$$ +L _ {\text {p e r c e p t i o n}} = w _ {1} * L _ {H D} + w _ {2} * L _ {b b o x} + w _ {3} * L _ {l o c} \tag {13} +$$ + +where $w_{1}, w_{2}, w_{3}$ are set to 10.0, 1.0, 10.0 in training. For the goal constructor, we employ the cross entropy loss for + +distance score $(L_{dis})$ and DAC score $(L_{dac})$ . $w_4, w_5$ are set to 1.0 and 0.005. + +$$ +L _ {\text {g o a l}} = w _ {4} * L _ {\text {d i s}} + w _ {5} * L _ {\text {d a c}} \tag {14} +$$ + +$$ +L _ {d i s} = - \sum_ {i = 1} ^ {N} \delta_ {i} ^ {d i s} \log \left(\hat {\delta_ {i}} ^ {d i s}\right) \tag {15} +$$ + +$$ +L _ {d a c} = - \delta^ {d a c} \log \hat {\delta} ^ {d a c} - (1 - \delta^ {d a c}) \log \left(1 - \hat {\delta} ^ {d a c}\right) \tag {16} +$$ + +$L_{1}$ loss is utilized for multimodal planner. + +$$ +L _ {\text {p l a n n e r}} = \left| \mathbf {v} _ {\mathbf {t}} - \hat {\mathbf {v}} _ {\mathbf {t}} \right| \tag {17} +$$ + +# 4. Experiments + +# 4.1. Dataset + +Our experiment is validated on the Openscene[6] dataset. Openscene includes 120 hours of autonomous driving data. Its end-to-end environment Navsim[7] uses 1192 and 136 scenarios for trainval and testing, a total of over 10w samples at $2\mathrm{Hz}$ . Each sample contains camera images from 8 perspectives, fused Lidar data from 5 sensors, ego status, and annotations for the map and objects. + +# 4.2. Metrics + +In the Navsim environment, the generated 2Hz, 4-second trajectories are interpolated via an LQR controller to yield 10Hz, 4-second trajectories. These trajectories are scored using closed-loop metrics, including No at-fault Collisions $S_{NC}$ , Drivable Area Compliance $S_{DAC}$ , Time to Collision $S_{TTC}$ with bounds, Ego Progress $S_{EP}$ , Comfort $S_{CF}$ , and Driving Direction Compliance $S_{DDC}$ . The final score is derived by aggregating these metrics. Due to practical constraints, $S_{DDC}$ is omitted from the calculation1. + +$$ +\begin{array}{l} S _ {P D M} = S _ {N C} \times S _ {D A C} \times s _ {T T C} \times \\ \left(\frac {5 \times S _ {E P} + 5 \times S _ {C F} + 2 \times S _ {D D C}}{1 2}\right) \tag {18} \\ \end{array} +$$ + +# 4.3. Baselines + +In Navsim, we compare against the following baselines: Constant Velocity Assumes constant speed from the current timestamp for forward movement. Ego Status MLP Takes only the current state as input and uses an MLP to generate the trajectory. PDM-Closed Using ground-truth perception as input, several trajectories are generated through a rule-based IDM method. The PDM scorer then selects the optimal trajectory from these as the output. Transfuser Uses both image and LiDAR inputs, fusing them via a transformer into a BEV feature, which is then used for trajectory generation. LTF A streamlined version + +
MethodEgo Stat.ImageLiDARVideo\(S_{NC} \uparrow\)\(S_{DAC} \uparrow\)\(S_{TTC} \uparrow\)\(S_{CF} \uparrow\)\(S_{EP} \uparrow\)\(S_{PDM} \uparrow\)
Constant Velocity✓68.057.850.010019.420.6
Ego Status MLP✓93.077.383.610062.865.6
LTF [3]✓✓97.492.892.410079.083.8
TransFuser [3]✓✓✓97.792.892.810079.284.0
UniAD [15]✓✓✓97.891.992.910078.883.4
PARA-Drive [30]✓✓✓✓97.992.493.099.879.384.0
GoalFlow (Ours)✓✓✓98.498.394.610085.090.3
GoalFlow†✓✓✓99.897.998.610085.492.1
Human‡10010010099.987.594.8
+ +Table 1. Comparisons with SOTA methods in PDM score metrics on Navsim [7] Test. Our method outperforms other approaches across all evaluation metrics. † uses the endpoint of the ground-truth trajectory as the goal point. ‡ uses the ground-truth trajectories to evaluate. + +
ModelDescriptionSNC↑SDAC↑STTC↑SCFSEP↑SPDM↑
-Transfuser[3]97.792.892.810079.084.0
M0Base Model97.994.294.210079.985.6
M1M0 + Distance Score Map98.596.494.910083.088.5
M2M1 + DAC Score Map98.697.594.710083.889.4
M3M2 + Trajectory Scorer98.498.394.610085.090.3
+ +Table 2. Ablation study on the influence of each component. $\mathcal{M}_0$ is the base model, which uses rectified flow without goal point guidance and averages all generated trajectories to produce the final output. $\mathcal{M}_1$ and $\mathcal{M}_2$ introduce the distance score map and DAC score map, respectively, to guide the rectified flow. $\mathcal{M}_3$ builds upon $\mathcal{M}_1$ by incorporating trajectory scorer. + +
TInf.TimeSNC↑SDAC↑STTC↑SCF↑SEP↑SPDM↑
20177.8ms98.398.194.310084.789.9
1092.4ms98.398.294.410084.990.1
549.0ms98.498.394.610084.490.3
110.4ms98.497.894.110084.588.9
+ +Table 3. Impact of different timesteps in inference. $T$ denotes the number of denoising steps during inference. The results indicate that the model's performance is robust to variations of denoising steps. + +
σSNC↑SDAC↑STTC↑SCF↑SEP↑SPDM↑
0.0598.398.294.410085.090.1
0.198.498.394.610085.090.3
0.287.476.069.432.056.249.0
0.368.348.144.82.2323.618.8
+ +Table 4. Impact of different values of $\sigma$ on the initial noise distribution. $\sigma$ is the standard deviation of $x_0$ . The results show that performance drops significantly when $\sigma$ exceeds 0.1, but remains stable for values below 0.1. + +of Transfuser, where the LiDAR backbone is replaced with a learnable embedding. It achieves results in NavSim similar to Transfuser. UniAD Employs multiple transformer architectures to process information differently, using queries + +to transfer information specifically for planning. PARA-Drive Differs from UniAD by performing mapping, planning, motion prediction, and occupancy prediction tasks in parallel based on the BEV feature. + +# 4.4. Model Setups and Parameters + +The training of rectified flow[24] follows classifier-free guidance[13], where features within the conditioning set are randomly masked to bolster model robustness. The last point of the ground-truth trajectory is used to guide flow matching in trajectory generation during training. In testing, the goal point for trajectory generation is set by selecting the highest-scoring point from the goal point vocabulary. The sampling process employs a smoothing method in [9] that re-scales the timesteps nonlinearly, instead of using uniform intervals. We generate 128/256 trajectories, from which the trajectory scorer identifies the optimal one. All training was conducted on 4 nodes, each equipped with 8 RTX 4090 or RTX 3090 GPUs. + +# 4.5. Results and Analysis + +Comparison with SOTA Methods. In Table 1, we compared our method with several state-of-the-art algorithms in end-to-end autonomous driving, highlighting the highest scores in bold. Testing in the Navsim environment revealed + +that GoalFlow consistently outperformed other methods in overall scores. Notably, our method surpasses the second-best approach by 5.5 points in the DAC score and by 5.7 points in the EP score, indicating that GoalFlow provides stronger constraints on keeping the vehicle within drivable areas, thus enhancing the safety of autonomous driving systems. Additionally, GoalFlow enables faster driving speeds while ensuring safety. Further experiments, where we replaced the predicted goal point with the endpoint of the ground truth trajectory, resulted in a score of 92.1, which is very close to the human trajectory score of 94.8. This demonstrates the strong guiding capability of the goal point in autonomous driving. + +Ablation Study on The Influence of Each Component. We conduct an ablation study of the influence of each component in Table 2. The $\mathcal{M}_0$ represents a model that generates trajectories using only the rectified flow. In our experiment results, the base $\mathcal{M}_0$ consistently outperforms baseline methods on Navsim, particularly excelling in DAC and TTC. This indicates that the base model, which is based on flow matching, has effectively learned interactions with map information and surrounding agents, demonstrating that the flow model alone possesses strong modeling capabilities. + +The $\mathcal{M}_1$ model builds on $\mathcal{M}_0$ by modeling the distance score distribution and selecting the point with the highest score to guide the rectified flow. We found that this results in the most significant improvement, demonstrating the effectiveness of decomposing the trajectory planning task. Specifically, we decompose the complex task into two simpler sub-tasks: goal point prediction and trajectory generation guided by the goal point. + +The $\mathcal{M}_2$ model builds upon $\mathcal{M}_1$ by incorporating the prediction of DAC score distribution. The main improvement is seen in the DAC score. By introducing multiple evaluators from different perspectives, the model benefits from a more robust assessment, resulting in improved performance. + +By incorporating trajectory scorer, which includes a trajectory selection and goal point checking mechanism, $\mathcal{M}_3$ further enhances the reliability of GoalFlow. + +Impact of Different Steps in Inference. We conducted experiments with different denoising steps during the inference process, as shown in Table 3. In these experiments, We found as the number of inference steps decreases from 20 to 1, the scores remained stable. Specifically, even with just a single inference step, excellent performance was achieved. This highlights the advantage of flow matching over diffusion-based frameworks: flow matching takes a direct, straight path, requiring fewer steps to transfer from noisy distribution to target distribution during inference. Additionally, as the inference steps are reduced from 20 to 1, the denoising time in inference of one sample decreases + +to $6\%$ of the original. This efficient inference process is especially critical for autonomous driving systems, where real-time performance is essential. + +Impact of Different Initial Noise in Training. In the experiments, the initial noise follows a Gaussian distribution $\mathcal{N}(0,\sigma^2 I)$ . We explored the impact of the noise variance on the generated trajectories in Table 4. The results reveal that noise settings have a significant impact on the scores. When the noise is set too high, the generated trajectories become excessively erratic; notably, with a $\sigma$ of 0.3, the Comfort score drops to only 2.23, indicating that the trajectory lacks coherent shape. Conversely, when the noise variance is too low, flow matching tends to degenerate into a regression model, reducing the trajectory diversity available for scoring. This lack of variety lowers overall scores. + +
DimBackboneSNC↑SDAC↑TTC↑SEP↑SPDM↑
256V2-9997.196.291.881.886.5
512V2-9997.397.692.583.088.1
1024V2-9998.697.594.785.089.4
256resnet3498.393.894.379.885.7
256V2-9997.196.291.881.886.5
+ +Table 5. Impact of Scaling Model. We examine the impact of scaling the Transformer's hidden dimension and changing the image backbone. Both increasing the hidden dimension and using a larger backbone improve performance. To isolate the effect of trajectory post-processing, we compare with $\mathcal{M}_2$ . + +Impact of Scaling Model. Inspired by [36], we present experiments on scaling the model based on the $\mathcal{M}_2$ in Table 5. Under the same V2-99 backbone, increasing the hidden dimension consistently improves performance, with the best results observed at a dimension of 1024. Additionally, we conducted experiments comparing different backbone architectures under the same dimension setting, using ResNet-34 and V2-99 as the image backbones. While V2-99 and ResNet-34 achieved similar scores, their score distributions displayed significant differences. We attribute this to ResNet-34's distinct approach to learning the goal point information as guidance compared to V2-99. + +# 5. Conclusion + +In this paper, we focus on generating accurate and efficient multimodal trajectories. We reviewed recent works on multimodal trajectory generation in autonomous driving and proposed a framework that generates precise goal points and effectively constrains the generative model with them, ultimately producing high-quality multimodal trajectories. We conducted experiments on the Navsim environment, demonstrating that GoalFlow achieves state-of-the-art performance. In the future, we aim to further investigate the impact of different guidance information on multimodal trajectory generation. + +# References + +[1] Shaoyu Chen, Bo Jiang, Hao Gao, Benchcheng Liao, Qing Xu, Qian Zhang, Chang Huang, Wenyu Liu, and Xinggang Wang. 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We detail the foundational elements enabling high-quality visual generation, including the data curation pipeline, model architecture design, flow formulation, and advanced infrastructure for efficient and robust large-scale training. The Goku models demonstrate superior performance in both qualitative and quantitative evaluations, setting new benchmarks across major tasks. Specifically, Goku achieves 0.76 on GenEval and 83.65 on DPG-Bench for text-to-image generation, and 84.85 on VBenchmark for text-to-video tasks. We believe that this work provides valuable insights and practical advancements for the research community in developing joint image-and-video generation models. + +# 1. Introduction + +Video generation has garnered significant attention owing to its transformative potential across a wide range of applications, such media content creation [62], advertising [3, 93], video games [63, 77, 88], and world model simulators [1, 8, 31]. Benefiting from advanced generative algorithms [30, 34, 52, 53], scalable model architectures [59, 78], vast amounts of internet-sourced data [14, 45, 57], and ongoing expansion of computing capabilities [18-20], remarkable advancements have been achieved in the field of video generation [7, 8, 35, 36, 42, 44, 47, 49, 62, 69, 89]. + +In this work, we introduce Goku, a family of rectified flow [52, 53] transformer models designed for joint image and video generation, paving the way toward industry-grade performance. Our approach emphasizes four key aspects: data curation, model architecture, flow formulation, and opti + +mized training infrastructure—each refined for high-quality, large-scale video generation. + +First, we present a comprehensive data processing pipeline designed to construct large-scale, high-quality image and video-text datasets. The pipeline integrates multiple advanced techniques, including video and image filtering based on aesthetic scores, OCR analysis, and subjective evaluations, to ensure exceptional visual and contextual quality. Furthermore, we employ multimodal large language models (MLLMs) [90] to generate dense and contextually aligned captions, which are subsequently refined using an additional Qwen2 [87] to enhance their accuracy and descriptive richness. As a result, we have curated a robust training dataset comprising approximately 36M video-text pairs and 160M image-text pairs, which are proven sufficient for training industry-level generative models. + +Secondly, we take a pioneering step by applying rectified flow formulation [52] for joint image and video generation, implemented through the Goku model family, which comprises Transformer architectures with 2B and 8B parameters. At its core, the Goku framework employs a 3D joint image-video variational autoencoder (VAE) to compress image and video inputs into a shared latent space, facilitating unified representation. This shared latent space is coupled with a full-attention [78] mechanism, enabling seamless joint training of image and video. This architecture delivers high-quality, coherent outputs across both images and videos, establishing a unified framework for visual generation tasks. + +Furthermore, to support the training of Goku at scale, we have developed a robust infrastructure tailored for large-scale model training. Our approach incorporates advanced parallelism strategies [41, 94] to manage memory efficiently during long-context training. Additionally, we employ ByteCheckpoint [79] for high-performance checkpointing and integrate fault-tolerant mechanisms from MegaS- + +![](images/eb5dad327611d161517e79c50cf702d7a474d07d320e2de9b56ea3d3431a9115.jpg) +A glass transparent emoji cartoon hand making the peace sign gesture, with fingers straight up and down + +![](images/01b47699cce09a33d70fc23e1ce27e78a0c6f9d6b6015cb044f181b326622465.jpg) + +![](images/2ed549b3675d8fcfc5dd3278f3b1ea29b28532276d4168552e882226e5d28d2b.jpg) +A native Warrior shaman Bengal Cat with a black and white leopard pattern, blue eyes, short fur, and portrait pose, colorful feathers and colorful ornaments, a regal oil-style portrait of the queen of native Kitty shaman white Cat with wings and headdress. Nordic is kind and motherly, it has black eye makeup and her hair is in messy. +An ancient artifact rests on a pedestal, the word "GOKU" etched onto its surface, glowing as if holding a hidden power within. + +![](images/3c8273e60cca9936ff5f927ca2eb808fa206bad37e7bc137dd643bf6a7296d4a.jpg) +A white bearded man's face emerges from a cloud of white butterflies, background is white + +![](images/39960b3f058cf25fb2aadbda9e20e973a536de360bd9401984fd991a5a053b9a.jpg) +An enchanted forest with a waterfall cascading over rocks, the word "GOKU" formed by glowing moss along the stone surface, lighting up the misty surroundings. + +![](images/d4edf51cddbda623797ca35a562b5e6f32cea409598d84346e7078487817b20c.jpg) +An extremely happy American Cocker Spaniel. + +![](images/7a0077be4bc09b11cff27df4cfc58caaaabae0f519430f1618ed18b506f90a54.jpg) +Goku Black, in Super Saiyan Rose form, stands in a destroyed cityscape. The word "SAIYAN" is etched into the ground with dark energy. + +![](images/081a3046422f767efd3ddcf71773cb25313baa34109f5f6f4b61e9b7877790ee.jpg) + +![](images/befac96fc83448f723909522628e23d67707bffae9b1b39d726417887831f830.jpg) +A flock of paper airplanes flutters through a dense jungle, weaving around trees as if they were migrating birds. + +(a) Text-to-Image Samples +![](images/eb9c6df944383832204779edff68d6968ddf96b8fc96234d2adcc02df4f36c60.jpg) +A giant panda sitting comfortably at a table, eating a hotspot meal. + +![](images/cb7fd8faa05e72033110c48a8c5ff021290333ea7637a4d67ee0fb8a3bcc42c7.jpg) + +![](images/3466e7a86781c1896fd2e1831641ac0c896dc68ef7234dd19e9b842815b4ebe8.jpg) + +![](images/4709645823dda443869e1e0a009bd5010e74ea096ed077624a5c0312717ff492.jpg) + +![](images/336c5d78072fc1eb3ceaab002312044d238cb84da5516f3c2cd2719e525f740c.jpg) + +![](images/092e3c0d75702875e894866c8f1b6c93377ddf38c2261b9fa2e1c419ef8053ca.jpg) + +![](images/db21883a5dffbbbf639eaf367355c60fff576c9ae9d05c8a2492468259b921ca.jpg) + +Figure 1. Generated samples from Goku. Key components are highlighted in RED. +![](images/62c27d9705b69c4f5b0557bee94725fa2c051886099a642139bbcf5c6cc1e643.jpg) +An individual standing in a kitchen, wearing an apron, and holding a frying pan positioned above a burner. + +![](images/dd95e3b4cb6a90ab6b2e470d03b484fcdc03a57cde3469115dac897f6df75f1e.jpg) +(b) Text-to-Video Samples + +![](images/70149f7aeb5c5bfe21a71afa281deb50157781e4e1d45c99604ec06bde22d232.jpg) + +![](images/c22943099534d918c49f7f4e8e0434ae8b84088a43c4da2d9854b406866c3c57.jpg) + +![](images/e72d8e1497af208b0899cd9c0a39c1f6620312058895b90a83d3119f6bd2d0c4.jpg) + +![](images/f75ab016f6b34230a58716a833f8c38c4ee414bbf1b3c1f9bda7f14b0399b597.jpg) + +scale [43] to ensure stability and scalability across large GPU clusters. These optimizations enable Goku to handle the computational and data challenges of generative modeling with exceptional efficiency and reliability. + +We evaluate Goku on both text-to-image and text-to-video benchmarks to highlight its competitive advantages. For text-to-image generation, Goku-T2I demonstrates strong performance across multiple benchmarks, including T2I-CompBench [39], GenEval [28], and DPG-Bench [38], excelling in both visual quality and text-image alignment. In + +text-to-video benchmarks, Goku-T2V achieves state-of-the-art performance on the UCF-101 [71] zero-shot generation task. Additionally, Goku-T2V attains an impressive score of 84.85 on VBenchmark [40], securing the top position on the leaderboard (as of 2025-01-25) and surpassing several leading commercial text-to-video models. Qualitative results, illustrated in Figure 1, further demonstrate the superior quality of the generated samples. These findings underscore Goku's effectiveness in videoi generation and its potential as a solution for both research and commercial applications. + +# 2. Goku: Generative Flow Models + +In this section, we present three core components of Goku, the image-video joint VAE [89], the Goku Transformer architecture, and the rectified flow formulation. These components are designed to work synergistically, forming a cohesive and scalable framework for joint image and video generation. During training, each raw video input $x \in \mathbb{R}^{T \times H \times W \times 3}$ (with images treated as a special case where $T = 1$ ) is encoded from the pixel space to a latent space using a 3D image-video joint VAE (Section 2.1). The encoded latents are then organized into mini-batches containing both video and image representations, facilitating the learning of a unified cross-modal representation. Subsequently, the rectified flow formulation (Section 2.3) is applied to these latents, leveraging a series of Transformer blocks (Section 2.2) to model complex temporal and spatial dependencies effectively. + +# 2.1. Image-Video Joint VAE + +Earlier research [25, 33, 65] demonstrates that diffusion and flow-based models can significantly improve efficiency and performance by modeling in latent space through a Variational Auto-Encoder (VAE) [25, 46]. Inspired by Sora [8], the open-source community has introduced 3D-VAE to explore spatio-temporal compression within latent spaces for video generation tasks [50, 89, 95]. To extend the advantages of latent space modeling across multiple media formats, including images and videos, we adopt a jointly trained Image-Video VAE [89] that handles both image and video data within a unified framework. Specifically, for videos, we apply a compression stride of $8 \times 8 \times 4$ across height, width, and temporal dimensions, respectively, while for images, the compression stride is set to $8 \times 8$ in spatial dimensions. + +# 2.2. Transformer Architectures + +The design of the Goku Transformer block builds upon GenTron [12], an extension of the class-conditioned diffusion transformer [59] for text-to-image/video tasks. It includes a self-attention module for capturing inter-token correlations, a cross-attention layer to integrate textual conditional embeddings (extracted via the Flan-T5 language model [16]), a feed-forward network (FFN) for feature projection, and a layer-wise adaLN-Zero block that incorporates timestep information to guide feature transformations. Additionally, we introduce several recent design enhancements to improve model performance and training stability, as detailed below. + +Plain Full Attention. In Transformer-based video generative models, previous approaches [7, 12, 69, 85] typically combine temporal attention with spatial attention to extend text-to-image generation to video. While this method reduces computational cost, it is sub-optimal for + +
ModelLayerModel Dim.FFN Dim.Attention Heads
Goku-1B281152460816
Goku-2B281792716828
Goku-8B4030721228848
+ +Table 1. Architecture configurations for Goku Models. Goku-1B model is only used for pilot experiments in Section 2.3 + +modeling complex temporal motions, as highlighted in prior work [62, 89]. In Goku, we adopt full attention to model multi-modal tokens (image and video) within a unified network. Given the large number of video tokens remaining after VAE processing—particularly for high-frame-rate, long-duration videos—we leverage FlashAttention [21, 68] and sequence parallelism [51] to optimize both GPU memory usage and computational efficiency. + +Patch n' Pack. To enable joint training on images and videos of varying aspect ratios and lengths, we follow the approach from NaViT [23], packing both modalities into a single minibatch along the sequence dimension. This method allows flexible mixing of training instances with different sequence lengths into a single batch, eliminating the need for data buckets [61]. + +3D RoPE Position Embedding. Rotary Position Embedding (RoPE) [72] has demonstrated effectiveness in LLMs by enabling greater sequence length flexibility and reducing inter-token dependencies as relative distances increase. During joint training, we apply 3D RoPE embeddings to image and video tokens. In our joint training framework, we extend 3D RoPE embeddings to image and video tokens, leveraging their extrapolation capability to accommodate varying resolutions. This adaptability makes RoPE particularly suited for handling diverse resolutions and video lengths. Furthermore, our empirical analysis revealed that RoPE converges faster than sinusoidal positional embeddings during transitions across different training stages + +Q-K Normalization. Training large-scale Transformers can occasionally result in loss spikes, which may lead to model corruption, manifesting as severe artifacts or even pure noise in generated images or videos. To mitigate this issue, we incorporate query-key normalization [22] to stabilize the training process. Specifically, we apply RMSNorm [92] to each query-key feature prior to attention computation, ensuring smoother and more reliable training dynamics. + +The overall Transformer model is constructed by stacking a sequence of blocks as described above. To address varying computational demands and performance requirements, we design three model variants, summarized in Table 1. The + +Goku-1B model serves as a lightweight option for pilot experiments. The Goku-2B variant consists of 28 layers, each with a model dimension of 1792 and 28 attention heads, providing a balance between computational efficiency and expressive capacity. In contrast, the larger Goku-8B variant features 40 layers, a model dimension of 3072, and 48 attention heads, delivering superior modeling capacity aimed at achieving high generation quality. + +# 2.3. Flow-based Training + +Our flow-based formulation is rooted in the rectified flow (RF) algorithm [2, 52, 53], where a sample is progressively transformed from a prior distribution, such as a standard normal distribution, to the target data distribution. This transformation is achieved by defining the forward process as a series of linear interpolations between the prior and target distributions. Specifically, given a real data sample $\mathbf{x}_1$ from the target distribution and a noise sample $\mathbf{x}_0 \sim \mathcal{N}(0,1)$ from the prior distribution, a training example is constructed through linear interpolation: + +$$ +\mathbf {x} _ {t} = t \cdot \mathbf {x} _ {1} + (1 - t) \cdot \mathbf {x} _ {0}, \tag {1} +$$ + +where $t \in [0,1]$ represents the interpolation coefficient. The model is trained to predict the velocity, defined as the time derivative of $\mathbf{x}_t$ , $\mathbf{v}_t = \frac{d\mathbf{x}_t}{dt}$ , which guides the transformation of intermediate samples $\mathbf{x}_t$ towards the real data $\mathbf{x}_1$ during inference. By establishing a direct, linear interpolation between data and noise, RF simplifies the modeling process, providing improved theoretical properties, conceptual clarity, and faster convergence across data distributions. + +Goku takes a pioneering step by adopting a flow-based formulation for joint image-and-video generation. We conduct a pilot experiment to validate the rapid convergence of flow-based training by performing class-conditional generation with Goku-1B a model specifically designed for these proof-of-concept experiments, on ImageNet-1K $(256\times 256)$ [24]. The model is configured with 28 layers, an attention dimension of 1152, and 16 attention heads. To evaluate performance, we compare key metrics, such as FID-50K and Inception Score (IS), for models trained using the denoising diffusion probabilistic model (DDPM) [34] and rectified flow. As shown in Table 2, RF demonstrates faster convergence than DDPM. For instance, Goku-1B (RF) achieves a lower FID-50K after 400k training steps compared to Goku-1B (DDPM), which requires 1000k steps to reach a similar level of performance. + +# 2.4. Training Details + +We propose a multi-stage training strategy. It starts with text-semantic pairing, advances to joint image-video training and cascaded resolutions, and concludes with modality-specific fine-tuning for optimal visual and temporal quality. Please refer to Appendix A for more details. + +
LossStepsFID ↓sFID ↓IS ↑Precision ↑Recall ↑
DDPM200k3.07954.3498226.47830.83870.5317
DDPM400k2.52314.3821265.06120.83990.5591
DDPM1000k2.25684.4887286.56010.83190.5849
Rectified Flow200k2.74724.6416232.30900.82390.5590
Rectified Flow400k2.15724.5022261.12030.82100.5871
+ +Table 2. Proof-of-concept experiments of class-conditional generation on ImageNet $256 \times 256$ . Rectified flow achieves faster convergence compared to DDPM. + +# 2.5. Image-to-Video + +To extend Goku for adapting an image as an additional condition for video generation, we employ a widely used strategy by using the first frame of each clip as the reference image [6, 29, 89]. The corresponding image tokens are broadcasted and concatenated with the paired noised video tokens along the channel dimension. To fully leverage the pretrained knowledge during fine-tuning, we introduce a single MLP layer for channel alignment, while preserving the rest of the model architecture identical to Goku-T2V. + +# 3. Infrastructure Optimization + +To achieve scalable and efficient training of Goku, we first adopt advanced parallelism strategies (Section 3.1), to handle the challenges of long-context, large-scale models. To further optimize memory usage and balance computation with communication, we implement fine-grained Activation Checkpointing (Section 3.2). Additionally, we integrate robust fault tolerance mechanisms from MegaScale, enabling automated fault detection and recovery with minimal disruption (Section 3.3). Finally, ByteCheckpoint is utilized to ensure efficient and scalable saving and loading of training states, supporting flexibility across diverse hardware configurations (Section 3.4). The details of these optimizations are introduced below. + +# 3.1. Model Parallelism Strategies + +The substantial model size and the exceptionally long sequence length (exceeding 220K tokens for the longest sequence) necessitate the adoption of multiple parallelism strategies to ensure efficient training. Specifically, we employ 3D parallelism to achieve scalability across three axes: input sequences, data, and model parameters. + +Sequence-Parallelism (SP) [41, 48, 51] slices the input across the sequence dimension for independent layers (e.g., LayerNorm) to eliminate redundant computations, reduce memory usage, and support padding for non-conforming input. We adopt Ulysses [41] as our implementation, which shards samples across the sequence parallel group from the start of the training loop. During attention computation, it + +uses all-to-all communication to distribute query, key, and value shards, allowing each worker to process the full sequence but only a subset of attention heads. After parallel computation of attention heads, another all-to-all communication aggregates the results, recombining all heads and the sharded sequence dimension. + +Fully Sharded Data Parallelism (FSDP) [94] partitions all parameters, gradients and optimizer states across the data parallel ranks. Instead of all-reduce in Distributed Data Parallelism, FSDP performs all-gather for parameters and reduce-scatter for gradients, enabling overlap with forward and backward computations to potentially reduce communication overhead. In our case, we adopt the HYBRID_SHARD strategy, which combines FULL_SHARD within a shard group and parameter replication across such groups, which effectively implements data parallelism (DP). This approach minimizes communication costs by limiting all-gather and reduce-scatter operations. + +# 3.2. Activation Checkpointing + +While the parallelism methods discussed in Section 3.1 provide significant memory savings and enable large-scaling training with long sequences, they inevitably introduce communication overhead among ranks, which can lead to suboptimal overall performance. To address this issue and better balance the computation and communication by maximizing their overlap in the profiling trace, we designed a fine-grained Activation Checkpointing (AC) [13] strategy. Specifically, we implemented selective activation checkpointing to minimize the number of layers requiring activation storage while maximizing GPU utilization. + +# 3.3. Cluster Fault Tolerance + +Scaling Goku training to large-scale GPU clusters inevitably introduces fault scenarios, which can reduce training efficiency. The likelihood of encountering failures increases with the number of nodes, as larger systems have a higher probability of at least one node failing. These disruptions can extend training time and increase costs. To enhance stability and efficiency at scale, we adopted fault tolerance techniques from MegaScale [43], including self-check diagnostics, multi-level monitoring, and fast restart/recovery mechanisms. These strategies effectively mitigate the impact of interruptions, enabling Goku to maintain robust performance in large-scale generative modeling tasks. + +# 3.4. Saving and Loading Training Stages + +Checkpointing training states—such as model parameters, exponential moving average (EMA) parameters, optimizer states, and random states—is crucial for training large-scale models, particularly given the increased likelihood of cluster + +![](images/051ba5840c28cfd19224b695713e46a826e895c769687f85e86619fe94f3bd6d.jpg) +Figure 2. The data curation pipeline in Goku. Given a large volume of video/image data collected from Internet, we generate high-quality video/image-text pairs through a series of data filtering, captioning and balancing steps. + +faults. Reloading checkpointed states ensures reproducibility, which is essential for model reliability and debugging potential issues, including those caused by unintentional errors or malicious attacks. + +To support scalable large-scale training, we adopt ByteCheckpoint [79] as our checkpointing solution. It not only enables parallel saving and loading of partitioned checkpoints with high I/O efficiency but also supports resharding distributed checkpoints. This flexibility allows seamless switching between different training scales, accommodating varying numbers of ranks and diverse storage backends. In our setup, checkpointing an 8B model across over thousands of GPUs blocks training for less than 4 seconds, which is negligible compared to the overall forward and backward computation time per iteration. + +# 4. Data Curation Pipeline + +
StageAmountResolutionDINO-Sim.AestheticOCRMotion
480p36M≥ 480×864≥0.85≥ 4.3<= 0.020.3 - 20.0
720p24M≥ 720×1280≥0.90≥ 4.5<= 0.010.5 - 15.0
1080p7M≥ 1080×1920≥0.90≥ 4.5<= 0.010.5 - 8.0
+ +Table 3. Overview of multi-stage training data. This table summarizes the thresholds for each filtering criterion, including resolution, DINO similarity, aesthetic score, OCR text coverage, motion score, and the corresponding data quantities. + +We unblock the data volume that is utilized for industry-grade video/image generation models. Our data curation pipeline, illustrated in Figure 2, consists of five main stages: (1) image and video collection, (2) video extraction and clipping, (3) image and video filtering, (4) captioning, and (5) data distribution balancing. We describe the details of data curation procedure below. + +# 4.1. Data Overview + +We collet raw image and video data from a variety of sources, including publicly available academic datasets, internet resources, and proprietary datasets obtained through partnerships with collaborating organizations. After rigorous filter + +ing, the final training dataset for Goku consists of approximately 160M image-text pairs and 36M video-text pairs, encompassing both publicly available datasets and internally curated proprietary datasets. The detailed composition of these resources is outlined as follows: + +- Text-to-Image Data. Our text-to-image training dataset includes 100M public samples from LAION [67] and 60M high-quality, internal samples. We use public data for pre-training and internal data for fine-tuning. +- Text-to-Video Data. Our T2V training dataset includes 11M public clips and 25M in-house clips. The former include Panda-70M [14], InternVid [83], OpenVid-1M [57], and Pexels [50]. + +# 4.2. Data Preprocessing + +We build a high-quality video dataset through preprocessing raw videos by standardizing duration, resolution, bitrate, and frame rate. Videos are segmented using PySceneDetect and refined with DINOv2. Clips undergo visual aesthetic evaluation, OCR-based text filtering, and RAFT-based motion filtering, with criteria adjusted by resolution. Semantic tags balance the dataset, emphasizing human-related content by adjusting representation across categories. More details are provided in Appendix C. + +# 4.3. Captioning + +Detailed captions are essential for enabling the model to generate text-aligned images/videos precisely. For images, we use InternVL2.0 [15] to generate dense captions for each sample. To caption video clips, we start with InternVL2.0 [15] for keyframe captions, followed by Tarsier2 [90] for video-wide captions. Note that the Tarsier2 model can inherently describe camera motion types (e.g., zoom in, pan right) in videos, eliminating the need for a separate prediction model and simplifying the overall pipeline compared to previous work such as [62]. Next, we utilize Qwen2 [87] to merge the keyframe and video captions. Besides, we also empirically found that adding the motion score (calculated by RAFT [75]) to the captions improves motion control for video generation. This approach enables users to specify different motion scores in prompts to guide the model in generating videos with varied motion dynamics. + +# 5. Experiments + +# 5.1. Text-to-Image Results + +we conduct a comprehensive quantitative evaluation of Gokut2I on widely recognized image generation benchmarks, including GenEval [28], T2I-CompBench [39], and DPG-Bench [38]. Details of these benchmarks could be found in Appendix B. The results are summarized in Table 4. + +
MethodText Enc.GenEval OverallT2I-CompBenchDPG Avg.
ColorShapeTexture
SDv1.5 [65]CLIP ViT-L/140.430.37300.36460.421963.18
DALL-E 2 [64]CLIP ViT-H/160.520.57500.54640.6374-
SDv2.1 [65]CLIP ViT-H/140.500.56940.44950.4982-
SDX [61]CLIP ViT-bigG0.550.63690.54080.563774.65
PixArt-α [11]Flan-T5-XXL0.480.68860.55820.704471.11
DALL-E 3 [5]Flan-T5-XXL0.67†0.8110†0.6750†0.8070†83.50†
GenTron [12]CLIP T5XXL-0.76740.57000.7150-
SD3 [26]Flan-T5-XXL0.74----
Show-o [86]Phi-1.50.53----
Transfusion [96]-0.63----
Chameleon [54]-0.39----
LlamaGen [73]FLAN-T5 XL0.32----
Emu 3 [81]-0.66†0.7913†0.5846†0.7422†80.60
Goku-T2I (2B)FLAN-T5 XL0.700.75210.48320.669183.65
Goku-T2I (2B)†0.76†0.7561†0.5759†0.7071†
+ +Table 4. Comparison with state-of-the-art models on image generation benchmarks. We evaluate on GenEval [28]; T2I-CompBench [39] and DPG-Bench [38]. Following [81], we use $\dagger$ to indicate the result with prompt rewriting. + +Performance on GenEval. To assess text-image alignment comprehensively, we employ the GenEval benchmark, which evaluates the correspondence between textual descriptions and visual content. Since Goku-T2I is primarily trained on dense generative captions, it exhibits a natural advantage when handling detailed prompts. To further explore this, we expand the original short prompts in GenEval with ChatGPT-40, preserving their semantics while enhancing descriptive detail. As shown in Table 4, Goku-T2I achieves strong performance with the original short prompts, surpassing most state-of-the-art models. With the rewritten prompts, Goku-T2I attains the highest score (0.76), demonstrating its exceptional capability in aligning detailed textual descriptions with generated images. + +Performance on T2I-CompBench. We further evaluate the alignment between generated images and textual conditions using the T2I-CompBench benchmark, which focuses on various object attributes such as color, shape, and texture. As illustrated in Table 4, Goku-T2I consistently outperforms several strong baselines, including PixArt- $\alpha$ [11], SDXL [61], and DALL-E 2 [56]. Notably, the inclusion of prompt rewriting leads to improved performance across all attributes, further highlighting Goku-T2I's robustness in text-image alignment. + +Performance on DPG-Bench. While the aforementioned benchmarks primarily evaluate text-image alignment with short prompts, DPG-Bench is designed to test model performance on dense prompt following. This challenging benchmark includes 1,000 detailed prompts, providing a rigorous test of a model's ability to generate visually accurate outputs for complex textual inputs. As shown in the last column of + +
MethodResolutionFVD (↓)IS (↑)
CogVideo (Chinese) [37]480×480751.3423.55
CogVideo (English) [37]480×480701.5925.27
Make-A-Video [69]256×256367.2333.00
VideoLDM [7]-550.6133.45
LVDM [33]256×256372.00-
MagicVideo [97]-655.00-
PixelDance [91]-242.8242.10
PYOCO [27]-355.1947.76
Emu-Video [29]256×256317.1042.7
SVD [6]240×360242.02-
Goku-2B (ours)256×256246.1745.77 ± 1.10
Goku-2B (ours)240×360254.4746.64 ± 1.08
Goku-2B (ours)128×128217.2442.30 ± 1.03
+ +Table 5. Zero-shot text-to-video performance on UCF-101. We generate videos of different resolutions, including $256 \times 256$ , $240 \times 360$ , $128 \times 128$ , for comprehensive comparisons. + +Table 4, Goku-T2I achieves the highest performance with an average score of 83.65, surpassing PixArt- $\alpha$ [11] (71.11), DALL-E 3 [5] (83.50), and EMU3 [81] (80.60). These results highlight Goku-T2I's superior ability to handle dense prompts and maintain high fidelity in text-image alignment. + +# 5.2. Text-to-Video Results + +Performance on UCF-101. We conduct experiments on UCF-101 [71] using zero-shot text-to-video setting. As UCF-101 only has class labels, we utilize an video-language model, Tarsier-34B [80], to generate detailed captions for all UCF-101 videos. These captions are then used to synthesize videos with Goku. Finally, we generated 13,320 videos at different resolutions with Goku-2B model for evaluation, including $256 \times 256$ , $240 \times 360$ and $128 \times 128$ . Following standard practice [70], we use the I3D model, pre-trained on Kinetics-400 [9], as the feature extractor. Based on the extracted features, we calculated Fréchet Video Distance (FVD) [76] to evaluate the fidelity of the generated videos. The results in Table 5 demonstrate that Goku consistently generates videos with lower FVD and higher IS. For instance, at a resolution of $128 \times 128$ , the FVD of videos generated by Goku is 217.24, achieving state-of-the-art performance and highlighting significant advantages over other methods. + +Performance on VBenchmark. As presented in Table 6, we evaluate Goku-T2V against state-of-the-art models on VBenchmark [40], a comprehensive benchmark designed to assess video generation quality across 16 dimensions. Goku-T2V achieves state-of-the-art overall performance on VBenchmark, showcasing its ability to generate high-quality videos across diverse attributes and scenarios. + +Among the key metrics, Goku-T2V demonstrates notable strength in human action representation, dynamic degree, and multiple object generation, reflecting its capacity for + +![](images/2bad8dc9443e3e0ecbd7bd435b4d122cea763cef4aea6a175b198032d144e029.jpg) + +![](images/f2b395de7b4783d2821c3c10973078f0e699c28920ae831adc19e91299b97f40.jpg) + +![](images/a19dd880c2ba1190aaafabf3922925453b9e056a531fc751617433ec8f1473aa.jpg) +GOKU-T2V(2B) + +![](images/7327b6b2f0fcc420cc545627a8d8b5465db3ff1004cf016448721906d3278a02.jpg) + +![](images/d42bc4412a8a009fcba5432e050bcc253338f02964a1dae58b5278bac96e63bb.jpg) + +![](images/8a642c4a60acdf15888ca55e4144f7587a7dc863f2e0adcb0b28a301855041b5.jpg) +GOKU-T2V(8B) + +![](images/6f44cf36f79501089d890fa6ae6ba2a26d84549987beb069f12da5027efb3c4d.jpg) +(a) Model Scaling +GOKU-T2V w/o Joint Training +(b) Joint Training +Figure 3. Ablation Studies of Model Scaling and Joint Training. Fig. (a) shows the comparison between Goku-T2V(2B) and GokuT2V(8B). Fig. (b) shows the comparisons between whether joint training is adopted or not. + +![](images/9a4b2c165ac8f68f435296b8956d28794ea6059f62689df06d3f53c903fceafd.jpg) +GOKU-T2V w/ Joint Training + +handling complex and diverse video content. Additionally, it achieves competitive results in appearance style, quality score, and semantic alignment, highlighting its balanced performance across multiple aspects. + +For detailed results on all 16 evaluation dimensions, we refer readers to Table 8 in the Appendix. This comprehensive analysis underscores Goku-T2V's superiority in video generation compared to prior approaches. + +# 5.3. Image-to-Video + +We fine-tune Goku-I2V from the T2V initialization with 4.5M text-image-video triplets, sourced from diverse domains to ensure robust generalization. Despite the relatively small number of fine-tuning steps (10k), our model demonstrates remarkable efficiency in animating reference image while maintaining strong alignment with the accompanying text. As illustrated in Figure 4, the generated videos exhibit high visual quality and temporal coherence, effectively capturing the semantic nuances described in the text. + +# 5.4. Image and Video Qualitative Visualizations + +For intuitive comparisons, we conduct qualitative assessments and present sampled results in Figure 12. The evaluation includes open-source models, such as CogVideoX [89] and Open-Sora-Plan [95], alongside closed-source commercial products, including DreamMachine [55], Pika [60], Vidu [4], and Kling [49]. The results reveal that some commercial models struggle to generate critical video elements when handling complex prompts. For instance, models like Pika, DreamMachine, and Vidu (rows 3–5) fail to render the + +
ModelsHuman ActionSceneDynamic DegreeMultiple ObjectsAppear. StyleQuality ScoreSemantic ScoreOverall
AnimateDiff-V292.6050.1940.8336.8822.4282.9069.7580.27
VideoCrafter-2.095.0055.2942.5040.6625.1382.2073.4280.44
OpenSora V1.285.8042.4747.2258.4123.8980.7173.3079.23
Show-195.6047.0344.4445.4723.0680.4272.9878.93
Gen-396.4054.5760.1453.6424.3184.1175.1782.32
Pika-1.086.2049.8347.5043.0822.2682.9271.7780.69
CogVideoX-5B99.4053.2070.9762.1124.9182.7577.0481.61
Kling93.4050.8646.9468.0519.6283.3975.6881.85
Mira63.8016.3460.3312.5221.8978.7844.2171.87
CausVid99.8056.5892.6972.1524.2785.6578.7584.27
Luma96.4058.9844.2682.6324.6683.4784.1783.61
HunyuanVideo94.4053.8870.8368.5519.8085.0975.8283.24
Goku (ours)97.6057.0876.1179.4823.0885.6081.8784.85
+ +Table 6. Comparison with leading T2V models on VBench. Goku achieves state-of-the-art overall performance. Detailed results across all 16 evaluation dimensions are provided in Table 8 in the Appendix. + +![](images/47738a37ec1d959f38f679d0810b9ce1c54731192f3250ec988fc6c354cc1c9d.jpg) +A lion running towards the left side of the scene, with flames engulfing its body. As it runs, the lion gradually transforms into a mass of flames.. + +![](images/f01d993428dbe1970a1da993d73983cc4947db2544e0fd714eb60580e00634ff.jpg) +A woman in workout gear is lifting weights at a gym, her biceps flexing with each lift, sweat visible on her forehead, with a closeup on her determined expression.. + +![](images/1b1d8594c069a586a472b50f880a2a4b9f9c295f0650f84b4b2cf99a97b08d4f.jpg) +A man surfing on a wave, with the camera following his movement and focusing on his face. He is smiling and giving a thumbs-up to the camera, ... +Figure 4. Samples of Goku-12V. Reference images are presented in the leftmost columns. We omitted redundant information from the long prompts, displaying only the key details in each one. Key words are highlighted in RED. + +skimming drone over water. While certain models succeed in generating the target drone, they often produce distorted subjects (rows 1-2) or static frames lacking motion consistency (row 6). In contrast, Goku-T2V (8B) demonstrates superior performance by accurately incorporating all details of the prompt, creating a coherent visual output with smooth motion. Additional comparisons are provided in the appendix for a more comprehensive evaluation. Furthermore, more video examples are available at the Goku homepage. + +# 5.5. Ablation Studies + +Model Scaling. We compared Goku-T2V models with 2B and 8B parameters. Results in Figure 3a indicate that model scaling helps mitigate the generation of distorted object structures, such as the arm in Figure 3a (row 1) and the wheel in Figure 3a (row 2). This aligns with findings observed in large multi-modality models. + +Joint Training. We further examine the impact of joint image-and-video training. Starting from the same pretrained Goku-T2I (8B) weights, we fine-tuned Goku-T2V (8B) on 480p videos for an equal number of training steps, with and without joint image-and-video training. As shown in Figure 3b, Goku-T2V without joint training tends to generate low-quality video frames, while the model with joint training more consistently produces photorealistic frames. + +# 6. Conclusion + +In this work, we introduced Goku, a novel joint image-and-video generation model designed for industry-standard performance. By combining meticulous data curation and a robust model architecture, Goku effectively integrates image and video modalities to produce high-quality outputs. 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However, their speed is limited by multi-path blocks, and some depend on high-performance teacher models for training. To overcome these issues, we propose Golden Cudgel Network (GCNet). Specifically, GCNet uses vertical multi-convolutions and horizontal multipaths for training, which are reparameterized into a single convolution for inference, optimizing both performance and speed. This design allows GCNet to self-enlarge during training and self-contract during inference, effectively becoming a "teacher model" without needing external ones. Experimental results show that GCNet outperforms existing state-of-the-art models in terms of performance and speed on the Cityscapes, CamVid, and Pascal VOC 2012 datasets. The code is available at https://github.com/gyyang23/GCNet. + +# 1. Introduction + +Semantic segmentation is a critical task in computer vision that classifies each pixel in an image into specific categories. It is vital in fields like autonomous driving [2], medical image analysis [24], and environmental monitoring [37]. While deep learning has significantly improved the performance of semantic segmentation models, they still face challenges with real-time image analysis, limiting their use in applications such as autonomous driving. Therefore, ongoing research and optimization of these algorithms are essential for practical deployment. + +To meet the demands of real-time applications, numerous semantic segmentation models have emerged in recent years, emphasizing both performance and inference speed. One of the earliest, ERFNet [25], reduced parameters and computational load by redesigning ResNet [17] blocks using 1D convolutional kernels and skip connec + +![](images/f0162b93d6111b71179bae57f6b401cd73c7d82847e1535c7ec966b58a7be278.jpg) +Figure 1. The trade-off between inference speed and performance for real-time semantic segmentation models on the Cityscapes validation set. + +tions. However, its single-branch architecture limits its ability to learn spatial information from high-resolution features. In response, BiSeNetV1 [34], BiSeNetV2 [35], and DDRNet [21] introduced two-branch architectures, with one branch focusing on spatial details and the other on deep semantic information. PIDNet [32] expanded this idea with a three-branch design, adding a branch for boundary information. Although multi-branch models have proven effective for enhancing spatial detail capture, SCTNet [33] takes a different approach by proposing a single-branch model that improves semantic representation through knowledge distillation from a high-performance transformer segmentation model [31]. + +While models mentioned above [21, 32, 33] have achieved impressive speed and performance, their use of Residual Blocks [17] and Conv-Former Blocks [33] can hinder inference speed. As shown in Figure 2, residual connection increase memory access frequency, and the complexity of Conv-Former Block, similar to transformer ar + +![](images/03261ab62757683e6f5040cbf72e74d57f7be762fd13a8135681cf89a6f801c7.jpg) +Figure 2. A comparison of the proposed GCBlock with multi-path blocks: (a) Residual Block [17], used by model [21, 32, 33]. (b) Conv-Former Block [33], used by model [33]. (c) GCBlock, a block that is scalable in both vertical and horizontal directions. + +chitectures, also affects memory access and inference efficiency. In contrast, single-path blocks [28] are better suited for real-time segmentation due to their unidirectional structure, which allows for faster processing and reduced memory overhead. Additionally, although SCTNet uses a single-branch architecture for inference, it relies on a high-performance teacher model during training, which raises costs. The necessity of pre-trained weights from the teacher model on a specific dataset further complicates training and increases resource demands. + +Based on the aforementioned description, two key issues currently exist: (1) the decrease in inference speed caused by multi-path blocks and transformer-like convolution structures, and (2) the reliance on high-performance teacher models during training. To address issue (1), we introduce the Golden Cudgel Block (GCBlock), which employs a configuration of vertical multi-convolutions and horizontal multi-paths during training. During inference, these convolutions and paths are reparameterized into a single $3 \times 3$ convolution. This design seeks to simultaneously leverage the training advantages of multi-path blocks, such as avoiding issues of gradient vanishing and explosion, and the inference advantages of single-path blocks. To solve issue (2), we propose the Golden Cudgel Network (GCNet), which stacks multiple GCBlocks. During training, GCNet enlarges itself to enhance its learning capacity, while during inference, it contracts to improve speed. From a broader perspective, GCNet can effectively transform itself into a "teacher model" without the need for an external one. + +To evaluate the performance and speed of the proposed GCNet, we conducted experiments on three datasets: Cityscapes [9], CamVid [1], and Pascal VOC 2012 [14]. The results indicate that GCNet achieves a superior balance between segmentation performance and inference speed. As shown in Figure 1, compared to other state-of-the-art real-time semantic segmentation models, GCNet demonstrates enhanced performance and faster speed. The main contributions of this paper are as follows: + +- We propose the Golden Cudgel Network family, a model designed to enhance performance through self-enlargement and increase inference speed through self-contraction without any loss in performance. +- We introduce the Golden Cudgel Block, which leverages the training advantages of multi-path blocks and the inference advantages of single-path blocks through reparameterization. +- Experiments conducted on three public datasets demonstrate that the proposed GCNet achieves a superior balance between performance and speed compared to other state-of-the-art real-time semantic segmentation models. In particular, without ImageNet pre-training, GCNet reaches $77.3\%$ mIoU and 193.3 FPS on the Cityscapes. + +# 2. Related Work + +# 2.1. High-performance Semantic Segmentation + +High-performance semantic segmentation models primarily focus on segmentation quality and accuracy, often at the expense of inference speed. FCN [26], one of the earliest deep learning-based models, achieved pixel-level segmentation by replacing fully connected layers in CNNs with convolutional layers. However, its heavy downsampling results in a loss of spatial detail. To mitigate this, the DeepLab series [3-5] integrated dilated convolutions [36] with varying rates to enhance the receptive field while preserving spatial resolution. Recently, transformer-based segmentation models [6, 7, 31] have emerged, leveraging self-attention to capture long-range dependencies and improve performance. Despite their effectiveness, these models remain unoptimized for inference speed, limiting their suitability for real-time applications. + +# 2.2. Real-time Semantic Segmentation + +Real-time semantic segmentation models aim to simultaneously enhance speed and performance. However, optimizing speed through adjustments to depth, width, or structure can compromise performance, necessitating strategies to balance both. Architecturally, these models fall into two categories: single-branch and multi-branch architectures. + +Single-branch Architecture: As single-branch architecture models, they [22, 25, 30] typically balance performance and speed by optimizing backbone blocks or designing lightweight segmentation heads. However, with the rise of multi-branch models that offer enhanced performance and speed, single-branch models face challenges. Despite this, numerous studies continue to advance single-branch models. For example, STDC [15] addresses the speed slow addition of branches in BiSeNet [34] by introducing the Detail Aggregation Module, which retains spatial information through a single-branch approach. SCTNet [33] utilizes knowledge distillation with SegFormer [31] as the teacher + +![](images/e8c7dabd93dad8e5f18b6486342ef7a2de9835c93c41e8aaea751694e3fa1a88.jpg) + +![](images/5a33747077f43c2ca814bd7f5a1a15901d48de8c5035b528cf1b124b7e6c168e.jpg) +Figure 3. The overall architecture of GCNet. After feature flow into two branches, the upper branch corresponds to the semantic branch, while the lower branch corresponds to the detail branch. The orange box indicates that the first block within the GCBlocks has a stride of 2, while the remaining blocks have a stride of 1. The green box signifies that all GCBlocks maintain a stride of 1. PPM refers to the Deep Aggregation Pyramid Pooling Module [21]. + +model, employing a Conv-Former Block to bridge the semantic gap between CNN and transformer features, allowing for more effective learning of rich semantic information. + +Multi-branch Architecture: Single-branch architecture models use skip connections to link feature maps between the backbone and head, preserving spatial details. In contrast, multi-branch models add branches to learn both spatial details and boundary information. BiSeNetV1 [34] and V2 [35] propose a two-branch architecture where one branch focuses on deep semantic information and the other on spatial details, with no weight sharing between them. Conversely, models like Fast-SCNN [23] and DDRNet [21] share some low-level backbone weights. Fast-SCNN extracts shallow features and splits them into two branches for feature retention and global feature extraction, while DDRNet performs multiple bilateral fusions to efficiently merge information. PIDNet [32] introduces a three-branch architecture to capture spatial detail, deep semantic information, and boundary information. + +Whether single-branch models or multi-branch models, although they continually compete in architectural design to optimize performance and speed, their inference speeds are limited by multi-path blocks, as shown in Figure 2. In contrast, our GCNet, based on a two-branch architecture, enhances its learning capability during training by vertically increasing convolutions and horizontally expanding paths. During inference, it improves inference speed by reparameterizing multi-convolution multi-path blocks into a single + +convolution, all without sacrificing performance. Although some studies [11-13] have employed similar methods to enhance model performance and speed in image classification tasks, such approaches have been seldom explored in semantic segmentation tasks. + +# 3. Methodology + +In this section, we first present the overall framework of GCNet. Then, we describe the training structure of the GCBlock and its reparameterization into a single convolution during inference. Finally, we detail the supervisory strategy and loss function used in model training. + +# 3.1. Golden Cudgel Network + +To address the issue of increased training costs associated with the use of teacher models, we propose the Golden Cudgel Network (GCNet). We establish a two-branch architecture as baseline model and subsequently enhance it by deepening the model with additional convolution and broadening it with multiple paths, thereby augmenting its learning capacity. After training, we reduce the model's convolution and the number of paths to improve inference speed, a process that does not compromise performance. From a macro perspective, the self-enlarged GCNet functions as the "teacher model", while the self-contracted GCNet serves as the "student model". + +As shown in Figure 3, GCNet is a two-branch archi + +Table 1. Details of the different versions of GCNet. H represents height, W represents width, and C represents channels. For GCNet-S, C is set to 32, while for GCNet-M and GCNet-L, C is set to 64. In rows $S_4$ , $S_5$ , and $S_6$ , the left side of each column indicates the dimensions of the semantic branch, while the right side indicates the dimensions of the detail branch. + +
StageOutput DimensionQuantity of Blocks
GCNet-S/MGCNet-L
InputH × W × 3
S1H/4 × W/4 × C
S2H/4 × W/4 × C45
S3H/8 × W/8 × 2C45
S4H/16 × W/16 × 4C, H/8 × W/8 × 2C5, 45, 5
S5H/32 × W/32 × 8C, H/8 × W/8 × 2C5, 45, 5
S6H/64 × W/64 × 16C, H/8 × W/8 × 4C2, 23, 3
+ +tecture model, with its backbone composed of stacked GCBlocks. After extracting shallow features (stage 3), the features flow into two branches: the semantic branch and the detail branch. The semantic branch is designed to learn deep semantic information, while the detail branch focuses on learning spatial detail information. After passing through stage 4 or stage 5, the features from the semantic branch are fused with those from the detail branch after channel compression and upsampling. Conversely, the features from the detail branch undergo channel expansion and downsampling before being integrated with the features from the semantic branch. This process enhances the richness of the features from both branches. We do not utilize various attention modules [16, 18, 29, 32] for feature fusion, as this would complicate the model and decrease inference speed. Instead, we utilize $3 \times 3$ convolutions for channel compression and expansion, along with bilinear interpolation for upsampling. After stage 6, the features from the semantic branch are processed through a pyramid pooling module [21] to generate richer feature representations, which are then upsampled and fused with the features from the detail branch before being passed to the segmentation head for prediction. The segmentation head of GCNet consists of a $3 \times 3$ convolution followed by a $1 \times 1$ convolution. The $3 \times 3$ convolution is used to integrate the features from both branches while adjusting the channel dimension to $O_{c}$ and the $1 \times 1$ convolution is used to align the number of classes. For instance, if the number of classes is 19, the $1 \times 1$ convolution will adjust $O_{c}$ to 19. Additionally, we implement an auxiliary segmentation head during training to further enhance GCNet's performance. + +As illustrated in Figure 3, the backbone of GCNet consists of six stages. Stage 1 serves as the Stem, comprising two $3 \times 3$ convolutions with a stride of 2, which is intended for rapid downsampling of the image. The sub + +sequent stages are made up of stacked GCBlocks. Notably, the orange box in the figure indicates that the first block within the GCBlocks has a stride of 2, while the remaining blocks have a stride of 1; the green box denotes that all GCBlocks maintain a stride of 1. To accommodate various application scenarios, we adjusted both the quantity of stacked GCBlocks and the convolution width of the GCBlocks at each stage, resulting in three distinct versions of GCNet: GCNet-S, GCNet-M, and GCNet-L, as detailed in Table 1. The OC of the segmentation heads for GCNet-S, GCNet-M, and GCNet-L are 64, 128, and 256, respectively. + +# 3.2. Golden Cudgel Block + +Structure. To address speed degradation from the complex structures of multi-path and transformer-like convolution blocks, we propose the Golden Cudgel Block (GCBlock). During training, GCBlock expands into a multi-convolution, multi-path structure to leverage the benefits of these blocks. During inference, it simplifies to a single convolution through reparameterization, enhancing efficiency. Specifically, based on the bottleneck structure [17], we achieve vertical reparameterization of convolutions into a single $3 \times 3$ convolution by removing activation functions between convolutional layers, keeping only one at the output. During our investigation, we found that after training, the reduction in model parameter values hindered the lossless fusion between the first $1 \times 1$ convolution and the $3 \times 3$ convolution within the bottleneck. Thus, we eliminated the first $1 \times 1$ convolution, retaining one $3 \times 3$ convolution and one $1 \times 1$ convolution. Additionally, we introduced $\mathrm{Path}_{1 \times 1 \times 1}$ (consisting of two $1 \times 1$ convolutions) and more $\mathrm{Path}_{3 \times 3 \times 1}$ (comprising one $3 \times 3$ and one $1 \times 1$ convolution) to enhance learning capability. Although GCBlock contains multiple convolutions and paths, these components integrate into a single $3 \times 3$ convolution during inference, ensuring both performance and speed. The structure of GCBlock are illustrated in Figure 3, where N indicating the number of $\mathrm{Path}_{3 \times 3 \times 1}$ . We will detail the process of vertically reparameterizing each path into a single $3 \times 3$ convolution and then summing them horizontally. Conv-Bn to Conv. To enhance the stability of training, Batch Normalization (BN) is typically applied after convolution to perform channel normalization and linear scaling. Before reparameterizing between convolutions, it is necessary to merge the convolution and BN. Let $\mu$ , $\sigma$ , $\gamma$ , and $\beta \in \mathbb{R}^{C_{out}}$ , represent the mean, variance, scaling factor, and bias in BN, respectively, and let $W \in \mathbb{R}^{C_{out} \times C_{in} \times k \times k}$ and $B \in \mathbb{R}^{C_{out}}$ denote the weight and bias of a $k \times k$ convolution. $C_{in}$ represents the number of input channels, $C_{out}$ and represents the number of output channels. The merging of the convolution and BN can be computed as follows: + +$$ +W ^ {\prime} = \frac {\gamma}{\sqrt {\sigma + \varepsilon}} W, B ^ {\prime} = \frac {(B - \mu) \gamma}{\sqrt {\sigma + \varepsilon}} + \beta , \tag {1} +$$ + +where $\varepsilon$ is a constant term used in BN to prevent division by zero, and it is typically set to 1e-5. + +$\mathbf{Path}_{3 \times 3.1 \times 1}$ to $\mathbf{Conv}_{3 \times 3}$ . For a concatenation consisting of a $3 \times 3$ convolution followed by a $1 \times 1$ convolution, if there are no batch normalization layers or activation functions in between, they can be merged into a single $3 \times 3$ convolution. Let the weight and bias of the $3 \times 3$ convolution be denoted as $W_{3 \times 3} \in \mathbb{R}^{C_{out1} \times (C_{in} \times 3 \times 3)}$ and $B_{3 \times 3} \in \mathbb{R}^{C_{out1}}$ , respectively, and the weight and bias of the $1 \times 1$ convolution be denoted as $W_{1 \times 1} \in \mathbb{R}^{C_{out2} \times (C_{out1} \times 1 \times 1)}$ and $B_{1 \times 1} \in \mathbb{R}^{C_{out2}}$ . Given an input $x$ , the output $y$ can be computed as follows: + +$$ +\begin{array}{l} y = W _ {1 \times 1} * \left(W _ {3 \times 3} * x + B _ {3 \times 3}\right) + B _ {1 \times 1} \tag {2} \\ = W _ {1 \times 1} \cdot I _ {2} \left(W _ {3 \times 3} \cdot I _ {1} (x) + B _ {3 \times 3}\right) + B _ {1 \times 1} \\ = W _ {1 \times 1} \cdot I _ {2} \left(W _ {3 \times 3} \cdot I _ {1} (x)\right) + W _ {1 \times 1} \cdot I _ {2} \left(B _ {3 \times 3}\right) + B _ {1 \times 1} \\ = W _ {1 \times 1} \cdot I _ {2} \left(W _ {3 \times 3} \cdot I _ {1} (x)\right) + W _ {1 \times 1} \cdot B _ {3 \times 3} + B _ {1 \times 1}, \\ \end{array} +$$ + +where $*$ denotes the convolution operation, while $\cdot$ represents matrix multiplication. To perform matrix operations, $I(\cdot)$ denotes the im2col operator, which is utilized to transform the input $x$ into a two-dimensional matrix based on the shape of the convolution weight. For instance, $I(\cdot)$ will convert the input $x$ with dimensions $C_{in} \times H \times W$ into a matrix of shape $(C_{in} \times 3 \times 3) \times (H' \times W')$ , according to the dimensions of $W_{3 \times 3}$ . Since $B_{3 \times 3}$ is a constant sequence, $W_{1 \times 1} \cdot I_2(B_{3 \times 3})$ is equivalent to $W_{1 \times 1} \cdot B_{3 \times 3}$ . Furthermore, since the shape of $W_{1 \times 1}$ is $C_{out2} \times (C_{out1} \times 1 \times 1)$ and the shape of $W_{3 \times 3} \cdot I_1(x)$ is $C_{out1} \times (H' \times W')$ , we can conclude that: + +$$ +\begin{array}{l} W _ {1 \times 1} \cdot I _ {2} \left(W _ {3 \times 3} \cdot I _ {1} (x)\right) \\ = W _ {1 \times 1} \cdot W _ {3 \times 3} \cdot I _ {1} (x). \tag {5} \\ \end{array} +$$ + +Subsequently, by substituting Equation 3 into Equation 2, the following result is obtained: + +$$ +\begin{array}{l} y = W _ {1 \times 1} \cdot I _ {2} \left(W _ {3 \times 3} \cdot I _ {1} (x)\right) + W _ {1 \times 1} \cdot B _ {3 \times 3} + B _ {1 \times 1} \\ = W _ {1 \times 1} \cdot W _ {3 \times 3} \cdot I _ {1} (x) + W _ {1 \times 1} \cdot B _ {3 \times 3} + B _ {1 \times 1} \\ = \left(W _ {1 \times 1} \cdot W _ {3 \times 3}\right) \cdot I _ {1} (x) + \left(W _ {1 \times 1} \cdot B _ {3 \times 3} + B _ {1 \times 1}\right) \\ = W _ {3 \times 3} ^ {\prime} \cdot I _ {1} (x) + B _ {3 \times 3} ^ {\prime}, \tag {4} \\ \end{array} +$$ + +where $W_{3 \times 3}^{\prime}$ represents the new weight, while $B_{3 \times 3}^{\prime}$ represents the new bias. It is evident that a concatenation consisting of a $3 \times 3$ convolution followed by a $1 \times 1$ convolution can be merged into a new $3 \times 3$ convolution without any loss in performance. + +$\mathbf{Path}_{1 \times 1.1 \times 1}$ to $\mathbf{Conv}_{3 \times 3}$ . A concatenation of two $1 \times 1$ convolutions can also be merged into a $3 \times 3$ convolution according to Equation 4. The reason is that the first $1 \times 1$ convolution can be viewed as a $3 \times 3$ convolution with a non-zero weight value at the center and zero weight values in the surrounding positions. Notably, to satisfy the conditions in Equation 4, the stride of the first $1 \times 1$ convolution is set to 2 during downsampling, rather than being + +applied to the subsequent $1 \times 1$ convolution. Theoretically, the $\mathrm{Path}_{\mathbf{1} \times \mathbf{1} - \mathbf{1} \times \mathbf{1}}$ can accommodate an arbitrary number of $1 \times 1$ convolutions; however, experiments have shown that stacking two $1 \times 1$ convolutions yields the best model performance. + +$\mathbf{Path}_{\mathrm{residual}}$ to $\mathbf{Conv}_{3\times 3}$ . For residual connection, we first construct a $1\times 1$ convolution with weight $W_{\mathrm{residual}}\in \mathbb{R}^{C_{out}\times (C_{in}\times 1\times 1)}$ ( $C_{out} = C_{in}$ ) and bias $B_{\mathrm{residual}}\in \mathbb{R}^{C_{out}}$ (set to 0) to equivalently replace it. Next, this $1\times 1$ convolution is transformed into a $3\times 3$ convolution. Specifically, we traverse $W_{\mathrm{residual}}$ using $C_{out}$ and $C_{in}$ . When $c_{out}$ equals $c_{in}$ during the traversal, the weight value at that position is set to 1; otherwise, it is set to 0. After completing the traversal, the resulting $1\times 1$ convolution is equivalent to the residual connection. Since a $1\times 1$ convolution is a special case of a $3\times 3$ convolution, it is straightforward to convert the $1\times 1$ convolution into a $3\times 3$ convolution. In $\mathbf{Path}_{\mathrm{residual}}$ , we use a BN layer, so it is also necessary to integrate the converted convolution with the BN. Notably, when the stride of the GCBlock is set to 2, the residual connection is not used. + +Multipath to Single Convolution. After reparameterizing each path into $3 \times 3$ convolutions, parallel sets of $n$ weights $W \in \mathbb{R}^{C_{out} \times (C_{in} \times 3 \times 3)}$ and $n$ biases $B \in \mathbb{R}^{C_{out}}$ are obtained. Let $W_{i}$ represent the $i$ -th weight and $B_{i}$ the $i$ -th bias, where $i$ is less than or equal to $n$ . Given an input $x$ , the output $y$ from multiple paths is calculated as: + +$$ +\begin{array}{l} y = \sum_ {i = 1} ^ {n} \left(W _ {i} * x + B _ {i}\right) \\ = \sum_ {i = 1} ^ {n} \left(W _ {i} \cdot I _ {i} (x) + B _ {i}\right) \tag {5} \\ = \left(\sum_ {i = 1} ^ {n} W _ {i}\right) \cdot I (x) + \sum_ {i = 1} ^ {n} B _ {i} \\ = W ^ {\prime} * x + B ^ {\prime} \\ \end{array} +$$ + +where $I_{i}$ is the $i$ -th im2col operator. Since the shape of $W_{i}$ is consistent, all $I_{i}$ are the same. This allows for direct summation of these $3 \times 3$ convolutions, enabling the acquisition of a new $3 \times 3$ convolution without performance loss. + +# 3.3. Deep Supervision and Loss Function + +Previous research [21, 32, 35] has demonstrated that adding an auxiliary segmentation head to appropriate positions in the model during training can improve the model's performance without increasing inference time. Building on prior work, we introduced an auxiliary segmentation head in GCNet, which is removed during inference. As illustrated in Figure 3, after the bilateral fusion in the stage 4, the features from the detail branch are passed to the auxiliary segmentation head for loss calculation. Notably, the structure of the auxiliary segmentation head is identical to that of the + +Table 2. Ablation study on $\text{Path}_{1 \times 1.1 \times 1}$ for GCNet-S. "Number" indicates the number of convolutions used in the path, "Memory" refers to the GPU memory utilized during training, and "Time" represents the training duration in hours. + +
NumberMemoryTimemIoU
020.58 GiB4.0 h76.1
121.87 GiB4.5 h76.6
224.61 GiB5.0 h76.7
327.31 GiB5.4 h76.4
+ +primary segmentation head. Based on the losses from both the segmentation head and the auxiliary segmentation head, the total loss can be expressed as: + +$$ +L = L _ {s h} + \alpha L _ {a s h}, \tag {6} +$$ + +where $L_{sh}$ represents the loss from the segmentation head, $L_{ash}$ denotes the loss from the auxiliary segmentation head, and $\alpha$ is the weight coefficient, which is set to 0.4 in GCNet. To effectively handle imbalanced data and difficult samples, we employed OHEM Cross Entropy [27] as the loss function, consistent with previous work [32]. + +# 4. Experients + +# 4.1. Datasets and Implementation Details + +To demonstrate the effectiveness of GCNet, we conducted experiments on three public datasets: Cityscapes [9], CamVid [1], and Pascal VOC 2012 [14]. During training on Cityscapes, we did not utilize ImageNet [10] pretrained weight and instead trained from scratch using four A100 GPUs. For training on CamVid and Pascal VOC 2012, we fine-tuned the model using weight from Cityscapes. During inference, we used a single A100 GPU. More details regarding the datasets, training settings, inference settings, and evaluation metrics can be found in Appendix A. + +# 4.2. Ablation Studies + +Number of Convolutions in $\mathsf{Path}_{1\times 1.1\times 1}$ . To validate the effectiveness of $\mathsf{Path}_{1\times 1.1\times 1}$ , we conducted an ablation study by varying the number of $1\times 1$ convolutions in this path. Specifically, we established a baseline consisting of a $\mathsf{Path}_{3\times 3.1\times 1}$ and a $\mathsf{Path}_{\mathrm{residual}}$ , and then incrementally increased the number of $1\times 1$ convolutions in $\mathsf{Path}_{1\times 1.1\times 1}$ from 0 to 4. As shown in Table 2, both the memory usage and training time increased with the number of convolutions, calculated based on four A100 GPUs. At 0 convolutions (baseline), the model only achieved $76.1\%$ mIoU. However, as the number of convolutions increased, the mIoU improved, reaching peak performance with two convolutions. Consequently, we set the number of $1\times 1$ convolutions in this path to 2. + +![](images/c6abd77c9bf901c0a9aab231695d98650e02021800c1a104a4764155a964decd.jpg) + +![](images/4e4c73d8b783551124695a84fc1bf3d50d835d38f38a4858d7d55ca601a83667.jpg) + +![](images/04eca7fcc1a00d032724340afab5075b63d05fd5e005d864b02e36a6f8ab2151.jpg) +Figure 4. Ablation study on $\mathrm{Path}_{3\times 3.1\times 1}$ for GCNet-S. "N" indicates the number of $\mathrm{Path}_{3\times 3.1\times 1}$ , while "Iter-20000" signifies that 20000 iterations were completed, and so on. + +More Path $_{3 \times 3_{-1} \times 1}$ . To validate the effectiveness of Path $_{3 \times 3_{-1} \times 1}$ , we conducted an ablation study by varying the number of this path. The baseline comprised a Path $_{3 \times 3_{-1} \times 1}$ , a Path $_{1 \times 1_{-1} \times 1}$ , and a Path $_{\text{residual}}$ . Although theoretically the number of Path $_{3 \times 3_{-1} \times 1}$ can be increased indefinitely, extensive research indicates that overly wide or deep models do not necessarily lead to improved performance; our experiments corroborate this finding. As shown in Figure 4, the model's mIoU begins to increase with the addition of Path $_{3 \times 3_{-1} \times 1}$ , peaking at $N = 4$ or $N = 5$ . However, at $N = 10$ , the model's performance deteriorates, with training time increasing by over $80\%$ compared to $N = 4$ . Additionally, we observed that with fewer iterations, increasing the number of Path $_{3 \times 3_{-1} \times 1}$ can significantly enhance performance (a $4.5\%$ increase at 20000 iterations). Considering the training cost and model performance, we set differ + +![](images/e20f3ff92e4e653e31d1212e4d4fdc5039d5b1b57217f047d1e267b8b89eee61.jpg) + +![](images/119f150104d1d14de50f6c91b9bdc8269b851c42642746efcaa9f1ae061a7b99.jpg) + +![](images/a5a95fde60cfa4f8750d5de481308e0d2d5454e829e60214c7b21b0ab66a85e7.jpg) + +![](images/99fb35a8d37689fdff3149a2a8583e564adcfa68a0fd082a904f8ee60f89b5e9.jpg) +Ground Truth +PIDNet-S +SCTNet-S +GCNet-S +Figure 5. Visualization of different segmentation models on the Cityscapes validation set. + +Table 3. Comparison on the Cityscapes validation set. " * " indicates that the model was implemented and retested by us (with convolution and batch normalization fused). "ImageNet" indicates whether the model utilizes ImageNet pretrained weight. + +
MethodResolutionGPUFPSParamsGFLOPsImageNetmIoU (%)
ICNet* [38]1024 × 2048A100181.324.9 M74.3X71.6
Fast-SCNN* [23]1024 × 2048A100325.91.4 M7.3X71.0
SwiftNetRN-18 [20]1024 × 2048GTX 1080Ti39.911.8 M104.0✓75.4
CGNet* [30]1024 × 2048A10073.90.5 M27.5X68.3
BiSeNetV1* [34]1024 × 2048A100116.813.3 M118.0✓74.4
BiSeNetV2* [35]1024 × 2048A100132.43.4 M98.4X73.6
STDC1* [15]1024 × 2048A100183.78.3 M67.5X71.8
STDC2* [15]1024 × 2048A100132.812.3 M93.8X74.9
HyperSeg-M [19]512 × 1024RTX 309059.110.1 M7.5✓76.2
HyperSeg-S [19]768 × 1536RTX 309045.710.2 M17.0✓78.2
PP-LiteSeg-T2 [22]768 × 1536RTX 309096.0--✓76.0
PP-LiteSeg-B2 [22]768 × 1536RTX 309068.2--✓78.2
DDRNet-23-Slim* [21]1024 × 2048A100166.45.7 M36.3X76.3
DDRNet-23* [21]1024 × 2048A100106.020.3 M143.0X78.0
PIDNet-S* [32]1024 × 2048A100128.77.7 M47.3X76.4
PIDNet-M* [32]1024 × 2048A10078.228.7 M177.0X78.2
PIDNet-L* [32]1024 × 2048A10064.237.3 M275.0X78.8
SCTNet-S-Seg50* [33]512 × 1024A100169.14.6 M7.1X71.0
SCTNet-S-Seg75* [33]768 × 1536A100168.74.6 M16.0X74.7
SCTNet-B-Seg50* [33]512 × 1024A100162.617.4 M28.1X75.0
SCTNet-B-Seg75* [33]768 × 1536A100157.317.4 M63.2X78.5
SCTNet-B-Seg100* [33]1024 × 2048A100117.017.4 M112.3X79.0
GCNet-S1024 × 2048A100193.39.2 M45.2X77.3
GCNet-M1024 × 2048A100105.034.2 M178.0X79.0
GCNet-L1024 × 2048A10088.045.2 M232.0X79.6
+ +ent values of N for the various versions of GCNet: $N = 4$ for GCNet-S, $N = 2$ for GCNet-M, and $N = 2$ for GCNet-L. + +# 4.3. Comparison with State-of-the-art Methods + +Cityscapes. The experimental results on the Cityscapes dataset are shown in Table 3. To ensure a fair comparison, we made every effort to reproduce each model on the same hardware and tested their inference speeds. The results indicate that our GCNet achieves a better balance between performance and speed. Specifically, GCNet-S achieves $77.3\%$ + +mIoU while reaching 193.3 FPS, significantly outperforming other models of similar scale. GCNet-M also performs admirably, surpassing both PIDNet-M and PIDNet-L in terms of both performance and speed, although it is slightly slower than SCTNet-B-Seg100. Furthermore, GCNet-L achieves the highest performance with $79.6\%$ mIoU. As shown in the table, despite GCNet having a higher number of parameters and GFLOPs compared to other models, these factors are not the decisive determinants of inference speed. In fact, inference speed is also influenced by the fre + +Table 4. Comparison on the CamVid test set and the Pascal VOC 2012 validation set. All models were implemented by us and retested on the A100. The inference resolution for CamVid was set at $720 \times 960$ , while for VOC it was set at $512 \times 2048$ . $\dagger$ indicates that ImageNet pretrained weight were used. + +
MethodCamVidVOC
FPSmIoU (%)FPSmIoU (%)
CGNet [30]102.669.4104.742.2
BiSeNetV1†[34]276.073.3214.356.0
BiSeNetV2 [35]240.675.8228.650.0
STDC1 [15]240.870.2227.052.9
STDC2 [15]149.871.4137.256.3
DDRNet-23-Slim [21]189.376.2174.654.2
DDRNet-23 [21]171.178.2165.455.8
PIDNet-S [32]142.877.2137.454.0
PIDNet-M [32]128.978.6123.157.5
PIDNet-L [32]108.478.7104.058.2
GCNet-S210.676.6196.954.9
GCNet-M190.078.5173.458.2
GCNet-L170.479.1145.158.8
+ +quency of memory accesses within the model. The single-path block design of GCNet reduces the number of memory accesses, thereby enhancing inference speed. We also visualized the segmentation results of PIDNet-S, SCTNet-S-Seg75, and GCNet-S, as illustrated in Figure 5. The figure indicates that GCNet exhibits higher accuracy in pixel classification. + +CamVid. The experimental results on the CamVid dataset are shown in Table 4. To ensure a fair comparison, we retrained the models listed in the table using the MMSegmentation framework and evaluated their inference speeds. The experimental results indicate that our GCNet-S achieves $76.6\%$ mIoU while also reaching 210.6 FPS. Although PIDNet-S has an mIoU that is $0.6\%$ higher than that of GCNet-S, its FPS is lower by 67.8. Notably, GCNet-L performs exceptionally well at a resolution of $720 \times 960$ . Compared to GCNet-S, while its FPS only decreases by 40.2, it achieves $79.1\%$ mIoU, surpassing all models in the PIDNet series in both performance and speed. + +Pascal VOC 2012. The experimental results on the Pascal VOC 2012 dataset are shown in Table 4. To ensure a fair comparison, we retrained the models listed in the table using the MMSegmentation framework and evaluated their inference speeds. The experimental results indicate that our GCNet-S achieves $54.9\%$ mIoU while also reaching 196.9 FPS. Similar to the results on the CamVid dataset, GCNet-L demonstrates remarkable performance and speed at a relatively low resolution $(512 \times 2048)$ , even outper + +![](images/d8a20665f0c11749f72cf079ca42b21cc7c6cb91119643ba8b44c9b19e4135d1.jpg) + +![](images/fdfd29f612913e4b1a91f0098ea07912993cffb32f44bb0d6f680e7edb60d061.jpg) + +![](images/78543688bc879ce86486c9046acb7dc3c643c243a8816509169ac243ff0777dc.jpg) +Figure 6. The comparison of GFLOPs, number of parameters, and FPS for GCNet during training versus inference. + +![](images/236f2dac93b0c4636bcb40636ec256f79090da65ab84ac8fd1aeedbabb83de26.jpg) + +forming PIDNet-S. Interestingly, we found that BiSeNetV1 performs better on the VOC dataset, exceeding BiSeNetV2 by $6\%$ in mIoU, with an FPS that is only 14.3 lower. While BiSeNetV1 excels on VOC, the overall performance across the three datasets shows that GCNet outperforms BiSeNetV1. + +# 4.4. Comparison of Training and Inference + +To visually compare the different configurations of GCNet, we calculated the GFLOPs, number of parameters, and FPS during training versus those during inference, as shown in Figure 6. The figure illustrates that GCNet requires significantly more computational resources during training and operates at a slower speed. However, after self-contracting, both GFLOPs and number of parameters are greatly reduced, while FPS experiences a substantial increase. Notably, the performance of both configurations remains equivalent. + +# 5. Conclusion + +In this study, we proposed GCNet for real-time semantic segmentation. GCNet achieves stronger performance and faster speed simultaneously through self-enlargement and self-contraction, as confirmed by experiments on three public datasets. Although GCNet operates at high speed, its parameter count and computational complexity are higher than those of other models, which limits its applicability on devices with constrained storage capacity. In the future, we plan to explore more powerful and parameter-efficient reparameterizable structures. + +Acknowledgment. This work is supported by Natural Science Foundation China (NSFC) No. 62372301 and No. U22A2097. + +# References + +[1] Gabriel J Brostow, Julien Fauqueur, and Roberto Cipolla. Semantic object classes in video: A high-definition ground truth database. 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This, however, comes at the expense of a computational complexity that is several orders of magnitude higher than today's commercial CODECs, and thus prohibitive for most practical applications. With this paper, we demonstrate that by focusing on modeling visual perception rather than the data distribution, we can achieve a very good trade-off between visual quality and bit rate similar to "generative" compression models such as HiFiC, while requiring less than $1\%$ of the multiply-accumulate operations (MACs) for decompression. We do this by optimizing C3, an overfitted image codec, for Wasserstein Distortion (WD), and evaluating the image reconstructions with a human rater study, showing that WD clearly outperforms LPIPS as an optimization objective. The study also reveals that WD outperforms other perceptual metrics such as LPIPS, DISTS, and MS-SSIM as a predictor of human ratings, remarkably achieving over $94\%$ Pearson correlation with Elo scores. + +# 1. Introduction + +Methods of lossy data compression are characterized by a long tradition of exploiting both: + +- correlations in the statistics of the compressed data, for example by linearly or nonlinearly predicting the next sample in audio codes, or by applying decorrelating transformations such as the DCT [2]; and +- information bottlenecks of human perception, for example by representing chrominance in images with lower resolution than luminance, or by modeling frequency masking in the auditory system. + +Owing to the conceptual connection between decoding of an image and sampling one from a conditional distribution, research on learned image compression has recently been + +greatly influenced by generative methods such as GANs [15] or diffusion models [9], which excel at probabilistic modeling of real-world data, as evidenced by the impressive quality of samples drawn from such models. The generated samples are visually so convincing that measures of sample quality (i.e., realism, formalized by divergences between the distribution of the source data and the distribution of generated data) have even been called "perception" [6]. + +Unfortunately, a model which is extremely good at sampling real-world data has to have a certain computational complexity, because the world (and hence the space of possible images) is very complex. This is evidenced by the complexity of generative models such as Imagen, Stable Diffusion, or DALL-E. When it comes to image compression, this would make it seem that we ultimately need highly complex methods to achieve high image quality. In other words: out of the three qualities, good (image quality), fast (decoding speed), and cheap (low bit rate), we must pick two, as in the old proverb. Luckily, while good probabilistic models can lead to remarkable perceived quality, the inverse does not hold: good image quality does not require precisely modeling the distribution of natural images, as we demonstrate in this paper. + +Here, we focus on modeling human perception (specifically, texture perception in the periphery of the human visual system [3, 13]) instead of the data distribution. We take an existing low-complexity neural codec, C3 [22], and replace its distortion loss by either of two variants of Wasserstein Distortion (WD) [34]: one which assumes the observer to gaze at each image location with equal probability, and one which uses EML-net [20], a saliency model, to predict image locations that are more likely to be scrutinized. To aid texture reproduction, we supply the codec with common randomness (CR), i.e., randomness available to both the encoder and the decoder, implemented using a pseudo-random number generator with identical seeds. + +These changes lead to significantly better image quality at the same bit rate compared to baseline C3 [22], illustrated in Fig. 1, but retain its low decoding complexity. The encoding complexity increases with the complexity of the loss func + +![](images/2787e7ca6dfc2d84808ef2e3882a38a1aa780cb8d1f037cb020bd854849eca6b.jpg) + +![](images/f320f779a87beb58205a7eb7fc930471d49bebf2b150c38a55ea6cd287d0317a.jpg) + +![](images/259192dfd8641fdaded7d8779e48a0b58eba579797a8b253eeab1567917c799a.jpg) +Figure 1. Crop of image 28 from the CLIC2020 professional dataset (best viewed on screen). Top left: Original image. Top right: C3 optimized for MSE, compressed to 0.172 bits/pixel. Bottom left: C3 optimized for WD with $\sigma = 8$ , compressed to 0.167 bits/pixel. Bottom right: C3 optimized for WD with $\sigma = 8$ , without common randomness, compressed to 0.180 bits/pixel. While optimization for MSE leads to flattened texture, as seen in the reproduction of the grass and the walls of the building, texture is vastly improved in the WD-optimized versions. Not providing common randomness to the decoder (bottom right) means the codec must reproduce all textures using deterministic structure such as straight lines (as in, e.g., the texture of the roof – note the lines not being consistent with the original, while providing a better approximation of the texture than the MSE version). This is not adequate for random textures such as the grass in front of the building, where providing common randomness significantly helps to maintain the visual quality of texture. + +![](images/6550c98a18cff86336554264b162f762df3313403e4c8da563a8eea78699a9b3.jpg) + +![](images/c8daf577be1fc5013e5713c545593e2584128ef8c81cdc87f136d8ffec042fd3.jpg) +Figure 2. Decoding an image with COOL-CHIC [25] and C3 [22]. A. A latent element $\widehat{\mathbf{z}}_{ij}^n$ (□) is autoregressively decoded by applying the entropy network $g_{\psi}$ to the spatial context $\mathrm{c}(\mathbf{z}^n;(i,j))$ (□), yielding parameters $\mu, \sigma$ of the Laplacian probability model used for entropy decoding the latent element. B. The decoded latent spatial arrays at multiple resolutions are first bilinearly upsampled to the target resolution and then transformed into pixel space using the synthesis network $f_{\theta}$ . We supply common randomness at multiple resolutions by drawing i.i.d. elements from a pseudo-random number generator with fixed seed [3], which is novel to the present work. The common randomness arrays are upsampled and concatenated with the upsampled latents. Figure adapted with permission from Kim et al. [22]. + +![](images/f809cfc0b928b9cef495fd6c23289540610f0059d7acd8e0d5f8a60b95326669.jpg) + +tion, which we mitigate by introducing a novel, approximate implementation of WD. We perform a human rating study comparing our method to several baselines, including generative and commercial CODECs. It reveals that our method achieves a trade-off between image quality and bit rate similar to generative methods, but with much lower decoding complexity. In addition, we find that WD predicts the human ratings remarkably well. + +# 2. C3 codec + +Our experiments are based on the COOL-CHIC family of methods [5, 25, 28, 29] and more specifically on C3 [22], a neural codec which rivals modern classical CODECs like VVC [1] in terms of rate-distortion performance, while maintaining a very low computational cost. These CODECs are built from three main components: a set of latent arrays, a synthesis network and an entropy network, each of which are optimized per image (see Fig. 2). + +The latents consist of a set of multi-resolution arrays, starting with the resolution of the image, followed by progressively smaller resolutions (by a factor of two in each dimension). To synthesize an image, these latents are bilinearly upsampled and concatenated to create a single multichannel array at the resolution of the image. This array is passed through a synthesis network $f_{\theta}$ , a small convolutional neural network, to output RGB values at every pixel location. The entropy network $g_{\psi}$ is used to model the conditional distribution of each latent element given its spatial context. The bit sequence is made up of the bits encoding the quantized and entropy coded latents (with probabilities estimated + +by $g_{\psi}$ ) as well as the bits required to store the quantized parameters of both $f_{\theta}$ and $g_{\psi}$ . + +The latent arrays and the parameters of the synthesis and entropy networks are jointly optimized for a rate-distortion objective, with distortion given by the MSE between the original and reconstructed image pixels, and rate approximated by the cross entropy of the latent arrays under the entropy model. Since the latent arrays are quantized, this optimization is done in a quantization-aware manner. For further details on the architecture and optimization, we refer the reader to Ladune et al. [25] and Kim et al. [22]. + +In this paper, we use the identical architecture and optimization procedure as C3 [22], except for two changes: 1. We supply common randomness arrays to the decoder in the form of pseudo-random i.i.d. standard Gaussian noise, which remains fixed during optimization and decoding. Since the seed is fixed, no additional information needs to be encoded. 2. We replace MSE by the Wasserstein Distortion between the original and its reconstruction. + +# 3. Wasserstein Distortion + +Wasserstein Distortion (WD) [34] is a distance metric between pairs of images which, similar to the popular LPIPS [42] and DISTS [10] metrics, can utilize feature embeddings. The feature space is interpreted as a perceptual space, in which distances are more predictive of subjective human notions of distance between images than distances between pixel intensities. While WD itself is agnostic to the feature space, we chose to rely on the well-known VGG embeddings [37], derived from training a convolutional neural + +![](images/eb1e335e91fce26fd11dfe012f7f2161579674a23cc5cef29bc551d2e2a317f2.jpg) +A. Extract VGG features + +![](images/95a67342d9f2cceb7ddfa99ab36e2bbb521d34c686ceff80dd0d2b15ede6569d.jpg) +B. Compute featurewise local statistics + +![](images/996cdf5ba611a20bec6bd6c35923f336bf7806aa82c4d36071d33e4977217f1c.jpg) +C. Compute & aggregate featurewise WD +Figure 3. Computation of Wasserstein Distortion (WD) between two images, $\mathcal{A}$ and $\mathcal{A}$ . A. We extract spatial feature maps $f_{i}$ from selected layers of a VGG network. B. For each feature $i$ , we estimate local first and second raw moments at multiple scales $\alpha$ by successively applying a linear downsampling operation $\mathcal{D}$ : $\mu_{i\alpha} = \mathcal{D}^{\alpha}f_{i}$ and $\rho_{i\alpha} = \mathcal{D}^{\alpha}f_{i}^{2}$ ; the local standard deviations are derived by taking $\nu_{i\alpha} = \sqrt{\rho_{i\alpha} - \mu_{i\alpha}^{2}}$ elementwise. Note that $\mu_{i0} = f_{i}$ and $\nu_{i0} = 0$ . C. The local WD values for feature $i$ and scale $\alpha$ are computed elementwise as $d_{i\alpha}^{\mathcal{A}} = \sqrt{(\mu_{i\alpha}^{\mathcal{A}} - \mu_{i\alpha}^{\mathcal{A}})^{2} + (v_{i\alpha}^{\mathcal{A}} - v_{i\alpha}^{\mathcal{A}})^{2}}$ . They are then spatially averaged, with weights $w_{i\alpha}$ derived from the $\sigma$ -map, yielding the scalar WD for feature $i$ , $d_{i}^{\mathcal{A}}$ . The total WD for the image pair is obtained by adding the contributions from all features. + +network on the ImageNet task, and also used by LPIPS. + +In contrast to LPIPS and DISTS, WD generalizes the notion of pointwise distances in a feature space by taking into account foveation and peripheral vision. WD is parameterized by a spatial $\sigma$ -map of the same resolution as the images. Assume feature maps $f_{i}$ also have that resolution. Then the local WD for feature $i$ at a location $(x,y)$ is the 2-Wasserstein divergence between the local empirical distributions of $f_{i}$ for both images, aggregated using a pooling kernel of size $\sigma(x,y)$ and centered at $f_{i}(x,y)$ . For feature maps that have different resolutions than the images, the pooling kernel sizes need to be adjusted accordingly. The WD values are then spatially averaged and summed over all features $i$ . As $\sigma$ goes to zero, WD converges to computing pointwise distances, as in LPIPS. This models human vision in the fovea (the center of gaze), which is most accurate in distinguishing deviations between the images. Larger $\sigma$ values model peripheral vision, where humans are capable of distinguishing deviations in texture characteristics, but fail at picking up on subtler deviations. (For a complete description of WD, refer to Qiu et al. [34].) + +The larger $\sigma$ , the more permissive is WD to texture resampling, i.e. replacing a visual texture with one that has similar statistics. For image compression, we exploit this by choosing smaller $\sigma$ in salient image regions that are likely to be directly looked at, and larger $\sigma$ in other regions. Making the distance metric more permissive in such regions allows the codec to allocate fewer bits in representing the local image content, while maintaining visual quality. + +Even after approximating empirical distributions as independent Gaussians, computing WD can be computationally costly, since it generally requires aggregation of local statistics with a different pooling kernel at each spatial location. + +We propose an approximate, but more efficient way of computing WD by discretizing $\sigma$ to powers of two (Fig. 3). For every feature map $f_{i}$ extracted from VGG (panel A), we estimate spatial maps of the local first and second raw moments by building a multi-scale cascade akin to a Gaussian pyramid [7] using a $3\times 3$ convolutional downsampling filter $\mathcal{D}$ (panel B). This yields a full spatial map of the local mean $\mu_{i\alpha}$ and standard deviation $\nu_{i\alpha}$ of the ith feature, for pooling regions of size $2^{\alpha} / r_{i}$ , where $\alpha$ is the scale index, and $r_i$ is the relative resolution of the ith feature map with respect to the images (e.g., 0.5 if $f_{i}$ is downsampled by a factor of 2). + +Local WD maps $d_{i\alpha}$ between the two images are computed elementwise from two sets of $\mu_{i\alpha}$ and $\nu_{i\alpha}$ computed on each image. This gives us dense maps of precomputed local WD distances, but only for specific pooling region sizes corresponding to $\sigma$ -values of $2^{\alpha} / r_i$ . We can approximate the WD for a desired $\sigma$ -value by interpolating WD values from these precomputed maps (panel C). First, the $\sigma$ -map is adapted for each feature $i$ and scale $\alpha$ by computing + +$$ +\sigma_ {i \alpha} = \max \left(\mathcal {D} _ {i \alpha} \left(r _ {i} \sigma\right), 1\right). \tag {1} +$$ + +This resizes all pooling regions by a factor $r_i$ , proportional to the resolution of $f_i$ , and also resamples the map with a resampling operation $D_{i\alpha}$ to match the resolution of $d_{i\alpha}$ . We then determine weight maps + +$$ +w _ {i \alpha} = \max \left(1 - \left| \log_ {2} \sigma_ {i \alpha} - \alpha \right|, 0\right) \tag {2} +$$ + +which are 1 wherever $\sigma$ is equal to $2^{\alpha} / r_{i}$ , and linearly fade to 0 as $\sigma$ approaches either $2^{\alpha + 1} / r_{i}$ or $2^{\alpha - 1} / r_{i}$ . Each $d_{i\alpha}$ is multiplied with $w_{i\alpha}$ , averaged across space, and summed across $\alpha$ , to yield one WD value $d_{i}$ for each feature $i$ . Although the precomputed maps for each scale $\alpha$ have differing + +![](images/c27d0263d2bf728d2bbcbf3c57ddc4eb289d7347aeed9741b2d3560d476534fb.jpg) +Figure 4. Human rating study results and decoder complexity. Left: Evaluation of image compression methods in terms of visual fidelity vs. bit rate. Error bars indicate 99th percentile. Squares indicate C3 using CR, circles indicate C3 without CR, and diamonds mark other compression methods. Right: Computational complexity of the decoder of the same methods for the middle bit rate. HiFiC slightly outperforms C3 in terms of visual quality vs. bit rate. However, it requires more than two orders of magnitude more computations at the decoder. Note that neural methods tend to have similar complexity across different bit rates and objectives. This is also true for C3; only the addition of CR increases the complexity slightly. The complexity of VVC can vary across bit rates, and can't strictly be shown in the same plot, since it doesn't use floating point operations; we plot an estimated equivalent on typical hardware [32]. + +resolutions, the weights for each spatial location in $f_{i}$ add up to one, effectively interpolating local WD maps from precomputed WD maps $d_{i\alpha}$ . Finally, WD values $d_{i}$ are aggregated across different features $i$ by summation. + +To determine an appropriate $\sigma$ -map, we examined two alternatives: First, we may simply chose $\sigma$ constant across the image, which could be interpreted as a belief that every image location is equally likely to be scrutinized by a human observer. In this case the value needs to be chosen conservatively, small enough that a desired level of exact detail in the reconstruction is preserved at all locations. Second, we may derive $\sigma$ from an actual gaze map obtained with an eye tracking device – or a prediction thereof. In our experiments, we obtained predictions from EML-net [20] in the form of a saliency map $s$ valued between 0 and 1 (Fig. 7). We converted $s$ to a spatial density $p$ using the ad-hoc elementwise formula: + +$$ +p = p _ {\min } + \left(1 - p _ {\min }\right) \cdot s / \bar {s}, \tag {3} +$$ + +with $p_{\mathrm{min}} = 0.5$ lower bounding the likelihood, and $\overline{s}$ indicating the spatial mean of $s$ . The resulting density $p$ is always positive and averages to one spatially, regardless of the image resolution. We further converted $p$ to $\sigma$ by computing elementwise: + +$$ +\sigma = \sigma_ {\max } \cdot p _ {\min } / p, \tag {4} +$$ + +where $\sigma_{\mathrm{max}}$ is the maximal value of $\sigma$ . This parameter needs to be chosen based on image resolution and viewing distance. + +# 4. Experimental results + +To evaluate the proposed method, we compared a total of 10 image compression methods on the Challenge on Learned Image Compression (CLIC) 2020 professional validation dataset in a human rater study: + +C3, optimized for MSE (C3/MSE) [22]; +- C3, optimized for a weighted version of MSE using $p$ derived from saliency (C3/wMSE); +C3, optimized for MS-SSIM [40] (C3/MS-SSIM); +C3 with CR, optimized for LPIPS [42] (C3/LPIPS); +C3 with CR, optimized for WD using constant $\sigma = 8$ (C3/WD8); +- C3 with CR, optimized for WD using a $\sigma$ -map derived from saliency with $\sigma_{\mathrm{max}} = 16$ (C3/WDs); +- Versatile Video Coding (VVC) [1], a state-of-the-art commercial image and video codec, as implemented by VTM 23.4 using the intra YUV444 configuration; +- MLIC+ [21], a learned image codec which is state of the art in terms of MSE vs. bit rate; +- CDC [41], a learned image codec based on diffusion; and +- HiFiC [31], a learned image codec based on an adversarial loss. + +For each of the methods, we obtained compressed images and their reconstructions targeting three dataset-average bit rates: 0.075, 0.15, and 0.3 bits/pixel (the same bit rates that CLIC uses). For CDC and HiFiC, we were not able to + +exactly match these target rates, since it would have required re-training. Still, we included all three available target rates for HiFiC, as well as the two lower target rates for CDC in the study. This gave us a total of 29 method/rate combinations, and hence 29 distinct reconstructions for each of the 41 images in the dataset. + +Our evaluation protocol closely follows the CLIC approach. For each individual rating, three images are available to the rater: On one side of the screen, a random $512 \times 432$ pixel crop of the original. On the other, the corresponding crop of two reconstructed images, between which the rater can flip by pressing a key. The rater is asked to select the reconstruction that looks more similar to the original. For $10\%$ of the ratings, one of the reconstructions is replaced by the original, which is used to assess rater reliability (golden questions). While the original is selected at random, the pair of compared methods/rates is dynamically selected to maximize expected information gain considering past ratings. The resulting Elo score for each method/rate minimizes the cross-entropy between observed and predicted ratings. + +The main result of our study is shown in Fig. 4. Methods optimized for MSE (C3/MSE, MLIC+, VVC) and the diffusion model CDC all achieve similar trade-offs between bit rate and visual quality, while their complexity varies substantially (with VVC being least complex). HiFiC and C3 optimized for WD achieve much better and comparable trade-offs, but our method requires two orders of magnitude fewer MACs at decoding time. + +We provide further comparisons in Fig. 5, including variants of C3 optimized for other perceptual metrics, and ablations for using saliency and common randomness. The results show that optimizing for WD significantly outperforms other metrics in terms of human preference, especially if saliency and CR are used. Removing saliency results in a drop in visual quality at high bit rates, while removing common randomness mostly affects low bit rates. Fig. 6 reveals that both switching the objective from MSE to WD, and providing CR to a WD-optimized codec lead to a smaller fraction of the bit rate being allocated to the highest-resolution array (array 1), which encodes detail, allowing other arrays to encode more information. This is in line with the intuition that both steps enable texture resampling: switching the objective allows the encoder to find instantiations of texture that are visually equivalent, but take fewer bits to encode with the C3 architecture (for example, the roof in Fig. 1), and providing CR enables certain stochastic textures to be reproduced by a form of "noise shaping" (the grass in Fig. 1). + +Fig. 5 also reveals that basing WD or MSE on saliency predictions gives both a moderate boost in terms of Elo + +![](images/2074b4ea1b70b0345b3cacbf832f1fcc08342fb68581e08b2e9f119400e34aba.jpg) +Figure 5. Human rating study results for alternative perceptual objectives, including WD without saliency. Error bars indicate 99th percentile. As loss functions, both MS-SSIM and LPIPS lead to instabilities. To achieve reasonable results, we clipped the gradients of the exponentiation operations in MS-SSIM (C3/MS-SSIM), and used a loss equally weighting LPIPS and MSE (C3/LPIPS). We also assessed the effect of weighting MSE using saliency (C3/wMSE). + +![](images/8400d88914a363782604cabcac51c163a6671d1d216c52ff39b5559d28e1f44f.jpg) +Figure 6. Dataset-average bit allocation into individual latent arrays of varying resolution from array 1 (highest resolution) to array 7 (lowest resolution) for three target bit rates (0.075, 0.15, and 0.3 bits/pixel), and three variants of C3: optimized for MSE [22], and optimized for WD with $\sigma = 8$ , supplied with CR or without. + +scores, but the visual improvement with MSE is not sufficient to make it competitive with better metrics. We find that it can substantially improve the quality of semantically important features such as text (Fig. 7). Additional visual examples are provided in the supplement. + +After observing the strong performance of WD as an + +![](images/b492e1b746c81d108f617d82ae4ca6f148c09cbe4a513562e2b05c2b9a6334ac.jpg) + +![](images/125f5cb237da9ed75f06a6f219308ab9ef71a7b144f7c43f1378263004bf434c.jpg) + +![](images/be1db4f7a23bb59ba44471585f275b508698643bfc4f1f39f4728b3a8864edd3.jpg) + +![](images/dff28879cd4837dbcaf9bf5e143b198fb4dcc889f22bd6aa9537813ca938613a.jpg) +Figure 7. Crop of image 32 from the CLIC2020 professional dataset (best viewed on screen). Top left: original image. Bottom left: Saliency map $s$ as derived from EML-net (0: black, 1: white). Top center: C3 optimized for MSE, compressed to 0.191 bits/pixel. Bottom center: C3 optimized for MSE, weighted with the density map $p$ , compressed to 0.202 bits/pixel. Top right: C3 optimized for WD with $\sigma = 8$ , compressed to 0.194 bits/pixel. Bottom right: C3 optimized for WD with $\sigma$ derived from the saliency map, compressed to 0.191 bits/pixel. Optimizing for MSE leads to flattened texture on the shirt and skin (center column), while WD retains an accurate perception of texture (right column). However, assuming a flat sigma map in WD is equivalent to assuming all image locations will be perceived via peripheral vision, meaning that the text on the camera is subject to texture resampling, making for instance the text on the lens ("ZENITAR-M") indecipherable (top right). This is clearly undesirable, as text is a semantically relevant feature. According to the predicted saliency, the camera will be the subject of visual scrutiny. Modulating $\sigma$ according to the saliency map accounts for this. The end result is an image with both improved texture reproduction as well as legible text (bottom right). Note that simply weighting MSE using predicted saliency does not improve texture reproduction (bottom center). + +![](images/242f195ef9ac7b1db49ca498f601e0dddcffad917c448bbc91f80ac46a7a15b5.jpg) + +![](images/6cf71db349881794cb8fc598592c7b1f4785ae65a7d7f2878af0836afd1a386e.jpg) + +
% correctPCCSRCC
PSNR61.27%0.3630.298
MS-SSIM [40]64.64%0.5400.601
NLPD [26]64.35%0.5390.606
LPIPS [42]69.96%0.7110.699
DISTS [10]67.35%0.7260.724
PIM-5 [4]69.83%0.7640.785
WD2 (σ = 2)72.84%--
WDs (σmax = 4)72.87%--
WD8 (σ = 8)-0.9360.902
WDs (σmax = 16)-0.9420.913
+ +Table 1. Perceptual metric predictivity of human ratings collected throughout our study. Left column: Percentage of 16659 binary ratings predicted correctly by each metric. Raters compared randomly selected image crops of $512 \times 432$ pixels. $\sigma$ needs to chosen based on display resolution, and the crops are displayed on screen with $\approx 4$ times lower resolution than the full images (which roughly have QXGA format). Hence, we chose 4 times smaller $\sigma$ values for WD to make crop predictions. Middle and right column: Correlation of metrics with Elo scores. We computed averaged metric values between all full reconstructions and their originals, yielding one metric value for each metric and each of 29 methods/rate combinations. We then assessed how well each metric predicted the 29 scores by computing the Pearson correlation coefficient (PCC) and Spearman's rank correlation coefficient (SRCC) between Elo scores and metric averages. + +optimization objective, we investigated how well it does as an image quality assessment (IQA) method. Tab. 1 shows that WD well outperforms existing metrics both in terms of predicting individual ratings on crops, as well as predicting the Elo rankings of methods/rates on full images. To put the result of nearly $73\%$ into perspective, note that agreement among raters on individual binary answers can vary around $80\%$ . Remarkably, with a PCC of $94\%$ , WD is an excellent linear predictor of Elo scores, which we did not anticipate. + +# 5. Discussion + +Image and video compression applications enforce draconian limitations on computational complexity, so much so that CODECs using generative methods are generally infeasible to deploy on today's (and even tomorrow's) mobile devices, for reasons of both latency and energy efficiency. Neural overfitted CODEcs were introduced in COIN [11] and NeRV [8] for images and video, respectively, introducing a new class of neural image compression methods that mirror the asymmetric computational complexity trade-off between the encoder (high complexity) and decoder (low complexity) of hybrid video CODEcs such as VVC [1]. Initial follow up work focused on reducing the encoding time [35, 38] or extending the capabilities of these CODEcs to various data modalities [12, 19, 39]. Better architectures and more refined quantization and domain specific optimizations have improved compression performance both for images [16-18, 36] and video [14, 23, 24, 27, 30]. However, many of these improvements come at the cost of increased computational complexity for decoding, weakening one of the key advantages of overfitted CODEcs in the first place. COOL-CHIC [25] and follow-up work [5, 28, 29] was introduced later, maintaining the low decoding cost of COIN and improving performance by not only learning a decoder network, but also latent arrays and an entropy model per image. C3 [22] further improved performance in terms of MSE vs. bit rate. + +In the present work, we introduce a neural image compression method which is nearly the same as C3, but optimized for Wasserstein Distortion. We evaluate it using a human + +rater study, which reveals that the method truly is good, cheap, and fast! To our knowledge, this is the first method to achieve a comparable quality-rate trade-off at this decoding complexity. It provides a compelling demonstration that generative methods are not necessary to achieve highly efficient image compression. With that said, encoding complexity remains a significant limitation of overfitted compression – even more so due to the complexity of computing WD instead of MSE during optimization. A naive implementation computing WD for arbitrary pooling sizes $\sigma$ would be computationally prohibitive. Our implementation, while not specifically optimized for speed, still leads to a $\approx 6$ -fold increase in wall time required for each optimization step. + +With regards to the strong performance of WD both as a loss function and IQA method in our study, we can ask why it performs better than LPIPS, even though we also use a feature space derived from VGG. There are three main differences between WD and LPIPS: 1. Our implementation of WD uses raw VGG features rather than fitting linear "finetuning" layers to human ratings. Instead, we include the same VGG features computed on two downsampled versions of the image. This adds the same visual features at larger scales, making the overall set of features more robust to scale effects. 2. To achieve stable results, we had to add MSE to the LPIPS loss at equal weights, which was not necessary with WD. The reason may be that we included the image pixels as a "0th" layer. Note that this is not equivalent, since 3. WD always compares local statistics (i.e. mean and standard deviation) aggregated according to the $\sigma$ -map rather than pixel or feature values directly, which is more in line with models of peripheral vision. + +It's worth noting that our choice of feature space and $\sigma$ -map is entirely ad-hoc. More work is needed to identify which types of visual features are most useful, and which may be redundant (in the spirit of Portilla and Simoncelli [33]). Better saliency models, perhaps targeted specifically at image compression, could be identified. 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Roy-Chowdhury, Srikanth V. Krishnamurthy, Başak Güler University of California, Riverside, CA + +hsami003@ucr.edu, ssen010@ucr.edu, amertc@ece.ucr.edu, krish@cs.ucr.edu, bguler@ece.ucr.edu + +# Abstract + +Federated learning (FL) allows multiple data-owners to collaboratively train machine learning models by exchanging local gradients, while keeping their private data on device. To simultaneously enhance privacy and training efficiency, recently parameter-efficient fine-tuning (PEFT) of large-scale pretrained models has gained substantial attention in FL. While keeping a pretrained (backbone) model frozen, each user fine-tunes only a few lightweight modules to be used in conjunction, to fit specific downstream applications. Accordingly, only the gradients with respect to these lightweight modules are shared with the server. In this work, we investigate how the privacy of the fine-tuning data of the users can be compromised via a malicious design of the pretrained model and trainable adapter modules. We demonstrate gradient inversion attacks on a popular PEFT mechanism, the adapter, which allow an attacker to reconstruct local data samples of a target user, using only the accessible adapter gradients. Via extensive experiments, we demonstrate that a large batch of fine-tuning images can be retrieved with high fidelity. Our attack highlights the need for privacy-preserving mechanisms for PEFT, while opening up several future directions. Our code is available at https://github.com/info-ucr/PEFTLeak. + +# 1. Introduction + +Federated learning (FL) is a collaborative training paradigm to train a machine learning model across multiple dataowners (users) [41]. Users perform training locally using their local data and send the local model updates/gradients to a central server. The server aggregates these to form a global model. By obviating the need to share raw local samples, FL has emerged as a promising framework in fields where data privacy is paramount such as healthcare. + +Recently, leveraging large-scale pretrained models in various downstream tasks has gained significant attention, owing to their remarkable training performance. Considering the potential of pretrained models, recent works have extended their application to FL [43, 47, 57]. However, + +these pretrained models often contain a massive number of parameters, which can be in the range of millions/billions. Full fine-tuning (FFT) of such large models and communicating the gradient parameters require often prohibitive computational infrastructure and bandwidth. This prevents users with low computation/communication resources from participating in training and potentially causing bias in the global model. Thus, recent works have explored parameter-efficient fine-tuning (PEFT) [8, 12, 13, 23, 24, 33, 40, 46], where in lieu of fine-tuning the entire pretrained model, only a small number of lightweight modules are trained; the backbone model is kept frozen. Due to marked reduction in resource consumption and training latency, PEFT has become widely popular in FL [29, 39, 52, 61, 66, 67]. + +Though FL is popular in privacy-sensitive tasks, an adversarial server can still reverse-engineer the local gradients received from the users to extract privacy-sensitive information about local data samples [20, 21, 25, 26, 37, 42, 44, 55, 59, 63, 64, 70]. These attacks can be grouped into: 1) gradient inversion attacks [17, 20, 21, 63] and, 2) membership inference attacks [42, 49, 55, 60]. Gradient inversion attacks reconstruct the raw data samples held by a target user using the gradient received from the user. In contrast, membership inference attacks seek whether a candidate sample belongs to the local dataset of a target user. The success of membership inference attacks under both FFT and PEFT is shown via a malicious design of the pretrained model [36, 60]. These works do not consider gradient inversion attacks, which can be more detrimental to privacy, as they can operate without the knowledge of candidate samples [16]. + +A gradient inversion attack is proposed in [16], by poisoning the pretrained vision transformer (ViT) parameters [14]. However, this attack relies on FFT and assumes that the attacker has access to the gradients corresponding to the entire model. Such attacks do not apply to PEFT methods, where the pretrained model remains frozen and the attacker loses access to the full (local) gradient. Due to this, PEFT has been considered to enhance privacy and limit the risk of exposing sensitive information [67]; it has been shown that conventional gradient inversion attacks [70] have a reduced success rate under PEFT. However, these attacks do not con + +![](images/4de6a22f3eacf5717d2f11d281b3d54f0c44ab0d4fb7e03ac42db36e8956648e.jpg) +Figure 1. A small scale setup of PEFT based FL with $U = 4$ users. In each training round, users fine-tune the lightweight adapter modules and send the adapter parameters to the server. The backbone model parameters are kept frozen. After aggregation, the server sends the global adapter parameters back to the users. + +sider more powerful adversaries where the attacker can deviate from the benign training protocol to breach privacy, such as changing the model architecture and/or parameters sent to the users [16-18]. + +In this work, we ask the question whether gradient inversion attacks are viable for PEFT. Specifically, we consider gradient inversion attacks on a popular PEFT mechanism, adapters, proposed in [23]. This method introduces lightweight modules, called adapters, inside the backbone model. Originally introduced for natural language processing tasks, adapters gained significant popularity in vision tasks recently [40, 53, 66]. In an FL setup, each user computes gradients with respect to these adapter parameters only and sends them to the server (attacker), while the backbone model is frozen and not updated during training [29, 66, 67]. The server computes an average of local adapter gradients to form the global (aggregated) adapter parameters. These global parameters are sent back to the users for the next training round. The adversary seeks access to the local image dataset used for local fine-tuning by the users. Compared to conventional gradient inversion attacks targeted at FFT, a major limitation in the PEFT setting (from the attacker's perspective) is that the attacker can only observe the local gradients for a small number of adapter parameters, as the frozen backbone model does not carry any new information. In this context, whether an attacker can recover sensitive training samples of a target user (victim) using the limited information provided by the adapter gradients is yet unknown. + +In response to the question above, we propose a novel inversion attack, PEFTLeak, that can successfully recover the data samples of the victim by only leveraging the gradients from the adapters. Our attack builds on poisoning the pretrained model and adapter modules, in a way to lead the victim to unintentionally leave a footprint of their raw + +data inside the adapter gradients. To the best of our knowledge, our work is the first to propose a successful inversion attack applicable to a PEFT method. Our attack highlights the need for stronger defenses for adapters, and provides a number of principles that can also be useful for investigating inversion attacks for other PEFT methods like prefix-tuning [33], bias-tuning [6], or low-rank adaptation [24]. + +Our contributions are summarized as follows: + +1. We demonstrate the first successful gradient inversion attack on PEFT. Our attack can successfully extract local data samples of a victim user using the gradients of lightweight adapters, as opposed to the full model. +2. Extensive experiments on CIFAR-10, CIFAR-100 [30] and TinyImageNet [31] demonstrate that the attacker can breach privacy of fine-tuning data with high-accuracy. +3. We further show that reducing the adapter dimension (number of parameters) does not guarantee privacy. For small dimensions our attack can be executed in multiple rounds to increase the number of reconstructed patches. +4. Our results suggest that PEFT mechanisms, though greatly reducing the number of parameters shared during training, should not be viewed as a defense against inversion attacks, and highlights the necessity of stronger defenses such as differentially private PEFT for FL. + +# 2. Related Works + +PEFT. PEFT mechanisms combat large computation and memory costs associated with fine-tuning the entire pretrained model. Such methods freeze the pretrained model while tuning only the bias parameters [6], introducing additional lightweight trainable modules [8, 12, 23, 40, 46], learnable tokens [27, 32, 33] or optimizing low-rank matrices [24, 58, 62]. To enhance training efficiency, recent works have extended PEFT to FL [50, 61, 66, 67]. + +Privacy attacks. Gradient inversion attacks retrieve local data samples using local gradients. Attacks from [20, 70] recover ground-truth images by minimizing the distance between the true and estimated gradients. Subsequent works leverage batch-normalization statistics [63], blind source separation [28] or a pretrained generative model [15, 26, 34] to recover a batch of images. These works consider fully connected or convolutional neural networks. Attacks on ViTs are explored under the FFT setting in [21, 37, 48, 64]. References [5, 10, 16-18, 68, 69] consider more powerful adversaries who can manipulate the model parameters/architecture to further improve reconstruction. + +Membership inference attacks seek whether a specific data sample belongs to the victim user [42, 49, 51]. Such attacks have been explored under both FFT and PEFT settings [2, 19, 55, 60]. Other works recover personally identifiable information or infer the presence of a target property [7, 9, 36, 38, 54]. In contrast, our goal in is to recover the fine-tuning dataset held by the victim user. + +![](images/f3df056e098181797b30d51d3f058455b6230354bbc3521d4b643ffd7553bacb.jpg) +Figure 2. ViT encoder with adapter modules. ViT encoder with stacked LayerNorm, MSA, MLP layers and residual connections. An adapter module is inserted after each MSA/MLP layer, consisting of two feed-forward blocks and a non-linearity in-between. + +# 3. Problem Formulation + +We consider a typical centralized FL framework with $U$ users. Training is controlled by a server -often an organization with abundant resources- who performs pretraining using proprietary data or publicly available proxy datasets. Fine-tuning enhances task-specific performance by leveraging data from end-users. User $i$ holds a local dataset $\mathcal{D}_i$ . At each training round, user $i$ downloads the current state of the global adapter parameters $\mathbf{w}_A \in \mathbb{R}^d$ from the server and performs training locally using its on-device dataset. The goal is to train $\mathbf{w}_A$ to minimize the global loss, + +$$ +\mathcal {L} \left(\mathbf {w} _ {F}, \mathbf {w} _ {A}\right) \triangleq \frac {1}{U} \sum_ {i \in [ U ]} \mathcal {L} _ {i} \left(\mathbf {w} _ {F}, \mathbf {w} _ {A}\right) \tag {1} +$$ + +where $\mathcal{L}_i$ is the local loss of user $i$ and $\mathbf{w}_F$ is the frozen pretrained model. The frozen parameters are used in forward propagation to compute the loss, but are not updated during backpropagation. This system is illustrated in Fig. 1. + +Threat Model. We consider a malicious server who can modify the pretrained model and global adapter parameters. The server sends the pretrained model to the users once prior to training, after which this model is frozen (not updated), hence does not carry any new information from the users. The server sends the global adapter parameters to the users at each training round, which are then updated by the users. After receiving the local adapter gradients, the server initiates the attack to recover the data belonging to the victim user. Our threat model is motivated by [10, 16-18]. + +ViT with adapters. In ViT, an image is split into multiple patches. Sequences of patch embeddings are generated first and then a distinct position encoding vector is added to + +each patch embedding. Next, these position-encoded embeddings are used as inputs to multiple stacked multi-head self-attention (MSA) and multi-layer perceptron (MLP) layers. Each MLP layer consists of two fully connected (FCN) layers with a GELU [22] activation function in-between. In addition, a class token is used to predict classes of the fine-tuning samples at the final classification layer (also known as classification head). For fine-tuning, an adapter block is inserted after each MSA and MLP layer [23, 40, 66] as shown in Fig. 2. Each adapter block consists of two FCN layers. The first layer projects the original embeddings of dimension $D$ into a lower dimension $r$ ( $r < < D$ ), followed by a non-linear activation function. The second layer maps the projected dimension back to the original dimension, $D$ . By choosing $r < < D$ , the number of trainable parameters are significantly reduced in PEFT compared to FFT. + +The most relevant work to ours is the recent inversion attack to FFT [16], where users send full transformer gradients to the server (as opposed to PEFT). The attacker maliciously modifies the transformer parameters to recover sensitive local training images. Let us denote the total number of patches as $N$ , images in the batch as $M$ , and the (sensitive) patch embeddings by $\{\mathbf{y}^{(n,m)}\}_{n \in [N], m \in [M]}$ , which is the sum of image patch embedding and position encoding vectors. The class token embedding is denoted by $\mathbf{y}^{(0,m)}$ . The attack allows uninterrupted flow of $\mathbf{y}^{(n,m)}$ until the MLP layer. Let $\mathbf{w}_j$ and $b_j$ , denote the weight vector and bias corresponding to neuron $j$ in the first FCN layer. The output for neuron $j$ can be written as, + +$$ +v _ {j} ^ {(n, m)} \triangleq \mathbf {w} _ {j} ^ {\mathrm {T}} \mathbf {y} ^ {(n, m)} + b _ {j} \forall n \in \{0, \dots , N \}, m \in [ M ] \tag {2} +$$ + +where the gradient of user $i$ with respect to $\mathbf{w}_j$ and $b_{j}$ is, + +$$ +\frac {\partial \mathcal {L} _ {i}}{\partial \mathbf {w} _ {j}} = \frac {1}{M (N + 1)} \sum_ {m = 1} ^ {M} \sum_ {n = 0} ^ {N} \frac {\partial \mathcal {L} _ {i}}{\partial v _ {j} ^ {(n , m)}} \mathbf {y} ^ {(n, m)} \tag {3} +$$ + +$$ +\frac {\partial \mathcal {L} _ {i}}{\partial b _ {j}} = \frac {1}{M (N + 1)} \sum_ {m = 1} ^ {M} \sum_ {n = 0} ^ {N} \frac {\partial \mathcal {L} _ {i}}{\partial v _ {j} ^ {(n , m)}} \tag {4} +$$ + +which represents the average of gradients for all patches and class tokens across the images. Let us assume only patch $n$ from image $m$ propagates through the activation function in neuron $j$ while all other patches are blocked. Then, + +$$ +\frac {\partial \mathcal {L} _ {i}}{\partial \mathbf {w} _ {j}} = \frac {1}{M (N + 1)} \frac {\partial \mathcal {L} _ {i}}{\partial v _ {j} ^ {(n , m)}} \mathbf {y} ^ {(n, m)}, +$$ + +$$ +\frac {\partial \mathcal {L} _ {i}}{\partial b _ {j}} = \frac {1}{M (N + 1)} \frac {\partial \mathcal {L} _ {i}}{\partial v _ {j} ^ {(n , m)}} +$$ + +and embedding $\mathbf{y}^{(n,m)}$ can be recovered as, + +$$ +\left. \frac {\partial \mathcal {L} _ {i}}{\partial \mathbf {w} _ {j}} \right/ \frac {\partial \mathcal {L} _ {i}}{\partial b _ {j}} = \mathbf {y} ^ {(n, m)} \tag {5} +$$ + +The attacker then designs the weight and bias parameters in the MLP layer with the constraint that no two patches/tokens activate the same set of neurons, by leveraging patch statistics obtained from a public dataset which was originally proposed in [17]. After recovering the embeddings $\mathbf{y}^{(n,m)}$ , one can recover the image patch embeddings by subtracting the position encoding vectors from $\mathbf{y}^{(n,m)}$ . + +Challenges. In adapter-based PEFT [23], MLP layers are initialized prior to training and kept frozen afterwards (not updated by users). As a result, these layers do not carry any information about the local fine-tuning data, making the aforementioned attack infeasible. A potential approach is then to use the adapter gradients to recover the image embeddings as in (5). For this, the target embeddings $\{\mathbf{y}^{(n,m)}\}_{n\in [N],m\in [M]}$ should propagate through all intermediate layers before the adapter without any significant shift in the original contents, which requires the frozen MSA and MLP layers act as identity mappings. The key challenge is then the projection to lower dimension in the adapter, due to which the attacker has access to a maximum of $r$ weight and bias gradients. As seen in [8, 23], the typical values for $r$ lie within the range of 1 to 64. As evident in (5), a single neuron's weight and bias gradients play a role in recovering a single image patch. Reconstruction rate increases with the number of available neurons, which was also shown in [17, 68]. The MLP layer of the ViT architecture from [14] has 3072 neurons. These 3072 neurons' gradients were leveraged for the attack in [16], leading to the successful recovery of a large batch of images. In contrast, fine-tuning results in modifying only a small set of parameters (corresponding to $r\leq 64$ neurons in the adapter) compared to the images, which makes it hard to reconstruct a large fraction of the images using this limited information. Contributions. We address these challenges by crafting a novel gradient inversion attack on adapter-based PEFT. To do so, we introduce a malicious design of the pretrained model and adapters, which can uncover a large number of private fine-tuning images with a much reduced observable space compared to what was available with FFT. Our attack tackles the dimensionality problem (limited number of neurons) for the adapter by leveraging the gradients from multiple adapter layers, and carefully designs the patch propagation structure to enable different adapter layers to recover images with different features. + +# 4. Framework + +We next describe the details of PEFTLeak. We consider the conventional ViT architecture from [14] as the pretrained model. The architecture along with inserted adapter modules is depicted in Fig. 2. LayerNorm, MSA and MLP layers are kept frozen while only adapter modules are trainable [8, 40]. We assume that the victim performs fine-tuning on a batch of $M$ images. We denote the $m^{th}$ image in the batch + +as $\mathbf{X}(m) \in \mathbb{R}^{C \times H \times W}$ for $m \in [M]$ , where $C$ is the number of channels, and $(H, W)$ denotes the image resolution. Each image is divided into $N$ patches of resolution $(P, P)$ . Next, each patch is flattened to a vector, and denoted as $\mathbf{x}^{(n, m)} \in \mathbb{R}^{P^2 C}$ for $n \in [N]$ , $m \in [M]$ . We assume that the range of input values in $\mathbf{x}^{(n, m)}$ are in $[-1, 1]$ [45, 68]. The patches are then mapped to a dimension $D$ through linear projection using the weight matrix $\mathbf{E} \in \mathbb{R}^{D \times P^2 C}$ from the pretrained model, + +$$ +\mathbf {x} _ {\text {m a p}} ^ {(n, m)} \triangleq \mathbf {E} \mathbf {x} ^ {(n, m)} \tag {6} +$$ + +for $n\in [N]$ .A class token $\mathbf{x}_{map}^{(0,m)}$ is used to predict the class of image $m$ in the classification layer, which propagates like the image patch embeddings throughout the intermediate layers. Next, position encoding vectors $\mathbf{E}_{pos}^{(n)}\in \mathbb{R}^D$ for $n\in \{0,\dots ,N\}$ are added to the embeddings, + +$$ +\mathbf {y} ^ {(n, m)} \triangleq \mathbf {x} _ {\text {m a p}} ^ {(n, m)} + \mathbf {E} _ {\text {p o s}} ^ {(n)} = \mathbf {E} \mathbf {x} ^ {(n, m)} + \mathbf {E} _ {\text {p o s}} ^ {(n)} \tag {7} +$$ + +Key intuition. At a high-level, our goal is to propagate the embeddings $\mathbf{y}^{(n,m)}$ up to the adapter layers without any significant distortion. This should be achieved by a one-time adversarial modification of the pretrained model, which is sent to the users prior to fine-tuning. As these layers are frozen and not modified by the users during fine-tuning, they provide no information about the local image patches. Adapter layers will then be utilized to recover the image patches. These trainable parameters are modified by the users during fine-tuning, and hence encode sensitive information about the local images. On the other hand, the dimensionality of a single adapter layer is not sufficient to recover a large batch of images. To that end, our attack is designed across multiple adapter layers, where different layers capture image patches with varying statistics. We next describe the design of the individual layers. + +# 4.1. First LayerNorm (LN1) + +After position encoding, the embeddings $\mathbf{y}^{(n,m)}$ enter a LayerNorm (LN1) layer, + +$$ +\mathbf {z} ^ {(n, m)} \triangleq \frac {\mathbf {y} ^ {(n , m)} - \mu^ {(n , m)}}{\sigma^ {(n , m)}} \odot \mathbf {w} _ {L N 1} + \mathbf {b} _ {L N 1} \tag {8} +$$ + +where $\mathbf{w}_{LN1},\mathbf{b}_{LN1}\in \mathbf{R}^{D}$ are the weight and bias parameters at LN1. $\mu^{(n,m)},\sigma^{(n,m)}$ denote the mean and standard deviation across the elements in $\mathbf{y}^{(n,m)}$ and $\odot$ denotes element-wise multiplication. As our goal is to ensure uninterrupted flow of information from the input layer, we want $\mathbf{z}^{(n,m)}\approx \mathbf{y}^{(n,m)}$ . For this, we design $\mathbf{E}$ to make the mean and standard deviation across $\mathbf{x}_{map}^{(n,m)}$ in (6) negligible for all $n\in [N],m\in [M]$ compared to the mean and standard deviation of $\mathbf{E}_{pos}^{(n)}$ . Selecting $\mathbf{E}_{pos}^{(n)}\sim \mathcal{N}(0,\sigma)$ with $\sigma = 10$ and $\mathbf{E} = 0.5\mathbf{I}_D$ satisfies these conditions, $\mu^{(n,m)}\approx 0$ , and $\sigma^{(n,m)}\approx \sigma$ for all $n\in \{0,\dots ,N\}$ . Then, by setting each element in $\mathbf{w}_{LN1}$ to $\sigma$ and $\mathbf{b}_{LN1}$ to $0$ , $\mathbf{z}^{(n,m)}\approx \mathbf{y}^{(n,m)}$ . + +# 4.2. Multi-head Self Attention (MSA) + +The output embeddings of LN1 enter the Multi-head Self Attention (MSA) layer. To enable undistorted propagation of input patch embeddings, we design the weight parameters in the MSA layer to act as identity mappings. Suppose that the MSA layer consists of $L$ heads where the embedding dimension of each head is $D_h \triangleq D / L$ . For head $h$ , denote the query, key and value weight matrices as $\mathbf{W}_Q^h$ , $\mathbf{W}_K^h$ and $\mathbf{W}_V^h$ , and biases as $\mathbf{b}_Q^h$ , $\mathbf{b}_K^h$ and $\mathbf{b}_V^h$ , respectively. Let, + +$$ +\mathbf {W} _ {Q} ^ {h} = \mathbf {W} _ {K} ^ {h} = \mathbf {W} _ {V} ^ {h} = \mathbf {I} _ {D _ {h} \times D _ {h}} \tag {9} +$$ + +$$ +\mathbf {b} _ {Q} ^ {h} = \mathbf {b} _ {K} ^ {h} = \mathbf {b} _ {V} ^ {h} = \mathbf {0} \tag {10} +$$ + +and define $(\mathbf{y}^{(n,m)})_h \triangleq \mathbf{y}^{(n,m)}[hD_h : (h + 1)D_h] \in \mathbb{R}^{D_h}$ as the $D_h$ elements from the $n^{th}$ patch embedding that propagates through head $h$ . Then, query, key and value matrices for head $h$ are given by, + +$$ +\mathbf {Q} ^ {h} \triangleq \left[ \begin{array}{c c c} \mathbf {W} _ {Q} ^ {h} (\mathbf {y} ^ {(0, m)}) _ {h} & \dots & \mathbf {W} _ {Q} ^ {h} (\mathbf {y} ^ {(N, m)}) _ {h} \end{array} \right] +$$ + +$$ +\mathbf {K} ^ {h} \triangleq \left[ \begin{array}{l l l} \mathbf {W} _ {K} ^ {h} (\mathbf {y} ^ {(0, m)}) _ {h} & \dots & \mathbf {W} _ {K} ^ {h} (\mathbf {y} ^ {(N, m)}) _ {h} \end{array} \right] +$$ + +$$ +\mathbf {V} ^ {h} \triangleq \left[ \begin{array}{l l l} \mathbf {W} _ {V} ^ {h} (\mathbf {y} ^ {(0, m)}) _ {h} & \dots & \mathbf {W} _ {V} ^ {h} (\mathbf {y} ^ {(N, m)}) _ {h} \end{array} \right] \tag {11} +$$ + +Note that position encoding vectors $\mathbf{E}_{pos}^{(n)}$ are generated independently from $\mathcal{N}(0,10)$ , hence for $n\neq t$ + +$$ +\left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {E} _ {p o s} ^ {(t)} > > \left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {E} _ {p o s} ^ {(n)} \tag {12} +$$ + +As a result, the attention matrix becomes an identity matrix, + +$$ +\mathbf {A} ^ {h} \triangleq s o f t m a x \left(\left(\mathbf {Q} ^ {h}\right) ^ {\mathrm {T}} \mathbf {K} ^ {h} / \sqrt {D _ {h}}\right) \cong \mathbf {I} _ {(N + 1) \times (N + 1)} +$$ + +After multiplying with the value matrix $\mathbf{V}^h$ , the self-attention output for head $h$ is $SA_h([y^{(0,m)}\dots y^{(N,m)}]) \triangleq \mathbf{A}^h (\mathbf{V}^h)^\mathrm{T}$ . Let $\mathbf{W}_{MSA} \in \mathbb{R}^{D\times D}$ denote the weight matrix that performs the linear transformation on the concatenated outputs from all heads. We set $\mathbf{W}_{MSA} = \mathbf{I}_{D\times D}$ , after which the MSA output is, + +$$ +\begin{array}{l} M S A ([ \mathbf {y} ^ {(0, m)} \dots \mathbf {y} ^ {(N, m)} ]) \\ \triangleq \left[ S A _ {1} \left(\left[ \mathbf {y} ^ {(0, m)} \dots \mathbf {y} ^ {(N, m)} \right]\right) \quad \dots \right. \\ \left. S A _ {L} \left(\left[ \mathbf {y} ^ {(0, m)} \dots \mathbf {y} ^ {(N, m)} \right]\right) \right] \times \mathbf {W} _ {M S A} (13) \\ \cong \left[ \left(\mathbf {y} ^ {(0, m)}\right) \quad \dots \quad \left(\mathbf {y} ^ {(N, m)}\right) \right] _ {(N + 1) \times D} ^ {\mathrm {T}} (14) \\ \end{array} +$$ + +which ensures the flow of $\mathbf{y}^{(n,m)}$ for $n\in [N],m\in [M]$ + +# 4.3. Adapter Layer + +The next layer is the adapter, consisting of two linear layers (one down-projection and one up-projection) with an activation function in-between. Down-projection projects the input embeddings of dimension $D$ to a lower dimension $r << D$ . Recall that adapter modules are trainable. By using the gradients in the down-projection layer along with + +![](images/7792d4865185ace278d417c2d0d86424e38c8e2c14f74fd3ee1f542bdd8ba735.jpg) +Figure 3. Image recovery from multiple adapters. A small-scale example with two adapters, each consisting of 3 neurons in the down-projection layer. The attacker aims to recover 4 images in the batch, where each image is divided into 4 patches. The biases for the two adapters are designed to recover patches from the second position. The plot represents the distribution of patch statistics, $(\mathbf{E}_{pos}^{(t)})^{\mathrm{T}}\mathbf{x}_{map}^{(t,m)}$ for $t = 2$ . The attacker targets images whose patch statistics lie in one of the four intervals (colored). Each adapter targets two intervals. By leveraging multiple adapters, the attacker can recover all the patches in the target position. + +the activation, one can try to recover the input embeddings $\{\mathbf{y}^{(n,m)}\}_{n\in [N],m\in [M]}$ as in (5). On the other hand, the number of neurons $r$ typically ranges from 1 to 64 [8, 23], which severely limits the number of images recovered, as reconstruction performance in (5) degrades when the number of neurons decreases [17, 68]. To enable recovery of a large batch of images, we propose to use the neurons from multiple adapters, where different layers are designed to recover images with different statistical properties. + +We first discuss how to recover a patch from a target position within an image. For a target position $t \in [N]$ , the goal is to allow the patches from position $t$ pass the activation function, and filter out the patches from all other positions $n \neq t$ . We allocate $k_{t} > r$ neurons to recover patches from position $t$ . As each adapter has $r$ neurons, $S_{t} \triangleq \frac{k_{t}}{r}$ adapters are used to recover patches from position $t$ , and $S \triangleq \sum_{n=1}^{N} S_{n}$ adapters to recover the patches from all positions $t \in [N]$ . Denote the set of neurons used for position $t$ as $\mathcal{N}_{t}$ . For each neuron $j \in \mathcal{N}_{t}$ , we set the corresponding weight vector to $\mathbf{E}_{pos}^{(t)}$ , after which the output for patch $t$ is, + +$$ +\begin{array}{l} v _ {j} ^ {(t, m)} = \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {y} ^ {(t, m)} + b _ {j} (15) \\ = \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {x} _ {\text {m a p}} ^ {(t, m)} + \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {E} _ {\text {p o s}} ^ {(t)} + b _ {j} (16) \\ \end{array} +$$ + +whereas for all other positions $n\in \{0,\dots ,N\} \backslash \{t\}$ + +$$ +\begin{array}{l} v _ {j} ^ {(n, m)} = (\mathbf {E} _ {p o s} ^ {(t)}) ^ {\mathrm {T}} \mathbf {y} ^ {(n, m)} + b _ {j} \\ = \left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {x} _ {m a p} ^ {(n, m)} + \left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {E} _ {p o s} ^ {(n)} + b _ {j} \tag {17} \\ \end{array} +$$ + +We next discuss how this design plays a key role in propagating patches from target position $t$ while blocking patches from all other positions. Note that the server does not know $(\mathbf{E}_{pos}^{(t)})^{\mathrm{T}}\mathbf{x}_{map}^{(t,m)}$ as it does not have access to local data. Along the lines of [17, 18], we assume the server can instead estimate an approximate distribution for this quantity by utilizing a public dataset, which resembles a Gaussian distribution from the central limit theorem [17]. Define, + +$$ +c _ {j} \triangleq \psi^ {- 1} \left(j / k _ {t}\right) \tag {18} +$$ + +where $\psi^{-1}(\cdot)$ is the inverse CDF of the estimated Gaussian. Then, the bias for neuron $j$ is designed as, + +$$ +b _ {j} \triangleq - \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {E} _ {\text {p o s}} ^ {(t)} - c _ {j} \tag {19} +$$ + +If for any given patch $t$ and image $m$ , + +$$ +c _ {j} < \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {x} _ {\text {m a p}} ^ {(t, m)} < c _ {j + 1} \tag {20} +$$ + +then, from (16), (19) and (20) we observe for patch $t$ + +$$ +v _ {j} ^ {(t, m)} = \left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {y} ^ {(t, m)} + b _ {j} = \left(\mathbf {E} _ {p o s} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {x} _ {m a p} ^ {(t, m)} - c _ {j} > 0 \tag {21} +$$ + +whereas for all other patches $n\in \{0,\dots ,N\} \backslash \{t\}$ + +$$ +v _ {j} ^ {(n, m)} = \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {y} ^ {(n, m)} + b _ {j} < < 0 \tag {22} +$$ + +which follows from (12), hence (22) filters out the patches from all other positions after the activation function. Next, for the target position $t$ , we need to ensure unique recovery of each image patch in the batch. For this, we utilize the technique from [17] to successively block images by the activation function. According to (16), (19) and (20), + +$$ +v _ {j + 1} ^ {(t, m)} = \left(\mathbf {E} _ {\text {p o s}} ^ {(t)}\right) ^ {\mathrm {T}} \mathbf {x} _ {\text {m a p}} ^ {(t, m)} - c _ {j + 1} < 0 \tag {23} +$$ + +hence $\mathbf{y}^{(t,m)}$ propagates through the activation function at neuron $j$ as in (21), but is blocked at neuron $j + 1$ as in (23). If no other image satisfies (20), then by leveraging the gradients for this pair of neurons, the attacker can recover, + +$$ +\left. \left(\frac {\partial \mathcal {L} _ {i}}{\partial \mathbf {w} _ {j}} - \frac {\partial \mathcal {L} _ {i}}{\partial \mathbf {w} _ {j + 1}}\right) / \left(\frac {\partial \mathcal {L} _ {i}}{\partial b _ {j}} - \frac {\partial \mathcal {L} _ {i}}{\partial b _ {j + 1}}\right) = \mathbf {y} ^ {(t, m)} \right. \tag {24} +$$ + +After computing $c_{j}$ for $j \in [k_t]$ as in (18), we can utilize $c_{(s - 1)r + 1},\ldots ,c_{sr}$ to design the biases of $r$ neurons as in (19) for the $s^{th}$ adapter for $s \in [S_t]$ . As long as only one patch lies within an interval $[c_j,c_{j + 1}]$ for $j \in [k_t]$ , perfect recovery can be achieved for that particular patch. From a single adapter, the attacker can recover at most $r - 1$ patches that lie within one of the $r - 1$ intervals. Attacks to more intervals can be deployed by utilizing $S_{t}$ adapters for position + +$t$ . We demonstrate an illustrative example in Fig. 3. After recovering the embedding $\mathbf{y}^{(t,m)}$ , the attacker can recover, + +$$ +\mathbf {x} ^ {(t, m)} = \mathbf {E} ^ {\dagger} \left(\mathbf {y} ^ {(t, m)} - \mathbf {E} _ {p o s} ^ {(t)}\right) \tag {25} +$$ + +where $\mathbf{E}^{\dagger}$ is the pseudoinverse of $\mathbf{E}$ in (6). The weight and bias for the up-projection are designed to produce zero output, to ensure we regain the target embeddings $\{\mathbf{y}^{(n,m)}\}_{n\in [N],m\in [M]}$ after the residual connection in Fig. 2. However, if we simply set all parameters to zero, the gradient for the preceding layer will be zero during backpropagation, making reconstruction impossible. We prevent this by setting the first neuron's weight to a small non-zero value $(\sim 10^{-6})$ . We next discuss how to propagate the current layer's output (embeddings $\mathbf{y}^{(n,m)}$ ), from one adapter layer to the next to continue reconstruction. + +# 4.4. Second LayerNorm (LN2) + +As shown in Fig. 2, the adapter output goes through a residual connection from the LN1 input, which is equal to $\mathbf{y}^{(n,m)}$ from (8). The output of the residual connection is then, + +$$ +\mathbf {e} ^ {(n, m)} \triangleq (1 + 1) \mathbf {y} ^ {(n, m)} \cong 2 \mathbf {y} ^ {(n, m)} \tag {26} +$$ + +for $n \in \{0, \dots, N\}$ , which enters another LayerNorm (LN2). Note that $\mathbf{y}^{(n,m)}$ has mean approximately equal to 0 and standard deviation $\sigma$ from (8). Therefore, $\mathbf{e}^{(n,m)}$ has mean 0 and standard deviation $2\sigma$ . The server can then set the elements in the LN2 weight vector to $\sigma$ and bias vector to 0 to retrieve back the original embeddings. + +$$ +\frac {\mathbf {e} ^ {(n , m)} - 0}{2 \sigma} \sigma + 0 \cong \mathbf {y} ^ {(n, m)} \tag {27} +$$ + +# 4.5. Multi Layer Perceptron (MLP) + +Next is the MLP layer, consisting of two linear layers with a GELU activation in-between. The first layer maps the embeddings to a higher dimension $4D$ , whereas the second layer maps them back to the original dimension $D$ [14]. Our goal is to propagate the embeddings $\mathbf{y}^{(n,m)}$ to the next adapter undistorted. For this, the MLP needs to act as an identity function. Let $\mathbf{W}_{MLP,1} \in \mathbb{R}^{4D \times D}$ be the weight matrix in the first layer, with row $p$ and column $q$ given as, + +$$ +\mathbf {W} _ {M L P, 1} [ p, q ] \triangleq \left\{ \begin{array}{l l} 1 & \text {i f} p = q \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {28} +$$ + +which makes the output equal to the original embeddings, $\mathbf{y}^{(n,m)}$ in the first $D$ coordinates, while the remaining $3D$ coordinates are 0. Note that original embeddings may contain negative values with a large magnitude, which will be filtered out by GELU, whereas values close to zero are subject to attenuation. To avoid this, we set the bias as $\mathbf{b}_{MLP,1}\triangleq \gamma \mathbf{1}_{4D}$ with a large value $\gamma = 10^4$ , where $\mathbf{1}_{4D}$ + +![](images/f2b332207259fe1125528f50815d7e2ce6ffb9e56179afd41e0d8be56d9b0cee.jpg) +Figure 4. CIFAR-100 (recovered images for a batch of 32 images). + +![](images/b52502cfbaf08605fb446da5afbbf0370a7ad3e0c60aabfce3c117c5abf0fc6f.jpg) + +
LPIPSSSIMMSE
MeanStdMeanStdMeanStd
CIFAR-100.100.090.740.110.210.12
CIFAR-1000.080.060.880.120.200.16
TinyImageNet0.120.040.760.101.060.82
+ +Table 1. Mean and standard deviation of MSE, LPIPS and SSIM scores for different datasets. + +is a $4D$ -dimensional vector containing all 1s. This ensures that the neuron outputs are not affected by GELU. By setting the weight matrix $\mathbf{W}_{MLP,2} \in \mathbb{R}^{D \times 4D}$ and bias $\mathbf{b}_{MLP,2} \in \mathbb{R}^D$ in the second linear layer as, + +$$ +\mathbf {W} _ {M L P, 2} [ p, q ] \triangleq \left\{ \begin{array}{l l} 1 & \text {i f} p = q \\ 0 & \text {o t h e r w i s e} \end{array} \right. \tag {29} +$$ + +and $\mathbf{b}_{MLP,2} \triangleq -\gamma \mathbf{1}_D$ , we ensure that the MLP output is equal to the original embeddings $\mathbf{y}^{(n,m)}$ for $n \in \{0, \dots, N\}$ , $m \in [M]$ . We adopt the same design in the subsequent LayerNorm, MSA and MLP layers. This ensures that the target embeddings $\mathbf{y}^{(n,m)}$ propagate through all intermediate layers towards the adapters. After recovering raw image patches, the final step is to group the patches that belong to the same image. For this, we use a similar approach to [18], which embeds a unique tag in the first MSA layer to each patch belonging to the same source image. + +# 5. Experiments + +Our experiments aim to answer the following questions: + +- How does PEFTLeak perform in terms of reconstruction? +- How is performance impacted with varying bottleneck dimension $r$ inside the adapters? +- How is performance impacted with increasing batch size? +- How do we benefit from leveraging the layers from all the adapter modules for reconstruction? + +Setup. We consider a distributed setting for image classification using ViT-B/16 [14] as the pretrained model. Each user holds data samples from CIFAR-10, CIFAR-100 [30] and TinyImageNet [31] datasets. The experiments are run on a 24 core AMD Ryzen device with NVIDIA RTX4000. + +Hyperparameters. In our experiments, each image is divided into patches of size (16, 16) in accordance with [14]. For CIFAR-10 and CIFAR-100, each image (with resolution (32, 32)) is divided into 4 patches. For TinyImageNet, each image (with resolution (64, 64)) is divided into 16 patches. The embedding dimension is $D = 768$ [14]. The bottleneck dimension for the adapters is $r = 64$ . + +Performance Metrics. Attack performance is evaluated using the mean squared error (MSE), and perceptual/structural similarity scores LPIPS [65] and SSIM [56] between recovered and ground-truth images. Lower MSE/LPIPS or higher SSIM implies better reconstruction. + +Results. In Fig. 4, we present the reconstructed images from the local gradient of a target user. The gradient is derived from training on a batch of 32 images from CIFAR100. Since each image is divided into 4 patches, there are $32 \times 4 = 128$ target patches that the attacker aims to recover. As we observe, 110-out-of-128 image patches (85.9% of the patches) are recovered. Gray patches indicate that the corresponding ground-truth patches are not recovered. In Fig. 5, we present the reconstructed images for TinyImageNet. Since in this case each image is divided into 16 patches, the attacker aims for $32 \times 16 = 512$ different patches. We observe that around 81% of the total patches are recovered. Reconstruction for CIFAR-10 is presented in App. C.1. In Table 1, we report the mean and standard deviation of MSE, LPIPS, and SSIM scores across the recovered patches. + +We next study the impact of batch size, bottleneck dimension, and number of adapter layers on reconstruction. These experiments are conducted using CIFAR-100. + +Reconstruction rate vs. batch size. We first evaluate the impact of batch size on the success rate. Since reconstruction is performed patch-wise, we compare the percentage of patches recovered across different batch sizes. As we observe in Fig. 6a, even for a batch size as large as 128, PEFTLeak recovers up to $72.6\%$ of the patches. + +Reconstruction rate vs. bottleneck dimension. We present the impact of bottleneck dimension $r$ on the attack efficiency in Fig. 6b. As $r$ increases, more patches are retrieved. Higher values of $r$ imply more neurons in the adapter layer that can be used for recovery. This sug + +![](images/0cc9d6800a807f49ffbf129a78c920fe028bb080eb4bd595993af545582ae110.jpg) +Figure 5. TinyImageNet (recovered images for a batch of 32 images). + +![](images/ff111f752390896b7383e739711673af3bdb436bc4c0c57894b8b8ac632b8012.jpg) + +![](images/0a4fb3abe8799657b9781e4c5c6157692b936e5df93a677cad917e403967d768.jpg) +(a) Varying batch size + +![](images/0eef2cb0d4e9b9f401aa1bfbb6d9694ae12555e06d0140cab86191eeafe05bc5.jpg) +(b) Varying $r$ + +![](images/2394b9b6b18c824b7902217c1a69b93cc9c37641f4db630568343e9b74b60608.jpg) +(c) Varying # adapter layers + +![](images/bcb80a7402f1bc5130f9898535e6ac1ee5c88c6c6a181f8672b00c72e44fb7b0.jpg) +Figure 6. Percentage of patches recovered with varying batch size, bottleneck dimension, and number of adapter layers used. +(a) Round 1 +Figure 7. Patches recovered over multiple rounds $(r = 8)$ + +![](images/f915de075f1b4c2fdbdabac36f20ee1bd94567bb77d2f28a6b4fdddd9b124e85.jpg) +(b) Round 2 + +![](images/c0377ac1bc683f8394403bc631ca974f7418bfb0527f12e5eac542b1e222104f.jpg) +(c) Round 4 + +![](images/bf42e8bd4fc509d40c72be058d96534f315d4d54356b86adc271565d88e24f06.jpg) +(d) Round 5 + +gests that choosing a small $r$ could be a potential defense against privacy attacks. However, as we show later, this can be countered by using multiple training rounds. + +Reconstruction rate vs. number of adapter layers. We further analyze the impact of the number of adapter layers on the attack success in Fig. 6c. We observe that as we use more layers for the attack, more patches can be recovered. Even though a single adapter may have insufficient neurons due to down-projection, the leakage rate is enhanced by leveraging multiple adapter layers. + +Attack over multiple training rounds. We next demonstrate how the attack can be executed over multiple training rounds to increase the number of reconstructed patches for a small bottleneck dimension, in particular for $r = 8$ . As + +![](images/f34a757cd94dfd2f586dda3c1afc4f4d4e2ac189c9e2427e7bea9b07f164b9ea.jpg) +Figure 8. Recovered images with attack from [20] (CIFAR-100). + +mentioned earlier, each user sends the adapter gradients to the server in each training round, while the pretrained model is kept frozen. The server sends the aggregated adapter parameters in each training round back to the users. Hence, the server can tamper with these adapter parameters so that in each round, different sets of intervals from (20) can be targeted. For the image in Fig. 7, we observe that only a single patch is recovered from gradients within a single training round. However, from gradients over 5 training rounds, the entire image is recovered. Hence, choosing a small value for $r$ does not guarantee privacy. + +Comparison with optimization-based baseline. In Fig. 8, we apply the optimization-based attack from [20] for the images in Fig. 4a (details are provided in App C.2). + +
Batch size816324864
% Patches recovered9084.773.266.562.6
+ +Table 2. Reconstruction with varying batch size (ImageNet). + +Scalability to high resolution dataset. Table 2 presents patch recovery on ImageNet [11], with image resolution (224, 224). Each image is divided into 196 patches of size (16, 16). Additional experiments are provided in App. C. + +# 6. Conclusion + +We show how an adversarial server can manipulate the pretrained model and adapter parameters to uncover users' local fine-tuning data in PEFT for FL, despite a significantly reduced embedding space. Our attacks demonstrate the critical need for privacy-aware PEFT mechanisms, with future directions including certifiable privacy guarantees. + +# 7. Acknowledgement + +The research was supported in part by the OUSD (R&E)/RT&L under Cooperative Agreement W911NF-20-2-0267, NSF CAREER Award CCF-2144927, ARO grant W911NF2210260, and the UCR OASIS Grant. 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(left) Decision boundaries of a $4^{th}$ -degree polynomial logistic regression model with 2D input. In this example, feature $x_{1}$ is class-specific and $x_{2}$ is domain-specific, while color represents classes and shapes represent domains. The samples with solid red and green colors are included in the training data, whereas the fainted samples are part of the hidden held-out test set. As a result, domain shift is represented by a change in $x_{2}$ . Although the classifier should only infer based on $x_{1}$ , traditional gradient descent leads to overfitting (top-left). The proposed method, GGA (bottom-left), introduces an annealing process that depends on gradient agreement, leading to models that generalize well to new, unobserved target domains. (right) Schematics of the parameter updates of ERM (top-right) and GGA (bottom-right). Parameters updated via ERM are driven by gradient conflict, whereas GGA searches for a point where gradients align before continuing descending towards a minima. + +![](images/f5c5fa9b3e28a49e08d392d9157f817deb5c0f9b4f84977c4805cd7454341f32.jpg) + +# Abstract + +Domain Generalization (DG) research has gained considerable traction as of late, since the ability to generalize to unseen data distributions is a requirement that eludes even state-of-the-art training algorithms. In this paper we observe that the initial iterations of model training play a key role in domain generalization effectiveness, since the loss landscape may be significantly different across the training and test distributions, contrary to the case of i.i.d. data. + +Conflicts between gradients of the loss components of each domain lead the optimization procedure to undesirable local minima that do not capture the domain-invariant features of the target classes. We propose alleviating domain conflicts in model optimization, by iteratively annealing the parameters of a model in the early stages of training and searching for points where gradients align between domains. By discovering a set of parameter values where gradients are updated towards the same direction for each data distribution present in the training set, the proposed + +Gradient-Guided Annealing (GGA) algorithm encourages models to seek out minima that exhibit improved robustness against domain shifts. The efficacy of GGA is evaluated on five widely accepted and challenging image classification domain generalization benchmarks, where its use alone is able to establish highly competitive or even state-of-the-art performance. Moreover, when combined with previously proposed domain-generalization algorithms it is able to consistently improve their effectiveness by significant margins1. + +# 1. Introduction + +The vast majority of neural networks today are trained via stochastic gradient descent methods, such as SGD [7] or ADAM [25], where the gradient direction guides the optimization through the loss landscape, aiming to converge to a minimum. What is more, it has been empirically shown that the astounding performance and generalization capabilities of these over-parameterized models stems from the fact that loss surfaces of large neural networks have multitudinous local minima [2, 42], most of which yield similar performance upon model convergence [12, 37]. + +The above optimization process assumes that all available data samples are independent and identically distributed (i.i.d.). When this assumption holds, the parameter values reached during training is likely to generalize to the test distribution. However, in several real-world scenarios the i.i.d. assumption is not met, and models are evaluated on similar but distinct out-of-distribution (OOD) data resulting from domain shifts to the training distribution, leading to a domain generalization (DG) [60] problem. In this case, the training loss minimum may lead to a poor parameter configuration for the test data. + +The disagreement of gradients across data from different domains during training, can provide an indication that the described problem occurs. This observation about gradient conflicts was initially made in the multi-task learning paradigm [58], where gradients of different tasks pointed to conflicting directions on the loss surface. To mitigate the effects of gradient conflicts, methods to balance the relative gradient magnitudes were proposed [11, 23], along with algorithms that remove disagreeing gradient components among tasks [45, 55]. Similarly, gradient conflicts were also addressed in the context of DG in [34], where gradients with different signs among domains were either muted or set to random values; as they are assumed to contain domain-specific information. With that being said, it has been empirically shown that even though the above issues arise, the correct selection and tuning of hyperparameters can be enough for vanilla network training to surpass + +even state-of-the-art algorithms [19]. This evidence leads us to believe that there exist local minima on the vanilla loss surface that lead to more robust and generalizable models. Depending on the starting parameter configuration, even a model optimized by traditional Empirical Risk Minimization can reach a solution that is locally optimal for all distinct domains. These hypotheses, along with problems poised by gradient disagreement, are demonstrated in Section 1.1 (illustrated in Fig. 1) and are further explored in Section 3.2. + +Starting from these ideas, we propose an alternative strategy for updating the parameters of a neural network during the optimization process, in an attempt to "set the model up for success". Specifically, inspired by Simulated Annealing Optimization [26], during the early stages of model training we iteratively anneal, i.e. randomly perturb the parameters of the model, and search for a set of parameter values where the gradients between all training domains agree, before minimizing the total loss across all training domains. We call this simple, yet effective, strategy Gradient-Guided Annealing or GGA. When evaluated on extensive and challenging DG benchmarks, GGA is able to boost the performance of the baseline by significant margins, even yielding state-of-the-art results without the application of additional data processing or augmentation techniques. Additionally, since GGA can be considered a general strategy for handling multi-domain datasets it can also be combined with previously proposed algorithms. Experimental results of the combined methods, demonstrate the efficacy of GGA, as it is able to enhance their generalization capacity and overall accuracy, boosting their performance over the baseline benchmarks. + +Our primary contributions are as follows: + +- We present Gradient-Guided Annealing (GGA), a DG method for training neural networks such that gradients align across domains. +- We validate the effectiveness of GGA on multiple, challenging Domain Generalization benchmarks both as a standalone algorithm and by combining it with previous state-of-the-art methods. +- We offer further evidence on the effectiveness of the proposed method by investigating the domain gradients during training and its sensitivity to the choice of hyperparameters. + +# 1.1. Gradient Disagreement and Domain Overfitting + +To demonstrate how the domain generalization problem manifests during optimization in the source domains during training, we consider the following simple synthetic binary classification problem. For training, data is sampled from a mixture of two domains, while testing takes place on a different, previously unseen, target domain. Each sample + +has two features, a class-specific feature $x_{1}$ and a domain-specific feature $x_{2}$ . Our goal is to learn a model on the source domains, that can discriminate between classes effectively on the unseen target domain. + +Concretely, for the source domains, we draw 200 points from a 2-D Gaussian distribution with an isotropic covariance matrix for each domain and class, i.e., + +$$ +\boldsymbol {x} _ {y} ^ {(d)} \sim \mathcal {N} \left(\boldsymbol {\mu} _ {y} ^ {(d)}, \sigma \boldsymbol {I} _ {2}\right) \tag {1} +$$ + +Where the subscript $y$ indicates the class and the exponent $d$ the domain, while $\pmb{\mu}_1^{(1)} = [-2.5, -2.5]$ , $\pmb{\mu}_1^{(2)} = [-2.5, 2.5]$ , $\pmb{\mu}_2^{(1)} = [2.5, -2.5]$ , $\pmb{\mu}_2^{(2)} = [2.5, 2.5]$ , $\sigma = 0.5$ and $\pmb{I}_2$ is the $2 \times 2$ identity matrix. We also draw an additional 400 samples from a held-out test domain with means at $\pmb{\mu}_1^{(3)} = [-2.5, -7.5]$ and $\pmb{\mu}_2^{(3)} = [2.5, -7.5]$ . The drawn samples are shown in the left column of Fig. 1. In this example, the classes can be distinguished solely on $x_1$ (the "class-specific" feature), while domains differ in terms of feature $x_2$ (the "domain-specific" feature). + +We train a $4^{\text{th}}$ degree polynomial logistic regression model trained with Empirical Risk Minimization (ERM, [49]) and binary cross-entropy loss using the SGD optimizer. In the top-left example of Fig. 1 the initial parameter conditions were such that training converged to a local minimum of the loss that leads the model to consider both $x_{1}$ and $x_{2}$ for its decisions. In this case, the model has clearly overfit its source domains and will fail when presented with out-of-distribution data from the held-out domain. An indicator of this was the fact that gradients of the loss for samples of different domains were dissimilar during training. This is in contrast to the bottom-left GGA model in Fig. 1 which mostly relies on $x_{1}$ to discriminate between classes. This model was trained by using the proposed gradient agreement strategy and although the resulting training loss is slightly higher, the model successfully generalizes to new domains. + +In the rest of the paper, we first discuss the most relevant works in the domain generalization literature (Section 2) and then present the proposed methodology (Section 3). Followingly, we present the experimental setup and results (Section 4), and finally conclude the paper with a discussion on limitations of our method and directions for future research (Section 5). + +# 2. Related Work + +Domain Generalization (DG) methods focus on learning a model from one or multiple source data sets, or domains, which can generalize to previously unseen, out-of-distribution target domains. Existing DG methods in the literature can be categorized into two major groups; single-source and multi-source. In addition to not having any knowledge about the unseen data, single-source algorithms + +do not leverage information regarding the presence of distinct domains in the training set. On the other hand, multisource methods utilize domain labels and often take advantage of the statistical differences in the sample distributions. Specifically, most popular algorithms include data augmentation [9, 59] which proves beneficial for regularizing over-parameterized neural networks and improving generalization, meta-learning [3, 14, 30, 57], which exposes models to domain shifts during training, and disentangled representation learning [4, 39, 51, 56], where models most commonly include modules or architectures that focus on decomposing learned representations into domain-specific and domain-invariant parts. Additionally, domain alignment [17, 35, 53] and causal representation learning algorithms [32, 33] have also been proposed in the literature towards producing robust models that retain their generalization capabilities on unseen data. Finally, ensemble learning methods [61] have also been proposed for DG, where techniques such as weight averaging [22] lead to improved generalization [10]. + +Gradient operations for DG. Lately, there has been a surging interest in addressing the DG problem from a gradient-aware perspective. The most relevant works to ours, leverage gradient information to learn generalized representations from the source datasets. For example, [21] proposes a self-challenging learning scheme, by muting the feature representations associated with the highest gradients and forcing the network to learn via alternative routes. In another work, the authors of [47] propose Fish, a first-order algorithm that approximates the optimization of the gradient inner product between domains. Inspired by gradient surgery in multi-task learning [55], [34] proposes aligning the gradient vectors among source domains by retaining the individual same-sign gradients, and either setting the rest to zero or random values. Finally, there has also been great interest into researching the properties of Sharpness-Aware Minimization (SAM) [16, 28, 52, 62], as it has been hypothesized that flatter minima lead to smaller DG gaps and improved generalization. + +Simulated Annealing for Deep Learning. Although explored in past literature, simulated annealing (SA) has not been explicitly proposed for DG. To avoid being "trapped" in local minima during model optimization, [8] proposes SA-GD, a simulated annealing method for gradient descent. Similarly, [40] shows that by sacrificing computation time, simulated annealing optimization can also improve the results of standard CNN architectures. In a more recent work, the authors of [44] propose SEAL and apply simulated annealing in the early layers of networks to prohibit them from learning overly specific representations and improve model generalization. Furthermore, there has also been research regarding the combination of SA with reinforcement learning (RL) algorithms, where RL is used to optimize specific + +hyperparameters of the SA process [13]. + +When compared to previously proposed methods which take into consideration gradient behaviour, GGA has some key differences. In contrast to gradient surgery algorithms [34, 55] that either mute, aggregate or set gradients to random values, and Fish [47] that approximately optimizes the inner-product between domain gradients, GGA searches for existing parameter space points where gradients of different domains have pairwise small angles. Furthermore, as GGA is applied in the early stages of training and for a limited number of training iterations, the high computational burden of traditional simulated annealing methods is avoided. + +# 3. Methods + +# 3.1. Preliminaries + +Consider a classification problem with $K$ classes. During model training we have access to a data set composed of distinct source data distributions (or domains), $\mathcal{S} = \{D_1, D_2, \ldots, D_{|\mathcal{S}|}\}$ . From each domain $D_i$ , we observe $n_i$ labeled data points, such that $(\boldsymbol{x}_j^{(i)}, y_j^{(i)}) \sim D_i$ for $j = 1, \ldots, n_i$ . Similarly, the test dataset consists of $\mathcal{T} = \left\{D_1^T, D_2^T, \ldots, D_{|\mathcal{T}|}^T\right\}$ unseen target data distributions, from which the model cannot retrieve any information during training. The goal is to learn a single labeling function $h(\boldsymbol{x}; \boldsymbol{\theta})$ , parameterized by $\boldsymbol{\theta}$ , which correctly maps input observations $\boldsymbol{x}_j^{(i)}$ to their labels $y_j^{(i)}$ for both the seen source and the unseen target domains. + +If $\mathcal{L}_i(\pmb {\theta}) = \frac{1}{n_i}\sum_{j = 1}^{n_i}\ell (h(\pmb{x}_j^{(i)};\pmb {\theta}),y_j^{(i)})$ represents the loss associated to the $i$ -th source data domain in the training set, we define the overall cost function $\mathcal{L}(\pmb {\theta}) = \frac{1}{|S|}\sum_{i = 1}^{|S|}\mathcal{L}_i(\pmb {\theta})$ , as the average loss over all available source domains. The function $\ell (\cdot ,\cdot)$ is a classification loss, in our case cross-entropy, that measures the error between the predicted label $\hat{y}$ of an input observation and its true label $y$ . The standard way of model training is Empirical Risk Minimization or ERM which uses the following objective on the training domain data + +$$ +\boldsymbol {\theta} ^ {*} = \arg_ {\boldsymbol {\theta}} \min \frac {1}{| \mathcal {S} |} \sum_ {i = 1} ^ {| \mathcal {S} |} \mathcal {L} _ {i} (\boldsymbol {\theta}) + \lambda R (\boldsymbol {\theta}) \tag {2} +$$ + +where $R(\cdot)$ is a regularization term and $\lambda$ a hyperparameter responsible for controlling the contribution of regularization to the loss, leading to a parameter vector $\pmb{\theta}^{*}$ . In practice, networks trained via ERM have been shown to overfit the data distributions present in the training set. Previous works (such as [47]) have observed that the directions of gradients for different domains during training play a significant role in model generalization. Given source domain losses $\mathcal{L}_i(\pmb{\theta})$ and $\mathcal{L}_j(\pmb{\theta})$ and their corresponding gradients $g_{i} = \nabla_{\pmb{\theta}}\mathcal{L}_{i}(\pmb {\theta})$ , $g_{j} = \nabla_{\pmb{\theta}}\mathcal{L}_{j}(\pmb {\theta})$ , gradient conflicts arise + +![](images/4de039a8df98cdb6bce6d93acd4cb2f8b1937aeca0315adb459c962c5b54ec8b.jpg) +Figure 2. Simplified generative model for multi-domain data. + +when the angle of the gradients grows e.g., above $|\pi /2|$ , or, equivalently, their cosine similarity $\frac{\pmb{g}_i^T\cdot\pmb{g}_j}{\|\pmb{g}_i\| \|\pmb{g}_j\|}$ becomes negative. In the following section, we further explore the role of gradient similarity as an indicator for domain overfitting. + +# 3.2. A Generative Model for Domain Generalization + +To assist with the development and understanding of the proposed method consider the generative model of Figure 2, summarized by the following process: + +$$ +\begin{array}{l} y \sim \operatorname {M u l t i n o u l l i} (p _ {1}, \dots , p _ {K}) \\ d \sim \text {M u l t i n o u l l i} (q _ {1}, \dots , q _ {L}) \\ \boldsymbol {z} _ {y} \sim p _ {y} \\ \boldsymbol {z} _ {d} \sim p _ {d} \\ e \sim p _ {e} \\ \boldsymbol {x} = f \left(\boldsymbol {z} _ {y}, \boldsymbol {z} _ {d}, \boldsymbol {e}\right) \\ \end{array} +$$ + +where $y$ is a variable corresponding to the class, $d$ is a variable corresponding to the domain (with $L = |\mathcal{S}| + |\mathcal{T}|$ ), $\boldsymbol{z}_y$ is a latent multivariate class-specific representation of class $y$ , drawn from an unknown distribution $p_y$ , and $\boldsymbol{z}_d$ is a latent multivariate domain-specific representation of the domain $d$ , drawn from an unknown distribution $p_d$ . Notice that these representations are disentangled, i.e., $\boldsymbol{z}_y$ does not depend on $d$ . The observed sample $\boldsymbol{x}$ , on the other hand, is derived using the function $f(\boldsymbol{z}_y, \boldsymbol{z}_d, \boldsymbol{e})$ that depends on both the class and domain representations, as well as independent nuisance variables, $\boldsymbol{e}$ . + +Without loss of generality, let's assume that we have two source domains $(|\mathcal{S}| = 2)$ and two classes $(K = 2)$ . Then, during model training we sample only from the source domains and use the loss $\mathcal{L} = \alpha_{1}\mathcal{L}_{1} + \alpha_{2}\mathcal{L}_{2}$ , + +$$ +\mathcal {L} _ {i} = - \mathbb {E} _ {d = i} [ \log h (y | \boldsymbol {x}; \boldsymbol {\theta}) ] \tag {3} +$$ + +where $h$ is the probability estimated by our model for class $y$ , $\alpha_{i}$ is the percentage of samples of domain $i$ , and $i = 1,2$ . The expectation is over samples that have been generated + +using the above process when $d = i$ . Each gradient update step depends on the loss gradient + +$$ +\begin{array}{l} \nabla_ {\boldsymbol {\theta}} \mathcal {L} = \alpha_ {1} \nabla_ {\boldsymbol {\theta}} \mathcal {L} _ {1} + \alpha_ {2} \nabla_ {\boldsymbol {\theta}} \mathcal {L} _ {2} \\ = - \alpha_ {1} \mathbb {E} _ {d = 1} \left[ \nabla_ {\boldsymbol {\theta}} \log h (y | \boldsymbol {x}; \boldsymbol {\theta}) \right] \tag {4} \\ - \alpha_ {2} \mathbb {E} _ {d = 2} [ \nabla_ {\boldsymbol {\theta}} \log h (y | \boldsymbol {x}; \boldsymbol {\theta}) ] \\ \end{array} +$$ + +where we have used the linearity of the expectation to obtain the expectation of the derivatives. Notice that the gradient update step depends on $\nabla_{\pmb{\theta}}\log h(y|\pmb{x};\pmb{\theta}) = \nabla_{\pmb{\theta}}\log h(y|f(\pmb{z}_y,\pmb{z}_d,\pmb{e};\pmb{\theta}))$ + +For models that use an internal domain-invariant representation (i.e., a representation that does not depend on $\mathbf{z}_d$ ) it will hold that $h(y|\mathbf{x}) = h(y|f(\mathbf{z}_y,\mathbf{z}_1,\mathbf{e})) = h(y|f(\mathbf{z}_y,\mathbf{z}_2,\mathbf{e}))$ , and therefore $\mathbb{E}_{d=1}[u(h(y|\mathbf{x}))] = \mathbb{E}_{d=2}[u(h(y|\mathbf{x}))]$ for any function $u$ . Thus, both the losses, $\mathcal{L}_i$ and their gradients, $\nabla_\theta \mathcal{L}_i$ , should be equal, in expectation, for different domains $i$ . This observation provides a necessary condition for domain-invariance, which in turn provisions the main motivation for the development of our method, presented in the following section. + +# 3.3. Gradient-Guided Annealing for DG + +The analysis presented in the previous section shows that we can use the agreement of gradients $\nabla \mathcal{L}_i$ as an indicator of domain invariance, since the less the model $h(\cdot |\pmb {\theta})$ depends on the domain $d$ , the more similar the expected value of the gradient, $\mathbb{E}[\nabla \mathcal{L}_d]$ , will be (see Eq. (4)). Inspired by Simulated Annealing [26], we achieve this by adding random noise to the parameters of the model in search for a point with high domain gradient agreement, as measured by the increase of the minimum gradient similarity across any pair of domains, + +$$ +\operatorname {grad} \operatorname {sim} = \min \left(\sum_ {\substack {i = 1, j = 1, \\ i \neq j}} ^ {i \leq | S |, j \leq | S |} \frac {\boldsymbol {g} _ {i} ^ {T} \cdot \boldsymbol {g} _ {j}}{\| \boldsymbol {g} _ {i} \| \| \boldsymbol {g} _ {j} \|}\right) \tag{5} +$$ + +In more detail, as it is common in DG literature, we start with a pre-trained model $f(\cdot ,\theta_0)$ and perform a small number of warmup training steps. This ensures that the model approaches a region of the parameter space that achieves a low loss for the target problem. We then calculate the minimum pairwise gradient similarity among source domains and begin searching the neighborhood of the parameter space for points where both: (a) the domain gradients agree and (b) the loss are reduced2. This is implemented through iterative random perturbations $\pmb{\theta}^{\prime}\gets \pmb {\theta} + \mathcal{U}(-\rho ,\rho)$ , where $\mathcal{U}$ is the multivariate uniform distribution. Each new point + +Algorithm 1 Implementing GGA in training + +Require: Pretrained DNN $h$ with parameters $\theta_0$ , training dataset with domains $S = \{D_i\}_1^{|S|}$ . Loss gradients $g$ . Learning rate $\eta$ , perturbation parameter $\rho$ , optimization step to start the annealing process $A_s$ , optimization step to end the annealing process $A_e$ , number of annealing iterations per optimization step $n_a$ . Total number of training iterations $n$ . + +1: for $t \gets 1$ to $n$ do +2: Sample a mini-batch: $\mathcal{B} \gets \mathcal{B}_{\mathcal{D}_1} + \ldots + \mathcal{B}_{\mathcal{D}_{|S|}}$ +3: if $A_{s} \leq t \leq A_{e}$ then +4: #Begin Gradient-Guided Annealing: +5: Compute the mini-batch loss at starting params: +6: $\mathcal{L}_B\gets \mathcal{L}(\mathcal{B};\pmb {\theta}_t)$ +7: Calculate minimum domain grad pair sim: +8: $\mathrm{sim}\gets \min \Big(\sum_{\substack{i = 1,j = 1,\\ i\neq j}}^{i\leq |\mathcal{S}|,j\leq |\mathcal{S}|}\frac{\pmb{g}_i^T\cdot\pmb{g}_j}{\|\pmb{g}_i\| \|\pmb{g}_j\|}\Big)$ +9: $\pmb{\theta}_{t} \gets \pmb{\theta}_{t-1}$ +10: for step $a\gets 1$ to $n_a$ do +11: $\pmb{\theta}_{a}\gets \pmb{\theta}_{t} + \mathcal{U}(-\rho ,\rho)$ +12: Calculate minimum domain grad pair sim: +13: $\operatorname{sim}_a \gets \min \left( \sum_{\substack{i = 1, j = 1, \\ i \neq j}}^{i \leq |\mathcal{S}|, j \leq |\mathcal{S}|} \frac{\pmb{g}_i^T \cdot \pmb{g}_j}{\|\pmb{g}_i\| \|\pmb{g}_j\|} \right)$ +14: Compute the mini-batch loss at new params: +15: $\mathcal{L}_a\gets \mathcal{L}(\mathcal{B};\pmb {\theta}_a)$ +16: if $(\mathrm{sim}_a > \mathrm{sim})\wedge (\mathcal{L}_a - \mathcal{L}_{\mathcal{B}} < 0.1)$ then +17: $\mathcal{L}_{\mathcal{B}}\gets \mathcal{L}_a,\pmb {\theta}_t\gets \pmb {\theta}_a,\mathrm{sim}\gets \mathrm{sim}_a$ +18: end if +19: end for +20: end if +21: #Update weights: +22: Compute mini-batch loss: $\mathcal{L}_{\mathcal{B}} = \mathcal{L}(\mathcal{B};\pmb{\theta}_t)$ +23: $\pmb{\theta}_{t + 1} = \pmb{\theta}_t - \eta \cdot \nabla \mathcal{L}_{\mathcal{B}}(\mathcal{B};\pmb{\theta}_t)$ +24: $t = t + 1$ +25: end for + +is selected only if it simultaneously achieves higher gradient agreement and lower loss (thus improving the Pareto front). After a fixed number of iterations, the point that has achieved the highest gradient agreement and the lowest loss is selected. This process is repeated after every training iteration step. After a number of optimization steps, we allow the model to be trained without parameter perturbations, following a standard SGD-based procedure, as usual. The GGA algorithm is presented in Algorithm 1. + +Table 1. Comparison of GGA with the ERM baseline. The top out-of-domain accuracies on five domain generalization benchmarks averaged over three trials, are presented. + +
AlgorithmPACSVLCSOfficeHomeTerraIncDomainNetAvg.
ERM85.5±0.277.3±0.466.5±0.346.1±1.843.8±0.363.9
GGA (ours)87.3±0.479.9±0.468.5±0.250.6±0.145.2±0.266.3
+ +Table 2. Comparison with state-of-the-art domain generalization methods. Out-of-domain accuracies on five domain generalization benchmarks are shown. Top performing methods are highlighted in bold while second-best are underlined. The results marked by $\dagger$ , $\ddagger$ are copied from Gulrajani and Lopez-Paz [19] and Wang et al. [52], respectively. For fair comparison, the training of each algorithm combined with GGA, were run on the respective codebases. Average accuracies and standard errors are calculated from three trials for the combination of GGA with past algorithms and from 5 trials for GGA. In green and red, we highlight the performance boost and decrease of applying GGA on top of each algorithm respectively, averaged over three trials. Due to computational resources, for DomainNet we do not combine GGA with previous methods. + +
AlgorithmPACSVLCSOfficeHomeTerraIncAvg.DomainNetTotal
Mixstyle‡[59]85.2±0.3 (+0.3)77.9±0.5 (+0.6)60.4±0.3 (+0.5)44.0±0.7 (+1.1)66.9 (+0.6)34.0±0.160.3
GroupDRO‡[43]84.4±0.8 (+1.4)76.7±0.6 (+0.6)66.0±0.7 (+2.2)43.2±1.1 (+1.5)67.6 (+1.4)33.3±0.260.7
MMD‡[31]84.7±0.5 (+0.8)77.5±0.9 (+1.3)66.3±0.1 (+1.6)42.2±1.6 (+6.3)67.7 (+2.5)23.4±9.558.8
AND-mask [46]84.4±0.9 (+0.1)78.1±0.9 (+0.3)65.6±0.4 (+1.2)44.6±0.3 (-0.4)68.2 (+0.3)37.2±0.662.0
ARM‡[57]85.1±0.4 (+0.5)77.6±0.3 (+0.9)64.8±0.3 (+2.0)45.5±0.3 (+0.8)68.3 (+1.1)35.5±0.261.7
IRM†[1]83.5±0.8 (-1.5)78.5±0.5 (-0.9)64.3±2.2 (-2.1)47.6±0.8 (-3.9)68.5 (-2.1)33.9±2.861.6
MTL‡[6]84.6±0.5 (+0.9)77.2±0.4 (+2.0)66.4±0.5 (+0.4)45.6±1.2 (+0.6)68.5 (+0.9)40.6±0.162.9
VREx†[27]84.9±0.6 (+0.6)78.3±0.2 (+0.1)66.4±0.6 (+1.3)46.4±0.6 (+2.0)69.0 (+1.0)33.6±2.961.9
MLDG†[30]84.9±1.0 (+0.7)77.2±0.4 (+1.3)66.8±0.6 (+1.2)47.7±0.2 (+1.1)69.2 (+1.2)41.2±0.163.6
Mixup†[54]84.6±0.6 (+1.2)77.4±0.6 (+1.8)68.1±0.3 (+1.0)47.9±0.8 (+2.0)69.5 (+1.5)39.2±0.163.4
SagNet†[36]86.3±0.2 (-1.0)77.8±0.5 (+0.9)68.1±0.1 (+0.3)48.6±1.0 (+0.7)70.2 (+0.4)40.3±0.164.2
CORAL†[48]86.2±0.3 (+0.7)78.8±0.6 (-0.4)68.7±0.3 (+0.2)47.6±1.0 (+0.3)70.3 (+0.2)41.5±0.164.5
RSC†[21]85.2±0.9 (+0.1)77.1±0.5 (+0.2)65.5±0.9 (+0.0)46.6±1.0 (+0.2)68.6 (+0.1)38.9±0.562.7
Fish‡[47]85.5±0.3 (+0.1)77.8±0.3 (+0.9)68.6±0.4 (-0.6)45.1±1.3 (+3.8)69.3 (+1.0)42.7±0.263.9
SAM‡[16]85.8±0.2 (+0.6)79.4±0.1 (+0.7)69.6±0.1 (+0.4)43.3±0.7 (+2.6)69.5 (+1.1)44.3±0.064.5
GSAM‡[62]85.9±0.1 (+0.4)79.1±0.2 (+1.0)69.3±0.0 (+0.3)47.0±0.8 (+0.6)70.3 (+0.2)44.6±0.265.1
SAGM‡[52]86.6±0.2 (+0.2)80.0±0.3 (-0.3)70.1±0.2 (-0.6)48.8±0.9 (-0.1)71.4 (-0.2)45.0±0.266.1
GGA (ours)87.3±0.479.9±0.468.5±0.250.6±0.171.745.2±0.266.3
+ +# 4. Experiments + +# 4.1. Experimental setup and implementation details + +In our experiments, we follow the protocol of DomainBed [19] and exhaustively evaluate our algorithm against state-of-the-art algorithms on five DG benchmarks, using the same dataset splits and model selection. For the hyperparameter search space, we follow [10] in order to avoid the high computational burden of DomainBed. The datasets included in the benchmarks are, PACS [29] (9,991 images, 7 classes, and 4 domains), VLCS [15] (10,729 images, 5 classes, and 4 domains), OfficeHome [50] (15,588 images, 65 classes, and 4 domains), TerraIncognita [5] (24,788 images, 10 classes, and 4 domains) and DomainNet [38] (586,575 images, 345 classes, and 6 domains). + +In all experiments, the leave-one-domain-out cross-validation protocol is followed. Specifically, in each run a single domain is left out as the target (test) domain, while the rest of the domains are used for training. The final performance of each algorithm is calculated by averaging the top-1 accuracy on the target domain, with different train-validation splits. For training, we utilize a ResNet-50 [20] pretrained on ImageNet [41] for the backbone feature extractor and ADAM for the optimizer. Regarding GGA, during training we let each algorithm run for several training iterations depending on the dataset and then begin the parameter space search, as described in Section 3. For the neighborhood size in the search process, we set $\rho$ to $0.0005^3$ + +and search for a total of $A = 250$ steps before moving to the next mini-batch of 48 samples from each domain, in each dataset. In all experiments, we perform search iterations for 100 different mini-batches during early training stages. The rest of the hyperparameters, such as learning rate, weight decay and dropout rate, are tuned according to [10] and are presented in Table 3. To account for the variability introduced in the random search of GGA, we repeat the experiments with 5 different seeds for each dataset. All models were trained on a cluster containing $4 \times 40$ GB NVIDIA A100 GPU cards, split into 8 20GB virtual MIG devices and $1 \times 24$ GB NVIDIA RTX A5000 GPU card. + +
HyperparameterPACSVLCSOHTIDN
Learning rate3e-51e-51e-51e-53e-5
Dropout0.50.50.50.50.5
Weight decay1e-41e-41e-41e-41e-4
Training Steps500050005000500015000
ρ5e-55e-55e-55e-55e-5
GGA Start-End100-150, 1500-1550100-200100-200500-600100-200
+ +Table 3. Hyperparameters for DG experiments. OH, TI and DN stand for OfficeHome, TerraIncognita and DomainNet respectively. $\rho$ is the parameter space search used during the annealing steps in GGA, while the last row indicates the training iterations during which GGA occurs. + +# 4.2. Comparative Evaluation + +The average OOD performances of the baseline vanilla ERM [49] and state-of-the-art DG methods on a total of 5 DG benchmarks, are reported in Tables 1 and 2 respectively. The results for each separate domain in each benchmark are reported in the Appendix. In the experiments, we apply GGA on-top of the rest of the DG algorithms and show that its properties generalize to other methods as well, boosting their overall performance. It should also be noted that GGA can be adapted to training scenarios where distributions shifts are present in training data. + +Initially, to validate whether the application of GGA in the early stages of model training leads to models with increased generalizability, we compare the results with the vanilla ERM baseline. As presented in Table 1, GGA is able to boost the performance of the baseline model by an average of $2.4\%$ on all benchmarks, demonstrating the efficacy of the proposed algorithm. For further evaluation, we also compare GGA with state-of-the-art DG methods [1, 6, 16, 18, 21, 27, 30, 31, 36, 43, 46-49, 52, 54, 57, 59, 62], before applying GGA to them as well. We note that we only include previous works that have implemented a ResNet-50 as the backbone encoder and do not use additional components or ensembles. In Table 2 we differentiate between the methods that operate on model gradients [16, 21, 47, 52, 62] and the rest of the algorithms. Even without its application + +to other methods, GGA is able to surpass most of the previously proposed algorithms, while also setting the state-of-the-art on PACS $(+0.7\%)$ and on the challenging TerraIncognita $(+1.8)$ dataset, while remaining competitive in the other two. What's more important is that the application of GGA in conjunction with the rest of the DG methods, proves beneficial and ultimately boosts their overall performance in almost each case by an average of around $1\%$ and in some cases up to even $6.3\%$ . With regards to IRM, which seems to be significantly impacted negatively by the application of GGA, its learning objective emphasizes on simultaneously minimizing the training loss of each source domain and not necessarily on the pairwise agreement of gradients among domains. It is therefore not able to converge to a good solution after the initial model's weights have been perturbed during training. + +From the experimental results, it is evident that the application of GGA and its search for parameter values where gradients align between domains is beneficial to model training. By introducing the proposed annealing step before the final stages of training, the majority of the models exceed their previous performance and exhibit improved generalization capabilities. + +# 4.3. Evaluating the impact of GGA on gradient disagreement + +As discussed in Section 3, when a training dataset is composed as a mixture of multiple domains, conflicting gradients between mini-batches drawn from each domain lead to models that do not infer based on domain-invariant features and which generalize to previously unseen data samples, but are hindered by domain-specific, spurious correlations. This is evident in the case of vanilla models trained via ERM where the average gradient similarity among domains continues to remain low upon reaching a local minima. Our hypothesis is that this behavior can be avoided by searching for a parameter set of common agreement between domains before optimizing via gradient descent. + +To demonstrate the operation of the proposed algorithm in practice against ERM, we calculate the average gradient cosine similarity between mini-batches from source domains during training for the VLCS dataset, along with the training loss in each iteration. As a result, each sub-figure in Figure 3 illustrates the progression of the training gradient alignment between domains, against the total training loss. + +As expected, in the very initial iterations the gradients of the pretrained model parameters point towards a common direction. However, in the case of ERM as training progresses and the loss is minimized, the domain gradients begin to disagree leading the model to converge to undesirable minima that do not generalize across domains. On the other hand, when GGA is applied the model searches for parameters such that gradients are aligned before continuing + +![](images/746cb623730640422d7e211f6de9bda9c757f74eb0c4f31efe156a54d414f04e.jpg) +Figure 3. Impact of GGA on gradient alignment during model training on the VLCS dataset. As illustrated, in the case of vanilla ERM, even though the training loss is minimized, the average cosine similarity among domain gradients remains low. In the case of GGA however, after the algorithm searches for points in the parameter space with increased gradient similarity, the gradients continue to agree during training, while the total training loss is also minimized. + +![](images/995c87b933a61e8fe7b925d0c2443310fef1c210f1788a09ce08e0f9d72b0aa3.jpg) + +![](images/afff18687fb6a9e2b1707543add04ea7c6d86256a5b30c8da7f25f900b744abf.jpg) + +![](images/2cf0954534f2cbfd205940a97e672f1885137404dc6786f41b2a6c8f3a9551da.jpg) + +![](images/16ba24d143aa7e27cfd84683cd67669806a27ce26fc1f413356266832cd18852.jpg) +Figure 4. Sensitivity analysis of the parameter space search magnitude $\rho$ and the training stage application of GGA. The analysis on PACS reveals smaller weight perturbations and gradient annealing during early training iterations lead to increased model performance. + +![](images/f02c1ed49f64fcfa23016d702e59d5738f0b69be37bb5b39cd512f3f9132945f.jpg) + +training. This is illustrated by the spike in gradient similarity, during iterations 100 up to 200. After GGA concludes, we observe that the model continues training by descending into minima where gradients agree among domains. + +# 4.4. Sensitivity Analysis + +The two core parameters of GGA, are the size of the parameter search $\rho$ and the moment of our methods implementation during training, i.e., during the early, mid or late training stages. To justify their selection, we conduct a sensitivity analysis (Fig. 4) by varying one of the above parameters while fixing the other at its optimal value. + +Regarding the magnitude of weight perturbations during the application of GGA, we found that the optimal value was $\rho = 5e - 5$ . As illustrated in Figure 4, a larger magnitude of perturbation led to decreased model performance. Intuitively, the application of larger noise to the model parameters leads to sets that are not close to the solution, making it increasingly difficult for the model to converge. On the other hand, smaller perturbations seem to have little to no effect on training, as the search is limited to spaces near the current parameters, which is why the model performance falls back close to that of ERM. With regards to the stage of training during which GGA will be applied, we found that the models yielded better performance when the search was initialized in earlier stages. We hypothesize that + +applying perturbations near the end of training displaces the model from a local optimum, requiring additional iterations to converge. + +# 5. Conclusions + +In this work, we investigated gradient conflicts in the context of domain generalization, leading to the development of GGA; a simple yet effective algorithm that identifies points in the parameter space where domain gradients align early in training before continuing optimization, ultimately enhancing model generalization. Through a comprehensive comparative analysis we have demonstrated the efficacy of GGA, which is able to achieve superior generalization capabilities in standard DG benchmarks and outperform SoTA baselines. What's more, as GGA is both model and method agnostic it can also be utilized by other algorithms. Interestingly, its combination with previous methods proves beneficial, as their majority yields improved performance over all benchmarks. Finally, we validate the impact of our algorithm on gradient alignment through additional experiments, showing that, unlike the baseline, domain gradients align during training. + +However, our method does not come without some key limitations. First of all, the annealing steps and gradient similarity computation add computational overhead. Furthermore, GGA relies on domain labels, making it inapplicable to single-source DG, where domain labels are not available during training. Its effectiveness is also batch-size dependent, as larger batches provide further information regarding gradient alignment and can lead to improved results. Future work will further explore gradient alignment in multi-domain settings and refine GGA to make annealing steps adaptive rather than random. + +Acknowledgement. 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Grenoble Alpes, CEA, List, F-38000 Grenoble, France. 2Prophesee, Paris, France. + +{manon.dampfhoffer, thomas.mesquida}@cea.fr cposch@propthesee.ai + +# Abstract + +Event-based cameras asynchronously detect changes in light intensity with high temporal resolution, making them a promising alternative to RGB camera for low-latency and low-power optical flow estimation. However, state-of-the-art convolutional neural network methods create frames from the event stream, therefore losing the opportunity to exploit events for both sparse computations and low-latency prediction. On the other hand, asynchronous event graph methods could leverage both, but at the cost of avoiding any form of time accumulation, which limits the prediction accuracy. In this paper, we propose to break this accuracy-latency trade-off with a novel architecture combining an asynchronous accumulation-free event branch and a periodic aggregation branch. The periodic branch performs feature aggregations on the event graphs of past data to extract global context information, which improves accuracy without introducing any latency. The solution could predict optical flow per event with a latency of tens of microseconds on asynchronous hardware, which represents a gain of three orders of magnitude with respect to state-of-the-art frame-based methods, with 48x less operations per second. We show that the solution can detect rapid motion changes faster than a periodic output. This work proposes, for the first time, an effective solution for ultra low-latency and low-power optical flow prediction from event cameras. + +# 1. Introduction + +Optical flow is the apparent relative motion of objects and surfaces in a scene (which could come from the motion of an object or from the observer itself) and is used in many downstream computer vision tasks, such as video stabilization [35], virtual reality [25], navigation [36] and obstacle avoidance [32]. Using an RGB camera, it can be measured as the pixel's displacement between two consecutive + +![](images/3ba1c03efbdb6393ee8d0d9bf89c3f58e200b294cb44fe8a03954ebc76b945ed.jpg) +Figure 1. Ultra-low latency optical flow prediction with asynchronous event graph neural networks and periodic aggregator. + +frames. However, the latency of the optical flow prediction is limited, both by the frame rate of the sensor and the computational time of the prediction algorithm. Therefore, rapid motion changes cannot be detected during this blind time, which can be critical in some real-time applications such as navigation [12]. The latency of the sensor can be decreased by increasing the frame rate, which comes at a high computational cost and can cause bandwidth problems. + +Event cameras are a promising alternative to RGB cameras in this context [11]. The pixels of event cameras function asynchronously and produce an event whenever a change in the light intensity is detected, at a temporal resolution of microseconds [17]. Therefore, they are particularly adapted for detecting fast motion changes with low latency. However, state-of-the-art convolutional neural networks (CNN) cannot handle the asynchronous flow of events and construct frames from events [7, 9, 13, 20, 21, 24, 30, 33, 38], loosing the opportunity to exploit the event information at low latency. Moreover, state-of-the-art methods are computationally-expensive [13, 20], limiting real-time implementation on embedded hardware with constrained resources. + +Therefore, the concept of event graphs (based on Graph + +Neural Networks - GNN) has emerged as a solution [5]. Events are represented in a continuously evolving graph, asynchronously triggering graph convolutions at the arrival of new events, that can allow event-level predictions at ultra-low latency [6, 12, 26]. This has motivated the creation of new asynchronous hardware to support these implementations [14, 34]. Moreover, by constraining edges of the graphs to be directed, from past-to-future only (preventing backward connections), the HUGNet approach [6] removes the additional latency of graph update for each new events, allowing ultra-low latency graph building. However, the latency constraint also prevents from using any form of accumulations in the GNN (e.g. pooling layers or normalizations on future data). This limits the aggregation of global context information, which is important for understanding the scene dynamics, and hence severely impacts the accuracy of the prediction. + +In this paper, we propose to break this accuracy-latency trade-off and leverage both asynchronous event graphs and periodic temporal accumulations. We propose a novel neural network architecture combining an accumulation-free asynchronous event branch and a periodic aggregation branch performing feature aggregations on the event graphs of past data. Therefore, the periodic branch can extract global context information, improving the accuracy of optical flow estimation, without increasing the prediction latency compared to the event branch alone. However, the periodic branch, only having access to past data, cannot accurately detect fast motion changes, and hence merging the periodic outputs with the event branch outputs is crucial. The proposed method could predict optical flow from event cameras with a total latency in the order of 10s of $\mu s$ in asynchronous hardware such as [34], while a standard frame-based approach would have a latency in the order of 10s of ms (Fig. 1). We further study if this reduction in the prediction latency also translates into a more accurate prediction of fast-changing optical flow. We show that, depending on the speed of change and the aggregation period of the periodic branch, the event prediction can outperform the periodic prediction at low latency by up to $59\%$ . + +Our contributions can be summarized as follows: + +- We propose a new version of the HUGNet [6] event graph, HUGNet2, entirely accumulation-free, and hence compatible with ultra low-latency per event prediction. +- We introduce a new architecture combining HUGNet2 with a Periodic Aggregator (PA), HUGNet2+PA, which largely improves the overall prediction accuracy compared to HUGNet2 alone, while introducing no latency. +- Our architecture can effectively leverage the most recent events in the event branch to detect a rapid motion change faster than a periodic output, and outperforms the state-of-the-art on the challenging Rock Scenes dataset [6]. +- The latency of our method is reduced by 3 orders of mag + +nitude compared to the state-of-the-art (from 10s of ms to 10s of $\mu$ s on asynchronous hardware), while also reducing number of operations (up to $48\mathrm{x}$ ) and parameters. + +# 2. Related Works + +Event-based Optical Flow Estimation. Moving edges are locally described in event data streams as 3D structures that can be analytically estimated online [3] or optimized offline using contrast maximization techniques [28, 29]. Assuming a constant speed, events can be grouped into features tracked over time that enable local motion estimations [18, 27]. Motion descriptors can also be extracted out of events using bio-inspired spiking handcrafted patterns [22]. However, all these techniques suffer from poor performance when the event stream is complex due to noise or textured objects. Inspired by image-based optical flow estimation, neural network methods create event frames, by counting events in each pixel during a certain temporal window, that can be processed by CNNs [7, 9, 13, 20, 21, 24, 30, 33, 38]. In addition, EV-FlowNet [38] use the last event timestamp in another input channel. STE-Flow [9] propose to adapt the event frame rate to the event density (i.e. each frame contains the same number of events), which allows a more accurate representation of high speed motions. ADM-Flow [20] introduce a learnable adaptive density module which can compensate for heterogeneous event density between event frames. Furthermore, Spiking Neural Networks [16, 31] have been proposed, as spiking computations can also be realized in an event-based manner on asynchronous hardware. + +Event Graph Neural Networks. Frame-based representations discard the precise temporal resolution of the event and can neither fully exploit the sparsity of events for sparse computations, nor the low latency of event cameras for low latency prediction. In order to overcome these issues, recent methods have proposed to represent event data as a graph, each event being represented as a node with connectivity according to spatio-temporal proximity, that can be processed by a GNN, for object classification [4, 8, 26, 34], object detection [12, 26], motion segmentation [23], or optical flow estimation [6]. Notably, event graphs can also predict at the node-level (i.e. event-level), which can be exploited in dense tasks such as optical flow estimation. Indeed, a prediction per event could allow to estimate locally the optical flow at low latency. However, fully leveraging this low-latency opportunity requires to impose constraints on the event graph operations. Indeed, when an event arrives, all the elements required for computing its output must be already available (without waiting), such that only the time of performing the graph convolution is required, which can be realized in microseconds [34]. In this context, [6] proposes the Hemi-spherical Update Graph method (HUGNet). At each new event, + +edges are constructed only on a hemi-spherical neighborhood of past events (i.e. the graph is directed, with past-to-future connections only), which reduces the latency of graph update to zero. However, current event graph methods [4, 6, 8, 23, 26, 34], use operations in the GNN relying on future data (e.g. pooling layers, graph-level normalization with on-the-fly statistics, or normal vectors across past and future events), that limits the latency of event-level prediction. Notably, [12] converts all GNN operations to an event-based version, showing for the first time a low-latency solution for an object detection application. In particular, they propose an event graph pooling that can be made asynchronous by keeping only directed edges of pooled nodes, but at the cost of severe accuracy degradation compared to a standard event graph pooling. + +# 3. Methods + +# 3.1. Event Graph and Periodic Aggregator + +We describe the proposed architecture composed of an asynchronous event-based branch and a periodic branch (Fig. 2). The event branch contains the graph building, a GNN (used as a feature extractor for both event and periodic branches), and an Event head. In the event branch, the computations are asynchronously triggered as events arrive, which allow sparse computations (proportional to the number of events), and ultra low-latency per event prediction. The periodic branch operates in parallel of the event branch and is composed of a PA module and a Periodic head that periodically outputs dense optical flow prediction. Note that the method only use event data (no images). + +# 3.1.1.Event Branch + +Events are output asynchronously from event cameras as $(x,y,t,p)$ features, corresponding to $x$ and $y$ pixel coordinates, the timestamp $t$ of the emission of the event, and its polarity $p$ (positive or negative, if the event corresponded to an increase or decrease of light intensity). A graph is represented as $\mathcal{G} = (\mathcal{V},\mathcal{E})$ , with $\mathcal{V}$ being a set of vertices, and $\mathcal{E}$ a set of edges. The vertices (and edges) are associated with features, on which GNN layers are applied to compute output features. In an event graph, events are represented as vertices, and edges are formed between events based on spatio-temporal proximity, commonly using a k Nearest Neighbors search (a node is connected to its $k$ closest nodes in the spatio-temporal 3D space) [6, 12, 34]. For enabling ultra-low latency prediction, we adopt the HUGNet [6] graph building, which constrains edges to be past-to-future directed, i.e. on recent past events only (that are already in memory). This means that the k Nearest Neighbors search is constrained to the hemi-spherical space around the event in $(-r_{xy}, + r_{xy})$ for $(x,y)$ coordinates and $(-r_t,0)$ for $t$ , $r_{xy}$ being the pixel radius and $r_t$ the temporal radius. + +For the GNN, we propose an improved version of HUGNet [6], called HUGNet2, that is compatible with low latency prediction. Indeed, as event graphs are highly heterogeneous, using instance normalization with on-the-fly statistics greatly improves the accuracy. However, this requires processing the graph over the entire sequence before any prediction can be made. Moreover, HUGNet uses normal vectors computed on a 3D neighborhood (including future events) around the event, which would also add latency. Therefore, HUGNet2 does not use neither normalization nor normal vectors. In addition, HUGNet2 replaces the SplineConv [10] in the first GNN layer, by a PointTransformerConv [37], which slightly improves the accuracy while reducing the number of parameters. + +GNN and PA outputs are merged in the Event branch. However, the PA output for the period T can only be available with a delay of 2 periods (Fig. 2c). Indeed, the computation can only start after the end of the accumulation period, and the PA module can take up to another frame to be computed (not more to allow real-time processing, but not less to reduce power consumption). That is why, in order to introduce no latency to the event branch, the merge is done with PA output immediately available when the event arrives (therefore corresponding to past events with a delay of 2 periods). In particular, the merge uses the output features of the event (computed in the GNN) and the PA(T-2) features in the pixel location of the event. + +The merged features are fed to the Event head, which predicts per event optical flow. This temporal shift may degrade the accuracy of the event prediction for fast motions. However, we will show that the Event head can leverage the event-level information contained in the GNN output features to faster detect motion changes. Note that, for training on a GPU, the graphs are built in advance and GNN layers are computed on an entire graph in parallel. However, on asynchronous hardware, the graph building and Event branch will be computed on-the-fly as events arrive (following the computation flow described in Fig. 2b). + +# 3.1.2. Periodic Branch + +The event branch has no pooling layers (which would require temporal accumulation and hence would introduce latency in the event computation flow) and therefore has a limited field of view. The goal of the periodic branch is to perform broader spatio-temporal aggregation of features allowing a better understanding of the global scene. Therefore, the PA module accumulates the output features of the GNN during a certain period, on which a spatio-temporal pooling operation is performed. This means that the pooling operation is performed on the features of the events accumulated during the period for each spatial location (temporal and spatial resolutions can be adjusted). The pooled features are processed by the PA module, composed of convolutional and recurrent layers to perform the spatio-temporal + +![](images/1b1bc00568674df953e662e86446f6589da4bf81dd58b4198c9a88cf79cc472e.jpg) +Figure 2. (a) Proposed architecture (HUGNet2+PA) combining event branch and periodic branch. (b) Computation flow of the event branch, performed asynchronously at each event. (c) Interactions between events and periodic branch. The event branch takes outputs of the periodic branch computed on past events (from period T-2 for events in period T) that are immediately available (no latency). + +![](images/736f948860318cfd3753b3a9b9de40010d9a229e61df5e6b7e7023fe20b633c8.jpg) + +![](images/36678198c48952fef0bc2b83bed696aa7034a9192d28c23c20e9970e42542d57.jpg) + +aggregation. The PA outputs are upsampled with bilinear interpolation in order to get back to the original pixel resolution, and then processed by the Periodic head. The Periodic head outputs Periodic predictions of dense optical flow (on every pixel location). + +# 3.2. Event Optical Flow Datasets + +MVSEC. The Multi Vehicle Stereo Event Camera dataset (MVSEC) [38, 39] includes indoor scenes from a flying drone and outdoor driving scenes, with $346 \times 260$ pixels resolution and groundtruth optical flow labels at $20 \mathrm{~Hz}$ . As the most common procedure [9, 13], we train the model on the outdoor_day2 sequence (which lasts about 610 seconds), and evaluate the model on the outdoor_day1 (240s) and indoor_flying sequences 1, 2 and 3 (240s). However, MVSEC scenes only contain slow and smooth motions, with a groundtruth at low frequency, and hence is not challenging enough the ability to detect fast motion changes. + +Rock Scenes. Rock Scenes [6] is a synthetic dataset specifically designed for evaluating very fast motion detection. Rock Scenes data feature record cover art images moving in front of a textured background, both having an uncorrelated movement with random sharp direction changes, with groundtruth optical flow at high resolution (500 Hz) and 100x100 pixel resolution. In particular, the motion changes (direction and speed) occur in one groundtruth timestep, i.e. 2 ms. The motion changes be + +ing easy to localize in the sequences, we can observe the latency of the method detect them. The sequences last between 2 and 6 seconds, with one hundred sequences for the train split (ten objects combined with ten scenes) and four sequences for the test split (two unseen objects objects combined with 2 unseen scenes). + +Data pre-processing. Event graph methods construct graphs on the raw events. However, constructing and processing graphs with large number of events is slow on GPU (which are not optimized for graph processing, contrary to the asynchronous hardware implementation that this method is targeting). Moreover event streams may contain a lot of redundant information. Therefore, following HUGNet [6], the datasets are filtered with a spatiotemporal contrast filter available in state-of-the-art event-cameras [1, 2]. In addition, MVSEC outdoor sequences are downsampled with a factor of 3 such that they have a similar event density as the indoor sequences. The event graphs are built for full sequences and then chopped into smaller sequences of $400\mathrm{ms}$ and $800\mathrm{ms}$ (with overlap of $200\mathrm{ms}$ ), for Rock Scenes and MVSEC respectively. + +# 3.3. Training and Evaluation Procedure + +Architecture details. For the graph building, the k Nearest Neighbor search is performed on a hemi-sphere with radius $r_{xy} = 8$ and 9 pixels, and $r_t = 80$ and 90ms, for MVSEC and Rock Scenes respectively, with $k = 32$ neighbors per node. + +We use the pixel coordinates and polarity as node input features (not including timestamp, as the absolute time should not influence the optical flow prediction and may lead to overfitting). HUGNet2 is composed of a PointTransformerConv [37] layer followed by 4 GCNConv [15] layers, each with 32 output features. Note that PointTransformerConv is more costly than GCNConv (which simply performs mean aggregations of the projected features of the neighbors), and hence is only used in the first layer where the input size is small. The output of the 5 layers are concatenated and fed to a fully connected layers of output size 64. The periodic branch then performs a feature-wise max pooling on the 64 output features of the GNN, in a pixel grid of 1/4th the spatial resolution of the original one in each dimension (the temporal resolution corresponds to the PA rate and is a parameter of study). The PA module is composed of a 2D convolutional layer (stride 2, 3x3 kernel, 64 channels), a SepConvGRU layer as in E-RAFT [13] (2D recurrent convolutions with 1x5 kernel performed first horizontally then vertically) with 64 output channels, and a 2D convolutional layer (3x3 kernel, 128 channels). The merge in the event branch simply concatenates the 64 GNN output features of a node with the 128 PA(T-2) output features at the same pixel coordinates. The Event and Periodic head are composed of fully connected layers (192-128-64-2 and 128-2, respectively), on each event (each pixel, respectively). + +Training details. AdamW [19] optimizer is used with batch size of 1, with learning rate starting at 5e-4 and divided by 2 if no relative change of 0.05 in the loss is observed during 10 epochs. The model is trained in a supervised manner using a smooth-L1-loss (as in HUGNet [6]) for both Event predictions and Periodic predictions. Data augmentation is used: random horizontal and vertical flips, temporal stretching with a factor between 0.5 and 1.5, random rotations from 0 to 360 degrees, and edge dropout (removing edges of the graph) with probability 0.25. In addition for MVSEC, random cropping of size $256 \times 256$ is used. As instance normalization with on-the-fly statistics could not be computed at low latency, it is only used as a warm-up for 100 epochs, and then removed while the models are fine-tuned for 100 more epochs. Experiments are performed on a NVIDIA A100 GPU with 40GB memory. + +Evaluation metrics. The Endpoint Error is defined as the L2-norm of the difference of the predicted vs. groundtruth optical flow [6, 13, 20, 38]. We evaluate the Sparse Endpoint Error (i.e. on pixels where there is at least an event) for both Event prediction (selecting the last event per groundtruth voxel) and Periodic prediction (upsampling or downsampling the prediction to match the groundtruth rate). In frame-based methods, the number of operations per second is fixed (number of operations per frames x frame rate). In event graph methods, the number of operations per event is fixed, but the number of events + +varies with time, therefore we use the average event density. The proposed architecture has both operations per event and fixed operations per period, in the event and periodic branches, respectively. The latency of our method on dedicated asynchronous hardware is estimated based on the FPGA implementation for event graph building and processing from [34], reporting a latency of $16\mu s$ per event. We estimate our latency at $\approx 50~\mu s$ considering that our graph building is similar and our number of operations per event in the GNN is $3x$ higher than theirs (and so the latency will be increased proportionally, given similar hardware resources and configuration). We estimate the latency of HUGNet [6] superior to $400~\mathrm{ms}$ as the method uses normalization with graph-level statistics, and hence the prediction cannot be made before the end of the sequence (400 ms in their experiments). The latency of frame-based methods is estimated to be in between 1 to 2 groundtruth frames, depending on the speed of the computation, similar to our periodic prediction (as explained previously in Fig. 2c). + +# 4. Results + +# 4.1. Comparison with State-of-the-Arts + +We benchmark the proposed approach in terms of accuracy and hardware efficiency metrics (number of parameters, operations and latency) against state-of-the-art methods on MVSEC (Table 1) and Rock Scenes (Table 2) datasets. We evaluate our proposed HUGNet2 alone, and the proposed combined architecture HUGNet2+PA with different period rates. Note that we provide the Endpoint Error of the low-latency Event prediction (and not of the Periodic prediction). On both datasets, HUGNet2 has a lower accuracy than HUGNet, but is also smaller (both in parameters and operations), and its latency is decreased by 4 orders of magnitude. Moreover, the proposed HUGNet2+PA outperforms both HUGNet2 and HUGNet with a moderate increase in the number of operations. We observe that the higher the PA frequency, the higher the accuracy, up to a certain point where the accuracy is no longer improved. This point depends on the dataset and the speed of change of optical flow with time. The rate corresponding to the groundtruth rate for MVSEC $(\mathrm{PA}_{20})$ , and to $1/5\mathrm{th}$ of the groundtruth rate for Rock Scenes $(\mathrm{PA}_{100})$ leads to the highest accuracy. On MVSEC, the proposed approach yields lower accuracy than state-of-the-art frame-based methods, however with a significant reduction in computational complexity and parameters memory (48x less operations per second and 17x less parameters than the state-of-the-art ADMFlow [20]). More importantly, we are the first to propose a solution for ultralow latency, with 3 orders of magnitude reduction (from 10s of ms to 10s of $\mu\mathrm{s}$ ) compared to previous methods. There is no state-of-the-art CNN methods on Rock Scenes, therefore we train ADMFlow [20] (at $20\mathrm{Hz}$ ), the state-of-the-art + +
PaperTypeEndpoint ErrorParametersOPs/eventOPs/frameOPs/sLatencyb
EV-FlowNet [38]CNN0.96c14.1 M-5.4 G107.0 G50-100 ms
Stoffregen et al. [30]CNN0.64dn.a.-n.a.n.a.50-100 ms
FireFlowNet [24]CNN1.220.06 M-5.1 G102.8 G50-100 ms
E-RAFT [13]CNN0.625.3 M-47.4 G948.8 G50-100 ms
STE-FlowNet [9]CNN0.56n.a.-n.a.n.a.50-100 ms
DCEIFlow [33]CNN0.51dn.a.-n.a.n.a.50-100 ms
ADMFlow [9]CNN0.49d7.0 M-47.5 G950.2 G50-100 ms
Spike-FlowNet [16]SNN0.79c14.1 M-4.4 G88.2 G50-100 ms
SdformerFlow [31]SNN0.85d54.9 M-9.1 G181.9 G50-100 ms
HUGNet [6]GNN1.72a0.14 M0.22 M-17.1 G>400 ms
HUGNet2GNN1.890.07 M0.18 M-13.7 G≈50 μs
HUGNet2+PA5GNN + CNN1.710.41 M0.16 M0.38 G14.1 G≈50 μs
HUGNet2+PA10GNN + CNN1.570.41 M0.16 M0.38 G16.0 G≈50 μs
HUGNet2+PA20GNN + CNN1.520.41 M0.16 M0.38 G19.8 G≈50 μs
+ +Table 1. Optical flow on MVSEC dataset (groundtruth at ${20}\mathrm{{Hz}},{76}\mathrm{k}$ event/s). ${}^{a}$ Our implementation. ${}^{b}$ See Section 3.3 for details. ${}^{c}$ Trained with self-supervised loss. ${}^{d}$ Trained on synthetic data. + +
PaperTypeEndpoint ErrorParametersOPs/eventOPs/frameOPs/sLatencyb
ADMFlow [20] (20 Hz)CNN0.048a7.0 M-12.5 G250 G50-100 ms
HUGNet [6]GNN0.037a0.14 M0.22 M-3.6 G>400 ms
HUGNet2GNN0.0660.07 M0.18 M-2.9 G≈50 μs
HUGNet2+PA20GNN + CNN0.0400.41 M0.16 M63 M3.8 G≈50 μs
HUGNet2+PA50GNN + CNN0.0330.41 M0.16 M63 M5.7 G≈50 μs
HUGNet2+PA100GNN + CNN0.0300.41 M0.16 M63 M8.8 G≈50 μs
+ +Table 2. Results on Rock Scenes dataset (groundtruth at ${500}\mathrm{{Hz}}$ ,16k event/s). ${}^{a}$ Our implementation. ${}^{b}$ See Section 3.3 for details. + +method on MVSEC, on Rock Scenes, using the open source code. Notably, our method outperforms ADMFlow on this dataset, while being more efficient. + +# 4.2. Low-latency Periodic vs. Event Predictions + +We analyse the ability of the method to detect fast motion changes, and its dependence on application-related and method-related factors. In particular, we study whether the use of recent event information from the GNN and past context information from the PA can be effectively merged, such that the Event head can predict a more accurate output while improving the latency of detection of fast motion changes. Therefore, we compare the Event prediction (based on the output of the GNN and PA(T-2)) for events in period T (Event), with the Periodic prediction for events in period T-2 (Periodic(T-2)), both being available without overhead in latency (in period T, Periodic(T-2) has been already computed). Event prediction is supposed to be available instantaneously here because its latency $(50\mu s)$ is very small compared to a groundtruth timestep $(2\mathrm{ms})$ + +Accuracy vs. number of operations. We evaluate + +the two predictions in average accuracy compared with the number of operations per second, depending on PA rate (Fig 3). Note that we compare both outputs on the Sparse Endpoint Error metric, because the Event prediction is only sparse. We also provide the respective number of operations per second per branch (Event vs. Periodic) to show their dependence on the application. Indeed, event density is higher in MVSEC, inducing more operations in the event branch, but the PA rate is smaller, decreasing the number of operations in the periodic branch, while it is the opposite in Rock Scenes. We observe a consistent error decrease (up to $59\%$ ) in the Event prediction compared to Periodic(T-2) prediction. This means that the Event head can effectively merge both types of features (GNN and PA(T-2)) and leverage the recent information contains in Event from the GNN, to improve the prediction compared to Periodic(T-2) (only using PA(T-2)). Notably, the Event prediction with low PA rate $(20 / 5\mathrm{Hz}$ for Rock Scenes / MVSEC respectively) matches the accuracy of the Periodic(T-2) prediction with high PA rate $(100 / 20\mathrm{Hz}$ respectively), while reducing the number of operations by $56\%$ / $29\%$ respectively. Moreover, the + +![](images/4fd6ac330506f4f82299d01d8f7edf581e257de48ad4973e51ca4b6f42fb45f5.jpg) +Figure 3. Endpoint Error vs. operations per seconds for the low-latency predictions (Event and Periodic(T-2)) with different PA rates for (a) Rock Scenes and (b) MVSEC. Operations per second per branch with different PA rates for (c) Rock Scenes and (d) MVSEC. + +![](images/d676b00ba508a644b7d68794409a6b27a7834f8f07a52917fa6f78a2ff630c5f.jpg) + +![](images/1d60f0ef87e33fd5631df881726028f0d18147a94c8b45e3f233a0f97b5629cb.jpg) + +![](images/7ea629d34ab6c8a3a15bb48351444ac3513e381db013ceb46639d05af303a727.jpg) + +lower the PA rate, the higher the accuracy of Event compared to Periodic(T-2) prediction, as the more Periodic(T-2) is impacted by the 2 periods delay. Moreover, the gain is higher on Rock Scenes than MVSEC, because very fast motion changes occur (in one groundtruth frame, which is at $500\mathrm{Hz}$ ), while changes in MVSEC are much smoother. + +Latency of detection of fast motion changes. We use the Rock Scenes dataset to evaluate more specifically the ability of the Event prediction to detect when a motion change occurs. Indeed, the optical flow changes are clearly visible and abrupt (in one groundtruth timestep), therefore it is ideal to observe the reaction time of the different predictions. We show the error of Event and Periodic(T-2) predictions with time for HUGNet2+PA $_{20}$ in Fig 4, with marks indicating the precise moments of optical flow change. In addition, visualisations of the corresponding optical flow predictions and groundtruth with time are provided. We can clearly see the impact of the delay on Periodic(T-2): a motion change can be detected with a minimum of 1 to 2 frames delay (depending on whether the change occurred at the beginning or end of the frame), meaning 50 to 100 ms for the PA at 20Hz, sometimes longer. On the other hand, the Event prediction error also increases at the moment of the motion change, but then decreases faster than the Periodic prediction. Interestingly, we observe that the error of Event and Periodic branches are similar most of the time, except after a motion change. This means that the Event head can leverage GNN features on recent events to differentiate from the Periodic branch outputs when there is enough evidence that the optical flow has changed and is not yet visible in PA(T-2). However, the Event prediction takes some time to correct the optical flow prediction, which is due to accumulating enough events to be able to characterize precisely the new optical flow. In particular, we observe that, after a motion change, the Event head predicts a decrease in optical flow magnitude and then an increase in the corrected direction (which would better correspond to a real-life situation, while in the dataset, the change is instantaneous). + +Comparison with ADMFlow [20]. The evolution of sparse Endpoint Error with time of the ADMFlow [20] prediction (our implementation, at $20\mathrm{Hz}$ ) at T and T-2 is compared with our Event prediction in Fig. 5. Just after a change, ADMFlow(T) is better than Event, because it has access to the event data in the frame that occurred after the change. However, using ADMFlow(T-2) prediction, we observe the lag after a change (as our Periodic(T-2)). On average, our Event prediction is better than both ADMFlow(T) and ADMFlow(T-2). We hypothesize that this is partly due to the extreme data sparsity in Rock Scenes (1.6 event/pixel/s). While ADMFlow is designed to take only 2 event aggregation periods as inputs for the prediction, our recurrent PA module functions over the entire sequence. Hence out method can accumulate information in longer periods, which improves the prediction accuracy when the motion is constant for a while. Nevertheless, the inherent limitation of frame-based methods remains valid: the lag between the emission of the event and the moment when the prediction is available impacts the latency of detection of fast motion changes. + +# 4.3. Discussion + +Our method addresses the multi-factorial trade-off between accuracy, latency and computational cost, which are impacted by many aspects. For instance, the larger the difference between the speed of motions to detect and the periodic aggregation rate, the larger the benefit of our approach leveraging events compared to a periodic output. Therefore, our method is expected to provide the largest benefits when the application requires to detect fast motions, that the frame rate of a frame-based method could not match for efficiency reasons. In this case, our method can detect those fast changes while maintaining a low rate of periodic aggregation. As shown previously, the accuracy of the Event prediction of HUGNet2+PA with PA at 5Hz (respectively 20Hz) matches the Periodic(T-2) predictions at 20Hz (respectively 100Hz) in MVSEC (respectively Rock Scenes), showing that our approach is highly efficient in terms of + +![](images/963d01b23d15525944c00d5b731a9a971be66cc757a84504973b235194d8c6e7.jpg) +Figure 4. (a) Endpoint Error as a function of time for Event and Periodic(T-2) predictions compared to groundtruth at timestep T, with HUGNet2+PA $_{20}$ , on a Rock Scenes test sequence. (b) Optical Flow predictions of Event and Periodic(T-2) vs. Groundtruth at selected groundtruth timesteps from (a). Arrows represent optical flow vectors (color masks indicate directions for the object and background). + +![](images/7a6dc84c9f375defd4968b65e56bccefe8c4d6aabba1da8fbf604adbb4a62d97.jpg) + +![](images/5ee83ed8cf50e1e17fed29c52adef2af4b7de339e062984bba4ca38d5cf376ef.jpg) +Figure 5. Endpoint error for HUGNet2+PA $_{20}$ and ADMFlow at $20\mathrm{Hz}$ on the same Rock Scenes sequence as Fig 4. + +accuracy and number of operations compared to a periodic output at low latency. + +Notably, our method is also impacted by the event density, which varies with time, including in similar environments, as event density depends on the motion in the scene. Indeed, higher event density can provide more information about optical flow, thus improving the accuracy, but also increases the computational cost of the Event branch. Moreover, not using event pooling in the GNN (only performing feature pooling in the Periodic branch) also limits the scalability of the GNN under power constraints, as the number of operations in every layer is impacted by the original event density. That is why our GNN uses a costly graph convolution layer only in the first layer, where the input size is small, to mitigate the number of operations. On the other hand, not pooling events also allows more predictions, as the Event branch outputs event-level predictions, which allows to faster adapt the optical flow estimation. Our PA module could be scaled for improving accuracy, by integrating more convolutional layers, other types of aggregation + +operations (e.g. correlation volumes), and iterative refinement [13], at the cost of more operations per frame. + +Furthermore, the benefit of our method not only depends on the application constraints (such as fast changing optical flow or event density), but also on the ability of the Event head to effectively leverage both GNN and PA outputs. Indeed, the Event head should be able to detect a potential mismatch between the two types of features, indicating that recent event features should dominate over the PA features. Therefore, future work could study the choice of the merge function and the architecture of the Event head to better interpret both features. Our method could also be extended to support image inputs in addition to events, in the multimodal scenario where an event camera and RGB camera are coupled to improve the overall prediction accuracy (similar to [12]). In this case, the image inputs would be processed by the periodic branch, in addition to taking inputs from the event branch. + +# 5. Conclusion + +We propose an efficient solution for optical flow estimation from event-based cameras at ultra-low latency and with minimal computational cost. Our solution combines event graph neural networks enabling low-latency per-event prediction, with a periodic aggregator module extracting context information, improving the accuracy of the event prediction without introducing latency to the event computation flow. Remarkably, our approach is the first to estimate optical flow with an estimated latency of 10s of $\mu$ s on asynchronous hardware, which represents a gain of 3 orders of magnitude compared to previous methods. 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The perceptual hashing of the model offers an efficient solution for retrieve the pirated models. Existing methods, such as handcrafted feature-based and dual-branch network-based perceptual hashing, have proven effective in detecting pirated models. However, these approaches often struggle to differentiate nonpirated models, leading to frequent false positives in model authentication and protection. To address this challenge, this paper proposes a structurally-aware perceptual model hashing technique that achieved reduced false positives while maintaining high true positive rates. Specifically, we introduce a method for converting the diverse neural network structures into graph structures suitable for DNN processing, then utilize a graph neural network to learn their structural features representation. Our approach integrates perceptual parameter-based model hashing, achieving robust performance with higher detection accuracy and fewer false positives. The experimental results show that the proposed method has only $3\%$ false alarm rate when detecting the non-pirated model, and the detection accuracy of the pirated model reaches more than $98\%$ . + +# 1. Introduction + +In recent years, a wide variety of neural networks [4, 5, 10, 13, 25, 31] have emerged and been applied to many aspects of daily life. Out of respect for human intelligence and to protect human ethics, the growing importance of neural network certification calls for specialized technologies to assist developers in verifying their models and in identifying potential misuse, such as fine-tuning, pruning, or tampering with replicated models. + +![](images/88bdafc79ae0606acc8db1762d1689604d780ec7c73f869b5a3b737df0528a8a.jpg) +Figure 1. An illustration of model perceptual hash for copyright protection and model verification. The left subfigure illustrates a scenario in which false positives occur in a model pirated detection scenario. User1 and User2 have their own models, which have completely different structures. The model hash vulnerability leads to misidentification of similar models during the discrimination due to the hash distance less than threshold $T$ . The right subfigure depicts the application in a model authentication scenario. The adversary creates a backdoor model and wishes to exploit a vulnerability in the model hash to authenticate it as a legitimate model. The adversary crafts a model modification so that its backdoor model matches the hash of the authenticated legitimate model, fooling the authentication system. + +Currently, three main techniques are used for model authentication and protection: model watermarking [6, 33], model fingerprinting [17, 23] and model perceptual hashing [2, 28]. Model watermarking embeds copyright information into a model's parameters, enabling legitimate users to extract the watermark and confirm the model's origin. To avoid the need for retraining, researchers have proposed model fingerprinting, which does not modify model parameters but instead designs adversarial examples to protect in- + +tellectual property. However, both methods struggle to efficiently detect infringing models among the vast number of existing models. To address this challenge, Chen et al. [2] and Xiong et al. [28] introduced model perceptual hashing, which is inspired by hash-based image retrieval methods [3, 24, 32]. Model perceptual hash method achieves effective detection of replicated and pirated models by using parameter distribution statistics or deep learning models to learn recognition rules. As shown in Fig. 1, when adversary acquires the owner's original model, the perceptual hashing method—whether modified through pruning or fine-tuning—generates hashes for both the original and pirated models, calculating the hash distance to identify piracy. Specifically, Chen's method employs hand-crafted feature extraction for hashing, which is convenient but relies on a single fixed feature dimension and is susceptible to targeted attacks. In contrast, Xiong et al. [28] utilize deep learning models to capture model characteristics from multiple dimensions, effectively addressing the limitations of manually extracted features. + +However, due to the absence of model structure information in the hashing process, the detection accuracy of DNN-based schemes is insufficient, leading to a risk of misidentifying non-pirated models with distinctly different structures as pirated ones. Current methods [28] are subject to higher false positives, i.e., a larger number of non-pirated models with different structures are recognized as stolen versions of a particular model at the time of detection. As shown in Fig. 1, the left side of the figure illustrates the model pirated detection scenario where two structurally dissimilar models are recognized as pirated models due to the hash distance being less than the threshold $T$ . The right side of the figure shows a scenario in which an adversary wants to utilize the model-aware hash misreporting vulnerability to authenticate a malicious model as a normal model in the model repository during the model authentication process. In other words, the high false positive rate of model perceptual hashing will not only lead to errors in model piracy detection. Moreover, in the model authentication scenario, it will be utilized by the adversary to authenticate the malicious neural network model as a legitimate model which will lead to more serious consequences. + +To address the challenge of achieving robust performance in both copy detection and distinguishing models with different structures, we introduce, for the first time, the inclusion of model structure information into perceptual hashing. Specifically, to encode diverse and complex model structures into unified statistical features, we propose a novel scheme that converts neural network structures into graph representations. In order to avoid multiple edges as well as circles that may result from the existing methods, we change the node connection strategy of the current scheme and design a model structure directed acyclic graph extrac + +tion strategy. Specifically, the original nodes representing layer inputs and layer outputs are directly connected to one or several intermediary nodes instead. These intermediary nodes can represent either fully connected layers or convolutional layers. Moreover, we train a model structure feature extractor on a large set of neural network graph data to generate structural features. Finally, we merge the trained network structure feature extractor with the parameter feature extractor via a merge layer to form a new three-branch network. Experimental results show that our proposed method has only $3\%$ false positive rate in distinguishing different structural models and has more than $98\%$ pirated model detection accuracy. Thus, our approach not only improves detection accuracy in copy detection scenarios but also enhances security in model authentication tasks. In summary, the main contributions of this work are as follows: + +- For the first time, we encode model structure information into model perceptual hashing, significantly improving detection accuracy in model copy detection and enhancing security in model authentication tasks. +- We design a conversion strategy that translates diverse and complex model structures into graph representations, making it more suitable for our graph embedding model to extract structural information. This approach effectively reduces the number of nodes and edges in the generated graphs, reducing memory complexity from $\mathcal{O}(mn)$ to $\mathcal{O}(m + n)$ compared to existing methods. +- Experiments demonstrate that our method significantly reduces false positive rates and improves the accuracy of distinguishing models with different structures. And it also improves the accuracy of piracy model detection. + +# 2. Related Work + +# 2.1. Graph Neural Networks (GNNs) + +Graph Neural Networks (GNNs) are generally divided into two categories: spectral graph convolutions and spatial graph convolutions. Spectral graph convolutions, based on the solid mathematical foundation of Graph Signal Processing (GSP) [8, 19, 21], aim to capture patterns in the frequency domain by leveraging the spectral properties of graphs. In contrast, spatial graph convolutions adopt the message-passing framework from Recurrent Graph Neural Networks (RecGNNs) [26], where node features are computed by aggregating the features of their neighboring nodes. Since message-passing networks like GCN [11] and GraphSAGE [7] are indistinguishable when confronted with certain graph structures. In order to solve this problem and enhance the representation capability of graph neural networks, Xu et al. proposed the graph isomorphism network (GIN) [29], which enhances the ability to distinguish different graph structures by assigning adjustable weights to the center node features. In this work, we adopt graph repre + +sensation learning to generate features for structural information of DNNs. + +# 2.2. Model Hashing + +Inspired by perceptual hashing in image processing [1, 15, 20], Chen et al. [2] were the first to propose a perceptual hashing method for models, leveraging Normal Test Statistics (NTS) of convolutional neural network parameters to detect pirated models. Their work claimed effective piracy detection for convolutional networks with promising results. However, their method failed to account for the diverse differences that may exist between non-pirated and original models, resulting in suboptimal perceptual hashing performance. Subsequently, Xiong et al. [28] introduced the use of a dual-branch network to replace statistical features and manual quantisation methods, partially addressing the issue of hash distance independence from model structure. However, the high false positive rate of their method posed challenges for practical applications. + +Based on these observations, we propose a structured hashing method that integrates model structure as part of the perceptual hash. Our method reduces the false alarm rate for different model detection to below $5\%$ under the same threshold while simultaneously improving the accuracy of pirated model detection at that threshold. + +# 3. Problem Formulation + +Given that the hash sequences $H_{a}$ and $H_{b}$ are generated for two neural network models, $M_{a}$ and $M_{b}$ , using a hash generator, the hash distance $D$ between $H_{a}$ and $H_{b}$ can be computed to assess the similarity or dissimilarity between models a and b. During the final hash calculation, we use mean squared error(MSE): + +$$ +\mathcal {D} \left(H _ {a}, H _ {b}\right) = \frac {1}{L} \times \sum_ {t = 1} ^ {L} \left(h _ {a _ {t}} - h _ {b _ {t}}\right) ^ {2}, \tag {1} +$$ + +where $h_{a_t} \in \{0,1\}^t$ and $h_{b_t} \in \{0,1\}^t$ represent the $t$ -th bit of hash sequences $H_a$ and $H_b$ , respectively, and $L$ denotes the length of the hash sequence. + +# 3.1. Robustness + +If the model to be tested is a common modified version of the query model (common modified version means a model that has undergone model fine-tuning and model pruning), then the hash distance between the test model $M_{a}$ and the query model $M_{b}$ should be less than threshold $T$ . formally, $\forall M_{a}, M_{b}$ , we have follow: + +$$ +\text {i f} M _ {a} = f \left(M _ {b}\right) \text {t h e n}, \mathcal {D} \left(H _ {a}, H _ {b}\right) < T, \tag {2} +$$ + +where $H_{a}, H_{b}$ and $f$ denote model hash of $M_{a}$ and $M_{b}$ and the common modifications, and $T$ is threshold. + +# 3.2. Discrimination + +The distance of model hash should be larger than threshold $T$ , if the model is a non-pirated model (i.e., a test model is neither the query model nor its common modified version). Formally, we have follow: + +$$ +\text {i f} M _ {a} \neq M _ {b} \text {t h e n}, \mathcal {D} \left(H _ {a}, H _ {b}\right) > T. \tag {3} +$$ + +# 4. Methodology + +To reduce security risks from high false positives in non-pirated model hashing and improve platform retrieval and model use efficiency, we propose a structured perceptual hashing method. As shown in Fig. 2, this method consists of two components: the parameter hashing module and the structure hashing module. When generating a hash for a model, we first separate its parameters and structure. The parameters are preprocessed and fed into the parameter hashing generator. And the structural information is first converted into a Directed Acyclic Graph (DAG) to facilitate feature learning. Then the DAGs are fed into the Model structure hash generator to generate the structure hash. In the end, structure hash and parameter hash are merged to generate the finally model hash. + +Given the lack of similar datasets, we adopt a pretraining and fine-tuning strategy to learn effective representations from the structural DAG. Specifically, we begin by pre-training a graph classification neural network on the MUTAG dataset to obtain a generalizable pre-trained model. We then use $30\%$ and $10\%$ of the generated model DAGs for fine-tuning and validation, respectively, to create the final structure hash generator. Additionally, we modify the pre-trained graph classification neural network to meet the specific requirements of our fine-tuning tasks, ensuring the generator performs as expected. + +# 4.1. Structure Hashing Module + +DNNs exhibit diverse structures with varying numbers and types of layers. To facilitate the use of deep learning models in processing DNN structure information, we convert the diverse model structures into features of uniform size. In this study, we first transform the model structure into a graph structure suitable for DNN processing and then use a DNN-based graph embedding algorithm to convert the graph structure into features of uniform size. As shown in Fig. 2, our structural information extraction module consists of two parts: the DAG extraction module and the structural feature generation module. + +DAG Extraction Module. In graph learning, neural networks often struggle to efficiently generate graphs for mainstream models, typically requiring space complexity of $\mathcal{O}(mn)$ or more (e.g., $\mathcal{O}(mnp)$ for convolutional layers, where $p$ is the number of kernels, and $m, n$ represent the input and output dimensions of each layer), which is impracti- + +cal for our task. Therefore, we optimized the graph generation process based on the properties of neural network models. Specifically, we adjusted the generation methods for fully connected and convolutional layers, changing the original two-layer design to a three-layer structure and avoiding designs that could lead to cyclic graphs. + +For fully connected layers, as shown in Fig. 2 (b), three groups of nodes are used: the top group corresponds to the input dimensions, the bottom group corresponds to the output dimensions, and the middle group corresponds the activation process between the input and output nodes. For convolutional layers, we also use three groups of nodes. However, unlike existing methods that represent the number of kernels with multiple edges, our intermediate layer contains nodes corresponding to each dimension of every kernel. For example, if there are two kernels, each of size $2 \times 2$ , the middle group would contain $2 \times 2 \times 2 = 8$ graph nodes. This approach not only avoids multiple edges and simplifies the graph into a directed acyclic graph (DAG) but also reduces space complexity to $\mathcal{O}(p \times (m + n))$ . We generated corresponding graphs for 497 models from the TIMM. + +Structural Feature Generation Module. After obtaining the DAG from the model structure, we input it into a graph neural network to generate the final structural features. We use graph isomorphism network [29] as generator in our method. We first pre-trained a graph classification network on the MUTAG dataset. However, since the graphs in MUTAG datasets are relatively small, directly adapting the trained network to our task would result in poor performance. Therefore, we performed finetuning using a subset of DAG data from our task to align the model with the structure of the generated DAGs. During finetuning, we applied noise to the original graph $G_{o}$ to generate a similar graph $G_{s}$ and a dissimilar graph $G_{d}$ . Specifically, we employ contrastive learning, defining two graphs as similar if the added nodes do not exceed $5\%$ of the original nodes within the same layer, and their feature vectors are as close as possible. Conversely, graphs with more than $5\%$ added nodes or new layers were considered dissimilar, and their feature vectors were expected to be as distant as possible. Ultimately, we obtained a 128-bit structure hash. Finally, we constructed a fusion layer composed of fully connected layers to merge the structure and parameter hashes into a 100-bit perceptual hash. + +# 4.2. Parameter Hashing Module + +In designing the parameter hashing module, we adopted the approach from mainstream practices. First, the parameters are preprocessed and divided into convolutional layer parameters and fully connected layer parameters, both of which are pruned to reduce redundancy. The pruned parameters are then input into the parameter hashing generator. Since we must handle parameters of various sizes and + +shapes, the first layer of the hashing generator employs a dynamic convolutional layer to map inputs of different dimensions into a unified space, ensuring effective processing by subsequent modules. Finally, the hashes from the convolutional and fully connected layers are merged through a fusion module to generate a 50-bit parameter hash. This approach reduces redundant computations through pruning, and the dynamic adjustment capabilities of the hashing generator ensure adaptability, providing a consistent hash representation for models of varying scales. + +# 4.3. Loss Functions + +The loss functions used in the experiment fall into three categories for various training stages: the parameter hash loss $\mathcal{L}_w$ , the structure hash loss $\mathcal{L}_s$ and the merge hash loss $\mathcal{L}_m$ : + +$$ +\mathcal {L} = \left\{ \begin{array}{l l} \mathcal {L} _ {w}, & \text {i f t r a i n p a r a m e t e r h a s h g e n e r a t o r ;} \\ \mathcal {L} _ {s}, & \text {i f t r a i n s t r u c t u r e h a s h g e n e r a t o r ;} \\ \mathcal {L} _ {m}, & \text {i f t r a i n m e r g e h a s h .} \end{array} \right. \tag {4} +$$ + +In Eq. (4), $\mathcal{L}_w$ is aimed at ensuring that the hash codes generated from similar models' parameters are closely clustered, while those from dissimilar ones are more dispersed. $\mathcal{L}_w$ consists of two parts: $\mathcal{D}(H_p,H_o)$ and $\mathcal{D}(H_{np},H_o)$ : + +$$ +\mathcal {L} _ {w} = \mathcal {D} \left(H _ {p}, H _ {o}\right) - \mathcal {D} \left(H _ {n p}, H _ {o}\right), \tag {5} +$$ + +where $H_{o}$ , $H_{p}$ and $H_{np}$ represent the hash codes of the original, pirated and non-pirated models' parameters, respectively. + +$\mathcal{L}_s$ in Eq. (4) is used to train structure hash generator. We employed different loss functions for various training phases: + +$$ +\mathcal {L} _ {s} = \left\{ \begin{array}{l l} \mathcal {L} _ {p}, & \text {w h e n p r e - t r a i n i n g p h a s e ;} \\ \mathcal {L} _ {f}, & \text {w h e n f i n e - t u n i n g p h a s e .} \end{array} , \right. \tag {6} +$$ + +where $\mathcal{L}_p$ represents mean squared error loss function: + +$$ +\mathcal {L} _ {p} = \frac {1}{n} \sum_ {i = 1} ^ {n} \left(y _ {i} - \hat {y} _ {i}\right) ^ {2}. \tag {7} +$$ + +To make the graph neural network better suited to the structural characteristics of our data, the pre-trained model is fine-tuned using the loss function $\mathcal{L}_f$ + +$$ +\mathcal {L} _ {f} = \mathcal {D} _ {e} \left(H _ {s}, H _ {o}\right) - \mathcal {D} _ {e} \left(H _ {d}, H _ {o}\right), \tag {8} +$$ + +where $H_{o}, H_{s}$ and $H_{d}$ represent the hash of original graph, the similar graph, and the dissimilar graph, respectively, and $\mathcal{D}_e(\cdot ,\cdot)$ is used to calculate the distance between two hashes. The specific formula is as follows: + +$$ +\mathcal {D} _ {e} \left(H _ {a}, H _ {b}\right) = \frac {1}{1 + e ^ {- \mathcal {D} _ {o} \left(H _ {a} , H _ {b}\right)}}, \tag {9} +$$ + +![](images/d8d0ba368e22fbde8e1a10b9815a68e9592c673cf1984297b479b7ec1b1a15ea.jpg) + +![](images/e74a1f2c51b4794f02ff173a8b63722a3538c9364bdf01a6f2d6db2a575721be.jpg) +Figure 2. Network framework of our proposed method. In part (a), model structure and model parameter matrices are firstly extracted. Model parameter metrics are fed into dual-branch network to generate parameter hash. While the model structure is extracted to get the DAG. The DAG is then fed into well-trained GIN to generate structure. Finally, structure hash and parameter hash are merged to generate the model hash. In part (b), we illustrates our DAG extraction method. The left diagram represents a linear layer with three input dimensions and four output dimensions; the middle diagram depicts a convolutional layer with two $1 \times 1$ convolutional kernels, having two inputs dimensions and four outputs dimensions; and the right diagram shows the layer norm, indicated by the dashed circle. And in part (c), the left diagram shows the model structure hash generator which is graph isomorphism network with 3 graph convolutional layers. + +![](images/fecc8076f8343ccaac14ec4b95cf79bb44eb4a3e0711095724b914a57d219938.jpg) + +where $\mathcal{D}(H_a, H_b)$ denotes the Euclidean distance between the graph embeddings $H_a$ and $H_b$ . Under this setup, the embedding distance for similar graphs should be as small as possible, while the distance for dissimilar graphs should be as large as possible. As the loss function $\mathcal{L}_f$ converges, $\mathcal{D}_e(H_s, H_o)$ approaches 0.5, indicating that the original and similar graphs are very close in embedding space, while $\mathcal{D}_e(H_d, H_o)$ approaches 1, showing that the original and dissimilar graphs are far apart. These outcomes ensure that the final loss $\mathcal{L}_f$ lies within the open interval $(-0.5, 0.5)$ . + +In the merge phase, the loss function integrates the parameter and structure hashes into the final perceptual hash. Thus, we expect the pirated model's perceptual hash to closely align with that of the original model, while that of the non-pirated model remains distant. The specific form of $\mathcal{L}_m$ is as follows: + +$$ +\mathcal {L} _ {m} = \mathcal {D} \left(H _ {p} ^ {T}, H _ {o} ^ {T}\right) - \mathcal {D} \left(H _ {n p} ^ {T}, H _ {o} ^ {T}\right), \tag {10} +$$ + +where $\mathcal{D}(\cdot ,\cdot)$ is same as Eq. (1) and $H_{o}^{T}$ , $H_{p}^{T}$ and $H_{np}^{T}$ denote the original, the pirated and the non-pirated model. + +# 4.4. Training details + +During the training stage, we first train the dual-branch network with $\mathcal{L}_w$ by 5,000 epochs to get a well-trained parameter hash generator. Concurrently, the structure hash generator, based on graph neural network, undergoes initial training with the $\mathcal{L}_p$ to enhance its feature recognition capability. Subsequently, $30\%$ of our dataset is allocated for fine-tuning, and the generator is refined using $\mathcal{L}_f$ over 200 epochs, yielding the final structure hash generator. The outputs of the dual-branch model are ultimately integrated with that of the structural branch, followed by joint fine-tuning of all three branches using $\mathcal{L}_m$ . + +# 5. Experiments + +# 5.1. Experimental Setup + +Model Dataset. We used ResNet (ResNet18, 34, 50, 101, 152) [9], VGG (VGG11, 13, 16, 19) [22], ShuffleNet [30], and MobileNetv2 [18] as the training set for the parameter identification module, and these mod + +
Non-pirated model identificationHash DistanceFalse Alarm RateAccuracy Rate
Max.Mean.Std.Min.T=0.1T=0.5T=0.1T=0.5
Proposed374.723248.889577.44290.082.69%10.45%97.31%88.55%
Baseline45.882511.315813.37709.50%17.46%91.51%82.54%
+ +Table 1. Statistics of hash distances, false alarm rates and identification accuracy rates for non-pirated models. + +
Hash DistanceAccuracy Rate
Max.Mean.Std.Min.T=0.1T=0.5T=1.0T=2.0
PiratesFine-tuningProposed0.020.00150.00190100.00%100.00%100.00%100.00%
Baseline0.21090.02410.0283096.88%100.00%100.00%100.00%
ModelL1Proposed0.01310.00140.00190100.00%100.00%100.00%100.00%
Identifi-cationpruningBaseline0.23620.02440.0295096.35%100.00%100.00%100.00%
RandomProposed0.0130.00150.00180100.00%100.00%100.00%100.00%
pruningBaseline0.20310.02560.0289095.50%100.00%100.00%100.00%
+ +Table 2. Statistics of hash distances and identification accuracy rates for pirated models. + +els were trained on classical vision task datasets, including CIFAR-10 [12], CIFAR-100 [12], MNIST [14], and FashionMNIST [27]. During fine-tuning, five models were saved per epoch (10 epochs total) to capture varying refinement stages. We evaluated generalization using 325 TIMM visual models as test data, resulting in a total of 2,569 models. Pruned/tampered models were dynamically generated during training. For structural hashing, MUTAG molecular graphs served as pretraining data (188 samples, avg. 17.9 nodes/19.8 edges), with performance enhancement achieved through fine-tuning on $30\%$ (98) of our TIMM-derived graph structures - the remaining $70\%$ (227) comprised the test set for large graph recognition validation. Training Strategy. The model hashing generator was trained on 1,683 models (75% of 2,569 original and corresponding fine-tuned models) with real-time generation of pruned/tampered variants from originals. Using AdaMax optimizer (learning rate=0.0001) for 5,000 iterations, the generator processed randomly selected pirated models including fine-tuned, pruned, and tampered versions. For structural hashing, we employed MUTAG molecular graphs (188 samples, avg. 17.9 nodes/19.8 edges) and enhanced generalization by fine-tuning on $30\%$ (98) of TIMM's 325 graph structures to enable scalable model hashing. + +Environment. All experiments were run on Linux platform with four RTX 4090 GPUs, using the PyTorch [16]. + +Comparison with Baseline Methods. We compared our approach with existing DNN-based perceptual hashing methods (e.g., Xiong [28]) from two perspectives: pirated model detection and non-pirated model distinction. And the result of the experiment shows in Tabs. 1 and 2. + +# 5.2. Non-pirated Model Distinction + +As a key focus of this study, we evaluated the ability to distinguish non-pirated models. We used the same validation + +dataset $\mathcal{D}_t^2$ and randomly selected two models to generate hash values in each experiment. We performed 1,000 tests in total, and the results are summarized in Tab. 1. Our method can achieve a non-pirated detection false positive rate of only $2.69\%$ at a $T$ that guarantees a higher piracy detection accuracy, compared to $9.5\%$ for the baseline method. According to the $T$ in Tab. 2, if the piracy detection accuracy is to be taken into account, the baseline false alarm rate will be $17.46\%$ . It is important to note that the identification accuracy for non-pirated models decreases as the threshold increases, which is different from the trend observed in pirated model detection. Thus, ideally, the distance between non-pirated models should be larger, while the distance between pirated models should be smaller. Therefore, as the threshold increases, both the maximum hash value recognized as a pirated model and the minimum hash value recognized as a non-pirated model increase, leading to an inverse trend in accuracy growth between the two tasks. + +# 5.3. Robustness Test + +# 5.3.1 Model Fine-tuning + +Following Sec. 3, we conducted experiments on pirated model detection under fine-tuning, pruning, and tampering scenarios. For fine-tuning tests, we used a validation dataset $\mathcal{D}_t^1$ consisting of $25\%$ of the original models and their fine-tuned versions, totaling $(2569 - 325) \times 0.25 = 561$ models. We generated two hash sequences for each original model and its fine-tuned version and calculated their hash distances $H_{p}$ . The results for fine-tuning detection are summarized in Tab. 2 under the "Fine-tuning" row, where our method achieves $100\%$ detection accuracy at the baseline's minimum threshold $T = 0.1$ , with a maximum hash distance of only 0.02. As shown in Fig. 3, our method makes better performance than baseline with different $T$ . + +
α = 1%α = 20%α = 50%
σ0.010.050.10.150.20.010.050.10.150.20.010.050.10.150.2
DMax.0.040.000.020.040.040.130.460.730.470.930.200.680.540.750.58
Mean.0.000.000.000.000.000.010.060.090.100.100.020.070.090.100.11
Std.0.000.000.000.010.010.020.080.090.090.100.030.080.090.100.10
Min.0.000.000.000.000.000.000.000.000.000.000.000.000.000.000.00
RpT=0.1100%100%100%100%100%98.96%81.46%74.48%69.04%67.66%95.41%77.89%71.30%64.87%60.06%
T=0.5100%100%100%100%100%100%100%99.70%96.20%94.70%100%99.85%93.78%95.60%92.94%
T=1.0100%100%100%100%100%100%100%100%100%100%100%100%100%100%100%
T=2.0100%100%100%100%100%100%100%100%100%100%100%100%100%100%100%
+ +Table 3. Statistics of hash distances and identification accuracy rates for pirated models under tampering operation. Here, $\alpha$ , $\sigma$ , $D$ , and $R_p$ denote the tampering rate, Gaussian noise deviation, hash distance, and detection accuracy at threshold $T$ , respectively. + +# 5.3.2 Model Pruning + +For pruning attack detection, we tested our hashing generator with both L1-norm pruning and random pruning. The validation dataset $\mathcal{D}_t^2$ consisted of $(11 \times 4) \times 0.25 + 325 = 336$ models. During the experiment, we randomly selected an original model and generated its pruned version in real-time, with the pruning rate $pr$ randomly chosen from 0.1 to 0.9 with the step of 0.1. We performed 1,000 experiments in total and recorded the corresponding hash distances. As shown in Tab. 2, the maximum hash distances for L1-norm and random pruning were 0.0131 and 0.013, respectively, while the baseline method yielded maximum distances of 0.2362 and 0.2301. Additionally, our method achieved the same $100\%$ detection accuracy as in the fine-tuning scenario, outperforming the baseline method, which reported only $96.3\%$ and $96.8\%$ accuracy for L1-norm and random pruning, respectively. Also shown in Fig. 3, performance of ours method is better. + +# 5.3.3 Model Tampering + +According to the definition, tampered versions of the original models should be regarded as pirated models and identified as such. To verify the robustness of our method under different tampering configurations, we conducted tests with varying tampering rates $\alpha$ , set at $1\%$ , $20\%$ , and $50\%$ . Additionally, the mean of the Gaussian noise $\varepsilon$ was set to 0, while the standard deviation $\sigma$ was assigned values of 0.01, 0.05, 0.10, 0.15, and 0.20. In each experiment, a model was randomly selected from $\Omega_2$ , and a tampered version was generated in real time by altering its parameters. Hash sequences were then generated for both the original and tampered models, and their hash distance $S_p$ was calculated. A total of 700 tampering operations were performed for each combination of $\sigma$ and $\alpha$ , resulting in $700 \times 3 \times 5 = 10,500$ hash distances and $3 \times 5 \times 4 = 60$ recognition accuracies. + +As shown in Tab. 3, the maximum hash distance was only 0.93, with both the mean and standard deviation below 0.10, indicating that most hash distances were small, and nearly all tampered pirated models were successfully identified. When $\alpha$ and the threshold $T$ were fixed, the recog + +![](images/da9ea2fe009247c71ef36899015a92977f0b7be261353de6a1412c292d4ccf5d.jpg) +Figure 3. Recognition accuracy comparison under different threshold $T$ . The figure respectively describes the accuracies of our scheme and the scheme of Xiong et al. under different thresholds in the scenarios of pruning and fine-tuning. + +nition accuracy decreased as $\sigma$ increased. This is because larger $\sigma$ values amplify the differences between the original and tampered models, resulting in greater hash distances. When $T$ was set to 0.5, 1.0, and 2.0, the recognition accuracy of pirated models consistently exceeded $90\%$ . + +# 5.4. Impact of Parameters on Hashing Performance + +# 5.4.1 Performance with Different Component + +Our ablation study compares: (1) direct concatenation vs. neural fusion (merge module) for hash integration, and (2) hard-coded computational graphs vs. graph learning networks for structural hash generation. Hard-coded structural hashes produce sparse vectors that amplify parametric hash dominance (e.g., $53.19\%$ vs. $89.55\%$ Non-pirated Model Identification at $\mathrm{T} = 0.5$ ), while graph learning resolves this imbalance. As shown in Tab. 5, our method achieves $100\%$ Fine-tuning and L1 Random accuracy at $\mathrm{T} = 0.1$ , outperforming baselines by $4.91 - 9.38\%$ across key metrics. + +
Hash DistanceAccuracy Rate
Max.Mean.Std.Min.T=0.1T=0.5T=1.0T=2.0
Pirated +ModelFine-tuning50-bit0.01890.00150.00190100.00%100.00%100.00%100.00%
75-bit0.01470.00110.00130100.00%100.00%100.00%100.00%
100-bit0.020.00150.00190100.00%100.00%100.00%100.00%
Identifi-cationRandom +pruning50-bit0.05780.00480.00470.0001100.00%100.00%100.00%100.00%
75-bit0.04550.00380.00370.0002100.00%100.00%100.00%100.00%
100-bit0.0120.00150.00180100.00%100.00%100.00%100.00%
Non-pirated model +identification50-bit417.545643.861170.41110.011995.16%89.78%82.80%76.88%
75-bit284.792726.13549.37060.003892.47%82.26%76.81%63.44%
100-bit366.808437.50563.72810.018195.48%89.50%81.01%78.93%
+ +Table 4. Performance under different length of model hash. + +
Accuracy RateThresholdFine tuningL1 RandomNon-pirated Model Identification
ConcatenationT=0.195.09%62.44%89.13%
T=0.5100.00%94.12%66.85%
Hard CodeT=0.190.62%46.41%95.74%
T=0.5100.00%98.64%53.19%
OursT=0.1100.00%100.00%97.31%
T=0.5100.00%100.00%89.55%
+ +# 5.4.2 Performance with Different Threshold + +To demonstrate the efficiency and low false alarm rate of the proposed scheme, we conducted experiments on the recognition accuracy under the same threshold and plotted the accuracy curves for identifying different types of pirated models across various thresholds, as shown in Fig. 3. Our scheme achieves $100\%$ recognition accuracy at a threshold of less than 0.05, whereas existing methods require a threshold of approximately 0.15 to achieve the same accuracy. Similarly, to further validate the low false positive rate of our proposed scheme, we performed experiments on the false positive rate under different thresholds. + +# 5.4.3 Performance with Different Length of Merge Hash + +To evaluate the impact of different fusion lengths $H_{w}$ and $H_{s}$ on hashing performance, we randomly selected 200 model pairs at lengths of 50, 75, and 100 bits across fin-tuning, random pruning, and dissimilar model scenarios. We assessed detection accuracy and false alarm rates using various thresholds, where smaller hash values are preferred in the fine-tuning and pruning contexts, and larger hash values are favored in dissimilar scenarios. A higher detection accuracy is desirable across all conditions. Tab. 4 summarizes the results for different hash lengths. Notably, a length of 100 bits demonstrated strong performance in both similar and dissimilar scenarios, leading us to adopt it as our final + +Table 5. Ablation study with concatenating and hard coding method. + +
Length
3264128
Accuracy Rate92.11%89.47%97.37%
\( \mathcal{L}_{nll} \)0.30190.35560.1826
+ +Table 6. Performance with different length of structure hash. + +fusion hash length in the experiments. + +# 5.4.4 Different Length of Structure Hash + +During the structure hash generator implementation, we tested hash lengths for optimal discrimination. Structural DAG detection tests with 32, 64, and 128 -bit outputs were conducted, results in Tab. 6, where $\mathcal{L}_{nll}$ denotes negative log - likelihood loss. Under the same training, 128 -bit hash showed better performance and accuracy. Thus, 128 bits was chosen for our experiments. + +# 6. Conclusion and Limitation + +We propose structure hashing, a model-perceptual method employing graph neural networks to extract structural fingerprints through directed acyclic graph (DAG) mapping. Our results demonstrate that structural integration with parameter hashing significantly improves piracy detection robustness (38% fewer false positives). 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However, due to the modality and domain gap between images and LiDAR point clouds, Image-to-Point Cloud Registration is a significant challenge, especially when the image and point cloud come from non-synchronized frames. To tackle these issues, we introduce the virtual point cloud as a bridge to alleviate the cross-modality gap between images and LiDAR point clouds. In this way, the modality gap is converted to the domain gap of point clouds. Moreover, we introduce a virtual-spherical representation achieving orthogonal decoupling between pixel location and predicted depth. As for the domain gap, we propose a distribution-based adaptive sample module to generate a unified distribution of two types of point clouds. Then, we explore the correct correspondence pattern consistency and prune the false correspondences through a graph-based selection process. Experimental results demonstrate that our method outperforms the state-of-the-art methods by more than $10.77\%$ and $12.53\%$ performance on the KITTI Odometry and nuScenes datasets, respectively. The results demonstrate that our method can effectively solve nonsynchronized random-frame registration. + +# 1. Introduction + +Image-to-Point Cloud registration is a fundamental research topic in 3D computer vision, which is widely applied in many applications, such as 3D reconstruction [1], robotic localization [2], and autonomous driving [3]. The objective of registration is to predict a rigid transformation aligning images and point clouds. Compared to the registration be + +![](images/8352b49694f199be5cde8ecbf314c76449ea486bb7d7aadf80a33e2bb4c845be.jpg) +Figure 1. Registration recalls on KITTI [8] dataset when compared with the same-frame and non-synchronized random-frame of the Image and LiDAR point cloud for registration. + +tween images and point clouds generated by RGBD cameras in indoor environments, outdoor scenarios are more challenging due to the larger modality gap between the images and point clouds captured by LiDAR. The significant relative poses of cameras and LiDAR scanners are difficult to estimate by traditional single modality registration [4, 5] or regress-based self-calibration methods [6, 7]. + +Previous methods [9, 10] utilized MLPs [11] on the point clouds branch and CNNs [12] on the images branch separately and generate 2D-3D correspondences by matching them in feature space. However, the modality gap between features may lead to impaired 2D-3D candidate correspondences due to a lack of structure and geometric consistency. To this end, recent works have started to utilize the virtual point cloud [13, 14] or voxel [15, 16] as a bridge to alleviate the modality gap, which improves the Image-to-Point Cloud registration performance effectively. Nevertheless, these methods still suffer from the domain gap caused by the distribution difference between the intermediate modality data and LiDAR point clouds. Moreover, existing methods require the point cloud and image from the same frame for registration; when they come from non-synchronized random frames, which is very common in practical scenarios, + +![](images/df71f57a457fc888ed20402b0e373e5305fac6868e099aa095249f337b53f519.jpg) +Figure 2. Registration recalls on KITTI [8] dataset when compared with the same-frame and non-synchronized random-frame of the Image and LiDAR point cloud for registration. + +performance degrades significantly, as Fig. 1 shows. + +While the Point Cloud-to-Point Cloud registration is limited by the lack of reliable correspondences in cases of low overlap, the primary issue in Image-to-Point Cloud registration is the interference caused by incorrect correspondences from 360-degree LiDAR point clouds. Most existing methods [9, 10, 15, 17] adopt a two-stage paradigm, where points that fall within the camera's view are first selected by frustum filtering, followed by the establishment of reliable correspondences. However, the registration performance is primarily constrained by the accuracy of camera frustum filtering, which neglects the spatial consistency inherent in reliable correspondences. The inconsistency between images and LiDAR point clouds from different frames amplifies the errors in frustum filtering, significantly degrading cross-modality registration, as Fig. 2 shows. + +To tackle these problems, we propose a graph-based correspondence selection method that develops a global exploration scheme for Image-to-Point Cloud registration. Firstly, we design a virtual-spherical representation of latent space, achieving orthogonal decoupling between pixel location and predicted depth. The coarse registration in virtual-spherical representation relies on relative spatial relationships, which can reduce errors caused by inaccurate depth estimation methods. Furthermore, to solve the domain gap issue, we utilize the distribution-based adaptive sample module based on Maximum Likelihood Estimation (MLE) on distance direction to get consistent distribution between LiDAR and virtual point clouds. To mitigate the errors introduced by the frustum selection-based registration methods, we propose a frustum selection-free method based on the pattern consistency of the reliable correspondences. Specifically, we introduce a graph-based correspondence selection module to enhance the consistency of the correct correspondence features and prune false correspondences. Our approach achieves many gains in performance in non-synchronized random-frame setting, demonstrating its effectiveness under extremely challenging scenarios. + +Overall, this paper has three main contributions: + +- We introduce a virtual-spherical representation of latent + +space for cross-modality registration. This enables the virtual point clouds generated from images to exhibit geometric feature representations closer to those of LiDAR point clouds while reducing errors in virtual point clouds caused by scale loss in depth estimation. + +- To tackle the domain gap between virtual and LiDAR point clouds, a distribution-based adaptive sample module is proposed to reshape the two types of point clouds in a similar distribution and density for registration. +- We propose a graph-based correspondence selection module to explore the pattern consistency of the correspondence features, which effectively avoids the errors introduced by frustum selection-based methods. Evaluations have shown superior performance of our proposed method under non-synchronized random-frame settings. + +# 2. Related work + +# 2.1. Point Cloud Registration + +Traditional point cloud registration methods [18-20] require a proper initial pose to resolve the rigid transformation. With the development of deep learning, learning-based methods [11, 21-25] have demonstrated promising performance in estimating transformation indoor scenarios. In contrast, LiDAR point cloud registration [26-28] for outdoor scenarios is more challenging due to its inherent sparsity and complexity of the environment. SDMNet [29] introduces a Sparse-to-Dense matching network for largescale outdoor LiDAR point cloud registration, which utilizes a spatial consistency to enhance the features and reject outliers. Recently, correspondence-based RANSAC-free methods [5, 30, 31] utilizing the coarse-to-fine strategy have shown great potential in point cloud registration. Meanwhile, graph-based methods [27, 32, 33] have attracted more attention in outlier pruning. However, these methods require huge computational complexity when searching for maximal cliques. In contrast, we only take graph learning to enhance the correspondence pattern consistency rather than conduct RANSAC [34] in graph searching. + +# 2.2. Image-to-Point Cloud Registration + +For cross-modality registration, 2D3D-MatchNet [35] and P2-Net [36] are early attempts to directly establish 2D-3D correspondences and employ PNP [37] to obtain a rigid transformation. Besides, DeepI2P [9] employs a frustum selection network to predict camera pose. CorrI2P [10] introduces a fusion network to get dense correspondences and utilize EPnP [37] for registration. Some works [16, 38, 39] follow the coarse-to-fine mechanism to build point set-topixel patch correspondences followed by a multi-scale refine for point-to-pixel correspondences. Other methods [14, 40] model the registration problem as the cross-modality retrieval, which searches the correspondences overlap in the + +![](images/3a5a968bda35f7fe8f5398a7f84b892d7e33f3ce6a200c1c857ee19cef671784.jpg) +Figure 3. The pipeline of our proposed graph-based Image-to-Point Cloud registration method. First, the image is transformed into a virtual point cloud through depth estimation. Then, LiDAR and virtual point cloud are represented in virtual-spherical representation. After that, the distribution-based adaptive sample module is leveraged to get a unified distribution of point clouds. The graph-based correspondence selection module is constructed based on the consistency of the correspondence feature pattern and generates correct correspondences. + +geometric space and feature space. Recently, intermediate modality data, such as voxel and virtual point cloud, have been introduced as a bridge to alleviate the modality gap. VP2P [15] constructs voxel-to-pixel correspondences and introduces the differentiable probabilistic PnP Solver for end-to-end optimization. Freereg [13] utilizes depth estimation to generate the virtual point cloud and construct the 3D correspondences based on pre-trained diffusion models. However, these methods fail to get robust registration when the image and point cloud come from non-synchronized random frames due to a lack of reliable correspondences. + +# 2.3. Online Automatic Self-Calibration + +Learning-based Online automatic self-calibration aims to regress the initial transformation matrix with a series of pairs of images and LiDAR point clouds as input. LccNet [6] projects mismatched LiDAR point clouds onto depth images, together with the same-frame images. CalibDepth [41] combines the monocular depth estimation and self-calibration task together for the training process. Zhu et al. [42] introduce graph neural network to improve the cross-modal regression performance by enhancing the features representation. However, learning-based online automatic self-calibration methods are designed in regression style to estimate very slight mis-calibration within $20^{\circ}$ for + +rotation and $1.5\mathrm{m}$ for translation. Furthermore, these methods require a series of images and LiDAR point cloud from a synchronized frame as input. In contrast, our method can predict the relative pose with a single pair of the image and LiDAR point cloud as input even if they are captured from the different frames, which is much more challenging. + +# 3. Method + +# 3.1. Overview + +In this paper, we propose a graph-based Image-to-Point Cloud registration method composed of three main stages: bridging the domain gap, feature extraction and fusion, and graph-based correspondence selection, as Fig. 3 shows. Firstly, we convert the image to the virtual point cloud utilizing a zoe-depth [43] as FreeReg [13]. Then, a virtual-spherical representation and a distribution-based adaptive sample module are introduced to bridge the domain gap between the LiDAR and virtual point clouds. Specifically, both point clouds are transformed into the virtual-spherical representation space to decouple the depth direction and pixel plane. Furthermore, we introduce an adaptive distribution sample module based on the maximum likelihood estimation (MLE), ensuring that both point clouds exhibit similar distribution and patterns. Secondly, LiDAR and virtual + +![](images/37cbbe9aca2d082993b1b9ff51df190b56853d182e2e0e2c31c8786275af9763.jpg) +Figure 4. Compared with the different sample strategies, the distribution-based adaptive sample can better maintain the distribution and pattern of the original point clouds. + +point clouds with unified distribution are input KPConv-based [44] feature extraction and fusion stage to generate coarse correspondence based on point features and descriptors matching. Thirdly, we construct a graph-based correspondence selection module to filter reliable correspondences based on their pattern consistency. We design correspondence selection loss to enhance the consistency of the correspondence and reject false pairs. Finally, given final correspondences with features, we perform rigid motion computation via singular value decomposition (SVD) [45]. + +# 3.2. Virtual-Spherical Representation + +Following the previous works [13, 14], we utilize depth estimation to generate the virtual point cloud as the bridge to convert the modality gap between the image and point cloud to the domain gap between two different types of point clouds. To further alleviate the domain gap, we design a virtual-spherical representation, a 3D latent space for registration in spherical coordinates to replace traditional Cartesian coordinates. In particular, we exploit the 3D spherical representation where the basis is defined by azimuth, elevation, and range. Then, we transform the virtual point cloud 3D location $(u,v,d)$ into $(\theta ,\varphi ,r)$ where the $\theta$ is azimuth, $\varphi$ is elevation, and $r$ stands for the distance between the point cloud and camera plane. The strength of the proposed spherical representation lies in the decoupling of the direction $(\theta ,\varphi)$ and distance $(r)$ components, ensuring their orthogonality by design, in contrast to the entanglement present in the Cartesian representation. Moreover, we resize the virtual point cloud in the $r$ axis to the LiDAR point cloud scale to mitigate the errors introduced by monocular depth estimation methods. Therefore, the virtual-spherical representation decouples point cloud position and distance, effectively alleviating the impact of errors caused by nonsynchronized random-frame registration. + +# 3.3. Distribution-based Adaptive Sample + +Given the LiDAR point cloud $\mathbf{X} \in \mathbb{R}^{M \times 3}$ and the virtual point cloud $\mathbf{Y} \in \mathbb{R}^{N \times 3}$ , we further alleviate the do + +![](images/4d53a4f9f5c0a5b8c3801daf593df3a2fa13c12b86ebd0de10ad8a766262a722.jpg) +Figure 5. Based on the CFD matrix, we generate the graph adjacency matrix when threshold $\varepsilon = 0.5$ . Then, we prune the false correspondence 2 and 4 through GNN. + +main gap utilizing the distribution-based adaptive sample module to generate unified distribution. Unlike previous works[46, 47] that modeled the distribution of LiDAR point clouds in terms of distance as a normal distribution, we found, by calculating the Kullback-Leibler (KL) divergence between the fitted distribution and the ground truth distribution, that a log-normal distribution on in the $r$ more closely approximates this distribution. As the direction and distance of the point cloud are orthogonal, the overall distribution can be represented as a log-normal distribution along the $r$ axis in the virtual-spherical representation. For the LiDAR point clouds $x(\theta ,\varphi ,r)\in X$ , the distribution on axis $r$ is $X\sim LN(\mu ,\sigma^2)$ , and probability density function is: + +$$ +f (x; \mu , \sigma) = \frac {1}{\sqrt {2 \pi} \sigma r} e ^ {\frac {(\ln r - \mu) ^ {2}}{2 \sigma^ {2}}}. \tag {1} +$$ + +Then, we apply the MLE to estimate $\hat{\mu}$ and $\hat{\sigma}$ for LiDAR point clouds. The log-normal MLE function is: + +$$ +\left\{ \begin{array}{l} \frac {\partial \ln L (\mu , \sigma^ {2})}{\partial \mu} = \frac {1}{\sigma^ {2}} \sum_ {i = 1} ^ {n} (\ln r _ {i} - \mu) = 0 \\ \frac {\partial \ln L (\mu , \sigma^ {2})}{\partial \sigma^ {2}} = - \frac {n}{2 \sigma^ {2}} + \frac {1}{2 \sigma^ {4}} \sum_ {i = 1} ^ {n} (\ln r _ {i} - \mu) ^ {2} = 0 \end{array} . \right. \tag {2} +$$ + +According to the Eq. 2 and we get the $\hat{\mu}$ and $\hat{\sigma}$ for the LiDAR point clouds probability density function: + +$$ +\left\{ \begin{array}{l} \hat {\mu} = \frac {1}{n} \sum_ {i = 1} ^ {n} \ln r _ {i} \\ \hat {\sigma} = \sqrt {\frac {1}{n} \sum_ {i = 1} ^ {n} \left(\ln r _ {i} - \frac {1}{n} \sum_ {i = 1} ^ {n} x _ {i}\right) ^ {2}}. \end{array} \right. \tag {3} +$$ + +Then, we sample the LiDAR and virtual point cloud based on the distribution of $LN(\hat{\mu},\hat{\sigma}^2)$ , which unified the distribution of two different types of point cloud. As Fig. 4 shows, the distribution-based adaptive sample module makes the virtual point cloud more similar to the LiDAR point cloud in distribution and patterns compared to the random sample and depth-based adaptive sample. + +# 3.4. Graph-based Correspondence Selection + +We establish the 3D-3D correspondences according to the point features of two types of point cloud descriptors and + +reproject them back to the image to generate coarse 2D-3D correspondences. Given two correspondences $C_i = (x_i, y_i)$ and $C_j = (x_j, y_j)$ , we denote the position descriptor distance as: + +$$ +d _ {i j} = \left| \left\| x _ {i} - x _ {j} \right\| _ {2} - \left\| y _ {i} - y _ {j} \right\| _ {2} \right|. \tag {4} +$$ + +Then, we define the pair-wise feature distance of correspondence as: + +$$ +S _ {d i s t} \left(C _ {i}, C _ {j}\right) = F _ {s} \left(\frac {\left(f _ {C _ {i}} - f _ {C _ {j}}\right) \cdot d _ {i j}}{\sigma_ {c d}}\right), \tag {5} +$$ + +where $f_{x}$ and $f_{y}$ are the feature of the point, $f_{C} = f_{x} - f_{y}$ is the feature of the correspondence, $F_{s}$ is a sinusoidal function proposed by [48], and $\sigma_{cd}$ is a hyperparameter that can tune the sensitivity of feature distance variations. Inspired by the recent work [49], we conduct KNN based on the correspondence feature distance (CFD) matrix to construct the original graph. The graph is denoted as $\mathcal{G} = (\mathcal{V},\mathcal{E})$ , where nodes are correspondences and edges are represented by the adjacency matrix $\mathcal{E}$ . As the Fig. 5 shows, we construct adjacency matrix $\mathcal{E}$ based on the CFD matrix. For feature distance threshold $\varepsilon$ , if the correspondence $C_i$ and $C_j$ in the same cluster, and distance $S_{dist} \leq \varepsilon$ , the weight of that edge would be 1; otherwise, the weight would be the 0. We adopt 2 layers of graph neural network (GNN) to make the reliable correspondence features get closer on the same edge and reject false correspondences. The GNN layer is defined as: + +$$ +F ^ {(l + 1)} = \operatorname {R e L U} \left(\widetilde {\mathbf {D}} ^ {- \frac {1}{2}} \widetilde {\mathbf {A}} \widetilde {\mathbf {D}} ^ {- \frac {1}{2}} F ^ {(l)} \mathbf {W} ^ {(l)}\right), \tag {6} +$$ + +where $F^{(l)}$ is the correspondence features, $\widetilde{\mathbf{D}}^{-\frac{1}{2}}\widetilde{\mathbf{A}}\widetilde{\mathbf{D}}^{-\frac{1}{2}}$ is the normalized adjacency matrix, and $\mathbf{W}^{(l)}$ is the projection matrices. After graph-based learning, the consistency of the correct correspondences gets better by pruning the false correspondences in the original graph. + +# 3.5. Loss Function + +The loss function for our end-to-end training can be divided into two parts: coarse correspondence generation loss and graph-based globe correspondence selection loss. As for the first part, we apply circle loss $\mathcal{L}_{desc}$ proposed in [50, 51] to supervise the point-wise position descriptor as follows, + +$$ +\begin{array}{l} \mathcal {L} _ {\text {p o s n .}} = \frac {1}{N} \sum_ {k = 1} ^ {N} \log \left[ 1 + \sum_ {i \in c _ {p}} \exp \left(\lambda_ {p} ^ {i} \left(d _ {k} ^ {i} - m _ {p}\right)\right) \right. \tag {7} \\ \cdot \sum_ {j \in \hat {c} _ {n}} \exp \left(\lambda_ {n} ^ {j} \left(m _ {n} - d _ {k} ^ {j}\right)\right) ], \\ \end{array} +$$ + +where $d_k^i = \left\| f_{x_i} - f_{y_j}\right\|_2$ denotes distance in feature space, and $m_p, m_n$ are positive and negative margins, respectively. The weights $\lambda_p^i = \theta (d_k^i - m_p)$ and $\lambda_n^j = \theta (m_n - d_k^j)$ are learning parameters for each positive and negative example. As for the second part, we utilize contrastive loss to supervise graph learning. False correspondences are pruned based on the CFD in the feature space, while correct correspondences have better consistency in pattern. We intro + +duce correspondences selection loss $L_{sel}$ to supervise this process as follows, + +$$ +\mathcal {L} _ {S e l.} = - \sum_ {i = 1} ^ {N} \log \frac {\exp \left(W _ {y _ {i}} f _ {g} ^ {i} + b _ {y _ {i}}\right)}{\sum_ {k = 1} ^ {K} \exp \left(W _ {k} f _ {g} ^ {i} + b _ {k}\right)}, \tag {8} +$$ + +where $y_{i}$ is the true label of correspondence feature $f_{g}^{i}$ , $K$ denotes the group number of the correspondences, and $N$ is mini-batch size. Then we get the combined loss function as, + +$$ +\mathcal {L} = \mathcal {L} _ {\text {p o s n .}} + \alpha \mathcal {L} _ {\text {S e l .}}. \tag {9} +$$ + +where $\alpha$ is hyper-parameters, balancing the impact of position match loss and correspondence selection loss. + +# 4. Experiment + +# 4.1. Datasets + +We follow previous works [9, 10, 14-17, 39] to conduct experiments on two widely used outdoor benchmarks, i.e., the KITTI Odometry [8] and nuScences [52] datasets. On both datasets, the images and point clouds are captured simultaneously with 2D cameras and 3D LiDARs. We evaluate the performance of our proposed method for both the same-frame pairs and non-synchronized random-frame pairs Image-to-Point Cloud registration. + +KITTI Odometry [8]. We follow the train/test split in DeepI2P [9], utilizing the 0-8 sequences for training, and 9-10 for testing. Besides, similar to DeepI2P [9], we generate the non-synchronized frame pairs by randomly selecting image and point cloud frame within $\pm 10m$ . The random mis-registration transformation is conducted with a 2D translation on the ground within $\pm 10m$ and a rotation around the up-axis within $[-2\pi, 2\pi]$ . The image size was set to $160 \times 512$ as[15] and the point cloud size to 40960 during training and testing, respectively. + +nuScenes [52]. We follow the setting utilized in CorrI2P [10] to build point clouds set at the size of radius $80m$ . Furthermore, we leverage the official SDK to generate nonsynchronized image-point cloud pairs, where the image frame and point cloud frame initial position are within $\pm 10m$ . We follow the official data split of nuScenes to utilize 850 scenes for training and 150 scenes for testing. The mis-registration transformation setting is conducted in the same way as the KITTI dataset. We downsample the image resolution to $160\times 320$ as [15] and the point cloud size to 40960 during training and testing, respectively. + +# 4.2. Experimental Settings + +Evaluation Metrics Following the previous works [9, 16], we evaluate the performance of the Image-to-Point Cloud registration with widely used metrics: Relative Translation Error (RTE), Relative Rotation Error (RRE), Registration Recall (RR). As for the Inlier Ratio (IR), unlike the single modality registration task, we take the correspondence as the inlier if the distance between the projected point and + +Table 1. The Image-to-Point Cloud registration experimental results on the KITTI [8] and nuScenes [52] datasets on the same-frame setting. Lower is better for RTE and RRE, higher is better for RR. The best results are indicated in bold. + +
MethodTypeKITTInuScenes
\(RTE(m)\)↓\(RRE(°)\)↓RR(%)↑\(RTE(m)\)↓\(RRE(°)\)↓RR(%)↑
vpc + GeoTransformer[5]Point-to-Point3.43 ± 5.866.15 ± 11.3770.342.08 ± 2.754.30 ± 3.4142.87
vpc + HunterPoint-to-Point4.12 ± 12.615.35 ± 8.8053.672.57 ± 2.403.78 ± 4.0348.65
DeepI2P(2D) [9]Image-to-Point3.59 ± 3.097.56 ± 7.6325.952.68 ± 2.024.80 ± 6.2140.10
CorrI2P [10]Image-to-Point3.78 ± 65.165.89 ± 20.3462.423.04 ± 12.483.73 ± 9.0349.00
VP2P [15]Image-to-Point0.75 ± 1.133.29 ± 7.9984.040.89 ± 1.442.15 ± 7.0588.33
2D-3D Matr [38]Image-to-Point0.82 ± 1.381.98 ± 2.3693.101.36 ± 1.691.77 ± 2.1790.62
RetrI2P [14]Image-to-Point0.67 ± 0.942.89 ± 3.2186.720.67 ± 0.871.84 ± 3.4189.47
FreeReg [13]Image-to-Point0.95 ± 1.052.06 ± 3.2191.68---
CFI2P [16]Image-to-Point0.63 ± 1.191.72 ± 2.5897.150.86 ± 1.471.83 ± 1.2895.23
GraphI2P(Ours)Image-to-Point0.32 ± 0.811.65 ± 1.3299.610.49 ± 1.221.73 ± 1.6399.48
+ +Table 2. The Image-to-Point Cloud registration experimental results on the KITTI [8] and nuScenes [52] datasets on the non-synchronized random-frame setting. Lower is better for RTE and RRE, higher is better for RR. The best results are indicated in bold. + +
MethodTypeKITTInuScenes
RTE(m) ↓RRE(°) ↓RR(%) ↑RTE(m) ↓RRE(°) ↓RR(%) ↑
vpc + GeoTransformer[5]Point-to-Point4.27 ± 7.148.67 ± 8.5535.284.08 ± 2.656.30 ± 3.4116.77
vpc + HunterPoint-to-Point4.59 ± 5.226.23 ± 5.1738.613.75 ± 4.074.22 ± 3.4031.90
DeepI2P(2D) [9]Image-to-Point5.15 ± 7.359.14 ± 8.0210.674.85 ± 5.197.15 ± 5.8223.36
CorrI2P [10]Image-to-Point4.24 ± 7.266.47 ± 5.2042.314.29 ± 5.056.40 ± 4.2636.79
VP2P [15]Image-to-Point2.05 ± 3.234.01 ± 6.3773.04---
2D-3D Matr [38]Image-to-Point1.86 ± 3.792.59 ± 4.4683.93---
RetrI2P [14]Image-to-Point1.61 ± 2.393.16 ± 2.8579.171.73 ± 2.343.42 ± 3.4177.50
FreeReg [13]Image-to-Point1.78 ± 1.762.89 ± 4.4783.68---
CFI2P [16]Image-to-Point1.95 ± 2.972.63 ± 3.1984.631.89 ± 3.443.20 ± 3.5381.05
GraphI2P(Ours)Image-to-Point0.68 ± 0.951.91 ± 2.0495.400.83 ± 1.402.21 ± 3.2693.58
+ +ground-truth pixel is smaller than a threshold $\tau_{d}$ as follows, + +$$ +\operatorname {I R} = \frac {1}{| \tilde {\mathcal {C}} |} \sum_ {(\mathbf {u} _ {i}, \mathbf {p} _ {i}) \in \tilde {\mathcal {C}}} \left[ \left[ \| \mathbf {u} _ {i} - \mathcal {F} _ {p} (\mathbf {K} \bar {\mathbf {T}} \mathbf {p} _ {i}) \| \leq \tau_ {d} \right] \right], \tag {10} +$$ + +where $\llbracket \cdot \rrbracket$ is the Iversion bracket and $\tilde{C}$ is the estimated correspondences set, $\bar{\mathbf{T}}$ is the transformation matrix (i.e., $\bar{\mathbf{T}} = [\bar{\mathbf{R}} |\bar{\mathbf{t}} ]$ ), and $\mathbf{K}$ is the camera intrinsic. We follow the VP2P [15] evaluation metrics to report the RTE, RRE, and RR performances rather than to follow the CorrI2P [10] settings, which removes the image-point cloud samples with serious errors before averaging. We further report the registration recall as VP2P [15] setting, which is the proportion of fine registrations with RTE $< 2m$ , RTE $< 5^{\circ}$ on the KITTI and nuScenes datasets. + +Compared methods. We compare our method with the state-of-the-art Image-to-Point Cloud registration methods CFI2P [16], and VP2P [15]. Moreover, as our method introduces a virtual point cloud as a bridge to alleviate the modality gap, we compare it to the Point Cloud-to-Point Cloud registration methods, such as GeoTransformer [5] and Hunter [31]. We also compare to the indoor state-of-the-art Image-to-Point Cloud registration method such as 2D3D-Matr [38]. To further verify the superiority of + +![](images/32ea0b10518d5ddcf9e1af10e3b87458658918578f72b79fe9dd7adb70b708c1.jpg) + +![](images/b6fc730cb3e83383fc95dba1ee5e1ae627d2da4f90b00c42282fbe971e40d23f.jpg) +Figure 6. Curves of IR across different thresholds. The first row is the results of the same-frame setting on KITTI and nuScenes datasets. The second row shows the results of the non-synchronized random-frame setting on both datasets. + +![](images/7f143c8c9d2b7dfd38abfc18e6b9c7766e5275f458884698d4bdbd28de13635f.jpg) + +![](images/80f11287416e40708263f8bbb6211ba2d4ec417f0b4f7eb149822675163e534a.jpg) + +our proposed method, we also compare it with the depth estimation-based methods FreeReg [13] and RetrI2P [14]. We evaluate all available methods in the same-frame setting and non-synchronized frame setting. + +Implementation details. Our registration framework first employs a pre-trained depth estimation model from zoe-depth [43], to generate dense depth maps and then convert them to virtual point clouds. To avoid the impact of the sky in the image in cross-modality registration, we follow the previous work [9, 10, 15] settings to crop the top + +![](images/1471e2878e898267e72c7d96cd91624a479b73257ce3bbfac31ea5b01ba7e1c4.jpg) +Figure 7. Visual comparison of Image-to-Point Cloud registration results on KITTI dataset. The initial offset of the input image and point cloud pairs is larger than $75^{\circ}$ and $10m$ . The yellow boxes highlight the mis-registration parts. + +![](images/eb8cefd26f35db1cb42ef9de9d34a9d8c3ef39a5cc1a1d30dea4704202385065.jpg) +Figure 8. Visual comparison of Image-to-Point Cloud registration results on nuScenes dataset. The initial offset of the input image and point cloud pairs is larger than $75^{\circ}$ and $10m$ . The yellow boxes highlight the mis-registration parts. + +50 pixels of the generated depth maps on both KITTI and nuScenes datasets. To conduct the end-to-end training process, we do not take the RANSAC [34] as previous work [9, 10] in the final registration step. All the experiments are conducted on an NVIDIA RTX 3090 GPU. + +# 4.3. Register Performance + +Quantitative comparison. The experiment results are demonstrated in Tab. 1 and Tab. 2, where we can observe that our method outperforms the state-of-the-art Image-to-Point Cloud method CFI2P [15] on both KITTI [8] dataset with $10.77\%$ and nuScenes [52] dataset with $12.53\%$ in registration recall significantly in non-synchronized random + +frame setting. Our method replaces the traditional frustum selection module with a graph-based globe correspondence selection module, avoiding the points classification error caused by the two-stage frameworks. Moreover, our method also demonstrates superiority on the same-frame registration with $2.46\%$ and $4.25\%$ , respectively. Due to the point clouds in the nuScenes dataset being captured by 32-line LiDAR, the cross-modality registration on that becomes more challenging, and our methods show more advances for the distribution adaptive sample module. To further verify the effectiveness of our proposed virtual point cloud-based method, we conduct more experiments compared with the latest Point Cloud-to-Point Cloud registra + +tion methods. The results in Tab. 1 and Tab. 2 reveal that classic Point-to-Point methods are unsuitable for application on virtual point clouds due to the significant domain and distribution gap between the real LiDAR and virtual point clouds. Besides, for a more detailed comparison of the registration performance, we demonstrate the IR of the correspondences between the image and point cloud with different threshold $\tau_{d}$ in pixels in Fig. 6. As a result, our method can achieve satisfactory cross-modality registration performance compared with existing methods, especially when the image and point cloud are from different frames. + +Qualitative comparison. We conduct a qualitative comparison with the recent state-of-the-art Image-to-Point Cloud registration methods such as CorrI2P [10], VP2P [15] and CFI2P [16] on KITTI and nuScenes datasets non-synchronized random-frame setting as Fig. 7 and Fig. 8 shows. For visual comparison, the point cloud is projected into images with the extrinsic parameters predicted by compared methods. Most of the initial offset of the input image and point cloud pairs is much larger than $75^{\circ}$ and $10m$ . We highlight the regions with significant discrepancies between the point cloud and the image using boxes, which simultaneously contain the marker object in both modalities. The larger boxes in the same row demonstrate more serious mis-registration. As observed from Fig. 7, we can observe that registration becomes more challenging in scenes lacking distinct landmarks, such as the first rows. Thanks to the adaptive sample module, our method performs better in different road environments where the streetlights and cars demonstrate that only our method achieves relatively satisfactory registration performance in the scenarios with more sparse point clouds, as Fig. 8 shows. + +# 4.4. Ablation Study + +The effect of each component of the framework. The importance of each component introduced in GraphI2P Sec. 3 is evaluated by ablating the method in Tab. 3. We conduct the ablation study with the non-synchronized random-frame setting on the KITTI dataset. Specifically, we compare three different variations: (1) $w/o$ V-S. Repre. is the variation removing the virtual-spherical representation module and conducting the experiment in Cartesian coordinate; (2) $w/o$ A-D. Sample is the variation removing the adaptive distribution sample module; (3) $w/o$ Graph Sel. is the variation removing the graph-based correspondence selection module. The results are demonstrated in Tab. 3, from which we can observe that our full framework achieves the best performances in overall variations. Such results prove the effectiveness of each component in our framework. Moreover, we can observe that the graph-based correspondence selection module plays the most important role in our framework, followed by the A-D sample module. + +The effect of input point cloud density. We further + +Table 3. The effect of each component of the framework. + +
RTE(m)↓RRE(°)↓RR(%) ↑
w/o V-S. Repre.0.86 ± 1.902.28 ± 2.4690.07
w/o A-D. Sample.1.33 ± 1.522.61 ± 1.9484.81
w/o Graph Sel.1.63 ± 2.513.12 ± 3.2980.25
Full0.68 ± 0.951.91 ± 2.0495.40
+ +explore the impact of the LiDAR point cloud density on our method performance with an on-synchronized random-frame setting on the KITTI dataset. The results in Table 4 show the trends of the registration recall decreasing with the density dropping. We can observe that when the point cloud density falls below a certain threshold, the registration performance significantly degrades. When the point cloud density exceeds 10,000 points, our method outperforms other methods, even these methods utilize more points. Therefore, when resources are limited, we can sample at least 10,000 points as a sufficient choice. + +Table 4. The effect of point cloud density. + +
PointRTE(m)↓RRE(°)↓RR(%)↑IR(%)
51202.83 ± 4.143.58 ± 4.8375.818.47
109601.37 ± 1.842.48 ± 0.9487.8539.18
204800.91 ± 1.342.37 ± 1.9493.6446.28
409600.68 ± 0.951.91 ± 2.0495.4070.63
+ +# 5. Conclusion + +In this paper, we introduce a graph-based Image-to-Point Cloud registration method, which can effectively solve the non-synchronized random-frame registration. In this way, the modality gap is converted to the domain gap of point clouds by introducing the depth estimation. Moreover, we propose a virtual-spherical representation and distribution-based adaptive sample module to narrow the domain gap between virtual and LiDAR point clouds. Then, we explore the reliable correspondence pattern consistency through a graph-based selection. Experimental results demonstrate that our method outperforms the state-of-the-art methods with $10.77\%$ and $12.53\%$ performance on the KITTI Odometry and nuScenes datasets in non-synchronized random-frame settings, respectively. More experiments on 3D random rotation should be conducted in the future. + +# 6. Acknowledgement + +This work was supported by the Beijing Natural Science Foundation (No. L242167), National Key Laboratory of Human-Machine Hybrid Augmented Intelligence, Xi'an Jiaotong University (No. HMHAI-202412). We would like to express our sincere gratitude to OPPO for their generous support of our work. + +# References + +[1] Anh-Duc Nguyen, Seonghwa Choi, Woojae Kim, Jongyoo Kim, Heeseok Oh, Jiwoo Kang, and Sanghoon Lee. Single-image 3D reconstruction: Rethinking point cloud deformation. IEEE Transactions on Neural Networks and Learning Systems, 35(5):6613-6627, 2024. 1 +[2] Paul-Edouard Sarlin, Daniel DeTone, Tsun-Yi Yang, Armen Avetisyan, Julian Straub, Tomasz Malisiewicz, Samuel Rota Bulo, Richard Newcombe, Peter Kontschieder, and Vasileios Balntas. Orienternet: Visual localization in 2D public maps with neural matching. 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However, the significant expense of collecting such action-labeled robot data presents a major bottleneck. Video data, a rich data source encompassing diverse behavioral and physical knowledge, emerges as a promising alternative. In this paper, we present GraphMimic, a novel paradigm that leverages video data via graph-to-graphs generative modeling, which pre-trains models to generate future graphs conditioned on the graph within a video frame. Specifically, GraphMimic abstracts video frames into object and visual action vertices, and constructs graphs for state representations. The graph generative modeling network then effectively models internal structures and spatial relationships within the constructed graphs, aiming to generate future graphs. The generated graphs serve as conditions for the control policy, mapping to robot actions. Our concise approach captures important spatial relations and enhances future graph generation accuracy, enabling the acquisition of robust policies from limited action-labeled data. Furthermore, the transferable graph representations facilitate the effective learning of manipulation skills from cross-embodiment videos. Our experiments exhibit that GraphMimic achieves superior performance using merely $20\%$ action-labeled data. Moreover, our method outperforms the state-of-the-art method by over $17\%$ and $23\%$ in simulation and real-world experiments, and delivers improvements of over $33\%$ in cross-embodiment transfer experiments. + +# 1. Introduction + +Imitation learning from demonstrations has become an effective paradigm for teaching robots to perform diverse be + +![](images/d795299479a5cc25a8604a5b2b70ae2e00fdd391e1b75f5caec3eb6a1d1d861e.jpg) +(a) Graph-to-Graphs Generative Modeling + +![](images/6dbe4deeaeca105e24c1c9948a54c905eaf1f1120bf1535629843c06971aec65.jpg) +(b) Comparisons with Baselines +Figure 1. Illustration of our GraphMimic. (a) GraphMimic constructs the graph within a video frame, and pre-trains models to generate future graphs, providing effective guidance for policy learning. (b) GraphMimic achieves superior performance using merely $20\%$ action-labeled data, and significantly outperforms strong video pre-training baseline methods. + +haviors [1]–[4]. However, demonstration collection often necessitates substantial human effort, posing a bottleneck for robot learning. Confronted with this challenge, videos emerge as a promising alternative, offering a rich data source encompassing behavioral and physical knowledge. + +Prior work has explored various approaches to leverage video data, including visual pre-training [5]–[11], learning reward functions [12]–[17]. However, these methods overlook the transition dynamics or encounter a significant sim-to-real gap. Recent research [18]–[23] attempted to address these by pre-training models on video data to predict subsequent images or points from the current ones, then leveraging such predictions to guide policy learning on action-labeled data. While these approaches have demonstrated potential, they + +directly model representations from pixel space, neglecting the modeling of important structures, typically the underlying internal structures of objects, the spatial relationships between objects, as well as the relationships between objects and effectors. Correspondingly, graph representations inherently encode spatial relational bias, enabling effective structural modeling. Furthermore, we can directly incorporate visual action vertices into constructed graphs, capturing the relationships between objects and effectors. Inspired by the encouraging properties of graph representation, we naturally ask the question: Can we formulate video pre-training as graph-to-graphs generative modeling, enabling policy learning on limited action-labeled data? + +To answer this question, we exploit the graph-to-graphs generative modeling scheme for effective video pre-training. However, several challenges must be overcome: (I) The source video and target scene often exhibit substantial embodiment discrepancy, hindering the transfer of learned action knowledge. To address this issue, we propose the action-informed transferable graph representation, which extracts visual action vertices by abstracting key interaction points of the embodiment, facilitating cross-embodiment transfer. Furthermore, the representation incorporates vertices on relevant objects, independent of specific embodiments. (II) The properties of distinct objects exhibit significant variability, such as stiffness, inhibiting the generative modeling network from capturing diverse object behaviors. To address this challenge, we propose to infer properties from historical observations and integrate them into graphs, facilitating predictions for objects with distinct properties. (III) Modeling long-range dependencies is crucial for capturing spatial relationships, but directly expanding edge construction range potentially overwhelms important internal structures. To optimize this trade-off, we present a hierarchical architecture, integrating global vertices for long-range information propagation, enabling the effective modeling of important internal structures and spatial relationships. + +Based on the above analysis, we present GraphMimic, a novel approach that formulates video pre-training as graph-to-graphs generative modeling. GraphMimic abstracts video frames into objects and visual action vertices, and constructs action-informed transferable graphs for state representations, providing spatial relational bias while facilitating cross-embediment transfer. Subsequently, the graph generative modeling network extracts object properties and establishes a hierarchical architecture to effectively model internal structures and spatial relationships, accurately generating future graphs conditioned on the constructed graphs. The generated graphs, as shown in Figure 1, function as guidance for the control policy, facilitating the mapping to robotic actions. Our concise approach effectively captures important structural information, improving graph generation accuracy and enabling robust policy learning from limited action-labeled + +data. Furthermore, the transferable graph representations facilitate the effective learning of manipulation skills from cross-embodiment videos. Our extensive experiments exhibit that our GraphMimic achieves superior performance with only $20\%$ of the data required by baselines, and significantly outperforms them with identical data volumes. + +Our main contributions can be summarized as follows: (I) We propose GraphMimic, a novel framework that bridges video pre-training to policy learning via graph-to-graphs generative modeling. GraphMimic constructs action-informed transferable graphs within video frames, and generates future graphs to provide precise and expressive guidance. (II) We propose an object property estimation approach to facilitate behavior predictions for diverse objects, and introduce a hierarchical architecture to capture local structures and spatial relationships. (III) Extensive experiments spanning over 140 tasks demonstrate that our method surpasses the state-of-the-art method by more than $17\%$ and $23\%$ in simulation and real-world experiments, and exhibits over $33\%$ enhancement in cross-embodiment transfer experiments. + +# 2. Related work + +# 2.1. Learning from Videos for Manipulation + +Learning from video data provides a promising paradigm to alleviate the reliance on expensive action-labeled robot data. To leverage easily accessible video data resources, multiple learning frameworks are proposed for robot learning. A plethora of recent research [9], [10], [24]–[27] focuses on learning task-relevant priors from videos to guide robot behaviors or derive a heuristic reward function for reinforcement learning. These methods encounter challenges in bridging the sim-to-real gap and constructing task-specific environments. Another line of work [6], [28], [29] explores leveraging large-scale human video data to pretrain visual representations for subsequent imitation learning tasks. However, a visual representation only describes the state at the current time step, largely neglecting the transition dynamics. More recently, several works [18]–[22], [30], [31] have explored video learning through video generation or flow generation. UniPi [18] proposes to leverage text-guided video generation to create versatile agents. ATM [21] leverages video demonstrations to pre-train a trajectory generation model, bridging video pre-training and policy learning. However, these methods directly model representations from pixel space, neglecting the modeling of important structures. + +# 2.2. Graph Representations for Manipulation + +A large body of work has studied leveraging graph representation for robotic manipulation. Among these, dynamic model learning methods [32]–[39] utilize graph neural networks (GNNs) to model object particles, studying the prediction of object particle motion under given robot actions. + +![](images/6ac14bcbb71afb0f4a32f3c56a8d3d2f5d4228b7265cf4c91c2a2aa0cfae4d89.jpg) + +![](images/1da38bc065a07b23f917e0c788e5eb71b4dcd30e418d186d89ef0c4d10544c05.jpg) +Figure 2. Illustration of our GraphMimic. (a) GraphMimic constructs graphs for video frame representations, we only show two visual action vertices for simplicity. GraphMimic subsequently predicts object properties and establishes the hierarchical structure, aiming to generate subsequent graphs. (b) The graph-guided policy is trained to predict robot actions based on these generated future graphs. + +DefGraphNets [37] predicts 3D stress and deformation fields in deformable object grasping, enabling efficient gradient-based grasp optimization. Wang et al. [33] propose dynamic-resolution particle representations and a GNN-based unified dynamics model for adaptive abstraction levels in visual model-predictive manipulation tasks. Another line of work [40]–[42] constructs graph abstraction-based reward function, and trains policies through reinforcement learning. The recent GraphIRL [42] employs graph abstraction on the videos followed by temporal matching to measure the task progress, and a dense reward function is employed to train reinforcement learning algorithms. However, these methods still struggle with a significant sim-to-real gap and the complexity of building task-specific environments. Different from the above-mentioned methods, this study explores the utilization of graph representations to extract motion guidance from video data, thereby reducing the reliance on expensive action-labeled robot data. + +# 3. Preliminary + +Graph neural networks (GNNs) [43]–[45] are a powerful tool for machine learning on graphs. They combine vertex feature information with the graph structure by recursively passing neural messages along the edges of the input graph. GNNs utilize the vertex features $\Phi$ and the graph structures $\mathcal{G} = (\mathcal{V},\mathcal{E})$ to learn representations, where $\mathcal{V}$ indicates the vertex set, and $\mathcal{E}$ denotes the edge set. At layer $l$ , the model first computes pairwise neural messages for all vertex pairs $(v_{i},v_{j})$ , where $v_{i},v_{j}\in \mathcal{V}$ , connected by edge $e_{ij}\in \mathcal{E}$ : + +$$ +m _ {i j} ^ {l} = \operatorname {M s g} \left(\Phi_ {i} ^ {l - 1}, \Phi_ {j} ^ {l - 1}, e _ {i j}\right). \tag {1} +$$ + +Subsequently, for each vertex $v_{i}$ , GNNs aggregate messages from the neighborhood $\mathcal{N}_{v_i}$ of vertex $v_{i}$ and calculate an + +aggregated message $M_{i}^{l}$ [46], [47]: + +$$ +M _ {i} ^ {l} = \operatorname {A g g} \left(\left\{m _ {i j} ^ {l} \mid v _ {j} \in \mathcal {N} _ {v _ {i}} \right\}\right). \tag {2} +$$ + +Finally, GNNs take the aggregated message $M_{i}^{l}$ along with the representation $\Phi_{i}^{l-1}$ from the previous layer, non-linearly transform them to obtain the representation $\Phi_{i}^{l}$ at layer $l$ : + +$$ +\Phi_ {i} ^ {l} = \operatorname {U p d a t e} \left(M _ {i} ^ {l}, \Phi_ {i} ^ {l - 1}\right). \tag {3} +$$ + +The features $\Phi^L$ from the last layer $L$ serve as the final representations $\mathcal{Z}$ . + +# 4. GraphMimic + +Considering the action-free video dataset $\mathcal{T}^o = \{(\tau_i^o,\ell_i)\}_{i = 1}^{N_o}$ and action-labeled robot demonstration dataset $\mathcal{T}^a = \{(\tau_i^a,\ell_i)\}_{i = 1}^{N_a}$ , where $\ell_{i}$ is the language instruction for the $i^{th}$ episode, $\tau_{i}^{o} = \{o_{i,t}\}_{t = 1}^{T}$ denotes the observation sequence consisting of camera images, and $\tau_{i}^{a} = \{o_{i,t},a_{i,t}\}_{t = 1}^{T}$ is the action-labeled sequence. The objective is to leverage the easily accessible, unlabeled videos $\mathcal{T}^o$ for pre-training, learning a policy to mimic the expert behavior. + +The overall pipeline of GraphMimic is illustrated in Figure 2. GraphMimic first constructs graphs within video frames. Then, the generative modeling network is pre-trained to generate future graphs conditioned on the constructed graphs. It predicts object properties and establishes the hierarchical structure to capture important local structures and spatial relationships, aiming to generate future graphs. The policy network predicts robot actions conditioned on these generated future graphs through few-shot learning from action-labeled demonstrations. + +# 4.1. Action-informed Transferable Graph + +We construct graph representation $\mathcal{G}_t = (\mathcal{V}_t, \mathcal{E}_t)$ based on the task description $\ell$ and an image observation $o_t$ at timestep + +$t$ , where $\mathcal{V}_t$ indicates the vertex set consisting of object and visual action vertices $\{\mathcal{V}_t^\Omega, \mathcal{V}_t^a\}$ , and $\mathcal{E}_t$ denotes the edge set representing interacting vertex pairs. + +Object vertices. The object graph dynamics describe the change in object state, irrelevant to the agent embodiment, enhancing the cross-embediment learning ability of GraphMimic. In the initial phase of task execution, we utilize Vision Language Models (VLMs) to derive and compile the task-related objects $\Omega$ into textual information [48], predicated on the text instruction $\ell$ and initial image observation $o_0$ . Subsequently, for time step $t$ in the task progression, an efficient segmentation model [49] is utilized to predict the corresponding object masks on the current image observation $o_t$ , followed by applying a uniform sampling strategy within these predicted masks, obtaining the vertex set $\mathcal{V}_t^{\Omega_i} = \{v_{k,t}^{\Omega_i}\}_{k=1}^{N_{\Omega_i}}$ with $N_{\Omega_i}$ vertex for object $\Omega_i$ . + +Visual action vertices. The incorporation of action vertices enables our approach to capture important object-embedment interactions. However, the morphological heterogeneity among diverse embodiments impedes direct motion transfer across different embodiments. To overcome this challenge, we abstract embodiments into key interaction points, capturing their topological information with objects. For human videos, a major source of video data, we extract fingertip positions as key interaction points $\mathcal{V}_t^a = \{v_{k,t}^a\}_{k=1}^{N_a}$ based on previous research indicating that fingertips are the most frequently contacted areas during object manipulation [50]–[53]. This approach enables GraphMimic to learn general principles of physical interactions with objects, focusing on the functional aspects of manipulation and facilitating cross-embedment transfer. + +Graph construction. Utilizing the object and visual action vertices, edges are established, yielding the graph representation $\mathcal{G}_t$ for the current observation. In our experiments, bidirectional edges are established between vertex pairs with distances less than $d$ . The transferable graph representations facilitate the effective learning of manipulation skills from cross-embediment videos. Additionally, it provides meaningful spatial relational bias for the graph generative modeling network, enhancing the structural modeling capacity and thus improving the graph generation accuracy. + +# 4.2. Property-aware Graph Generative Modeling + +The objective is to pre-train a model on videos for forecasting future graph sequences. The graph generative modeling network then predicts the graphs $\mathcal{G}_{t:t + F_{\mathcal{G}}}$ over the $F_{\mathcal{G}}$ future steps, conditioned on the current image observation $o_t$ , historical observations $o_{t - H:t}$ , and a language instruction $\ell$ . + +Object property estimation. Objects exhibiting divergent properties tend to manifest distinct motion patterns. A straightforward approach for providing such awareness to the network is to condition it on human-provided parameters [54], such as stiffness. However, most of the demon- + +![](images/95aa0b20afc96b64bd71f1ea05ef2a3c914cb0deb1e3a22b0a4327da5c50256a.jpg) +Figure 3. (a) Object features are extracted from the historical graphs, and these features are fed into an LSTM network to model long-term dependencies, predicting object properties. (b) We cluster the vertices and designate a global vertex for each cluster, then construct edges to connect within the hierarchical structure. + +![](images/b226d21a8761c183b66de14501e72a25532bd620daac2dfd5de4bbcf9745e099.jpg) + +stration data lacks accurate numerical values, hindering the model training. Moreover, defining these parameters by hand presents a barrier to fast and easy deployment of the network. Instead, we propose a concise and automatic approach that utilizes a sequence of consecutive past observations to infer learned object properties $\phi_t^\Omega$ . As shown in Figure 3 (a), we first retrieve object-centric graphs $\mathcal{G}_{t-H:t}^{\Omega_i}$ from graphs $\mathcal{G}_{t-H:t}$ , where the vertex set $\mathcal{V}^{\Omega_i}$ comprises solely vertices on object $\Omega_i$ , and the edge set $\mathcal{E}^{\Omega_i}$ is restricted to edges whose incident vertices both correspond to $\Omega_i$ . We then leverage an online tracking algorithm [55] to obtain the vertex set $\mathcal{V}_{t-H:t}^{\Omega_i}$ across historical observations. Subsequently, the vertex embedding $\Phi_{k,t}^{\Omega_i} \in \Phi_t^{\Omega_i}$ for the $k^{th}$ vertex $v_{k,t}^{\Omega_i}$ is generated by incorporating the historical position information $x_{k,t-H:t}^v$ , and the vertex attribute $c_{k,t}^v$ , which denotes the semantic category of vertex $v_{k,t}$ . Then, an L-layer GNN network performs iterative message passing to aggregate information along the established edges. The resulting features $\mathcal{Z}_{k,t}^{\Omega_i}$ are average pooled across vertices to form the object graph features $\bar{\mathcal{Z}}_t^{\Omega_i}$ as follows: + +$$ +\Phi_ {t} ^ {\Omega_ {i}} = \operatorname {M L P} \left(\left[ x _ {t - H: t} ^ {v}, c _ {t} ^ {v} \right]\right), v \in \mathcal {V} ^ {\Omega_ {i}}, +$$ + +$$ +\mathcal {Z} _ {t} ^ {\Omega_ {i}} = \operatorname {G N N} \left(\Phi_ {t} ^ {\Omega_ {i}}, \mathcal {G} _ {t} ^ {\Omega_ {i}}\right), \tag {4} +$$ + +$$ +\bar {\mathcal {Z}} _ {t} ^ {\Omega_ {i}} = \operatorname {P o o l} \left(\mathcal {Z} _ {t} ^ {\Omega_ {i}}\right). +$$ + +To establish the long-range temporal dependencies and enhance the property prediction precision, the features $\bar{\mathcal{Z}}_t^{\Omega_i}$ are fed into the long short-term memory (LSTM) module [56], and the output hidden embedding is projected to the property features $\phi_t^{\Omega_i}$ as follows: + +$$ +h _ {t}, c _ {t} = \operatorname {L S T M} \left(\tilde {\mathcal {Z}} _ {t} ^ {\Omega_ {i}}, h _ {t - 1}, c _ {t - 1}\right), \quad \phi_ {t} ^ {\Omega_ {i}} = \operatorname {M L P} \left(h _ {t}\right), \tag {5} +$$ + +where $h_t$ denotes the hidden embedding at the timestep $t$ , and $c_t$ indicates the cell embedding at the timestep $t$ . + +Hierarchical graph modeling. The estimated property features $\phi_t^\Omega$ are incorporated into the constructed graphs $\mathcal{G}_t$ . The graph generative modeling network then captures local + +structures and spatial relationships to predict future graphs. To model long-range dependencies for capturing spatial relationships, we introduce an additional hierarchical level to facilitate direct long-range message propagation. For each action and object vertex set, as shown in Figure 3 (b), we employ K-means clustering algorithm to partition the vertices into non-overlapping clusters based on their spatial locations, and the root global vertex $\mathcal{V}_{k,t}^{g}\in \mathcal{V}_{t}^{g}$ is added to each cluster, with its spatial position being the average of the spatial positions of all leaf vertices within the cluster. We then construct edges to connect within the hierarchical structure: (I) an edge set $\mathcal{E}_t^{\mathrm{L2R}}$ that contains directed edges from each leaf vertex to the corresponding root global vertex, (II) an edge set $\mathcal{E}_t^{\mathrm{R2L}}$ containing directed edges from each root to its leaf vertices, and (III) a pairwise directed edge set between all root global vertex $\mathcal{E}_t^{\mathrm{R2R}}$ . The resulting hierarchical graph $\mathcal{G}_t^h = \{\mathcal{V}_t^h,\mathcal{E}_t^h\}$ is constructed as: + +$$ +\mathcal {V} _ {t} ^ {h} = \mathcal {V} _ {t} \cup \mathcal {V} _ {t} ^ {g}, \quad \mathcal {E} _ {t} ^ {h} = \mathcal {E} _ {t} \cup \mathcal {E} _ {t} ^ {\mathrm {L 2 R}} \cup \mathcal {E} _ {t} ^ {\mathrm {R 2 L}} \cup \mathcal {E} _ {t} ^ {\mathrm {R 2 R}}. \tag {6} +$$ + +The constructed hierarchical graph is embedded through the GNN network. The position information over $H$ history timesteps $x_{k,t - H:t}^v$ , the vertex attribute $c_{k,t}^v$ , and the estimated property $\phi_{k,t}$ are integrated to form the vertex embedding. Then, an L-layer GNN network aggregates information along the established edges to derive the resulting vertex features $\mathcal{Z}_t^h$ as follows: + +$$ +\begin{array}{l} \Phi_ {t} ^ {h} = \operatorname {M L P} \left[ x _ {t - H: t} ^ {v}, c _ {t} ^ {v}, \phi_ {t} \right], v \in \mathcal {V} _ {t} ^ {h}, \tag {7} \\ \mathcal {Z} _ {t} ^ {h} = \mathrm {G N N} (\Phi_ {t} ^ {h}, \mathcal {G} _ {t} ^ {h}). \\ \end{array} +$$ + +Graph generation. The transformer-based generator incorporates the graph embedding $\mathcal{Z}_t^h$ , image embedding $\mathcal{Z}_t^o$ , and the language instruction embedding $\mathcal{Z}^\ell$ , yielding graph features $\mathcal{T}_t^h$ . The text condition is encoded via a pre-trained Bert [57], while the observation image is encoded through the ResNet [58]. Subsequently, the graph features $\mathcal{T}_t^h$ are provided to a two-layer MLP prediction head for future graph sequence generation. Since the edge associations directly depend on the positional relationships between vertices, our generation procedure can be simplified to generate vertex spatial locations $x_{t:t + F_{\mathcal{G}}}$ . The edge set is derived based on a spatial distance threshold $d$ , yielding future graphs $\mathcal{G}_{t:t + F_{\mathcal{G}}}$ . + +# 4.3. Graph Guided Policy Learning + +Our graph-conditioned policy takes the generated graphs $\mathcal{G}_{t:t + F_{\mathcal{G}}}$ , the current observation $o_t$ , and the robot proprioception $\rho_t$ as input, predicting a sequence of actions $\{a_t,\dots ,a_{t + F_a}\}$ . As shown in Figure 2(b), our policy comprises the state encoder and action head. + +State Encoder. The state encoder, comprising standard transformer blocks [59], encodes all modalities $\{\mathcal{G}_{t:t + F_{\mathcal{G}}},o_t,\rho_t\}$ at timestep $t$ to generate the state representation $s_t$ . We project each modality with modality-specific encoders into a shared embedding space, where the GNN (Eq. 7) is utilized to encode graphs, a ResNet processes + +the observation image $o_t$ , and a MLP encodes the proprioceptive information $\rho_t$ . The projected tokens $\{\mathcal{Z}_t^\mathcal{G}, \mathcal{Z}_t^o, \mathcal{Z}_t^\rho\}$ across all modalities and views are added with the modality-specific learnable positional embedding, and concatenated with a learned CLS token, then the self-attention is performed to aggregate information to the CLS token [57], the resulting CLS token is utilized as the state representation $s_t$ . Action Head. We treat each timestep's state independently, and parameterize actions using an MLP action head. To effectively integrate the guiding information from the predicted graph sequences, we concatenate the state CLS token $s_t$ with the graph tokens $\mathcal{Z}_t^\mathcal{G}$ to obtain the policy condition $\mathcal{Z}_t^c$ . Then, the MLP action head is utilized to generate the action sequences $a_{t:t + F_a}$ based on the $\mathcal{Z}_t^c$ . + +# 4.4. Model Training + +The graph generative modeling network is pre-trained on the video dataset. We employ a cotracker [60] to track these graph vertices throughout the entire video, obtaining their spatial positions and deriving graph sequences. Our loss function computes the mean squared error (MSE) between the predicted vertex positions $x_{t:t + F_{\mathcal{G}}}$ and the ground truth $x_{t:t + F_{\mathcal{G}}}^*$ in the pixel space. The graph-conditioned policy is then trained on a few-shot dataset with annotated robot actions. We combine actions $a_{t:t + F_a}^*$ with tracked future graph sequences $\mathcal{G}_{t:t + F_{\mathcal{G}}}$ , observations $o_t$ , and proprioception $\rho_t$ to construct the training dataset $\{a_{t:t + F_a}^*, \mathcal{G}_{t:t + F_{\mathcal{G}}}, o_t, \rho_t\}$ . Our graph-conditioned policy is trained with MSE loss. + +# 5. Experiments + +Baselines. GraphMimic is compared with four representative methods: (1) BC represents vanilla behavioral cloning, which trains a policy solely on action-labeled expert demonstrations. It uses a policy architecture identical to GraphMimic, but excludes graph conditions and instead utilizes language embeddings for task specification; (2) R3M [7], which employs contrastive learning to align video and language representations. We adopt pre-trained Ego4D weights and fine-tune the weights on our video dataset, to initialize the BC policy's visual encoder; (3) UniPi [18], which trains a text-conditioned video diffusion model to generate fine-grained video plans, followed by an inverse dynamics model trained on the action-labeled data. (4) ATM [21], which trains a track generation model, and a corresponding track-guided policy for action prediction. The comparisons with Diffusion policy (DP) [61] and Im2Flow2Act [30] are provided in Appendix ?? and Appendix ?? + +# 5.1. Video Pre-training for Imitation Learning + +We first investigate the capacity of GraphMimic to provide accurate and expressive state representations, enhancing robot task performance and reducing data requirements. + +Table 1. Average success rate on LIBERO benchmark. 50 videos are collected for pre-training, 'Num of L-demos' indicates the number of action-labeled demonstrations utilized for training. Results are averaged over three seeds. + +
MethodsNum of L-demosLibero-SpatialLibero-ObjectLibero-GoalLibero-LongLibero-90
BC-Full-Trainset500.71 ± 0.030.71 ± 0.080.76 ± 0.010.24 ± 0.020.38 ± 0.01
BC100.39 ± 0.080.51 ± 0.130.42 ± 0.040.16 ± 0.030.29 ± 0.01
R3M [29]100.49 ± 0.040.52 ± 0.020.05 ± 0.010.09 ± 0.030.09 ± 0.00
UniPi [18]100.69 ± 0.040.59 ± 0.030.11 ± 0.020.05 ± 0.020.07 ± 0.01
ATM [21]100.68 ± 0.020.68 ± 0.060.77 ± 0.010.39 ± 0.150.48 ± 0.02
Ours (20%)20.75 ± 0.020.75 ± 0.020.74 ± 0.030.43 ± 0.050.52 ± 0.02
Ours100.88 ± 0.020.89 ± 0.020.87 ± 0.030.56 ± 0.030.67 ± 0.01
+ +Table 2. Success rates on real-world manipulation experiments. 50 videos are collected for pre-training, 'Num of L-demos' indicates the number of action-labeled demonstrations utilized for training. + +
MethodsBC-Full-TrainsetBCR3MUniPiATMOurs (20%)Ours
Overall0.440.100.130.480.530.630.76
MethodsNum of L-demosOpen drawerStack blockOpen ovenPut fruit on platePress buttonPour from cup to cup
BC-Full-Trainset500.70.70.40.70.60.4
BC100.30.20.20.20.10.0
R3M [29]100.40.30.20.30.00.0
UniPi [18]100.60.60.50.70.60.5
ATM [21]100.80.60.70.70.70.5
Ours (20%)20.70.70.70.80.70.6
Ours100.80.80.80.90.80.8
MethodsNum of L-demosSweep tableInsert boxPush boxFold clothFold and put clothStraighten rope
BC-Full-Trainset500.60.50.20.30.00.2
BC100.10.00.00.10.00.0
R3M [29]100.10.10.00.10.00.1
UniPi [18]100.70.50.30.30.10.3
ATM [21]100.70.40.50.40.10.3
Ours (20%)20.60.60.50.70.40.5
Ours100.80.60.70.80.60.7
+ +Simulation experiment setup. Our evaluation utilizes the LIBERO benchmark [62], encompassing 130 language-conditioned manipulation tasks. This benchmark comprises five distinct suites. We compare with baselines on each suite separately. Baseline methods are trained on 10 action-labeled demonstration trajectories and 50 action-free videos of the robot for each task. For each task, we train each method with three different random seeds. + +Simulation experiment results. The performance of comparison methods is summarized in Table 1, demonstrating that our method surpasses all other methods in all task suites. Our method, trained with only 2 action-labeled trajectories for each task, outperforms the latest methods ATM, and UniPi, which employ five times as many action-labeled trajectories. Moreover, our GraphMimic achieves superior performance even when compared to BC trained on the complete dataset. When trained with 10 action-labeled trajectories for each task, our method significantly surpasses all baselines, achieving an improvement of over $17\%$ . + +Real-world experiment setup. We collect 10 action-labeled trajectories and 50 action-free demonstration videos for each + +task, and train policies on all training data using task descriptions as language conditions. Success criteria are human-evaluated and the success rate is calculated from 10 randomized object positions and orientations. + +Real-world experiment results. Quantitative results in Table 2 illustrate GraphMimic consistently and significantly outperforms BC and other video pre-training baselines. Remarkably, GraphMimic maintains superior performance even when utilizing merely $20\%$ of action-labeled data required by baseline, consistently exceeding other video pretraining methods. Additionally, our approach exhibits robust failure recovery capabilities. We posit that the graph modeling of topological relationships between objects and actions allows GraphMimic to learn general principles of object interactions, yielding a substantial performance enhancement. + +# 5.2. Cross-embodiment Transfer + +We then investigate the capacity of GraphMimic to provide easily transferable manipulation knowledge, facilitating learning from cross-embodiment video data. + +Robot-to-robot experiment setup. The cross-robot transfer + +Table 3. Robot-to-robot experiment results on LIBERO benchmark. We collect 50 videos from a Franka arm and 10 action-labeled demonstrations from a UR arm for each task. 'Num of L-demos' indicates the number of action-labeled demonstrations utilized for training. Results are averaged over three seeds. + +
MethodsNum of L-demosLibero-SpatialLibero-ObjectLibero-GoalLibero-LongLibero-90
BC100.42 ± 0.050.54 ± 0.090.41 ± 0.040.17 ± 0.040.27 ± 0.01
R3M [29]100.39 ± 0.030.44 ± 0.040.03 ± 0.030.06 ± 0.050.07 ± 0.02
UniPi [18]100.03 ± 0.020.04 ± 0.010.03 ± 0.020.01 ± 0.010.01 ± 0.01
ATM [21]100.45 ± 0.040.56 ± 0.090.41 ± 0.040.17 ± 0.090.28 ± 0.04
Ours (20%)20.69 ± 0.050.71 ± 0.030.67 ± 0.050.34 ± 0.060.47 ± 0.02
Ours100.81 ± 0.040.85 ± 0.020.81 ± 0.050.46 ± 0.030.60 ± 0.02
+ +Table 4. Human-to-robot transfer experiment results on real-world. We collect 50 videos of a human performing the task and 10 action-labeled robot demonstrations for each task. 'Num of L-demos' indicates the number of action-labeled demonstrations utilized for training. + +
MethodsBCR3MUniPiATMOurs (20%)Ours
Overall0.100.110.110.270.490.64
MethodsNum of L-demosOpen drawerStack blockOpen ovenPut fruit on platePress buttonPour from cup to cup
BC100.30.20.20.20.10.0
R3M [29]100.30.20.20.20.00.0
UniPi [18]100.20.10.10.10.20.0
ATM [21]100.40.40.40.50.20.2
Ours (20%)20.70.40.60.70.50.4
Ours100.70.60.70.80.70.6
MethodsNum of L-demosSweep tableInsert boxPush boxFold clothFold and put clothStraighten rope
BC100.10.00.00.10.00.0
R3M [29]100.20.10.00.10.00.0
UniPi [18]100.10.10.10.20.00.1
ATM [21]100.30.20.20.30.10.0
Ours (20%)20.50.40.40.60.30.4
Ours100.60.60.60.70.50.6
+ +experiments are conducted on LIBERO benchmark [62], we collect 10 action-labeled demonstration trajectories of the UR arm and 50 action-free video demonstration trajectories of the Franka arm for each task. Baselines are validated employing the UR arm. All other settings remain consistent with the simulation experiments detailed in Sec. 5.1. + +Robot-to-robot experiment results. The experimental results of baselines and our method are presented in Table 3, indicating that our GraphMimic still obviously outperforms comparison methods. Our approach demonstrates superior performance when trained on merely two action-labeled trajectories per task, and achieves an outstanding $70\%$ success rate with ten trajectories, whereas UniPi and ATM exhibit substantial performance declines under such conditions. This disparity is attributed to the excessive incorporation of embodiment-specific information, impeding cross-embediment generalization capabilities. Our GraphMimic focuses on object dynamics and the key interaction points, enabling our method to provide meaningful action information while enhancing its capability to learn from cross-embediment videos. + +Human-to-robot experiment setup. The human-to-robot transfer experiments are conducted in a real-world setting, + +wherein we collect 10 action-labeled trajectories of the Franka arm and 50 action-free videos from humans for each task. All other configurations remain consistent with the real-world experiments delineated in Sec. 5.1. + +Human-to-robot experiment results. Human videos constitute a major data source for cross-embediment videos. Experimental results, summarized in Table 4, indicate that GraphMimic effectively facilitates the transfer of manipulation knowledge from human videos to robotic systems, providing expressive guidance for control policy learning. Our method demonstrates enhanced performance compared to alternative video pretraining approaches, substantiating its ability to provide effective state representation for cross-embediment video learning. + +# 5.3. Ablation Analysis + +Comprehensive ablation studies are conducted to investigate the fundamental designs of our GraphMimic approach. The effects of these design decisions are assessed by measuring the success rates in robot-to-robot transfer experiments. More ablation studies are provided in Appendix ?? + +State representations. Table 5(a) analyzes three distinct state representations. The variant employing grid samples to + +Table 5. Ablation experiments with GraphMimic on robot-to-robot transfer experiments. Default settings are marked in gray . (a) State representations. (b) Visual action representations. + +
VariantsSpatialObjectGoalLong
Graph with grid vertices0.510.600.430.25
Flow with related points0.660.650.530.23
Graph with related vertices0.810.850.810.46
+ +(c) Object representations. + +
VariantsSpatialObjectGoalLong
Manipulated objects0.710.760.670.31
All objects0.550.660.520.27
Task-related objects0.810.850.810.46
+ +Table 6. Ablation study on the object property estimation module. Default settings are marked in gray. + +
VariantsReal-worldHuman-to-robot
No estimation0.660.57
No LSTM0.730.60
Graph+LSTM0.760.64
+ +generate vertices and construct graphs exhibits diminished performance. Furthermore, the variant focusing on related points, including objects and key interaction points, but utilizing point representation, also exhibits diminished performance. Experimental results demonstrate that the related regions extracted from our proposed object and action representations effectively and compactly capture manipulation-related information, and the graph representation is capable of capturing important local structures and spatial relationships, thereby enhancing the performance of our method. + +Visual action representations. Table 5(b) presents variants and their respective performance. The first variant excludes the visual action vertices, resulting in a significant performance decline. The second variant directly samples vertices within the robot masks. However, the action representation extracted by this variant considers excessive embodiment-specific information, thereby constraining the efficacy of cross-embediment transfer. The results exhibit that our interaction points-based representation can provide meaningful action information while emphasizing the functional facets of manipulation over specific anatomical details. + +Object representations. We conduct an analysis on the impact on the object representations, as shown in Table 5 (c). Experimental findings indicate that both isolated focus on the manipulated object and comprehensive consideration of all objects result in suboptimal performance. The former approach restricts the acquisition of spatial relationships across objects, diminishing robustness to positional variations. The latter, albeit facilitating comprehensive relational modeling, introduces a dynamic-static imbalance due to prevalent stationary objects, compromising graph prediction accuracy. + +Hierarchical modeling. Table 5 (d) analyzes the impact of the hierarchical architecture in the graph generative mod + +
VariantsSpatialObjectGoalLong
No action0.410.610.420.18
End-effector0.560.590.510.19
Interaction points0.810.850.810.46
+ +(d) Hierarchical modeling. + +
VariantsSpatialObjectGoalLong
Local connection0.730.790.710.38
Global connection0.750.720.730.37
Hierarchical architecture0.810.850.810.46
+ +eling network. Empirical findings indicate that solely relying on either local connections $\mathcal{E}$ or global connections $\{\mathcal{E}_t^{\mathrm{L2R}},\mathcal{E}_t^{\mathrm{R2R}},\mathcal{E}_t^{\mathrm{R2L}}\}$ , leads to suboptimal performance. In contrast, our proposed hierarchical architecture demonstrates the ability to effectively model local structures while concurrently capturing spatial relationships. + +Object property estimation. We conduct an analysis concerning the effect of object property estimation on real-world experiments (Sec. 5.1) and human-to-robot transfer experiments (Sec. 5.2). As shown in Table 6, our proposed object property estimation approach significantly improves the method's capacity to capture diverse object behaviors. Typically, the integration of long-term temporal dependencies proves crucial for enhancing property estimation accuracy. + +# 6. Conclusion + +In this paper, we present GraphMimic, a novel paradigm that formulates video pre-training as graph-to-graphs generative modeling. GraphMimic constructs graphs within video frames. Then, the graph generative modeling network extracts object properties and establishes a hierarchical architecture to effectively model local structures and spatial relationships, aiming to generate future graph sequences. The predicted graphs serve as conditions for the control policy, mapping to robot actions. Our concise approach effectively captures important structural information, enabling robust policy learning from limited action-labeled data. Moreover, the transferable graph representations facilitate the effective learning of manipulation skills from cross-embodiment videos. Our extensive experiments across 140 tasks exhibit that our method outperforms the state-of-the-art method by over $17\%$ and $23\%$ in simulation and real-world manipulation tasks, and delivers substantial improvements of over $33\%$ in cross-embodiment transfer experiments. + +Limitations. Despite the promising performance exhibited by GraphMimic, current SOTA tracking models still struggle with low-texture objects during large motions, compromising training data quality. We believe that the progression of tracking models will mitigate this limitation. Appendix ?? provides detailed discussions. + +# References + +[1] A. Mandlekar, D. Xu, J. Wong, et al., "What matters in learning from offline human demonstrations for robot manipulation," arXiv preprint arXiv:2108.03298, 2021. +[2] A. O'Neill, A. Rehman, A. Gupta, et al., "Open x-embodiment: Robotic learning datasets and rt-x models," arXiv preprint arXiv:2310.08864, 2023. +[3] H.-S. Fang, H. Fang, Z. 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This problem naturally appears as an object-matching task, which underlies various real-world computer vision applications, e.g., image registration, point cloud registration, stereo matching, and 3D reconstruction. Gradient-based algorithms have been widely used to solve GW, and our main idea is to utilize the following remarkable property that emerges in GW with cyclic symmetry: By setting the initial solution to have cyclic symmetry, all intermediate solutions and matrices that appear in the gradient-based algorithms have the same cyclic symmetry until convergence. Based on this property, our gradient-based algorithms restrict the solution space to have cyclic symmetry and update only one symmetric part of solutions and matrices at each iteration, resulting in faster computation. Moreover, our algorithms solve the optimal transport problem at each iteration, which also exhibits cyclic symmetry. This problem can be solved efficiently, and as a result, our algorithms perform significantly faster. Experiments showed the effectiveness of our algorithms in synthetic and real-world data with strict and approximate cyclic symmetry. + +# 1. Introduction + +Given a discrete probability measure and a metric matrix on each of two discrete metric-measure spaces, the discrete Gromov-Wasserstein problem (GW) finds a coupling that is as close to an isometry between the two measures as possible. The coupling distortion from isometry is quantifiable and is called Gromov-Wasserstein distance (GWD). The GWD is an effective tool that compares or matches two metric-measure spaces, and thus GW has been studied in various research areas, e.g., object matching [25, 28, 42], generative modeling [10], and domain adaptation [12]. + +Existing approaches to solve GW include gradient-based algorithms, and the conditional gradient method (CG) was proposed recently [41]. This algorithm iterates the following three processes until convergence: (i) it computes the + +gradient of the objective function in GW at the current solution, (ii) solves the optimal transport problem (OT) [20] with the computed gradient as the cost to obtain the update direction, and (iii) updates the current solution in that direction. In addition, the entropy-regularized GW (EGW) has attracted much attention [28, 31, 49] because it offers a concise and fast projected gradient method (PG). This algorithm iterates the same processes as CG until convergence but solves the entropy-regularized OT (EOT) [13] instead of OT. As another line of work to solve GW faster, algorithms using special structures of input data have been proposed, e.g., algorithms for GW with low-rank [29] or hierarchical [48] structures of input data. Besides, several algorithms provide closed-form solutions to GW with some special structures of input data, such as 1-dimensional input data [42] and tree metric structure [23]. + +In this paper, we propose novel fast algorithms for GW with a new and ubiquitous special structure, cyclic symmetry, of input data. Specifically, we assume $K$ -order cyclic symmetry of input data; the input $m$ - and $n$ -dimensional probability measures are given as concatenations of $K$ copies of $m' \coloneqq m / K$ - and $n' \coloneqq n / K$ -dimensional vectors, respectively, and the input $m \times m$ and $n \times n$ metric matrices are block circulant matrices consisting of $K$ matrices with size $m' \times m'$ and $n' \times n'$ , respectively (see Assumption 1). Such GW with cyclic symmetry naturally appears as an object-matching task, which underlies various real-world computer vision applications (see Sec. 4). To solve this new GW efficiently, we developed fast versions of CG and PG using cyclic symmetry. Our main idea is to utilize the following remarkable property that emerges in this new problem: By setting the initial solution as a $m \times n$ block circulant matrix consisting of $K$ matrices with size $m' \times n'$ , all intermediate solutions and matrices that appear in CG and PG also become $m \times n$ block circulant matrices consisting of $K$ matrices with size $m' \times n'$ until convergence (see Theorem 1 and the later discussion). This property ensures that we can restrict the solution space to such a block circulant matrix in CG and PG and update only the $K$ matrices with size $m' \times n'$ instead of the whole $m \times n$ matrix, which results in fast versions of CG and PG. We call this fast + +CG Cyclic CG (C-CG) and this fast PG Cyclic PG (C-PG). Moreover, OT and EOT that must be solved in C-CG and C-PG also exhibit cyclic symmetry. These problems can be solved efficiently [36], and as a result, C-CG and C-PG perform significantly faster than the original CG and PG. In this paper, we theoretically show the time complexities of C-CG and C-PG in Secs. 5.2 and 5.3, respectively. + +In summary, this paper is the first to introduce the concept of symmetry to solve GW faster and proposes fast cyclic symmetry-aware algorithms C-CG and C-PG. We validated the effectiveness of our algorithms in experiments on synthetic and real-world data with strict and approximate cyclic symmetry. + +# 2. Related Works + +Mémoli [25] initially formulated the Gromov-Wasserstein problem (GW) for object matching even defined on different metric-measure spaces. The Gromov-Wasserstein distance relaxes the Gromov-Hausdorff distance and quantifies the coupling distortion between two measures from being isometry. GW is a relaxation of the quadratic assignment problem that is NP-hard. Thus, several relaxations for this problem could be also used for GW, such as SDP relaxation [19, 21] and eigenvalue relaxation [9, 24]. However, the former runs slowly due to the increased number of variables, while the latter has looser approximation bounds. Recently, the conditional gradient method (CG), which is also known as the Frank-Wolfe algorithm, was proposed to solve GW directly [41]. This algorithm at each iteration boils down to compute the gradient of the objective function in GW and solve the optimal transport problem (OT) [20] by the network simplex algorithm [1]. Moreover, the entropy-regularized GW (EGW) has attracted much attention [28, 31, 49] because it offers a concise and fast projected gradient method (PG). This algorithm is similar to CG but solves the entropy-regularized OT instead of OT by the Sinkhorn-Knopp algorithm [30]. This paper focuses on the algorithms CG for GW and PG for EGW because they are widely used in the Gromov-Wasserstein research field. + +To solve GW faster, various algorithms that use special structures of input data have been proposed [23, 29, 42, 48]. Scalable algorithm [48] uses the hierarchical structure of input data and recursively solves GW for each layer. Low-rank algorithm [29] uses the low-rank structure of the input metrics and couplings. Besides, several algorithms using special structures of input data provide closed-form solutions to GW. Sliced algorithm [42] assumes input probability measures on the 1-dimensional real line and the squared Euclidean distance metrics; such GW becomes the Gromov-Monge problem that has a closed-form solution. Since the 1-dimensional line is a special case of the tree structure, the algorithm using tree metric structures of input data was also proposed [23]. Unlike the above algorithms, + +this paper is the first to introduce the use of a new and ubiquitous special structure, cyclic symmetry. + +The optimal transport problem (OT) was formulated as the linear programming problem by [20], and the entropy-regularized OT (EOT) has attracted attention recently because this problem can be solved faster than OT [13]. These problems seek an optimal coupling to minimize the total cost of transporting a probability measure toward another one on the same metric-measure space. Similar to the research progress in GW, many algorithms have been proposed to solve OT faster using special structures of input data, e.g., low-rankness [2, 38], translation invariant [17, 27], hierarchy [16], and submodularity [3] of input data. More recently, using cyclic symmetry of input data for OT was proposed [36]. This structure and the convexity of OT can reduce OT to a small problem with significantly fewer variables, resulting in faster computation. Similar to this research, we use cyclic symmetry of input data to solve GW faster, but this is more challenging and non-trivial because GW is non-convex while OT is convex. + +# 3. Preliminary + +Notations. We denote the set of non-negative real numbers by $\mathbb{R}_{\geq 0}$ . For matrices $\mathbf{X}, \mathbf{Y} \in \mathbb{R}^{d \times d}$ , we denote the Frobenius inner product by $\langle \mathbf{X}, \mathbf{Y} \rangle = \sum_{i,j=0}^{d-1} X_{ij} Y_{ij}$ . We define the probability simplex as $\Delta^d := \{\mathbf{x} \in \mathbb{R}_{\geq 0}^d \mid \sum_{i=0}^{d-1} x_i = 1\}$ . The $d$ -dimensional all-ones vector is written as $\mathbf{1}_d$ . We use $\mathbf{X}^{\circ 2}$ to represent element-wise squaring of $\mathbf{X}$ , meaning $(\mathbf{X}^{\circ 2})_{ij} = X_{ij}^2$ . The matrix norm is given by $\| \mathbf{X} \|_{\infty} := \max_{i,j} |X_{ij}|$ . We define the entropy of $\mathbf{X}$ as $H(\mathbf{X}) := -\sum_{i,j=0}^{d-1} X_{ij} (\log X_{ij} - 1)$ . We denote the elementwise division by $\varnothing$ . We denote the Kronecker product of matrices by $\otimes$ . When a matrix $\mathbf{X}$ can be written as + +$$ +\mathbf {X} = \left( \begin{array}{c c c c} \mathbf {X} _ {0} & \mathbf {X} _ {1} & \dots & \mathbf {X} _ {K - 1} \\ \mathbf {X} _ {K - 1} & \mathbf {X} _ {0} & \ddots & \vdots \\ \vdots & \ddots & \ddots & \mathbf {X} _ {1} \\ \mathbf {X} _ {1} & \dots & \mathbf {X} _ {K - 1} & \mathbf {X} _ {0} \end{array} \right), +$$ + +using $\mathbf{X}_0, \mathbf{X}_1, \ldots, \mathbf{X}_{K-1} \in \mathbb{R}^{d_1 \times d_2}$ , the matrix $\mathbf{X}$ is referred to as a $(d_1, d_2, K)$ -block circulant matrix generated by $\mathbf{X}_0, \mathbf{X}_1, \ldots, \mathbf{X}_{K-1}$ . + +# 3.1. Entropic Gromov-Wasserstein Problem + +We first define the original 2-Gromov-Wasserstein problem (GW) introduced by [25]. Let $\mathbb{X} = (\mathcal{X},d_{\mathcal{X}},\mathbf{a})$ be a metric-measure space where $\mathcal{X} = \{x_0,\dots ,x_{m - 1}\}$ is a finite set with an associated metric $d_{\mathcal{X}}$ and a discrete probability measure $\mathbf{a}\in \Delta^m$ . Similarly, let $\mathbb{Y} = (\mathcal{Y},d_{\mathcal{Y}},\mathbf{b})$ be another discrete metric-measure space with a discrete probability measure $\mathbf{b}\in \Delta^n$ . Given similarity matrices $\mathbf{C}\in \mathbb{R}_{\geq 0}^{m\times m}$ and $\mathbf{D}\in \mathbb{R}_{\geq 0}^{n\times n}$ where $C_{ii'}\coloneqq d_{\mathcal{X}}(x_i,x_{i'})$ and + +$D_{jj'} \coloneqq d_{\mathcal{Y}}(y_j, y_{j'})$ , we define GW between $\mathbb{X}$ and $\mathbb{Y}$ as the following constrained non-convex optimization problem: + +$$ +\underset {\mathbf {T} \in \Pi (\mathbf {a}, \mathbf {b})} {\min } \sum_ {i, i ^ {\prime}, j, j ^ {\prime}} \left(C _ {i i ^ {\prime}} - D _ {j j ^ {\prime}}\right) ^ {2} T _ {i j} T _ {i ^ {\prime} j ^ {\prime}}, \tag {1} +$$ + +where $\mathbf{T}$ is a coupling matrix between $\mathbb{X}$ and $\mathbb{Y}$ , and $\Pi (\mathbf{a},\mathbf{b})\coloneqq \{\mathbf{X}\in \mathbb{R}_{\geq 0}^{m\times n}\mid \mathbf{X}\mathbf{1}_n = \mathbf{a},\mathbf{X}^\top \mathbf{1}_m = \mathbf{b}\}$ . The optimal objective function value of (1) is called Gromov-Wasserstein distance (GWD). Through a simple calculation, the objective function in (1) can be rewritten in matrix form as $\left\langle \mathbf{Q} - 2\mathbf{CTD}^{\top},\mathbf{T}\right\rangle$ , where $\mathbf{Q}\coloneqq \mathbf{C}^{\circ 2}\mathbf{a}\mathbf{1}_n^{\top} + \mathbf{1}_m\mathbf{b}^{\top}(\mathbf{D}^{\circ 2})^{\top}$ . Hereafter, we will use this matrix form. + +In this paper, we consider the entropy-regularized GW (EGW), which is an extension of GW with the entropy regularizer introduced by [28]: + +$$ +\min _ {\mathbf {T} \in \Pi (\mathbf {a}, \mathbf {b})} \left\langle \mathbf {Q} - 2 \mathbf {C T D} ^ {\top}, \mathbf {T} \right\rangle - \varepsilon H (\mathbf {T}), \tag {2} +$$ + +where $\varepsilon \geq 0$ . Apparently, EGW is identical to the original GW when $\varepsilon = 0$ . + +# 3.2. Gradient-based Algorithms for EGW + +Several algorithms have been proposed to solve EGW. In this paper, we focus on two representative algorithms that use gradient information: the Conditional Gradient method (CG) [41] and the Projected Gradient method (PG) [28]. + +CG is an iterative algorithm for solving GW, i.e., (2) with $\varepsilon = 0$ . At each iteration, this algorithm approximates the objective function linearly around the current solution and then updates the solution in the direction obtained by minimizing the linear approximation within the feasible region. + +PG is an iterative algorithm for solving EGW, i.e., (2) with $\varepsilon > 0$ . At each iteration, this algorithm updates the current solution in the direction of the gradient of the objective function in EGW using exponentiated gradient descent [22] and then projects the updated solution back onto the feasible region with the Kullback-Leibler metric. + +Although these algorithms differ in the problems they address (GW and EGW) and their algorithm design principles (e.g., how the feasible region is handled), the procedures can be described in a unified manner as below. Let $\mathbf{T}^{(\tau)}$ be the current solution and $\mathbf{G}^{(\tau)}$ denotes the gradient of the first term of (2) at $\mathbf{T}^{(\tau)}$ . First, $\mathbf{G}^{(\tau)}$ is calculated as + +$$ +\mathbf {G} ^ {(\tau)} = \mathbf {Q} - 2 \left(\mathbf {C} ^ {\top} \mathbf {T} ^ {(\tau)} \mathbf {D} + \mathbf {C T} ^ {(\tau)} \mathbf {D} ^ {\top}\right). \tag {3} +$$ + +Then, we solve the following problem: + +$$ +\mathbf {S} ^ {(\tau)} = \underset {\mathbf {S} \in \Pi (\mathbf {a}, \mathbf {b})} {\operatorname {a r g m i n}} \left\langle \mathbf {G} ^ {(\tau)}, \mathbf {S} \right\rangle - \varepsilon H (\mathbf {S}). \tag {4} +$$ + +Finally, $\mathbf{T}^{(\tau)}$ is updated to the next solution $\mathbf{T}^{(\tau +1)}$ : + +$$ +\mathbf {T} ^ {(\tau + 1)} = (1 - \lambda) \mathbf {T} ^ {(\tau)} + \lambda \mathbf {S} ^ {(\tau)}, \tag {5} +$$ + +where $0 \leq \lambda \leq 1$ is the step size. + +In CG, the problem (4) is identical to the optimal transport problem (OT) introduced by [20] because $\varepsilon = 0$ . This problem can be solved efficiently using the network simplex algorithm [1]. The step size $\lambda$ can be determined by line search based on Armijo or Wolfe conditions [6, 46]. + +In PG, the problem (4) is identical to the entropy-regularized OT introduced by [13] because $\varepsilon > 0$ , and it can be solved efficiently via the Sinkhorn-Knopp algorithm for its dual problem [30]. The step size $\lambda$ is fixed to 1. + +# 4. C-EGW: EGW with Cyclic Symmetry + +This section explains our assumption of cyclic symmetry for EGW (2). We assume that $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{C}$ and $\mathbf{D}$ in (2) have the following $K$ -order cyclic symmetry. + +Assumption 1. A common divisor $K$ exists for $m$ and $n$ . The probability vectors $\mathbf{a}$ and $\mathbf{b}$ in (2) can be written as + +$$ +\mathbf {a} = \mathbf {1} _ {K} \otimes \boldsymbol {\alpha}, \quad \mathbf {b} = \mathbf {1} _ {K} \otimes \boldsymbol {\beta}, +$$ + +where $\alpha \in \mathbb{R}_{\geq 0}^{m'}, \beta \in \mathbb{R}_{\geq 0}^{n'}$ and $m' := \frac{m}{K}, n' := \frac{n}{K}$ are integers. Furthermore, in (2), the similarity matrix $\mathbf{C}$ is an $(m', m', K)$ -block circulant matrix generated by $\mathbf{C}_0, \ldots, \mathbf{C}_{K-1} \in \mathbb{R}_{\geq 0}^{m' \times m'}$ and $\mathbf{D}$ is an $(n', n', K)$ -block circulant matrix generated by $\mathbf{D}_0, \ldots, \mathbf{D}_{K-1} \in \mathbb{R}_{\geq 0}^{n' \times n'}$ . + +In this paper, we call EGW (2) with Assumption 1 Cyclic $EGW(C-EGW)$ . This problem naturally appears as one approach to the object-matching task, which underlies various computer vision applications, as below. + +Example 1 (Image Matching with Cyclic Symmetry). Image matching task, which seeks a coupling of similar features between images, is essential for various visual applications such as face recognition [51], image registration [33, 40], stereo matching [4, 35], and image retrieval [18, 43]. Since images often exhibit inherent cyclic symmetry, the image matching task often uses cyclic symmetry to improve accuracy [4, 26, 32, 35, 43, 51]. We here consider an image matching task between two images with $90^{\circ}$ rotational symmetry, i.e., 4-order cyclic symmetry, as shown in Fig. 1. We define $\mathbf{a}$ and $\mathbf{b}$ as concatenations of image features (or simply intensity values) at each symmetric region in each image of Fig. 1, and $\mathbf{C}$ and $\mathbf{D}$ as the Euclidean distance matrix between the pixel positions. These $\mathbf{a}, \mathbf{b}, \mathbf{C}$ and $\mathbf{D}$ satisfy Assumption 1 with $K = 4$ , and thus this image matching task will become C-EGW with $K = 4$ . + +![](images/5f55c8bac4f51b76d68af96f209bb0767ab53ba8b58eaeaeecb87fb526723981.jpg) +Figure 1. Images with 4-order cyclic symmetry. + +![](images/39470f5ad89fd8bc25ef4640e0743b036862e6966cb806157d76f7b9178a649e.jpg) + +Example 2 (Point Cloud Matching with Cyclic Symmetry). Point cloud matching task, which seeks a coupling of similar geometric features between point clouds, is essential for various 3D applications such as point cloud registration [5, 50] and 3D reconstruction [39, 47]. Since 3D objects, especially artificial ones, often exhibit inherent cyclic symmetry, the point clouds obtained from such 3D objects also exhibit cyclic symmetry. Thus, the point cloud matching task often uses this structure to improve accuracy [34, 39, 45]. We here consider a point cloud matching task between two point clouds with mirror symmetry, i.e., 2-order cyclic symmetry, as shown in Fig. 2. We define $\mathbf{a}$ and $\mathbf{b}$ as uniform weights (or intensity values of points), each of which has a total of 1, and $\mathbf{C}$ and $\mathbf{D}$ as the Euclidean distance matrices for pairwise 3D point positions of each object in Fig. 2. These $\mathbf{a},\mathbf{b},\mathbf{C}$ and $\mathbf{D}$ satisfy Assumption 1 with $K = 2$ , and thus this point cloud matching task will become C-EGW with $K = 2$ . + +![](images/12af8eae5560dd945c9dffa8c377743b19249cc1dea7a7d292af31456ffd8786.jpg) +Figure 2. Point clouds with 2-order cyclic symmetry + +![](images/1e069edd8e1468b247f2b79fe84b83562fa45a30de89e13d34d30737efa759f8.jpg) + +We can show that $\mathbf{Q}$ has a block circulant structure in C-EGW, which will be used in the next section. + +Lemma 1. Under Assumption 1, the matrix $\mathbf{Q}$ in (2) is an $(m', n', K)$ -block circulant matrix generated by $\widehat{\mathbf{Q}}, \ldots, \widehat{\mathbf{Q}}$ , where $\widehat{\mathbf{Q}} := \sum_{i=0}^{K-1} \mathbf{C}_i^{\circ 2} \alpha \mathbf{1}_{n'}^\top + \mathbf{1}_{m'} \beta^\top (\mathbf{D}_i^{\circ 2})^\top$ . + +Note that all proofs are in the Appendix. + +# 5. Fast Algorithms for C-EGW + +In this section, we propose fast algorithms to solve C-EGW. + +# 5.1. Block Circulant Intermediate Matrices + +We first demonstrate that in CG and PG, introduced in Sec. 3.2, the cyclic symmetry structure of matrices generated during the algorithms, including all intermediate solutions, can be preserved under Assumption 1. + +Theorem 1. Assume that $\mathbf{T}^{(\tau)}$ is an $(m', n', K)$ -block circulant matrix. Then, under Assumption 1, $\mathbf{G}^{(\tau)}$ given by (3) is an $(m', n', K)$ -block circulant matrix. Moreover, there exists an $(m', n', K)$ -block circulant matrix $\mathbf{S}^{(\tau)}$ which is an optimal solution to the problem (4). Furthermore, when $\mathbf{S}^{(\tau)}$ is an $(m', n', K)$ -block circulant matrix, $\mathbf{T}^{(\tau + 1)}$ given by (5) remains an $(m', n', K)$ -block circulant matrix. + +By repeatedly applying Theorem 1, we can see that by setting the initial solution $\mathbf{T}^{(0)}$ in C-EGW as an $(m', n', K)$ -block circulant matrix, it is possible to ensure that $\mathbf{T}^{(\tau)}, \mathbf{G}^{(\tau)}$ , and $\mathbf{S}^{(\tau)}$ all become $(m', n', K)$ -block circulant matrices in CG and PG until convergence (see Fig. 3). + +![](images/fd4fe8f5343b903ba81beedfde9d0ec679e77cc8fb9ff5f5b3bee27c138c3434.jpg) +Figure 3. An illustrative flow diagram of repeatedly applying Theorem 1 for $\tau = 0, 1, 2$ . + +This remarkable property ensures that we can restrict the solution space to $(m', n', K)$ -block circulant matrices in CG and PG. Therefore, we hereafter restrict $\mathbf{T}^{(\tau)}, \mathbf{G}^{(\tau)}$ , and $\mathbf{S}^{(\tau)}$ to $(m', n', K)$ -block circulant matrices generated by $\mathbf{T}_0^{(\tau)}, \ldots, \mathbf{T}_{K-1}^{(\tau)} \in \mathbb{R}_{\geq 0}^{m' \times n'}$ , $\mathbf{G}_0^{(\tau)}, \ldots, \mathbf{G}_{K-1}^{(\tau)} \in \mathbb{R}_{\geq 0}^{m' \times n'}$ , and $\mathbf{S}_0^{(\tau)}, \ldots, \mathbf{S}_{K-1}^{(\tau)} \in \mathbb{R}_{\geq 0}^{m' \times n'}$ , respectively. Using this restriction and Lemma 1, we can rewrite (3) as + +$$ +\mathbf {G} _ {k} ^ {(\tau)} = \widehat {\mathbf {Q}} - 2 \sum_ {i, j = 0} ^ {K - 1} \left(\mathbf {C} _ {i} ^ {\top} \mathbf {T} _ {j - i} ^ {(\tau)} \mathbf {D} _ {j - k} + \mathbf {C} _ {i} \mathbf {T} _ {j - i} ^ {(\tau)} \mathbf {D} _ {j - k} ^ {\top}\right), \tag {6} +$$ + +where $\mathbf{T}_{j - i}^{(\tau)}$ and $\mathbf{D}_{j - k}$ are simplifications of $\mathbf{T}_{j - i\mod K}^{(\tau)}$ and $\mathbf{D}_{j - k\mod K}$ , respectively. We can rewrite (4) as + +$$ +\begin{array}{l} \mathbf {S} _ {0} ^ {(\tau)}, \ldots , \mathbf {S} _ {K - 1} ^ {(\tau)} \\ = \underset {\mathbf {S} _ {0}, \dots , \mathbf {S} _ {K - 1} \in \Gamma (\boldsymbol {\alpha}, \boldsymbol {\beta})} {\operatorname {a r g m i n}} \sum_ {k = 0} ^ {K - 1} \left\langle \mathbf {G} _ {k} ^ {(\tau)}, \mathbf {S} _ {k} \right\rangle - \varepsilon H (\mathbf {S} _ {k}), \tag {7} \\ \end{array} +$$ + +where $\Gamma (\pmb {\alpha},\pmb {\beta})\coloneqq \{\mathbf{X}_0,\dots ,\mathbf{X}_{K - 1}\in \mathbb{R}_{\geq 0}^{m'\times n'}|$ $\sum_{k = 0}^{K - 1}\mathbf{X}_k\mathbf{1}_{n'} = \pmb {\alpha},\sum_{k = 0}^{K - 1}\mathbf{X}_k^\top \mathbf{1}_{m'} = \pmb {\beta}\} .$ We can rewrite (5) as + +$$ +\mathbf {T} _ {k} ^ {(\tau + 1)} = (1 - \lambda) \mathbf {T} _ {k} ^ {(\tau)} + \lambda \mathbf {S} _ {k} ^ {(\tau)}. \tag {8} +$$ + +# 5.2. Fast Conditional Gradient Method for C-GW + +We here propose a fast CG for C-GW, i.e., (2) with $\varepsilon = 0$ and Assumption 1. The processes (6)-(8) can be computed faster than the original ones (3)-(5) because they update only $K$ matrices with the size $m' \times n'$ . Moreover, because (7) with $\varepsilon = 0$ is equivalent to OT with cyclic symmetry in [36], we can show the following proposition, which extends Theorem 1 in [36] to the case where $m \neq n$ . The proof is almost the same as the $m = n$ case. + +Proposition 1. We consider the following OT + +$$ +\mathbf {Z} ^ {(\tau)} = \underset {\mathbf {Z} \in \mathrm {I I} ^ {\prime} (\alpha , \beta)} {\operatorname {a r g m i n}} \left\langle \mathbf {W} ^ {(\tau)}, \mathbf {Z} \right\rangle , \tag {9} +$$ + +where $\Pi'(\alpha, \beta) \coloneqq \{\mathbf{X} \in \mathbb{R}_{\geq 0}^{m' \times n'} \mid \mathbf{X}\mathbf{1}_{n'} = \alpha, \mathbf{X}^\top \mathbf{1}_{m'} = \beta\}$ and + +$$ +W _ {i j} ^ {(\tau)} := \min _ {0 \leq k \leq K - 1} G _ {i j k} ^ {(\tau)}. \tag {10} +$$ + +# Algorithm 1 C-CG for C-GW + +Input: $\mathbf{a} \in \Delta^m$ , $\mathbf{b} \in \Delta^n$ , $\mathbf{C} \in \mathbb{R}_{\geq 0}^{m \times m}$ , $\mathbf{D} \in \mathbb{R}_{\geq 0}^{n \times n}$ which satisfy Assumption 1 and $\varepsilon = 0$ + +1: Initialize $\mathbf{T}^{(0)}$ as an $(m', n', K)$ -block circulant matrix generated by $\mathbf{T}_0^{(0)}, \ldots, \mathbf{T}_{K-1}^{(0)} \in \mathbb{R}_{>0}^{m' \times n'}$ . +2: for $\tau = 0,1,\ldots$ do +3: Calculate $\mathbf{G}_0^{(\tau)},\ldots ,\mathbf{G}_{K - 1}^{(\tau)}$ by (6) +4: Calculate $\mathbf{W}^{(\tau)}$ whose entry is given by (10) +5: Solve (9) to obtain $\mathbf{Z}^{(\tau)}$ +6: Calculate $S_{ijk}^{(\tau)}$ for $i, j, k$ by the relationship (11) +7: Calculate $\mathbf{T}_0^{(\tau +1)},\ldots ,\mathbf{T}_{K - 1}^{(\tau +1)}$ by (8) + +# 8: end for + +Then, we will obtain the optimal solution to (7) with $\varepsilon = 0$ , $\mathbf{S}_0^*$ , ..., $\mathbf{S}_{K - 1}^*$ , as follows. + +$$ +S _ {i j k} ^ {*} = \left\{ \begin{array}{l l} Z _ {i j} ^ {(\tau)} & \text {i f} k = \min \left(\underset {0 \leq k \leq K - 1} {\operatorname {a r g m i n}} G _ {i j k} ^ {(\tau)}\right), \\ 0 & \text {o t h e r w i s e .} \end{array} \right. \tag {11} +$$ + +Proposition 1 indicates that we will obtain the optimal solution to (7) with $\varepsilon = 0$ by solving the small OT (9) instead, which has significantly few only $m'n'$ variables. Therefore, the original processes (3), (4), and (5) in CG can be reduced to the small ones (6), (9), and (8), respectively. We call the proposed algorithm Cyclic Conditional Gradient method (C-CG), summarized in Algorithm 1. + +We evaluate the time complexity of C-CG (Algorithm 1). It mainly depends on the matrix-vector product in (6) and solving the small OT (9). The former requires $O(mn(m' + n'))$ , which is improved from $O(mn(m + n))$ in CG that uses (3). From the report of [37], the latter requires $O((m' + n')m'n'\log(m' + n')\log((m' + n')\|\mathbf{W}^{(\tau)}\|_{\infty}))$ when using the network simplex algorithm to solve (9), which is improved from $O((m + n)m n\log(m + n)\log((m + n)\| \mathbf{G}^{(\tau)} \|_{\infty}))$ in CG that solves (4) in terms of the dimensional reduction and $\| \mathbf{W}^{(\tau)} \|_{\infty} \leq \| \mathbf{G}^{(\tau)} \|_{\infty}$ by (10). Therefore, for C-GW, C-CG will achieve a better time complexity than CG. Note that, in C-CG, the time complexity of line search to determine $\lambda$ in (8) will also be improved because the objective function value of (2) can be assessed by using only the block matrices $\{\mathbf{C}_k^{(\tau)}, \mathbf{D}_k^{(\tau)}, \mathbf{T}_k^{(\tau)}\}_{k=0}^{K-1}$ . + +# 5.3. Fast Projected Gradient Method for C-EGW + +We here propose a fast PG for C-EGW, i.e., (2) with $\varepsilon > 0$ and Assumption 1. Similar to the discussion in Sec. 5.2, because (7) with $\varepsilon > 0$ is equivalent to EOT with cyclic symmetry in [36], we can show the following proposition, which extends Theorem 2 in [36] to the case where $m \neq n$ . The proof is almost the same as the $m = n$ case. + +# Algorithm 2 C-PG for C-EGW + +Input: $\mathbf{a} \in \Delta^m$ , $\mathbf{b} \in \Delta^n$ , $\mathbf{C} \in \mathbb{R}_{\geq 0}^{m \times m}$ , $\mathbf{D} \in \mathbb{R}_{\geq 0}^{n \times n}$ which satisfy Assumption 1 and $\varepsilon > 0$ + +1: Initialize $\mathbf{T}^{(0)}$ as an $(m', n', K)$ -block circulant matrix generated by $\mathbf{T}_0^{(0)}, \ldots, \mathbf{T}_{K-1}^{(0)} \in \mathbb{R}_{>0}^{m' \times n'}$ . +2: for $\tau = 0,1,\ldots$ do +3: Calculate $\mathbf{G}_0^{(\tau)},\ldots ,\mathbf{G}_{K - 1}^{(\tau)}$ by (6) +4: Calculate $\mathbf{L}^{(\tau)}$ whose entry is given by (13) +5: Solve (12) via Remark 1 to obtain $\mathbf{p}$ and $\mathbf{q}$ . +6: Calculate $S_{ijk}^{(\tau)}$ for $i,j,k$ by the relationship (14) +7: Calculate $\mathbf{T}_0^{(\tau +1)},\ldots ,\mathbf{T}_{K - 1}^{(\tau +1)}$ by (8) +8: end for + +Proposition 2. The Fenchel dual of (7) with $\varepsilon >0$ is + +$$ +\underset {\mathbf {u} \in \mathbb {R} ^ {m ^ {\prime}}, \mathbf {v} \in \mathbb {R} ^ {n ^ {\prime}}} {\operatorname {a r g m a x}} \langle \mathbf {u}, \boldsymbol {\alpha} \rangle + \langle \mathbf {v}, \boldsymbol {\beta} \rangle - \varepsilon \sum_ {i = 0} ^ {m ^ {\prime} - 1} \sum_ {j = 0} ^ {n ^ {\prime} - 1} p _ {i} L _ {i j} ^ {(\tau)} q _ {j}, \tag {12} +$$ + +where $p_i = \exp (u_i / \varepsilon),q_j = \exp (v_j / \varepsilon)$ , and + +$$ +L _ {i j} ^ {(\tau)} := \sum_ {k = 0} ^ {K - 1} \exp \left(- \frac {G _ {i j k} ^ {(\tau)}}{\varepsilon}\right). \tag {13} +$$ + +Let $u_{i}^{*}$ and $v_{j}^{*}$ be the optimal solutions to (12), we can describe $p_{i}^{*} = \exp (u_{i}^{*} / \varepsilon)$ and $q_{j}^{*} = \exp (v_{j}^{*} / \varepsilon)$ , respectively. Then, we will obtain the optimal solutions to (7), $\mathbf{S}_0^*,\ldots ,\mathbf{S}_{K - 1}^*$ as follows. + +$$ +S _ {i j k} ^ {*} = p _ {i} ^ {*} q _ {j} ^ {*} \exp \left(- \frac {G _ {i j k} ^ {(\tau)}}{\varepsilon}\right). \tag {14} +$$ + +Proposition 2 indicates that we will obtain the optimal solution to (7) with $\varepsilon > 0$ by solving the small dual problem (12) instead, which has significantly few only $m' + n'$ variables. Therefore, the original processes (3), (4), and (5) in PG can be reduced to the small ones (6), (12), and (8), respectively. We call the proposed algorithm Cyclic Projected Gradient method (C-PG), summarized in Algorithm 2. + +Remark 1. The problem (12) can be solved efficiently using the Sinkhorn-Knopp algorithm [13, 30]; instead of optimizing $\mathbf{u}$ and $\mathbf{v}$ directly, we iteratively optimize $\mathbf{p}$ and $\mathbf{q}$ as $\mathbf{p} \gets \alpha \oslash (\mathbf{L}^{(\tau)}\mathbf{q})$ and $\mathbf{q} \gets \beta \oslash ((\mathbf{L}^{(\tau)})^\top \mathbf{p})$ . + +We evaluate the time complexity of C-PG (Algorithm 2). It mainly depends on the matrix-vector product in (6) and solving the small dual problem of EOT (12). The former is the same as in Algorithm 1. The latter using the Sinkhorn-Knopp algorithm [13, 30] requires $O(m'n')$ at each iteration, which is improved from $O(mn)$ in PG that solves (4) using the same algorithm. Therefore, for C-EGW, C-PG will achieve a better time complexity than PG. + +# 6. Experiments + +To validate the effectiveness of our algorithms, C-CG and C-PG, we conducted experiments on synthetic and real-world data with strict and approximate cyclic symmetry, respectively. Specifically, the synthetic data provide a, b, C and D that satisfy Assumption 1 strictly but the real-world data provide them that satisfy Assumption 1 approximately due to slight distortion and displacement. We cannot apply C-CG and C-PG to such real-world cases directly because they rely on Assumption 1 strictly. However, we can adapt them via a simple preprocess called symmetric alignment (details will appear in Sec. 6.3). We here compared four algorithms: CG using the network simplex algorithm [41], C-CG using the network simplex algorithm (Algorithm 1), PG [28], and C-PG (Algorithm 2). As an initial solution for CG or PG, we created a uniform random matrix in $[0,1]^{m\times n}$ and scaled it to lie within $\Pi (\mathbf{a},\mathbf{b})$ using the Sinkhorn-Knopp algorithm [30]. Also, as an initial solution for C-CG or C-PG, we created $K$ uniform random matrices in $[0,1]^{m^{\prime}\times n^{\prime}}$ , scaled each of them to lie within $\Pi^{\prime}(\frac{1}{K}\alpha ,\frac{1}{K}\beta)$ using the Sinkhorn-Knopp algorithm, and then constructed an $(m^{\prime},n^{\prime},K)$ -block circulant matrix generated by the scaled $K$ matrices. For each algorithm, we checked GWD, defined by the objective function value of (1), and the computation time, measured from data input to solution output. Each algorithm ran until the update of the GWD value was below $1.0\times 10^{-6}$ . All experiments were performed in Python on an Ubuntu 20.04 desktop with AMD Ryzen Threadripper 3970X 32-core CPU and 256 GB memory. In CG and C-CG, we determined $\lambda$ using the Armijo line-search in SciPy library [44] and used the network simplex algorithm in LEMON [15]. + +# 6.1. Performance Analysis with Synthetic Data + +We here evaluated whether our C-CG and C-PG show GWDs compatible with those of CG and PG but faster computations, respectively, in different synthetic data. + +We created 100 random pairs of synthetic 2D point sets with 10-order rotational symmetry on a 2D plane (for details, see Appendix C). The number of 2D points in each point set was 2000. Thus, $m = n = 2000$ . For the input data to each algorithm, we set $\mathbf{a} = \frac{1}{m}\mathbf{1}_m$ and $\mathbf{b} = \frac{1}{n}\mathbf{1}_n$ , and $\mathbf{C}$ and $\mathbf{D}$ as the Euclidean distance matrices for pairwise 2D point positions of each point set. The input data $\mathbf{a},\mathbf{b},\mathbf{C}$ and $\mathbf{D}$ satisfy Assumption 1 with $K = 10$ strictly. Because this input data also satisfy Assumption 1 for all $K$ that are divisors of 10 greater than 1, i.e., $K\in \{2,5,10\}$ , we conducted experiments for using each $K$ in C-CG and C-PG; using a larger $K$ makes C-CG and C-PG faster. In PG and C-PG, we set $\varepsilon = 0.004$ as low as possible while avoiding overflow, which is often caused by the Sinkhorn iterations [13]. + +Table 1 lists the results. C-CG showed GWDs compat + +
Algo.KGWD (×10-3)# of iterationsTime (s)
CG [41]-3.75 ± 2.1310.08 ± 5.7116.82 ± 10.49
C-CG23.76 ± 2.149.60 ± 5.843.52 ± 2.17
53.74 ± 2.148.87 ± 5.451.01 ± 0.62
103.75 ± 2.138.97 ± 4.270.64 ± 0.3
PG [28]-6.88 ± 2.1319.56 ± 20.06.73 ± 6.78
C-PG26.88 ± 2.1520.60 ± 18.633.56 ± 3.20
56.89 ± 2.1417.97 ± 16.211.47 ± 1.33
106.89 ± 2.1317.41 ± 17.130.94 ± 0.93
+ +Table 1. Performance analysis with synthetic data in Sec. 6.1. "Algo." means "Algorithm." "#" means "the number." "s" is the symbol for seconds. Mean $\pm$ SD is shown in each result. + +![](images/fd888aa753b569120ea01c2272983562ec161601437cc1a6955ff30aec36f619.jpg) +Figure 4. Sensitivity to different initial solutions in Sec. 6.2. Each of Synthetic 1 to 5 indicates the different synthetic pair data. The time listed to the right of each algorithm name represents Mean $\pm$ SD of the computation time to obtain all GWDs. Note that PG and C-PG showed larger GWDs than those of CG and C-CG because they solved C-EGW having the entropy regularizer. + +ible with those of CG but faster computation times when a larger $K$ value was used. This trend was also observed between PG and C-PG. These results validated the effectiveness of C-CG and C-PG for C-EGW; they achieve faster computations than CG and PG when using the higher cyclic symmetry structure hidden in the input data (i.e., larger $K$ value) without degrading GWDs. + +# 6.2. Sensitivity to Different Initial Solutions + +Since GW is non-convex, the result depends on an initial solution. In C-CG and C-PG, the initial solution is restricted to an $(m', n', K)$ -block circulant matrix. This raises a concern that C-CG and C-PG may reach a worse solution than CG and PG, which allows for more flexible initial solutions. Therefore, we here evaluated the sensitivity of each algorithm to different initial solutions in the same synthetic data. + +As in Sec. 6.1, we created 5 random pairs of synthetic 2D point sets with 2-order rotational symmetry and set the input data $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{C}$ and $\mathbf{D}$ to each algorithm. We randomly set 50 different initial solutions for each algorithm in each synthetic pair data. Other settings were the same in Sec. 6.1. + +Figure 4 shows the results. In the same synthetic pair + +data, C-CG and C-PG showed GWDs compatible with those of CG and PG but faster computation times, respectively. These results indicate that the constraint in C-CG and C-PG, which restricts the initial solution to an $(m', n', K)$ -block circulant matrix, does not always degrade GWDs. + +# 6.3.2D Shape Analysis with Real-World Data + +Similar to the existing Gromov-Wasserstein studies [8, 31], we evaluated whether GWDs obtained by our algorithms are useful to distinguish different 2D objects even if the objects have approximate cyclic symmetry. + +We used the publicly available 2D structure dataset [7] and selected ten objects from each of the four classes, bone, glass, butterfly, and bell, with approximate mirror symmetry ( $K = 2$ ). Each object consists of 100 to 200 vertices and triangles, and we used the vertices as a representative feature for the object as in [8, 31]. For the input data to CG and PG, we selected a pair of objects with $m$ and $n$ vertices, respectively, and set $\mathbf{a} = \frac{1}{m}\mathbf{1}_m$ and $\mathbf{b} = \frac{1}{n}\mathbf{1}_n$ . Then, we defined C and D as the Euclidean distance matrices for pairwise vertex positions of each object. Because these real-world 2D objects satisfy Assumption 1 approximately due to slight displacement and distortion of shape, we cannot apply C-CG and C-PG to these data directly. Therefore, for the input data to C-CG and C-PG, we here first aligned the vertices of each object to exhibit strict mirror symmetry (for details, see Appendix D) and then set $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{C}$ and $\mathbf{D}$ in the same manner of CG and PG. This alignment preprocess is called symmetric alignment, mentioned at the beginning of Sec. 6. Figure 5 left panels show the original vertices and aligned ones of each object; we can see that the shape differences were not significant. Note that we also tested CG and PG with the symmetric alignment in this experiment for a fair comparison. For PG and C-PG, we set $\varepsilon = 0.002$ . + +For the evaluation, we computed the pairwise GWD between all objects using each algorithm. Also, to evaluate the discriminative power of the pairwise GWD obtained by each algorithm, we conducted a simple classification task as in [8, 25]; one object is randomly selected from each class and performs 1-nearest neighbor classification of the remaining objects using the pairwise GWD. This classification was repeated 10000 times, and we obtained a confusion matrix for each algorithm. That is, $(i,j)$ -th entry of the confusion matrix indicates the probability that the classifier, which is based on the pairwise GWD obtained by each algorithm, will assign class $j$ to an object with the true class $i$ . + +Figure 6 shows the results. CG produced almost the same pairwise GWDs and confusion matrices when using and not using the symmetric alignment. Also, because the symmetric alignment preprocess was so much faster than CG itself, the difference in total computation time to obtain the pairwise GWD between CG and CG with the symmetric alignment was negligible. In contrast, C-CG showed better + +![](images/6586e71eea730c90b376276b9b43eceeddd9a85b8ca128d528f90ca572cd85ae.jpg) +Figure 5. Input data examples in Sec. 6.3 (left) and Sec. 6.4 (right). + +![](images/24c62b2babe10e569b04804859bb73f7ef572e8ffdf4b74f567bd1207820ba95.jpg) + +results than CG: (i) its pairwise GWD showed larger values between different classes, (ii) its confusion matrix was closer to the identity matrix, which indicates the classifications were done more successfully, and (iii) its total computation time was the fastest. The reason for (i) and (ii) is that CG, with or without the symmetric alignment, often reached worse local solutions due to its large solution space, while C-CG often reached better local solutions thanks to its smaller solution space that considers cyclic symmetry of input data. This implies that C-CG can properly use the inherent cyclic symmetry of input data emerging clearly by the symmetric alignment (for details, see Appendix E). This trend was also observed among PG, PG with the symmetric alignment, and C-PG. These results indicate that combining C-CG and C-PG with the symmetric alignment can be more effective than CG and PG in distinguishing different real-world 2D objects with approximate cyclic symmetry. + +# 6.4. 3D Shape Analysis with Real-World Data + +Following the existing studies [8, 25, 31], we also conducted experiments on a 3D object version of Sec. 6.3, which have more complex shapes and bigger data size. + +We used the publicly available 3D structure dataset [11] and selected ten objects from each of the four classes, plane, bag, bottle, and chair, respectively, with approximate mirror symmetry ( $K = 2$ ) along the YZ-axes plane. Each object is provided as 3D mesh data, and we approximated the object as a point cloud with 2000 points using trimesh library [14]. In the same manner of Sec. 6.3, we set the input data $\mathbf{a}$ , $\mathbf{b}$ , $\mathbf{C}$ and $\mathbf{D}$ to CG and PG by using each pair of the original point clouds, and set them to C-CG and C-PG by using each pair of the symmetrically aligned point clouds exhibiting strict mirror symmetry. For details of the symmetric alignment for these point clouds, see Appendix F. Figure 5 right panels show the original point cloud and the aligned ones of each 3D object. Other settings were the same in Sec. 6.3. + +Figure 7 shows the results. Similar to Sec. 6.3, C-CG and C-PG showed better pairwise GWDs, confusion matrices, and faster computations than those of CG and PG, respectively. These results indicate that combining C-CG and C-PG with the symmetric alignment can be more effective than CG and PG in distinguishing different real-world 3D objects with approximate cyclic symmetry. + +![](images/fad31414650cbe86b00cce2fdb5bca972b86ed0846f7bbdb4e9d9b02fea7e9a9.jpg) +Figure 6. Experimental results in Sec. 6.3. Top panels show the pairwise GWD between all objects using each algorithm. Bottom panels show the confusion matrices obtained by each pairwise GWD. The time listed under each algorithm name represents the total computation time to obtain each pairwise GWD, which includes the symmetric alignment time if used. + +![](images/1e16eac70a0c39461c2578d42d0ae2db0ba56b72104e73524ac3cdf18d25ebc2.jpg) +Figure 7. Experimental results in Sec. 6.4. The details are the same in Fig. 6. + +# 7. Discussions and Limitations + +We here list the future issues: (I) Our algorithms rely on Assumption 1 and need the symmetric alignment for objects with approximate cyclic symmetry. We experimentally confirmed that this process is not as computationally heavy as the main process of solving C-EGW in Secs. 6.3 and 6.4. However, in more complex real-world settings, it may lead to slower runtime or worse solutions. Thus, a theoretically guaranteed fast algorithm with symmetric alignment is desirable. (II) Our algorithms are limited to cyclic symmetry and must know its order $K$ in advance. Generalizing for other symmetries without prior knowledge of their order is left for future work. (III) The output of our algorithms is restricted to the $(m', n', K')$ -block circulant matrix. However, there exists an instance of C-EGW whose globally optimal solution is never such a matrix (for details, see Appendix G). A fast algorithm that guarantees reaching a globally optimal solution by using cyclic symmetry is desirable. (IV) As a first step, we incorporated cyclic symmetry + +into the two most widely used GW algorithms, namely CG and PG. Extending this approach to other GW algorithms is a promising direction for future research. (V) Combining other special structures, such as low-rank and hierarchical structures, with symmetry has excellent potential but is nontrivial because our approach may break such structures. We will explore this potential in the future. + +# 8. Conclusion + +We introduced a new problem, EGW with cyclic symmetry (C-EGW), and proposed novel fast algorithms for C-EGW. Our algorithms restrict the solution space to have cyclic symmetry with theoretical guarantees, thereby dramatically reducing the number of variables in the gradient-based algorithms and achieving fast computation. Diverse experiments showed the effectiveness of our algorithms in synthetic and real-world data with cyclic symmetry. This paper was the first to explore the possibility of symmetry in solving GW faster, paving the way for future followers. + +# References + +[1] Ravindra K Ahuja, Thomas L Magnanti, and James B Orlin. Network Flows: Theory, Algorithms, and Applications. 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GroomLight achieves high-fidelity reconstruction of human hair appearance from real-world images, enabling realistic rendering under diverse lighting conditions. Here, in each column, we present relighting results of a same subject under two different environments, using the appearance model reconstructed by GroomLight. One input view with the similar head pose is shown at the top right corner. + +![](images/9e9fc8d3001e502aac8ea59d01361ea72153c8639f5dc2a38d9c7d4357b263dc.jpg) + +![](images/26e8e3562040462731f6faed2e7ab83977a69594d47b1691a50c7eaeed8b631a.jpg) + +![](images/59ccebf94d9b39af73400defc149b2d53735c077fe15d83b55038c0ea0763019.jpg) + +![](images/ac84de2d63d75da2b66b087c4963732862687e5e13ba9c4d56d26074884f4276.jpg) + +![](images/fdc12cfb5459974c823ce07cf6116f97c51267bc91dac018dff721c44dd8017f.jpg) + +![](images/a1021e93f224ac703e0bc2aef5efc144f9e628b36cb903cbc734602b55466f61.jpg) + +![](images/652749464eb0873846893f22dbf8adea1805b179c2d057301890284aa6bc19b6.jpg) + +![](images/1ca0e09733932b2322c216d2f310e0526c93be62592838877179f893bf73650b.jpg) + +# Abstract + +We present GroomLight, a novel method for relightable hair appearance modeling from multi-view images. Existing hair capture methods struggle to balance photorealistic rendering with relighting capabilities. Analytical material models, while physically grounded, often fail to fully capture appearance details. Conversely, neural rendering approaches excel at view synthesis but generalize poorly to novel lighting conditions. GroomLight addresses this challenge by combining the strengths of both paradigms. It employs an extended hair BSDF model to capture primary light transport and a light-aware residual model to reconstruct the remaining details. We further propose a hybrid inverse rendering pipeline to optimize both components, enabling high-fidelity relighting, view synthesis, + +and material editing. Extensive evaluations on real-world hair data demonstrate state-of-the-art performance of our method. Our project website is at: https://syntec-research.github.io/GroomLight. + +# 1. Introduction + +Hair capture is a long-standing problem in computer graphics and vision, and plays an essential role in human digitization. While substantial progress has been made in strand-accurate geometry reconstruction, hair appearance modeling and photorealistic relighting remain open challenges. + +As part of efforts towards physics-based photorealistic rendering, analytical material models for hair have been extensively studied. Following this path, inverse rendering approaches [43] seek to match renderings to input images by + +optimizing hair material properties, specifically the bidirectional scattering distribution function (BSDF). A key advantage of such approaches lies in their exceptional ability to generalize to novel viewpoints, unseen lighting, and altered hair geometry. However, even with sophisticated differentiable renderers, the reconstruction methods suffer from system errors stemming from factors such as imperfect geometry reconstruction, inaccurate lighting calibration, simplified light scattering models without diffraction and interference effects, etc. Consequently, these methods struggle to reproduce critical appearance details, hindering their successful application to real images. + +Meanwhile, recent advances in image-based neural rendering have achieved impressive success in hair view synthesis. By employing primitives specifically tailored for strand structures, such as hybrid neural volumes [48], neural strand features [37], and linked cylindrical Gaussians [27], these methods exhibit a superior capability in capturing fine-grained appearance details from multi-view inputs. However, lacking a physics-grounded appearance parameterization, these primitives tend to entangle geometry, appearance, and associated illumination conditions, leading to overfitting of input images at the expense of generalization capability. Consequently, significant quality degradation is constantly observed in their relighting results. + +Towards high-quality hair relighting, our motivation is to leverage the complementary strengths of both physically based material models and neural rendering representations. This involves employing analytical BSDF models to reconstruct the primary light transport while relying on neural rendering to capture subtle appearance details. + +In this work, we introduce GroomLight, a hair appearance modeling method that reconstructs relightable hair appearance from OLAT (one-light-at-a-time) images. For the very first time, GroomLight enables high-fidelity and fully functional relighting for photorealistic human hair. Our appearance representation consists of two key components: 1) an extended hair BSDF model robust to natural hair color variations and imperfections in the reference hair geometry; and 2) a light-aware residual model that captures remaining details utilizing light- and view-conditioned dual-level spherical harmonics (SH) associated with a Gaussian-based hair representation. On top of that, we propose a hybrid inverse rendering pipeline that combines a physics-based differentiable renderer with neural image-based rendering to optimize the appearance. + +We extensively evaluate our method on real-world hair data, demonstrating state-of-the-art relighting and view synthesis results under diverse lighting conditions. Moreover, our pipeline naturally supports versatile applications, including material editing and dynamic animation rendering, and seamlessly integrates with conventional CG workflows. + +# 2. Related Work + +# 2.1. Hair Appearance Modeling + +Besides geometry capture from single- [5, 6, 8, 16] or multiview [18, 28, 33, 34, 56], hair appearance modeling has also been a long-standing challenge. We provide a brief overview of physics- and neural-based methods that model the complex appearance of hair fibers. + +Physically Based Models. Physically based hair appearance models describe light transport resulting from scattering on and within hair fibers. Building upon the foundational work on fiber reflectance [23], Marschner et al. [30] and subsequent research [11-13, 17, 25, 38, 62-64] have derived hair BSDFs that encapsulate hair scattering effects into analytical reflection and transmission lobes. These BSDF models, when used in conjunction with a path tracer [22], can generate highly realistic images of hair. Variations of hair BSDF models have also been employed to render textile fibers [1] and animal fur [53, 54]. While most models rely on geometric optics, incorporating waveoptical effects can further enhance realism [2, 50, 51]. Nevertheless, analytical physically based BSDFs may lack the expressive capacity and flexibility to perfectly match the appearance of real hair, potentially leading to inaccuracies in re-rendering crucial appearance features such as specular highlights and color variations. + +Neural Representations. Neural networks offer a powerful means of representing high-fidelity human hair appearance. Generative models [9, 21, 36, 44, 49] have been trained for realistic hair synthesis. Neural rendering techniques [45] leverage scene representations such as neural radiance field (NeRF) [29, 31, 37], 3D Gaussian Splatting (3DGS) [24, 27, 35, 52], and implicit geometry and texture networks [10, 15, 41, 58] to learn portrait appearance from images. While neural models can produce high-quality, photorealistic results, they often lack robust relighting capabilities and can be challenging to animate or edit manually. + +# 2.2. Inverse Rendering of Hair + +Inverse rendering aims to estimate appearance parameters from visual observations using analysis-by-synthesis techniques. Sun et al. [43] estimate hair BSDF [11] parameters by measuring differences between sparse hair samples and synthetic ground truth observations. Their approach relies on an approximation of the observed color based on idealized lighting conditions and demonstrates results on synthetic data with accurate hair geometry reconstructed from ground truth segmentation, camera and lighting information. Chai et al. [7] propose an image-based rendering technique for hair relighting. Neural-based relighting [3, 32, 42, 55, 57] and Gaussian-based inverse rendering methods [4, 14, 20, 39, 40, 59] often combine neural representations with simplified physically based rendering + +![](images/63f26fef95621b8d3e9e9b0b41363a0565d89c0b3a6c64c7dd2d303fcb104835.jpg) +Stage 1: BSDF Optimization +Stage 2: Residual Optimization + +functions, which may not accurately model complex phenomena such as multiple scattering and shadowing. Luo et al. [27] leverage 3D Gaussians to capture hair appearance and design a scattering approximation method for relighting. However, their method remains fundamentally based on Gaussian splatting with baked-in appearance, and the approximation function may not fully capture real-world light scattering in human hair, potentially leading to suboptimal rendering results. In contrast, we propose a hybrid inverse rendering pipeline that fully leverages the strengths of both physically based and neural rendering representations. + +# 3. Method + +# 3.1. Overview + +Our approach employs a two-level representation of hair appearance. This comprises: 1) an extended BSDF model ( $\S 3.2$ ), which utilizes a physics-based parameterization to capture the primary appearance characteristics of real-world hair strands; and 2) an implicit light-aware residual model ( $\S 3.3$ ) that captures light- and view-dependent details not fully encompassed by the analytical BSDF formulation. + +Accordingly, our hybrid inverse rendering pipeline (§3.4) constructs these appearance models in two stages. First, inverse rendering optimization is performed within the analytical BSDF parameter space, which is extended to accommodate spatial variations in hair material and improve robustness against potential misalignment in the input hair geometry. Subsequently, leveraging a 3D Gaussian-based representation of individual strands, we optimize light-aware dual-level spherical harmonics to model the remaining appearance residuals. + +![](images/219c92f706b966992af18db28032618f0ec58974cd1a367aa01c2bbc5cc48abf.jpg) +Figure 2. Our hybrid inverse rendering pipeline employs a two-stage optimization scheme. Given input OLAT images and the reconstructed hair geometry (here we visualize the 1/10 downsampled version), we first estimate the physical parameters of the extended hair BSDF model (Stage 1, §3.2), and then leverage a light-aware residual model to capture fine-grained appearance details (Stage 2, §3.3). +Figure 3. Impact of light scattering. We compare the effects of varying the maximum number of ray bounces during path tracing ( $\infty$ means the integrator will not enforce any hard cutoff on the number of bounces). Our method employs 8 bounces to achieve high quality rendering at practical efficiency. + +Input Data. Our method operates on multi-camera OLAT captures. We capture our input data in a light stage, featuring an array of 50 cameras and 331 light sources, uniformly distributed over the dome. From the complete set of frames $\mathcal{I}$ , we exclude views where cameras do not prominently feature hair or where the subject is strictly back-lit (to mitigate artifacts arising from low exposure). The reference hair geometry $S$ and parametric head mesh $\mathcal{H}$ are pre-reconstructed from the same OLAT input using the state-of-the-art strand-level hair capture technique of GroomCap [61], which typically yields 150K scalp-rooted strands. Additionally, we perform 2D segmentation using SAM [26] to obtain a set of hair masks $\mathcal{M}$ for input frame images. + +# 3.2. Extended Hair BSDF Model + +Our strand-based hair BSDF is based on the analytical fiber reflectance model by Chiang et al. [11]. Each strand's geometry is approximated as a cylindrical B-spline curve with a uniform radius, which we set to the average radius of human hair $(40\mu m)$ . For each point on the fiber, the perceived + +reflectance is parameterized as a function of the incident $\theta_{i}$ and exitant $\theta_{o}$ lighting inclinations, their relative azimuth $\phi = \phi_{o} - \phi_{i}$ , and the physical parameters $\Psi$ of the material: + +$$ +\mathrm {S} \left(\theta_ {i}, \theta_ {o}, \phi ; \Psi\right) = \sum_ {p = 0} ^ {\infty} \mathrm {M} _ {p} \left(\theta_ {i}, \theta_ {o}; \Psi\right) \mathrm {N} _ {p} (\phi ; \Psi), \tag {1} +$$ + +where the reflectance $S$ is decomposed into separate lobes according to the path of light propagation $p$ (i.e., $p \in \{R, TT, TRT, \ldots\}$ ), which counts the reflections and transmissions in the fiber cylinder. Each lobe consists of $\mathbf{M}_p$ and $\mathbf{N}_p$ , i.e., the longitudinal and azimuthal scattering functions, respectively. Fig. 3 shows the light scattering effects in hair rendering, where single-bounce illumination (only $p = 0$ is evaluated) leads to degenerated results, while more scattering events contribute to more realistic rendering. + +The material parameters $\Psi$ of the BSDF model, to be optimized during inverse rendering, include absorption coefficients $\sigma_{a}$ , longitudinal $\beta_{M}$ and azimuthal $\beta_{N}$ roughnesses, and interior $i_{ior}$ and exterior $e_{ior}$ indices of refraction [11]. + +Scalp-Aligned Albedo Parameterization. By assuming homogeneous material parameters $\Psi$ (Eq.1), a uniform hair albedo is enforced across all strand points, which cannot model the nuanced color variations commonly observed in real world, naturally or artificially, ranging from root-to-tip gradients within a single strand to subtle differences across wisps. To address this limitation, following previous work [37, 47, 60, 61], we propose a scalp-aligned parameterization that introduces sufficient degrees of freedom to capture spatial color variation, while maintaining natural regularization and preventing over-parameterization. + +Specifically, recall that all input strands $S$ are rooted on the parametric head $\mathcal{H}$ . We pre-define a scalp region $\mathcal{H}_S$ on the head surface and unwrap it to a 2D parameterization, namely the scalp space. For each strand $s\in S$ , we project its root to the corresponding attachment point on $\mathcal{H}_S$ and embed it into the scalp space at coordinates $u_{s}$ via barycentric interpolation. We also convert each strand $s$ to a B-spline curve $s^*$ by uniformly sampling $n_c$ control points. The hair is finally formulated as a regular 3D volume, conceptually equivalent to $n_c$ layers of textures with resolutions of $(w_{u},h_{u})$ . An arbitrary point $p$ on strand $s$ is mapped to this volume based on the strand's root coordinate $u_{s}$ and the point's relative on-strand coordinate $w_{p}^{s}$ . We utilize this scalp-aligned parameterization to encode absorption coefficients $\sigma_{a}\in \mathbb{R}^{n_{c}\times w_{u}\times h_{u}}$ , which determine the albedo. + +Compared to world-space voxelization, this parameterization ensures that points on the same strand share the same texture coordinate, and nearby texels map to points on adjacent strands. Decoupled from specific geometric styles, this inherent structure leads to more controllable degree of freedom and effective regularization across texture layers. + +Rotation Correctives. In contrast to previous works [43] + +that benefit from clean images and relatively precise hair geometry obtained from synthetic renderings, our pipeline must contend with imperfections in hair reconstruction that introduces discrepancies between the reconstructed and ground-truth strand shapes. This poses challenges for inverse rendering, particularly problematic for specular highlights, which are highly sensitive to the accuracy of strand tangents. To mitigate sub-optimal roughness optimization due to misplaced highlights, we propose a lightweight corrective to the BSDF model that, rather than directly refining the curve geometry, optimizes a constrained rotation transformation for each strand segment to compensate for inaccuracies in the tangent directions. + +Specifically, we formulate this rotation corrective $R$ within the same scalp-aligned parameterization used for the absorption coefficients $\sigma_{a}$ . This corrective encodes a rotation matrix $R$ for each strand control point, represented using the Rodrigues formula. When evaluating a BSDF sample, its local shading frame $\{n,t,b\}$ , defined by the normal $n$ , tangent $t$ , and bitangent $b$ , is rotated by $R$ to yield a corrected frame $\{Rn,Rt,Rb\}$ for shading. + +# 3.3. Light-Aware Residual Model + +While our BSDF model effectively reconstruct the large-scale appearance of hair and generalizes well to novel views and lighting conditions, relying solely on this analytical model leads to over-smoothed results due to a broad range of imperfect assumptions such as simulated lighting, missing diffraction and interference in the BSDF model, etc., which limits its capacity to capture subtle, yet visually critical, local details. + +We introduce a residual term to model the remaining discrepancies between the physics-based rendering obtained the optimized BSDF and the real-world observations. To ensure desired consistency and generalization, this residual model is designed to be both light-aware and strand-aligned, to enable robust relighting capabilities and facilitate a compact, geometry-aware parameterization. + +Specifically, we leverage 3D Gaussian Splitting (3DGS) [24] for scene representation. However, instead of optimizing free-form Gaussians as in the vanilla 3DGS formulation, we enforce identical anisotropic Gaussians for all kernels, and place them along the input strand geometry to form a chained sequence. During optimization, we fix the geometric parameters of all Gaussians (position, covariance, and opacity) and focus solely on optimizing their appearance parameters, as detailed below. This strategy is motivated by our primary focus on appearance modeling, recognizing that the initial Gaussian configuration already inherits good strand geometry from the input. + +Dual-Level Spherical Harmonics. We introduce a dual-level spherical harmonics (SH) function as the appearance representation for the residual model, which is both view- + +and light-dependent, achieved by nesting two levels of SH. Given a dual-level SH, denoted as $\mathbf{C}_{vl}$ , the final Gaussian color $c$ is calculated as a function of the camera view $d_v$ and incident lighting $d_l$ directions (in global coordinates): + +$$ +\begin{array}{l} c = \mathbf {C} _ {v} (d _ {v}), \\ \mathbf {C} _ {v} = \mathbf {C} _ {v l} (d _ {l}). \tag {2} \\ \end{array} +$$ + +With both SH levels using the same degree $l$ , the parameter size of each dual-level SH is $\mathbf{C}_{vl} \in \mathbb{R}^{(l + 1)^2 \times (l + 1)^2 \times 3}$ and $\mathbf{C}_v \in \mathbb{R}^{(l + 1)^2 \times 3}$ . To maintain compact appearance parameters, we attach $k$ dual-level SHs to each strand as anchor SHs. During rasterization, for each Gaussian primitive at location $p$ belonging to strand $s$ , its dual-level SH parameters are linearly interpolated from its nearest two anchor SHs based on its relative on-strand coordinate $w_p^s$ . + +# 3.4. Hybrid Inverse Rendering + +Given the input hair geometry $S$ and multi-camera OLAT images $\mathcal{I}$ , we optimize the hair appearance, including both the analytical BSDF model and the residual model, using our hybrid inverse rendering in two stages. + +Stage 1: BSDF Optimization. The first stage optimizes the physical parameters $\Psi$ of the BSDF model using differentiable path tracing. Due to the large number of scattering events, we use path replay backpropagation [46] to efficiently compute gradients of the used photometric loss: + +$$ +\mathcal {L} _ {r g b} = \sum_ {I \in \mathcal {I}} \| I - \mathrm {R} (\Psi , \mathcal {S}, \mathcal {C} (I), \mathcal {L} (I)) \| _ {1}, \tag {3} +$$ + +where $\mathbf{R}$ represents the rendering function, $I \in \mathcal{I}$ denotes one ground truth view image, and $\mathcal{C}(I)$ and $\mathcal{L}(I)$ are the calibrated camera and lighting information associated with the image $I$ , respectively. + +With our albedo parameterization and rotation corrections, the complete set of parameters for the hair BSDF model is represented as $\Psi = \{\pmb {\sigma},\pmb {R},\beta_N,\beta_M,e_{ior},i_{ior}\}$ . To ensure smooth variation along each strand, we add regularization terms for the spatially varying variables in the scalp-aligned volume: + +$$ +\mathcal {L} _ {\sigma} = \sum_ {i = 1} ^ {n _ {c} - 1} \| \boldsymbol {\sigma} _ {i} - \boldsymbol {\sigma} _ {i - 1} \| _ {1}, \tag {4} +$$ + +$$ +\mathcal {L} _ {R} = \sum_ {i = 1} ^ {n _ {c} - 1} \| \boldsymbol {R} _ {i} - \boldsymbol {R} _ {i - 1} \| _ {1}. \tag {5} +$$ + +Finally, the complete loss function for the first inverse rendering stage is: + +$$ +\mathcal {L} _ {B S D F} = \mathcal {L} _ {r g b} + \lambda_ {\sigma} \mathcal {L} _ {\sigma} + \lambda_ {R} \mathcal {L} _ {R}, \tag {6} +$$ + +where $\lambda_{\sigma} = 0.5$ and $\lambda_{R} = 10$ control the strength of both regularization terms. + +Stage 2: Residual Optimization. Once the BSDF optimization in Stage 1 is complete, we proceed to optimize the residual model. This involves fitting the remaining differences between the rendered images and the input views. Specifically, we optimize the dual-level spherical harmonics parameters of the residual appearance by minimizing the following residual loss: + +$$ +\mathcal {L} _ {r e s} = \sum_ {I \in \mathcal {I}} \| I - \left(I _ {\text {r e n d e r}} + I _ {r e s}\right) \| _ {2} ^ {2}, \tag {7} +$$ + +where $I_{\text{render}}$ represents the path-traced rendering using the optimized BSDF parameters from Stage 1, and $I_{\text{res}}$ is the residual image rendered via 3D Gaussian rasterization. Note that in stage 2 we employ $L_2$ loss which we find leads to more robust performance. + +Implementation Details. The inverse rendering pipeline in Stage 1 is built upon the differentiable renderer of Mitsuba 3 [19]. We approximate the lighting using measured IES profiles, with lighting positions initialized via OLAT calibration. We jointly optimize the BSDF parameters $\Psi$ and the lighting parameters, including positions, orientations, and intensities since the lighting calibration might not be perfectly accurate. In each optimization iteration, we randomly select 8 images from all camera views and lighting conditions, and aggregate gradients across these images. For a given capture, we run 1000 iterations, which takes about 20 hours on a single NVIDIA A100 GPU (40 GiB). + +In Stage 2, we downsample the input hair to approximately $52\mathrm{K}$ strands, each represented by 100 segments. Cylindrical Gaussians are attached to these strand segments, with their positions and covariance matrices derived from the location and orientation of the the corresponding hair segments. Each strand is associated with 8 anchor SHs with SH degree $l = 3$ , and per-segment SH parameters are obtained through interpolation between its two nearest anchor SHs. During optimization, we optimize the SH appearance parameters and keep all geometric properties fixed. We train the residual Gaussians for $160\mathrm{K}$ iterations on 8 NVIDIA A100 GPUs (40 GiB), which takes about 12 hours. + +# 4. Experiments + +In this section, we first explain our experimental setup, including the dataset, baselines, and evaluation metrics. Then we present and discuss the experiment results, including comparisons and ablation study, in detail. + +# 4.1. Setup + +Dataset. We capture our test data from 10 subjects (§3.1). These subjects feature diverse hair characteristics, including variations in length (short, medium, and long), style (curly, wavy, and straight), and color (black, blond, and gray). + +![](images/7fc4c9898091e46a70ea440b251d0cb98a16be6d46c1c4a72fbe7460ec464455.jpg) +Figure 4. Qualitative evaluation of rendering results at novel testing views under novel lighting conditions of our method and baselines. + +![](images/755383f9fca81b1bde536872270fa9a21321913d590a916c2da74e31ae40f8ef.jpg) +Ours (Stage1 OrigBSDF) + +![](images/3bd15356a4da4a8d73b8745c08a7bd0624244464a4a0606b5d887c52d00d6f79.jpg) +Ours (Stage1 NoCorr) + +![](images/6d7e8c145945a99b8b192b7cd724673b57535d8cb44bb294c3394b4fee328789.jpg) +Ours (Stage1 Full) + +![](images/2f9c38f06b3a413f9a3cc3d88a8dd8d72eef01a46059de541e5f5584391a1305.jpg) +Ours (Full) + +![](images/417a750b778ae225f156e9ab70872311c2fca2ccc096d9c0b370e217d7020e24.jpg) +Groundtruth + +
MethodPSNR (↑)SSIM (↑)LPIPS (↓)
HairInverse [43]26.500.67670.3171
GaussianHair [27]27.220.73400.2920
Ours (Stage1 OrigBSDF)27.750.73500.2772
Ours (Stage1 NoCorr)28.580.74100.2690
Ours (Stage1 Full)28.670.74230.2653
Ours (Full)29.710.77270.2461
+ +Table 1. Quantitative results on view reconstruction of baseline comparisons and ablation study. + +The hair geometry is reconstructed by GroomCap [61] from views under uniform lighting. For each subject, we use 160 lighting conditions and approximately 48 cameras views for training. We designate 2 novel views (one front and one back view) and 160 novel lightings for evaluation. + +Baselines. To assess the quality of view synthesis and relighting, we compare GroomLight with two adapted state-of-the-art baselines quantitatively and qualitatively: + +- HairInverse [43]: An inverse rendering method based on an analytical BSDF material model. The original method performs image-space optimization on selected pixels without involving differentiable renderers and presents results only on synthetic data. We re-implement this baseline, adapting to our algorithm, which iterative optimizes BSDF parameters based on photometric losses. +- GaussianHair [27]: A 3DGS-based [24] neural rendering method for hair. We re-implement this baseline by reusing our chained cylindrical Gaussians and applying our residual appearance model, i.e., dual-level SH, to the full image. This differs from their hair scattering model, which employs optimized SH base colors and manually tuned material parameters. + +Evaluation Metrics. We evaluate all methods using the following photometric error metrics: Peak Signal-to-Noise + +![](images/a96741a00fe412e13684a1dd44f072c84360254c165933cf2da57096db807e39.jpg) +Figure 5. Ablation study of components in our method. Starting from Stage 1 only with original BSDF model (Stage1 origBSDF), we sequentially add spatially-varying albedo (Stage1 NoCorr), rotation correctives (Stage1 Full), and the residual model (Full). + +![](images/43eb723bafd290fd08a201d86b0519cf657b1636ec4e2c21776a6c3c3c862654.jpg) +Original Hair + +![](images/8462d129332d5d04cc099f4a8dd5323283a69b1c6fe6e7ec1da95986afa37989.jpg) + +![](images/3b53d0be6de570db28cf44389aa2e8210ce36fb5f8e39c63d6eb9471fe1bd988.jpg) +Edited Hair + +![](images/101acf48fedf7343a6a4f048e706b010712b6ff8c855f6d60c7e7a2fb841be9e.jpg) + +![](images/521f874dcd719762a783a582546267306af24bb254b7fd0c6e34ce509637d397.jpg) +Figure 6. Appearance editing. Top row: decreasing roughness of hair BSDF to add more highlights. Bottom row: editing the albedo parameters to change the color for specific hair wisps. + +Ratio (PSNR), Structural Similarity Index Measure (SSIM), and Learned Perceptual Image Patch Similarity (LPIPS). + +# 4.2. Comparisons + +We compare our method with both HairInverse and GaussianHair baselines on testing view reconstruction under diverse lightings. As demonstrated in Tab. 1, our method outperforms both baselines by a large margin across all metrics. We also show qualitative comparisons in Fig. 4. + +HairInverse [43], based on homogeneous hair BSDF material, estimates its parameters from the average color of the hair region. This model lacks the flexibility to represent the diverse textures found in real-world hair. + +While 3DGS-based GaussianHair [27] achieves reasonable view reconstruction results, it often overfits to training views and lightings, leading to poor generalization. + +As shown in Fig. 4, GroomLight effectively reconstructs coarse hair appearances in stage 1 (Ours Stage1). By incor + +![](images/d21c56dd9abe91bb62dbf77aaf074957182c20b3e36151acfabe2197fca6a924.jpg) +Figure 7. Dynamic rendering. We show rendering results of animated hair sequences using our optimized appearance model. + +porting the residual model in Stage 2, we achieve photorealistic final renderings (Ours Full) with enhanced details. + +# 4.3. Ablation Study + +We conduct an ablation study to evaluate the contribution of each proposed component in our method, including the spatially varying albedo parameterization and rotation correctives in Stage 1, and the residual module of Stage 2. + +Extended BSDF. We augment the base hair BSDF with a scalp-aligned albedo parameterization to enable spatially-varying hair color and introduce rotation correctives to compensate for inaccuracies in the reference geometry. We present the performance of different variants in Tab. 1: including Stage1 OrigBSDF (Stage 1 only using the original version of hair BSDF [11]), Stage1 NoCorr (adding the albedo parameterization), Stage1 Full (adding both the albedo parameterization and rotation correctives). The results demonstrate that each component contributes to improved reconstruction quality. As shown in Fig. 5, the original hair BSDF, assuming homogeneous materials, produces a uniform color across all strands. The spatially-varying albedo facilitates the reconstruction of more detailed hair texture, while the rotation correctives further enhance the accuracy of light reflectance, particularly for highlights. + +Residual Model. We incorporate the residual model to address the inherent limitations of analytical BSDF models, which are based on approximations of physical behaviors. This residual model helps capture fine-grained texture details and highlights (Full), leading to more accurate results (Tab. 1) and enhanced photorealism as shown in Fig. 5. + +# 4.4. Applications + +The generalization capabilities of our hair appearance model naturally lends itself to various downstream applications that are previously challenging. + +Relighting. Fig. 1 shows our relighting results under diverse environment lighting conditions. To provide the lighting direction input for our residual module, we approximate the light source in HDR environment maps as the position with maximum radiance. Our method achieves high-fidelity rendering quality across a wide range of lighting scenarios. + +Appearance Editing. Our spatially-varying albedo parameterization enables convenient appearance editing (Fig. 6). By directly modifying the absorption coefficients for hair strands on the scalp space embedding, we can achieve various color effects. In addition to albedo editing, our representation supports rendering diverse highlight patterns by changing the roughness parameters. + +Dynamic Rendering. Our method also generalizes to novel hair geometry. By animating the reconstructed hair using off-the-shelf simulation tools, we can render the sequence using the optimized appearance model, including BSDF and residual parameters, as shown in Fig. 7. Please refer to the supplementary video for the entire sequence. + +# 5. Conclusion + +We introduce GroomLight, a novel method for capturing and relighting photorealistic hair. Our approach combines the strengths of both physically based rendering and neural representation learning within a hybrid inverse rendering framework. We propose an extended analytical BSDF model that effectively captures the primary appearance of hair while remaining robust to variations in hair color and inaccuracies in the underlying geometry. To further enhance visual fidelity, we introduce a light-aware residual model based on dual-level spherical harmonics and a 3D Gaussian-based scene representation. GroomLight achieves state-of-the-art performance on inverse rendering for relightable human hair appearance modeling from real-world input data, which could benefit a wide specturm of applications in virtual reality, digital fashion, movie industry, and more. + +Limitations and Future Work. GroomLight relies on light stage capture setup to obtain lighting and camera calibrations, which limits its applicability to in-the-wild data where lighting and camera information are unknown. In addition, our pipeline is based on offline optimization and renders images at about 1 FPS during inference, which cannot support real-time applications. Furthermore, our method requires relatively accurate geometry and segmentation masks to prevent artifacts arising from the inclusion of unwanted textures from clothing, the face, or the background. We aim as future work to improve the efficiency of our pipeline, leverage large-scale datasets and neural networks to enable generalization of our method for in-the-wild image inputs. + +# Acknowledgement + +We thank Tiancheng Sun, Stefanos Zafeiriou, and Erroll Wood for their helpful discussions; Jay Busch, Cynthia Herrera, Christoph Rhemann, Di Qiu, and Xu Chen for their assistance with data capture and processing; and all of our capture models. 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In particular, we address five critical real-world challenges in text-instruction-based grounding: hallucinated references, multi-object scenarios, reasoning, multi-granularity, and part-level references. By leveraging knowledge distillation from a pre-trained teacher model, our approach generates high-quality instruction-response pairs linked to existing pixel-level annotations, minimizing the need for costly human annotation. The resulting dataset, Ground-V, captures rich object localization knowledge and nuanced pixel-level referring expressions. Experiment results show that models trained on Ground-V exhibit substantial improvements across diverse grounding tasks. Specifically, incorporating Ground-V during training directly achieve an average accuracy boost of $4.4\%$ for LISA and a $7.9\%$ for PSALM across six benchmarks on the gIoU metric. It also sets new state-of-the-art results on standard benchmarks such as RefCOCO/+/g. Notably, on gRefCOCO, we achieve an N-Acc of $83.3\%$ , exceeding the previous state-of-the-art by more than $20\%$ . + +# 1. Introduction + +Picture this: you are at a fruit bar and someone asks you to "add more fruits with high antioxidants." Without hesitation, your mind automatically translates this abstract request into action - your eyes scanning for and pinpointing apples, pomegranates, or blueberries. This seemingly simple process demonstrates an important human cognitive ability: connecting prior knowledge with visual recognition, navigating multiple levels of abstraction, and precisely localizing objects based on imprecise instructions. While humans perform such tasks naturally, current state-of-the-art com + +![](images/b6176c9022f5a7805581aa33005fc2bb0541f4e7dfc0892d7c38c9c58742c89b.jpg) +Figure 1. Performance comparison of LISA and PSALM models w/ and w/o our Ground-V dataset during training. Incorporating Ground-V consistently enhances both models' performance across benchmarks, achieving an average improvement of $4.4\%$ for LISA and $7.9\%$ for PSALM on the gIoU metric across six benchmarks. + +puter vision specialist [23, 38, 47, 58], despite their excellent performance on standard object detection or segmentation benchmarks, struggle to interpret abstract natural language instructions for precise visual grounding, particularly when handling complex instructions and visual scenarios. + +Advances in large vision-language models (VLMs) [1, 7, 20, 21, 56] have shown promise toward bridging this gap. These models exhibit strong capabilities in general multimodal tasks such as recognition, perception, and multimodal reasoning. To further enhance VLMs' ability to not only recognize and understand images but also localize specific regions of interest in pixel level, i.e. segmentation, researchers have proposed architectural designs to incorporate the strengths of computer vision specialists. By learning special grounding tokens in VLMs [13, 39, 44, 53] and using them as inputs for computer vision specialists like SAM [12], these models are beginning to unlock emerging capabilities such as reasoning-driven segmentation [13]. + +However, we find that current VLMs for segmentation are often unreliable under complex instructions or challenging visual scenarios1. For example, in an image with multiple red, green, and yellow apples, when asked to segment only the red apples, these VLMs often produce inaccurate results by including apples of other colors. This problem becomes more pronounced with complex instructions, such as "segment the partially eaten red apple next to the ceramic bowl", where VLMs typically ignore contextual details, segmenting random "red apples" without considering whether they are partially eaten or near the specified bowl. We conjecture that one root cause of these limitations in the current VLM training data used for grounding tasks: while humans naturally describe visual scenes using rich, nuanced language, most grounding datasets contain only simple, direct references. This disconnect between human-like descriptive complexity and oversimplified training data limits these VLMs' ability to translate the understanding of complex instructions into precise localization in the real world. + +Inspired by the success of data scaling in language instruction-following [6, 42], we ask a natural question: can scaling of pixel-grounded instruction following data bridge this gap? To explore this, we scale such data by incorporating richer scenarios and increasing the number of samples. We develop an automated data generation workflow with minimal human annotation (only for the test data) to tackle five critical challenges in real-world referring segmentation: (1) multi-object interactions, (2) multigranular instructions, (3) hallucinated references, (4) reasoning, and (5) part references. Using this workflow, we introduce Ground-V (where "V" denotes the Roman numeral for five), a comprehensive dataset of 500K instruction-segmentation pairs. We find that training with Ground-V effectively connects the multimodal understanding capabilities of VLMs with the grounding expertise of segmentation specialists, eliciting pixel-level grounding under complex text instructions. Importantly, our dataset can be seamlessly integrated into the training of existing models, yielding immediate performance improvements, as shown in Figure 1. Experiment results demonstrate that models trained with Ground-V not only achieve state-of-the-art performance on standard benchmarks (e.g., RefCOCO-series [29, 50] and gRefCOCO [19]) but also show substantial improvements of up to $20\%$ on our more challenging test set. In summary, we make the following contributions: + +- We develop an automated data generation workflow with minimal human input to address five critical challenges in real-world referring segmentation. To our knowledge, we are the first work to systematically consider these challenging scenarios and enable scalable generation of pixel-grounded instruction-following data. + +- Using the proposed data generation workflow, we introduce Ground-V, a comprehensive dataset of 500K instruction-segmentation pairs for visual grounding. The large-scale training set is crafted to enhance model performance in complex scenarios. We also provide a detailed evaluation protocol with human-annotated test data to accurately assess model performance. +- We conduct thorough evaluations on both public datasets and the human-annotated test set of Ground-V, achieving new state-of-the-art results. Specifically, we achieve $70.6\%$ gIoU and $83.7\%$ N-Acc on gRefCOCO on average, surpassing previous state-of-the-art by $5.7\%$ in gIoU and $20.9\%$ in N-Acc. On the more challenging Ground-V test set, we achieve an average boost of $15.4\%$ in gIoU over the state-of-the-art PSALM model [53]. + +# 2. Related Work + +Specialist Models for Referring Segmentation Recent advances in object segmentation have led to several powerful state-of-the-art models, such as Mask2Former [4], SegNext [9], and SAM [12, 37], which exhibit strong generalization across different scenes and object classes. Despite their benchmark-leading performance, these models lack a nuanced understanding of and interaction with natural language. This limitation is apparent in referring segmentation tasks [29, 50], where the objective is to segment target objects based on descriptive language instructions. There have been strong interest in developing specialists for referring segmentation [8, 43, 48, 49, 51, 55]. Recent advances include PolyFormer [22], which frames the task as sequential polygon generation through a sequence-to-sequence framework; UNINEXT [47], which incorporates text inputs to unify instance-perception tasks; and SEEM [58], which encodes user intents into prompts within a joint visual-semantic space. Nevertheless, most of these methods focus on architectural unification and multi-task compatibility – leaving the critical challenge of handling complex language instructions in real-world scenarios unaddressed. + +Generalist Vision-Language Models Large VLMs extend the capabilities of LLMs by incorporating visual components – typically through vision encoders and/or decoders connected via specialized stitching mechanisms [1, 14, 20, 21, 30, 52, 57]. These models have made rapid advancements alongside LLMs and have garnered significant attention for their impressive multi-modal capabilities in tasks such as recognition, captioning, reasoning, and visual question answering. However, most generalist VLMs are limited to text-based outputs, typically lacking built-in capabilities for vision-centric tasks like segmentation and detection. Recent studies [33, 35, 40] have also identified various visual shortcomings in these generalist VLMs, such as weak spatial reasoning and localization awareness, highlighting the need for enhanced visual processing capabilities. + +Reasoning +![](images/538ce35c79930978337858e5ad4331242e548146b6c00c1502fb2942e9fda3eb.jpg) +Instruction: What can I use for my oral hygiene? + +Multi-Granularity +![](images/4469ccf7dcb26973c410778ff00bd6a36f6f08423d8f236f410247e8e360e04b.jpg) +Original Labels: bottle, phone, table Fine-grained Labels: Corona Extra beer, Samsung, wooden dining table Abstract Labels: drink, electronics, furniture + +Figure 2. Illustration of the diverse scenarios covered in our Ground-V dataset. These include reasoning-based segmentation (top left), multi-granular instructions (center), multi-object and hallucination handling (top right), and part-whole relationships (bottom left). Each example demonstrates how our dataset provides rich, nuanced instructions and corresponding segmentations. +![](images/1643b299841ef20e7cf2804b2069cda4cb3d1ed0cf343627a63db310d5d78f9d.jpg) +Answer: You can use the tooth brush $<\mathrm{seg}1>$ that is placed on the sink $<\mathrm{seg}2>$ . + +Instruction: How can I set the appropriate time for heating my food? + +Answer: You can set the time by pressing the button $<\mathrm{seg}1>$ on the microwave. + +# Part Reference + +Multi-Object & Hallucination +![](images/8467aa21924bf827ea11a4ce8cf6352eb21fe082b19893f29ec9a3f4cf7eb1e2.jpg) +Instruction (Multi-object): Can you locate all the cars? +Answer: Sure, they are [seg 1], [seg 2], ... [seg n] + +Instruction (Hallucination): Can you segment truck traffic sign writing right lane, and the car moving to the right? + +Answer: The requested objects cannot be segmented because they are not present in the image. Specifically, there is no truck (only multiple cars), and the traffic sign writes "left lane", not "right lane". Also, these cars are parking there and no car is shown moving to the right. + +VLMs for Segmentation Several recent works have tried to equip VLMs with the ability to generate segmentation masks. LISA [13] is a pioneering approach that introduces a learnable segmentation token within VLMs, using it as a prompt embedding for the SAM decoder to predict segmentation masks. Building on LISA, u-LLaVA [46] extends support to object grounding tasks. However, LISA is limited to single-object scenarios, prompting later works like GLaMM [36], PerceptionGPT [31], PixelLM [53], GSVA [44], and PSALM [53] to address multi-object scenarios through various learnable condition tokens. Despite strong performance on standard benchmarks, we observe that these models become highly unreliable when handling more complex instructions. We hypothesize that this limitation arises from the models' potential being constrained by the limited richness of their training data, despite being designed specifically for referring segmentation. + +# 3. Ground-V + +This section outlines five key dimensions essential for effective reasoning-based segmentation in real-world scenarios: multi-granular instructions, multi-object handling, hallucinated references, part references, and reasoning-driven segmentation. We propose a scalable approach to curate the training and test sets in Ground-V, incorporating these five dimensions, as shown in Figure 3 and Table 1. + +# 3.1. Five Real-World Challenges + +Multi-granularity Objects in the real world can be described at various levels of conceptual specificity. For instance, a corgi could be referred to as a specific breed ("corgi"), a general category ("dog"), a functional role ("pet"), or a broad biological classification ("animal"). Humans tend to use higher-level, abstract references when uncertain about specific details. To capture this variability in referring specificity, we implement a hierarchical label structure incorporating both abstract and fine-grained annotations. An abstract label can cover multiple objects, while fine-grained distinctions can be made within the same class. + +Multi-object In addition to handling single-object referring expressions at multiple levels of granularity, we also address the simultaneous segmentation of multiple objects by introducing instructions that reference more than five objects. This task aligns with the generalized referring expression setting [19] but presents a greater challenge that requires the VLM to handle quantity effectively. + +Part Reference We aim to enable VLMs to ground finer object parts for compositional localization. For instance, in the Figure 2 microwave example, if a robot needs to use the microwave, it must not only locate the microwave but also identify and segment its button. To support this, we incorporate part annotations from the PACO dataset [34] and rephrase the labels into natural language instructions. + +![](images/5bf76544ad394d02f6a468cb793f4a4d954d03fe1e74c4c8043e362762d87ba1.jpg) +(a) G5 Data Generation Workflow +Figure 3. (a) Overview of the G5 data generation pipeline. We identify key real-world challenges, including hallucination, multi-object scenarios, reasoning, multi-granularity, and part-level reference. For each dimension, we design few-shot prompts to generate instruction-response pairs. Using these prompts alongside corresponding images, we guide Claude to produce instruction-response pairs. Finally, human annotators validate the evaluation set to ensure accuracy and reliability. (b) Here we give an example few-shot prompt for generating hallucination-mitigation data, covering three levels: object-level, attribute-level, and relation-level. (c) We display a sample of the generated instructions and responses, paired with segmentation masks from the original data source, which supports training and evaluation. For hallucination-mitigation data, however, no segmentation mask is included because the instruction is designed to mislead the model deliberately; a correctly functioning model should not produce a segmentation mask in this scenario. + +Data Generation Prompt: You will be provided with an image and a set of object classes. Your task is to generate elements that are not present in the image at three levels and provide explanations of the reason: + +- Object-Level: Identify and generate an object class not present in image. +- Attribute-Level: Generate an existing object with a new attribute combination absent in the image. +- Relation-Level: Create a new relationship between existing objects that is not depicted in the image. + +![](images/ff5249dfa45bfc2d59187ec7dc1872ba45b41bf711fafe530c6ae5ce2f2c0da5.jpg) +Example 1 out of n: + +- Object: orange +- Attribute: Purple flower +- Relation: Vase on the floor + +Answer: There is no orange, purple flower, and the vase is not on the floor. The image shows a bouquet of roses in a glass vase placed on a surface along with some books and figurines. + +(b) Example Few-shot prompt (for Hallucination) +(c) Resulting Instruction-Response Pairs +![](images/e56c2d42932ee53fa485fd12c78adec317d8b3631adb6685ccae0de79a4c3fd9.jpg) +Instruction: Can you segment motorcycles woman in green shirt, and the man walking on brick path? + +Answer: There are no motorcycles, woman in green shirt, nor man walking on brick path in the image. The image depicts an outdoor scene with people, bicycles lying on the ground, and residential buildings in the background. There is a woman wearing white sweater and a man playing frisbee. + +
DatasetsReasoningMulti-ObjectHallucinationPart ReferenceMulti-Granularity# of Instruction pairs
ReasonSeg✓✗✗✗✗1.2K
MUSE✓✓✗✗✗214K
Ground-V (acronym “G5”)✓✓✓✓✓481K
+ +Table 1. Comparison between our proposed Ground-V and existing datasets designed for VLM segmentation, including ReasonSeg [13] and MUSE [39]. Our dataset surpasses previous ones in both comprehensiveness and scale. + +
SubsetTrain SetTest Set (Human Annotated)
# Images# InstructionsAvg. Objects / Instr.# Images# InstructionsAvg. Objects / Instr.
Multi-Object28,90236,85010.011,2511,5859.96
Hallucination21,01963,0577.215,00015,0007.36
Reasoning41,62441,6246.454,8174,8176.72
Part Reference41,807105,9081.942,03610,3911.89
Multi-Granularity (Coarse)35,26880,4983.155,00011,5363.19
Multi-Granularity (Fine)30,04195,8781.914,28214,2621.88
Total50,000423,8154.095,00057,5914.20
+ +Table 2. Statistics of the Ground-V train and test sets. + +Reasoning A key advantage of using VLMs for grounding tasks is their ability to leverage reasoning to interpret and act on abstract instructions that are nuanced and require contextual understanding (e.g., "steak" vs. "food with more protein"). In such cases, the model should be able to comprehend the underlying context and produce appropriate segmentation masks. Building on the reasoning segmentation setup in [13], we extend this framework by allowing the model to handle instructions that involve either multi- + +ple objects or a single object, in contrast to ReasonSeg [13], which is limited to single-object responses. + +Hallucinated Reference To prevent potential hallucinations in real-world segmentation tasks, such as segmenting objects that are not present in the image despite being instructed to do so, we introduce three types of no-target scenarios to evaluate the model's robustness against hallucinated references: object, attribute, and relation. Here, object hallucinations refers to items that are absent from + +the image, attribute hallucinations pertains to properties not associated with the objects, and relation hallucinations involves nonexistent relationships between objects, such as incorrect spatial positioning. We assign empty segmentation masks to these inputs and provide text descriptions that explain why they should be excluded from segmentation. + +# 3.2. Ground-V Data Generation Workflow + +We develop an automatic and scalable approach to generate instruction-segmentation pairs (we also provide bounding boxes), along with potential text answers for each sample. The overall pipeline is illustrated in Figure 3. + +Detailed Data Generation Process For each of the five aforementioned dimensions, we manually craft a 3-shot demonstration, with each shot consisting of an image, an instruction, and a corresponding answer. These examples serve as in-context demonstrations [2] for querying a teacher VLM, Claude 3 Sonnet3, which then generates new instruction-response pairs based on the query images. This process is applied to generate both the training and evaluation sets. For the evaluation set, we conduct a second round of re-validation using Claude 3.5 Sonnet as a judge model, regenerating instruction-answer pairs when the original outputs are deemed incorrect. Finally, human annotators manually inspect the whole evaluation set to ensure correctness. We use COCO 2017 [18] train and validation split as our image source as well as segmentation masks and bounding boxes as annotations for training and evaluation sets. During the data generation, Claude is prompted to link the instructions and text answers with corresponding object annotations (e.g., segmentation masks). In total, we have curated 50,000 images for training set and 5,000 images for evaluation set. The detailed statistics are shown in Table 2. We provide some exemplar data in Figure 2. More details such as words frequency, category distribution, and detailed prompts can be found in the supplementary materials. + +Human Annotations To ensure accurate model evaluation, we conduct rigorous human annotation on the test data. Each instruction pair includes an image, a question and one or multiple segmentation masks, each labeled with an object name. During annotation, annotators view the image, question, and all segmentation masks with object names simultaneously to ensure they have full contextual information. Annotators then examine each object within each segmentation mask, one by one, following the order of the mask index, to verify if it accurately and relevantly answers the question by selecting YES, NO or UNSURE. For hallucination mitigation, annotators assess three types of hallucinations for each image: 1) if the mentioned object itself is absent from the image, 2) if the relationship between objects is not present in the image, and 3) if the object's attribute incorrectly assigned or not present in the image. Each image + +instruction pair is reviewed independently by two different human annotators, and only those verified as correct (YES) by both are included in the test set, resulting in the removal of $23.1\%$ of the original test data due to erroneous or unsure labels. We provide further details in the supplementary materials about the human annotation process. + +# 4. Experiments and Results + +# 4.1. Experiment Setup + +Implementation Details To assess Ground-V's effectiveness, we train two representative models: LISA [13] and PSALM [53]. These models feature distinct architectures and backbones, highlighting the generality of our dataset. For a fair comparison, we keep all training hyperparameters and evaluation settings consistent with their original configurations, changing only the data by incorporating our own. + +- LISA LISA [13] builds on LLaVA [20], and incorporates a CLIP image encoder [32] and Vicuna-7B [5] as the LLM with a new segmentation token added to its vocabulary. During the forward pass, the last-layer embedding of the segmentation token is decoded into a segmentation mask using the fine-tuned SAM pixel decoder [12]. +- PSALM PSALM [53] uses Phi-1.5 (1.5B) [15] as the LLM, a Swin Transformer [25] as the vision encoder, and Mask2Former [4] as the pixel decoder, with 100 mask tokens. For referring expression tasks, the mask with the highest confidence score is selected as the prediction. For other tasks, all masks with confidence scores above 0.6 are chosen as the final predictions. + +Evaluation Benchmarks and Metrics We evaluate on both public datasets and our more challenging Ground-V test set. Details for each benchmark are listed below: + +- (Generalized) referring expression segmentation We use the commonly adopted RefCOCO+/g [29, 50] to evaluate referring expression segmentation (RES) with cumulative IoU (cIoU). The UNC split is used for RefCOCO and RefCOCO+, while the UMD split is used for RefCOCOg. For generalized referring expression segmentation (GRES), we evaluate on gRefCOCO [19], which includes multi-target and no-target scenarios. The primary metrics are generalized IoU (gIoU), cIoU, and N-Accuracy (N-Acc) measuring the model's ability to identify no-target samples. For no-target samples, a prediction with no foreground pixels is considered a true positive (TP), while any prediction with foreground pixels is a false negative (FN). N-acc, defined as $\mathrm{N - acc} = \frac{\mathrm{TP}}{\mathrm{TP} + \mathrm{FN}}$ , is often referred to as the True Positive Rate (TPR) in other domains, and it measures the model's ability to correctly identify no-target samples. For our benchmark, gIoU is the primary metric for segmentation accuracy, while N-Acc is used for the hallucination subset. Higher values for these metrics indicate better performance. + +
MethodRefCOCORefCOCO+RefCOCOgAverage
valtestAtestBvaltestAtestBvaltest
SpecialistSEEM-L------65.6--
PolyFormer-L76.978.574.872.275.766.771.271.273.4
UNINEXT-L80.382.677.870.074.962.673.473.774.4
UNINEXT-H82.283.481.372.576.466.274.776.476.6
VLM-BasedGLaMM79.583.276.972.678.764.674.274.975.6
u-LLava80.482.777.872.276.666.874.875.675.9
PerceptionGPT75.379.172.168.974.061.970.771.971.7
PixelLM73.076.568.266.371.758.369.370.569.2
GSVA77.779.974.268.071.561.573.273.972.5
LISA70.273.467.759.263.953.063.264.764.4
LISA-G573.975.568.463.165.754.764.966.966.6
PSALM83.684.781.672.975.570.173.874.477.1
PSALM-G583.985.082.173.175.869.874.874.277.3
+ +Table 3. Comparison with the state-of-the-art methods on three referring image segmentation benchmarks (RefCOCO, RefCOCO+, and RefCOCOg) using the cIoU metric. Models shaded in light gray are trained with the inclusion of our proposed Ground-V. Our models achieve the best performance on most of the subsets. + +
MethodvaltestAtestBAverage
gIoUcIoUN-AccgIoUcIoUN-AccgIoUcIoUN-AccgIoUcIoUN-Acc
SpecialistMattNet48.247.541.259.358.744.046.145.341.351.250.542.2
LTS52.752.3-62.661.9-50.449.9----
LAVT58.457.649.365.965.349.355.855.048.560.059.349.0
ReLA63.662.456.470.069.359.061.059.958.464.963.957.9
VLM-basedGSVA63.361.762.470.169.665.361.360.360.664.963.962.8
LISA32.238.72.748.552.66.339.744.85.040.145.44.7
LISA-G546.748.436.463.263.739.951.353.944.153.755.340.1
PSALM43.342.027.754.552.420.352.550.625.650.148.324.5
PSALM-G564.667.383.374.571.883.272.772.384.670.670.583.7
GSVA (ft)66.566.466.071.172.864.762.263.262.566.667.564.4
LISA (ft)63.361.756.570.169.263.561.360.358.464.963.759.5
LISA-G5 (ft)68.265.661.374.672.666.966.365.063.269.767.763.8
PSALM (ft)-69.378.3-74.873.4-71.379.6-71.877.1
PSALM-G5 (ft)67.368.087.277.375.289.778.973.190.674.572.189.2
+ +Table 4. Performance comparison on the gRefCOCO datasets using cIoU, gIoU, and N-Acc metrics. Models trained on our dataset (shaded in light gray) achieve the best performance, both with and without fine-tuning (ft) on gRefCOCO. + +
MethodMulti-granularMulti-objectHallucinationReasoningPart Reference
Abstract (gIoU)FG (gIoU)gIoUN-AccgIoUcIoUgIoUcIoU
GSVA45.046.730.49.340.141.221.932.4
GSVA-G547.8 (2.8↑)51.4 (4.7↑)39.6 (9.2↑)37.5 (28.2↑)50.8 (10.7↑)48.9 (7.7↑)24.1 (2.2↑)35.6 (3.2↑)
LISA35.347.133.18.742.249.915.633.9
LISA-G544.5 (9.2↑)55.0 (7.9↑)39.2 (6.1↑)17.9 (9.2↑)45.1 (2.9↑)55.8 (5.9↑)21.4 (5.8↑)35.2 (1.3↑)
PSALM37.940.127.320.553.753.919.334.2
PSALM-G558.7 (20.8↑)54.7 (14.6↑)39.5 (12.2↑)33.9 (13.4↑)72.9 (19.2↑)72.2 (18.3↑)27.4 (8.1↑)41.9 (7.6↑)
+ +Table 5. Performance comparison of models trained with and without proposed Ground-V, evaluated on the disjoint test set of Ground-V. + +- Described object segmentation We evaluate the described object segmentation task using the Description Detection Dataset $(\mathrm{D}^{3})$ [45], reformulating it from de + +tection to segmentation using the ground-truth segmentation masks. This task is more challenging than GRES, as it involves unrestricted language descriptions and ex + +pressions of absence (e.g., "man without a hat"). We use gIoU, cIoU, and N-Acc as the evaluation metrics. + +- Ground-V (ours) We divide the evaluation partition of the Ground-V into five subsets: multi-granular, multi-object, hallucinated reference, reasoning, and part reference. The multi-granular subset, divided into abstract and fine-grained (FG) levels, is designed to evaluate the model's ability to understand and segment concepts at different granularities and is assessed using the gIoU metric. The multi-object subset assesses segmentation of multiple objects, also using gIoU. The hallucinated reference subset measures the model's ability to avoid hallucinated segmentation with the N-Acc metric. The reasoning subset assesses reasoning skills through gIoU and cIoU. Finally, the part reference subset evaluates the model's understanding of specific reference to object parts with both gIoU and cIoU metrics. This structured evaluation approach offers a thorough analysis of model performance across key challenges in visual grounding. + +Baselines We compare both specialist models and VLM-based models on these benchmarks. For specialists, we report the performance of SEEM-L [58], PolyFormer-L [22], and UNINEXT-L/H [47] on RefCOCO+/g. We also compare with representative SoTA VLMs such as LISA [13], GLaMM [36], u-LLaVA [46], PerceptionGPT [31], PixelLM [39], GSVA [44], and PSALM [53]. On the gRefCOCO dataset, we also include comparisons with specialist models trained specifically on this dataset, including MattNet [51], LTS [8], LAVT [48] and ReLA [19]. + +# 4.2. Quantitative Results + +Results on (G)RES benchmarks The results on RefCOCO, RefCOCO+, and RefCOCOg are presented in Table 3. Our model achieves state-of-the-art performance on most subsets, outperforming both specialist and VLM-based models. On gRefCOCO in Table 4, our model outperforms existing methods by a significant margin, both with and without post-hoc fine-tuning (ft), especially in N-Acc that measures the ability to abstain no-target instructions. This demonstrates that training on our dataset generalizes well to other benchmarks, as the diverse instructions, such as multi-granular text inputs, enhance the model's understanding of general referring expressions. Additionally, our hallucination mitigation data helps the model accurately identify when referenced objects are absent. + +Results on $\mathbf{D}^{3}$ dataset Table 6 presents the results on the $\mathrm{D}^{3}$ dataset. After incorporating our proposed GroundV during training, both LISA and PSALM exhibit significant performance improvements across all metrics. Notably, PSALM trained on our dataset achieves $9.0\%$ and $23.5\%$ gains in gIoU and N-Acc, respectively, highlighting enhanced accuracy in understanding complex language descriptions and avoiding false segmentations of non-existent + +
ModelgIoUcIoUN-Acc
LISA31.936.812.8
LISA-G535.3 (3.4↑)41.4 (4.6↑)26.5 (13.7↑)
PSALM49.546.042.5
PSALM-G558.5 (9.0↑)51.0 (5.0↑)66.0 (23.5↑)
+ +Table 6. Performance comparison on $\mathbf{D}^3$ dataset with and without Ground-V during training. Models trained on our data (shaded in light gray) show significant improvement on this unseen dataset. + +
DatasetgIoUcIoU
Ground-V72.972.2
Rephrased Ground-V71.572.3
+ +Table 7. Performance comparison on Ground-V Reasoning subset before and after rephrasing, showing that our model is robust to language priors, with improvements not due to overfitting. + +
ModelPOPEVizwizMMBenchSciQA-Img
LLaVA-v1.5-7B85.950.064.366.8
LLaVA-v1.5-7B-Ours86.253.665.169.9
+ +Table 8. Performance comparison on general VQA tasks with and without Ground-V during LLaVA vision instruction tuning. + +objects. These results demonstrate the efficacy of our constructed reasoning, multi-object, and hallucination data categories, which generalize well to unseen datasets. + +Results on Ground-V The results on the test partition of Ground-V are presented in Table 5. As shown, training on our dataset leads to significant improvements over the original PSALM across all subsets and metrics, with performance gains ranging from $10\%$ to $20\%$ . Specifically, our model shows notable enhancements in each of the five challenging dimensions considered in the curation of Ground-V. These results underscore the value of our curated dataset in enhancing model performance, especially in handling complex visual scenarios and mitigating hallucinations. + +Generalization Beyond Language Priors Since both the training and evaluation data in Ground-V are generated using the same workflow, we assess whether the performance improvements are due to overfitting to a consistent language style. To test this, we employ an off-the-shelf VLM, Qwen2-VL [41], to rephrase the instructions while ensuring that the underlying answers remain unchanged. We focus this experiment on the reasoning subset, where language input has a more significant impact on reasoning-based segmentation. For example, we rephrase the original instruction, "What can we use to make a dinner? Find the objects," to "Give a step-by-step guide for making a dinner. Segment the related objects in the image." This allows us to evaluate if the model's performance is robust to variations in + +![](images/bfda1659b7e23b36fe198253b7be7a58ecec28024d8326660ec34459541a373f.jpg) +Figure 4. Our model demonstrates improved understanding of object attributes, enhanced reasoning capabilities, more precise segmentation of smaller object parts, and the ability to reject instructions when the target object is not present in the image. + +language style. As shown in Table 7, the performance remains consistent after rephrasing, indicating that the model trained on our dataset is robust to variations in language priors. This suggests that the improvements are not merely due to overfitting to specific language styles but reflect the model's ability to generalize to those challenging scenarios. Will generalist VLMs benefit from Ground-V? We explore whether generalist VLMs like LLaVA [20] can benefit from Ground-V by integrating its hallucination subset during the visual instruction tuning stage. This subset is text only, making it flexible for integration with existing visual instruction datasets, while the other subsets include text and segmentation mask pairs4. We evaluate on public VQA benchmarks such as POPE [16], Vizwiz [10], MM-Bench [24] and SciQA [27] with results compiled in Table 8. Remarkably, we observe consistent performance improvements across all benchmarks, demonstrating that even generalist VLMs can benefit from Ground-V. + +# 4.3. Qualitative Results + +Figure 4 shows qualitative comparisons between PSALM (top row) and our model (bottom row) under the same instructions. Compared to the baseline PSALM, our model effectively navigates multi-granularity, multi-object contexts, and part-based references, accurately avoiding incorrect segmentation of irrelevant objects under ambiguous instructions. For example, in the first and second columns, our model accurately interprets instructions at different specificity levels: it correctly segments the left-facing dog in the first column (fine-grained instance-level reference) and includes both the cat and dog in the second column under the broader instruction for "pets" (abstract category). The third to fourth columns demonstrate our model's + +reasoning abilities, such as in the fourth column, where it accurately identifies and segments part of a laptop as a MacBook based on the Apple logo. In the fifth to seventh columns, our model effectively mitigates hallucination by rejecting an misleading instruction, noting the absence of mentioned objects (e.g., "person playing badminton") in the image, while PSALM mistakenly segments conceptually similar objects (e.g., "person playing tennis"). + +# 5. Discussion + +In this paper, we explore a data-centric approach to enhance VLMs' ability to ground complex instructions with nuanced object references by developing an instruction-following data generation workflow and introducing a new dataset called Ground-V. By systematically addressing five critical challenges in open-world visual grounding - multi-object interactions, multi-granularity, hallucination prevention, part-level reference, and reasoning - Ground-V significantly improves the segmentation accuracy of VLMs across challenging scenarios. Experiment results demonstrated that models trained on Ground-V achieve significant performance gains, with the best-performing models surpassing previous state-of-the-art results on standard benchmarks such as RefCOCO/g/+, gRefCOCO, and $D^3$ . These findings highlight Ground-V's potential to bridge the gap between linguistics and pixel-level visual perception, advancing visual grounding in complex real-world applications. We hope our work encourages more scalable approaches to augment existing abundant computer vision data to unlock new capabilities in multimodal grounding. + +Limitations and Future Work While models trained on our dataset show strong performance, we acknowledge the presence of noise in the training data due to its automatic generation by off-the-shelf models. Future work could explore ways to mitigate data noise in an automated manner. + +# References + +[1] Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. 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For example, for an intelligent robot, it is necessary to accurately ground the affordance of an object and grasp it according to human instructions. In this paper, we introduce a novel task that grounds 3D object affordance based on language instructions, visual observations and interactions, which is inspired by cognitive science. We collect an Affordance Grounding dataset with Points, Images and Language instructions (AGPIL) to support the proposed task. In the 3D physical world, due to observation orientation, object rotation, or spatial occlusion, we can only get a partial observation of the object. So this dataset includes affordance estimations of objects from full-view, partial-view, and rotation-view perspectives. To accomplish this task, we propose LMAffordance3D, the first multi-modal, language-guided 3D affordance grounding network, which applies a vision-language model to fuse 2D and 3D spatial features with semantic features. Comprehensive experiments on AGPIL demonstrate the effectiveness and superiority of our method on this task, even in unseen experimental settings. Our project is available at https://sites.google.com/view/lmaffordance3d. + +# 1. Introduction + +Affordance is the property of an object that suggest how it can be used [10]. Grounding 3D object affordance aims to classify, detect, or segment the object's affordances in a scene with the input of images, videos, and point clouds, which plays an important role in robotics, human-object interactions (HOI), scene understanding, functionality understanding, and other fields [3, 14]. + +Although there are numerous studies [6, 8, 27, 30] focusing on grounding object affordances from 2D images + +![](images/9d5f92dd8a7de6bc632eaf390c77a19d2f251ad1582fd1f1ea9c1da80d212167.jpg) +Figure 1. Illustration for the affordance grounding task. Inspired by cognitive science, when humans encounter a new object, they learn its affordance through language instructions, vision information from eyes, and human-machine interactions, thus obtaining its affordance. + +or videos, the knowledge of affordances derived from 2D data remains challenging to apply in 3D space. Some works [5,44] have been dedicated to using 3D data to ground object affordances. They learn from geometry to segment out affordance regions from point clouds. However, they exhibit limited generalization for grounding unseen object affordances and tend to show confusion when encountering similar objects. [47]. Actually, humans learn the affordances of a new object from demonstrations in images or videos, as well as from verbal instructions. It is a complex and comprehensive task that involves understanding of language instructions, geometric relationships, and scene information. Cognitive science research [12] also indicates that visual information and auditory language cues humans perceive can enhance their ability to use or manipulate new objects. Inspired by this, we introduce a novel task that grounds 3D object affordance based on language instructions, visual observations, and interactions. + +In this paper, we present AGPIL, which is the first multimodal and multi-view dataset for grounding 3D object affordance. For the full-view dataset, each frame of data includes a language instruction, an image of human-object interactions, and point clouds of the object's entire external surface. In the 3D physical world, due to observation ori + +
DatasetYearInputOutputViewNumber
ImagePoint cloudLanguage
PAD [26]2021✓XX2D Segmentation-4002
CAD-120++ [11]2022✓XX2D Box-32327
AGD20K [27]2022✓XX2D Heatmap-20061
3D AffordanceNet [5]2021X✓X3D HeatmapF, P, R56307
GAPartNet [9]2023X✓X3D Segmentation & PoseP, R8489
PIAD [47]2023✓✓X3D HeatmapF7012
LASO [19]2024X✓✓3D HeatmapF19751
AGPIL (Ours)2024✓✓✓3D HeatmapF, P, R30972
+ +Table 1. Comparison of affordance grounding dataset. Here we mainly compare the input, output, view, and dataset scale for different datasets. F, P, and R respectively refer to full-view, partial-view, and rotation-view. + +entation, object rotation, or spatial occlusion, we can only acquire partial scans of the object. So we also build the partial-view and rotation-view datasets. The partial-view dataset includes only one side or part of the object's point clouds, while the rotation-view dataset contains part of the object's point clouds with random rotation along the x, y, and z axes. In addition, each view of datasets has two settings: seen and unseen, which can comprehensively test the model's generalization performance. + +To address the task of grounding 3D object affordance, we propose LMAffordance3D, which is an end-to-end multi-modal, language-guided 3D affordance grounding framework based on the vision-language model (VLM). And This framework operates as a one-stage method. The key idea is to integrate 2D and 3D spatial features and project them into a text space via multilayer perceptron (MLP). We then concatenate all the features as input for the vision-language model. Using a decoder, we fuse the output from the vision-language model with the 2D and 3D spatial features, subsequently employing a segmentation head to delineate affordance regions. + +In summary, our contributions are mainly two-fold: + +- We introduce a novel task that grounds 3D object affordance based on language instructions, visual observations, and interactions. And we present AGPIL which is composed of 30972 point-image-text pairs, covering 17 affordance categories and 23 object classes. It has full-view, partial-view, and rotation-view in seen and unseen settings. To the best of our knowledge, this is the first multi-modal and multi-view 3D affordance dataset with well-defined probabilistic affordance score annotations. +- We establish a comprehensive benchmark based on AGPIL for three different views in two settings. And we propose LMAffordance3D as a baseline, which is a novel end-to-end multi-modal, language-guided 3D affordance grounding framework based on VLM. The results show the effectiveness and better generalization capabilities of our fusion framework. + +# 2. Related Works + +# 2.1. Vision-Language Models + +Due to the remarkable performance of large language models (LLMs) such as LlaMA [7, 40, 41], Qwen [1] and GPT [36] in natural language processing tasks, many scholars have extended them to the visual domain, giving rise to a series of large vision-language models (VLMs), such as LLaVA [20-22], Qwen-VL [2], GPT-4o [15], and so on. Leveraging the prior knowledge learned by these large models, they have been applied in 3D visual grounding task. LLM-Grounder [46] utilizes an LLM to decompose complex natural language queries into semantic parts and employs a visual grounding tool to identify objects in a 3D scene. VLM-Grounder [45] utilizes a VLM based on image sequences and language to achieve zero-shot 3D visual grounding. Unlike previous work on object-level grounding tasks, we define our task as utilizing multi-modal data from point clouds and images to ground 3D object affordances based on human language instructions, which is a part-level 3D grounding task. + +# 2.2. Affordance Grounding + +Affordance grounding is to identify the locations where interactions are possible, which is important for human-object interaction. AffordanceLLM [34] uses LLaVA [21] for 2D visual affordance grounding based and it demonstrates the importance of 3D information in affordance grounding. However, it obtains a 2D heatmap of affordance based on the image and depth map, which is not convenient to map it to 3D space for human or robot operation. Several studies have focused on 3D affordance. For instance, 3D AffordanceNet [5] predicts a 3D heatmap based on point clouds. And some methods leverage multi-modal data to predict 3D affordance, such as IAG [47], OpenAD [32], and LASO [19]. However, IAG relies on the 2D detection bounding boxes of interactive objects, which limits the task's scalability. OpenAD uses simple labels for text input, lacking support for context-rich language instructions. Moreover, LASO overlooks challenges posed by incom + +![](images/e36fbea9a76f25aeeae68fd1aa5887dd1b61ec40bbeb529a1242543c43ee3a55.jpg) +(a) Example of image data. + +![](images/cd2e3b0bcf106990987c26d13d01e58c80907a34a61b4b7e9eeca93e59cfca78.jpg) + +![](images/fe6d2c8805a8ebc4253045b0af7d91fec17777e1e9cb7b0a0ab2db8074fdc097.jpg) +(b) Example of point cloud and affordance data. + +![](images/d992a978a6a7e4dc60ce6e4698be18cee787a44196739c8337d02e5808d9ced6.jpg) +(c) Distribution of instruction data. + +![](images/fe1778889841726db2fd68e2a275c9896127e82c10f7b8b154af0ad96f9db30f.jpg) +(d) Distribution of image data. + +![](images/6abaa608b4e0b250863795c4c84103b7a606cda2e1103bd9bf8860b5fd2f86ea.jpg) +(e) Distribution of point cloud data. + +![](images/106996b68a3f16a2aed05f5f9bdcdd3f5d50e405111340eacc8b24d92844c6e5.jpg) +(f) Distribution of affordance data. + +plete point clouds and object rotations in the real world. + +In order to improve the generalization of grounding 3D affordance of unseen objects, various approaches can be adopted, such as contrastive learning [43], zero-shot learning [16], reinforcement learning [31], supervised learning based on vision-language models [34] and so on. For zero-shot learning, there are issues such as incorrect HOI prompt generation and low granularity. And contrastive learning is sensitive to data augmentation strategies and is limited by similarity metric of comparing different things. Reinforcement learning typically requires a large amount of interaction data, which is time-consuming for training. In this paper, we use a vision-language model to ground 3D object affordance in full-view, partial-view and rotation-view, which can be easily extended to other new scenarios in the real world. + +# 3. Dataset + +# 3.1. Collection and Generation + +We collect the 3D affordance grounding dataset (AGPIL), which contains point clouds, images and language instructions. The point clouds are mainly collected from 3D AffordanceNet [5]. According to the differences in the point + +![](images/e14c121cb458ef9885233d718af9cbcbfa4e0028c8b1b2d2bc84caec1a45cddf.jpg) +Figure 2. Examples and statistics of the AGPIL dataset. Figures (a) and (b) are examples of images, point clouds, and a certain affordance that we randomly selected from the dataset. Figure (c) shows a word cloud generated according to the frequency of each word appearing in the language instructions. Figures (d) and (e) respectively show the distribution of affordances corresponding to different objects in image and point cloud data. The horizontal axis represents the types of objects, and the vertical axis represents the quantity. Different colors indicate different affordances. Figure (f) illustrates the distribution of image and point cloud data corresponding to each affordance. It indicates that images and point clouds are not a one-to-one match, as a single image may correspond to multiple objects. +Figure 3. Language instructions generation. In this example, the affordance is "cut" and the object category is "knife". + +clouds, the dataset has three parts: full-view, partial-view, and rotation-view. The term "full-view" indicates that the data include the point clouds of all the surfaces of an object. Both "partial-view" and "rotation-view" signify that the data include only part of the point clouds of an object's surfaces, with the distinction being whether or not there is rotation. And the rotation of the object along the x, y, and z axes is random. The images are mainly collected from AGD20K [28] and PIAD [47]. The image should depict the interaction between objects and humans, corresponding to the affordance of the object in the point clouds. Unlike PIAD, our dataset does not contain 2D bounding boxes of the interactive subject and object for each image. To improve efficiency, we use GPT-4o [15] combined with an im + +![](images/c7f80c20b584682f657e5b68ffa2e5b01aad9cdacd624c1dd42151af45c3ed07.jpg) +Figure 4. Method. The structure of the proposed LMAffordance3D model, which consists of four major components: 1) a vision encoder that processes multi-modal data, including images and point clouds, to encode and fuse the 2D and 3D features; 2) a vision-language model and its associated component (tokenizer and adapter) that takes in the instruction token, 2D and 3D vision token for fusion; 3) a decoder that uses 2D and 3D spatial features as query, instructional features as key and semantic feature as value to predict the affordance feature; 4) a head for segmenting and grounding 3D object affordance. + +age and a carefully designed prompt to generate each language instruction. The prompt is "Please describe the interactive relationships in the image in one phrase, reflecting the actions and the object being acted upon". To ensure accuracy, we carefully score the generated texts based on consistency, word choice accuracy, semantic completeness and conciseness, and sentence structure diversity. For texts with lower scores, we regenerate or manually refine them. The diagram which illustrates the generation of language instructions is shown in the Fig. 3. + +# 3.2. Annotation + +For the affordance of objects, we use the segmented annotations from 3D AffordanceNet [5], which enables part-level prediction. And we render a 3D heatmap based on confidence scores with different colors. Each annotation is a (2048, 17) matrix, where 2048 represents the number of points in the point cloud, and 17 represents the number of affordance types. Each element in the matrix indicates the probability of a point providing a specific affordance, with a range from 0 to 1. If all elements in a column are 0.0, it indicates that the object does not have the corresponding affordance. In our task, we only use the 3D heatmap of a single type of affordance corresponding to the image and language instruction in the point cloud annotation for training. The prediction is a (2048, 1) matrix during inference. In this way, we can predict different affordances in the point clouds with different images and language instructions. + +# 3.3. Statistic Analysis + +As Tab. 1 shows, we compare the open affordance dataset with AGPIL. Our total dataset consists of 41,628 point clouds, 30,972 images, and 30,972 language instructions, encompassing 23 object categories and 17 types of affordances. Each object has an average of 2.4 functional parts. In particular, objects in the images and point clouds + +are not captured from the same scene and they are paired based on object categories. Our dataset has two settings: Seen and Unseen. In the seen dataset, the categories of objects and affordances in the training and test sets are consistent, while in the unseen dataset, they are inconsistent. More examples and statistics about the dataset are illustrated in Fig. 2. + +# 4. Method + +# 4.1. Overview + +In this section, we propose LMAffordance3D, a framework that learns from language instructions, visual observations and interactions for grounding 3D object affordance. As illustrated in Fig. 4, LMAffordance3D is composed of four major components: 1) a vision encoder that processes multi-modal data, including images and point clouds, to encode and fuse the 2D and 3D features, where an RGB image contains information about the colors, scenes, and interactions between objects, while point clouds contain different information about the shape, size, and geometry of objects. 2) a vision-language model and its associated components (tokenizer and adapter) that take in the instruction token, 2D and 3D vision token for fusion; 3) a decoder that uses 2D and 3D spatial features as query, instructional features as key and semantic feature as value to predict the affordance feature; 4) a head for segmenting and grounding 3D object affordance. We will introduce the components of LMAffordance3D in Sec. 4.2. And we present the loss function in Sec. 4.3. + +# 4.2. LMAffordance3D + +Vision encoder. In the vision-language community [17, 18, 20-22, 48], the most common method for vision-language alignment is to use a pre-trained CLIP [35] model and project image features into the semantic space. How + +
SettingMetricsFull-viewPartial-viewRotation-view
3D A.N.IAGO.ADP.R.Ours3D A.N.IAGO.ADP.R.Ours3D A.N.IAGO.ADP.R.Ours
SeenAUC ↑0.80670.84850.85840.87660.88950.76090.80850.81450.82120.84780.59540.67910.73250.75640.7823
IOU ↑0.13410.20510.19930.20020.21230.10770.14540.15620.16130.17550.04520.08040.09110.10120.1161
SIM ↑0.48330.54500.58660.59530.61020.47850.53620.56520.57960.59280.38920.43590.47830.49840.5191
MAE ↓0.11410.09800.09440.09050.08160.12620.10420.10060.09870.09210.16480.13450.12360.13020.1182
UnseenAUC ↑0.66520.71840.73750.75450.77410.64190.67180.70140.72110.76020.58210.59940.59890.60880.6303
IOU ↑0.05220.07950.07810.08130.09030.04250.06120.06710.06820.07240.02770.03110.03560.03790.0415
SIM ↑0.30120.35200.37040.38490.40890.33470.35680.37660.38940.41440.35520.36230.36220.36310.3842
MAE ↓0.15560.12700.11930.11780.09450.16010.15180.14280.12620.11830.17440.17090.15060.15030.1398
+ +Table 2. Benchmark. We present the overall results of all comparative methods on different views and settings. "3D A.N." refers to "3D AffordanceNet", "O.AD" refers to "OpenAD", and "P.R." refers to "PointRefer" + +ever, we need to process images $I_{I}\in \mathbb{R}^{B\times 3\times H\times W}$ and point clouds $I_P\in \mathbb{R}^{B\times 3\times 2048}$ data for fusion in this task. And the large flops and parameter size of the CLIP models pose challenges for deployment in robotics. So we design a multi-modal vision encoder, in which the 2D vision encoder uses ResNet18 [13] to extract 2D features $F_{2D}\in \mathbb{R}^{B\times C_I\times H\times W}$ , and the 3D vision encoder uses PointNet++ [33] to extract 3D features $F_{3D}\in \mathbb{R}^{B\times C_P\times N_P}$ . Then fusion module uses MLP and self-attention to obtain multi-modal spatial features $F_{S}\in \mathbb{R}^{B\times N_{S}\times C_{S}}$ . + +Vision-language model. Vision-language model as the brain of agent is used for comprehending natural language instructions, integrating semantic features and spatial features to obtain affordance features. Specifically, we choose LLaVA-7B as the backbone networks for the vision-language model. Given the action instruction, we apply the tokenizer to convert the instruction into textual feature $F_{T} \in \mathbb{R}^{B \times N_{L} \times C_{L}}$ . We use an adapter, which consists of two linear layers and an activation layer. It takes spatial features $F_{S} \in \mathbb{R}^{B \times N_{S} \times C_{S}}$ as input and maps them to a semantic space while making an increase in the channel dimension to obtain projected features $F_{SP} \in \mathbb{R}^{B \times N_{S} \times C_{L}}$ . These projected features $F_{SP}$ are then concatenated with textual features $F_{T}$ as the input of vision-language model. And the output of vision-language model is its hidden state. + +Decoder. In order to fuse all kinds of feature to get the affordance features, we design a decoder based on cross-attention. We split the output of vision-language model into instructional features and semantic features. Then we use spatial features as the query, instructional features as the key, and semantic features as the value, and obtain the affordance feature $F_{A} \in \mathbb{R}^{B \times N_{A} \times C_{A}}$ with the decoder. + +Head. Here we upsample the affordance feature $F_{A}$ for propagation and use a head composed of two linear layers, a activation layer, a batch normalization layer and a sigmoid layer to obtain 3D object affordance $O \in \mathbb{R}^{B \times 2048 \times 1}$ . + +# 4.3. Loss Function + +We predict the probability that each point cloud belongs to the corresponding affordance, ranging from 0 to 1. In order to supervise the point-wise 3D heatmap on point clouds, + +we use a weighted sum of focal loss [38] and dice loss [29] as the final loss function: + +$$ +L o s s = \omega_ {f} L _ {f} + \omega_ {d} L _ {d} \tag {1} +$$ + +where $\omega_{f}$ and $\omega_{d}$ represent the weight of the focal loss and dice loss respectively. + +# 5. Experiments + +# 5.1. Benchmark + +Metrics. In accordance with PIAD [47], we use four metrics to build the AGPIL benchmark: AUC [23], aIoU [37], SIM [39], and MAE [42]. The AUC computes the area under the ROC curve to assess the significance map on a 3D point cloud heatmap. The aIoU is the average intersection over union, which is used to evaluate the proximity between the affordance prediction and the ground truth. SIM measures the similarity between the predicted map and the ground truth map. MAE is the mean absolute error between the predicted probabilities and the ground truth. For AUC, aIoU, and SIM, higher is better, while for MAE, lower is better. + +Baselines. Since there are no prior works on grounding 3D object affordance based on language, images, and point clouds, we choose 3D AffordanceNet [33], IAG [47], OpenAD [32], and PointRefer [19] as baselines. We evaluate them in both seen and unseen settings, as well as under different perspectives including full-view, partial-view, and rotation-view. This allows us to comprehensively understand the model's generalization ability and performance across different object categories and viewpoints. + +Training and testing setup. Our model is implemented using PyTorch and all training and testing experiments are conducted on a single V100 GPU. We train the model with the AdamW optimizer [24] and a cosine learning rate scheduler [25]. The initial learning rate is 1e-4 and the weight decay is set to 0.06. We train the models with the first 2000 iteration steps for warm-up [13]. The number of training epochs is set to 20 and the training batch size is set to 6. The image 2D vision encoder ResNet18 uses parameters pretrained on ImageNet [4], while the point cloud 3D vision + +
FMetricsgrasppressstabopenlaysitcutcont.disp.wrap.supp.pushlistenwearmoveliftpour
SeenAUC↑0.8590.8980.9970.9320.9350.9570.9450.8710.9070.6890.8460.8010.9100.7330.7760.9730.945
aIOU↑0.2030.1360.3540.2390.2940.3580.1560.1990.2930.0600.1110.0290.1600.0520.0980.4070.232
SIM↑0.6500.4010.6510.3980.6930.7190.6810.5670.6550.6450.7160.5700.6830.5640.6120.4970.597
MAE↓0.0980.0590.0170.0500.0860.0650.0560.0890.0950.1280.0970.0820.0870.1380.1350.0200.075
UnseenAUC↑0.3630.8540.9320.8940.7880.7190.9210.8660.6810.556-------
aIOU↑0.0080.0380.0530.1030.1220.1090.1040.1500.0470.025-------
SIM↑0.3190.3040.3560.2150.4270.3760.5330.5220.2770.562-------
MAE↓0.2050.0650.0530.0580.1270.1100.0590.0980.1110.134-------
PMetricsgrasppressstabopenlaysitcutcont.disp.wrap.supp.pushlistenwearmoveliftpour
SeenAUC↑0.8180.8360.9870.8630.7910.9520.9090.8060.8570.6470.8320.7810.8580.7090.8110.9630.907
aIOU↑0.1510.1270.3770.2120.1340.3130.1550.1280.2640.0410.0860.0290.1030.0360.0950.3930.214
SIM↑0.6080.4110.5220.4040.4650.7020.7510.4980.6020.7440.7310.5490.5100.6570.6220.5000.637
MAE↓0.1150.0780.0350.0740.1010.0580.0650.1030.1170.1370.1020.1100.0990.1350.1190.0630.089
UnseenAUC↑0.3580.7480.9390.8800.8010.7420.8790.8110.5770.604-------
aIOU↑0.0040.0280.0570.1000.1410.0930.0470.0920.0430.043-------
SIM↑0.3580.2540.4290.2710.4510.3620.4500.5140.2320.621-------
MAE↓0.0920.1060.0880.0930.1260.1200.0920.1160.1880.153-------
RMetricsgrasppressstabopenlaysitcutcont.disp.wrap.supp.pushlistenwearmoveliftpour
SeenAUC↑0.7580.7260.8370.7850.8200.8680.8350.6830.7780.6080.7520.8610.7760.5860.7650.7770.829
aIOU↑0.1250.0420.1780.1080.1060.1900.1020.0410.1900.0320.0690.0220.0970.0180.0550.2460.145
SIM↑0.5940.2590.5620.2940.4610.5370.6500.4320.5670.7060.6590.5940.5430.6480.5990.4660.541
MAE↓0.1160.1170.0650.1060.1610.0980.1030.1350.1650.1380.1360.0810.1030.1280.1360.0570.119
UnseenAUC↑0.7880.6430.9920.5650.7600.6020.9250.5760.5330.583-------
aIOU↑0.0290.0240.4220.0060.1100.0450.1230.0270.0550.031-------
SIM↑0.5890.2080.5870.1680.4310.3370.6280.4850.2490.656-------
MAE↓0.1010.1440.0280.0820.1730.1750.0790.1470.2330.152-------
+ +Table 3. Evaluation metrics for different affordance with LMAffordance3D. We compare on seen and unseen setting in different views, where F represents full-view, P represents partial-view, and R represents rotation-view. "cont." refers to "contain", "disp." refers to "display", "wrap." refers to "wrapgrasp", and "supp." refers to "support". "-" indicates that there is no corresponding affordance category in the test set, hence no metrics. + +encoder is trained from scratch. The vision-language model uses llava-v1.6-vicuna-7b, and its parameters are frozen. During training, automatic mixed precision (AMP) is introduced to accelerate training and reduce memory usage. Furthermore, given that images and point clouds do not need to be strictly one-to-one paired, we pair images and point clouds online during training. In one training step, an image can be paired with two point clouds, effectively augmenting the training samples. During training, the loss of one image and all paired point clouds is accumulated, and gradients are calculated based on the accumulated loss. During inference, an image is paired with only one point cloud to predict the result of affordance. + +# 5.2. Results and Analysis + +Quantitative results. We build a benchmark based on the AGPIL dataset, as shown in the Tab. 2. It can be observed that our method outperforms the compared baselines, and there is a significant performance improvement in the unseen setting compared to the seen setting. This improvement can be attributed to the extensive world knowledge and prior information in the large language model. In the same experimental setup, the metrics for the full view are greater than those for the partial view, which in turn are greater than those for the rotation view. In the Tab. 3, we + +present the evaluation metrics for different affordances using LMAffordance3D in detail. In the seen setting, both the training and testing datasets include all affordance categories. However, in the unseen setting, the training dataset is limited to seven categories: support, push, listen, wear, move, lift, and pour. The test dataset, on the other hand, consists of ten categories: grasp, press, stab, open, lay, sit, cut, contain, display, and wrapgrasp. The results indicate that our model demonstrates good generalization performance. + +Qualitative analysis. As shown in the Fig. 5, we compare the results of affordance prediction using different methods across various views and settings. When in full view, the model is able to observe the object from various angles, maximizing its grasp of the geometric and morphological information of the object. This setting can provide the model with the most complete information, allowing for comprehensive affordance analysis. In partial view, the model can only observe a partial view of the object, simulating real-world situations where full information about the object is inaccessible due to occlusion or viewpoint limitations. This experiment tests the model's robustness when information is incomplete. In rotation view, the object is rotated, and only partial views of the object are observed. It evaluates the model's robustness in handling object pose + +![](images/57284e176156db98add3117ea9e66efb80cb4f026a27d7ad0cf4cebda6f04a13.jpg) +Figure 5. Visualization. We select several examples from the test set under different views and experimental settings, showcasing the model's inputs and outputs, and comparing them with the ground truth (GT). + +rotations or changes in observer perspective. The figure clearly shows that our method achieves significantly better results, confirming the validity of our setting and demonstrating the superiority of our method. + +# 5.3. Ablation Study + +We conduct ablation experiments on the AGPIL dataset to evaluate the influence of interaction images and language instructions on the model. The results are shown in Tab. 4. + +To assess whether the visual cues from RGB images affect affordance accuracy, we can find that the performance without image input decreases in both seen and unseen settings, with a significant drop in the unseen setting. This demonstrates the necessity of interactive image input for this task. + +To explore the impact of different language instructions on the experiment, we select four different settings: + +- Full: We use the content generated by GPT-4o as the instruction. + +- Action & Object: We use an action and an object name, that is, a verb and a noun as an instruction, such as "grasp bottle". +- Action: The instruction includes only an action, for example, "grasp". +- None: An empty instruction. + +We can observe that full instructions yield a higher performance compared to other simpler prompts. This demonstrates that full instructions contain more knowledge and information, which are more beneficial for the pre-trained large language model to understand the intent. + +# 5.4. Generalization to Real World + +To evaluate the generalization ability of our model in the real world, we collect some data from everyday life for testing. And the language instructions and affordance categories are unseen to the model, which poses a greater challenge. As illustrated in the Fig. 6, the inference results + +
ViewSettingImageInstructionAUC↑aIOU↑SIM↑MAE↓
Full-viewSeen✓Full0.88950.21230.61020.0816
XFull0.88270.20370.60450.0881
✓Action & Object0.88290.20570.60580.0829
✓Action0.88130.20460.60340.0842
✓None0.82630.17050.53940.1018
Unseen✓Full0.77410.09030.40890.0945
XFull0.76040.08560.39900.1213
✓Action & Object0.77120.07830.40080.0968
✓Action0.76670.07740.39800.0997
✓None0.67410.03710.30360.1282
Partial-viewSeen✓Full0.84780.17550.59280.0921
XFull0.83830.16420.58540.0972
✓Action & Object0.84570.17210.58820.0924
✓Action0.84250.17060.58660.0937
✓None0.82810.15120.57020.0996
Unseen✓Full0.76020.07240.41440.1183
XFull0.74260.07010.40220.1311
✓Action & Object0.76000.06920.40960.1216
✓Action0.75870.05980.40700.1198
✓None0.65130.04750.34120.1566
Rotation-viewSeen✓Full0.78230.11610.51910.1182
XFull0.77320.10630.50670.1214
✓Action & Object0.77420.11630.51880.1238
✓Action0.77310.11590.51550.1189
✓None0.70520.0850.46570.1394
Unseen✓Full0.63030.04150.38420.1398
XFull0.61260.04010.37090.1512
✓Action & Object0.62830.04130.37940.1390
✓Action0.62770.04120.37820.1403
✓None0.58990.03690.37020.1489
+ +Table 4. Ablation Study. We investigate the impact of interaction images and language instructions on model performance relative to the baseline, with the best results highlighted in bold. + +![](images/ae5ba182977167a25e222d6d4eead6adbfa3f10e4a25e4cbafac101520b08de2.jpg) +Figure 6. Real world. We provide two examples in which the verbs "throw" and "clean" in the language instructions are not in our dataset and are unseen by the model. + +indicate that the model effectively leverages the strengths of vision-language models. By utilizing the prior world knowledge learned during the pre-training process and finetuning it on our dataset, the model can be easily transferred to other new scenarios in real world, achieving a complex and comprehensive understanding of semantics and spatial relationships. + +# 6. Conclusion + +In this paper, we introduce the task of grounding 3D object affordance based on language instructions, visual observations, and interactions. We present the first 3D affordance dataset combining images, point clouds, and language instructions, covering full-view, partial-view, and rotation-view. And inspired by cognitive science, we propose LMAffordance3D which leverages a vision-language framework to fuse 2D, 3D spatial features with semantic features, achieving part-level affordance estimation. We conduct experiments in both seen and unseen settings, and the results demonstrate the effectiveness and better generalization capabilities of our approach. + +In future work, it will be interesting to explore model quantization and compression, and deploy them on robots to achieve real-time inference, combined with planning and control modules to accomplish tasks such as manipulation and operation. Moreover, since the objects in our dataset are all rigid, investigating affordance prediction for flexible objects is another promising direction for future research. + +# Acknowledgment + +This work was supported in part by the Joint Funds of the National Natural Science Foundation of China under Grant U24A20128, and in part by the National Nature Science Foundation of China under Grant 62173293. + +# References + +[1] Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al. Qwen technical report. arXiv preprint arXiv:2309.16609, 2023. 2 +[2] Jinze Bai, Shuai Bai, Shusheng Yang, Shijie Wang, Sinan Tan, Peng Wang, Junyang Lin, Chang Zhou, and Jingren Zhou. Qwen-vl: A frontier large vision-language model with versatile abilities. arXiv preprint arXiv:2308.12966, 2023. 2 +[3] Dongpan Chen, Dehui Kong, Jinghua Li, Shaofan Wang, and Baocai Yin. A survey of visual affordance recognition based on deep learning. 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the image appears to be a young adult female... + +Background, Lightning, Occlusion The lighting is... The background is... + +The person's face is partially obscured by a bandage on their nose... + +Pose, Gaze, Emotion: + +The person looks happy and is making a peace sign with the right hand, slightly raised. The head is tilted ..., and the person are looking directly at the camera. + +Detailed Description (Ours) + +Skin condition: + +The individual has normal skin with a tan complexion, and exhibits mild brown spot... + +The face is adorned with paintings a various stickers, including...Addition person has a small silver nose ring. + +The person in the image appears to be in a cheerful and playful mood. The facial expression is characterized by a broad smile, with the corners... + +Overall Description (Ours) + +Overall Evaluation and Reasoning: The person in the image has a youthful and playful appearance, which is reflected in ... + +![](images/2db7d4419ae7a48df5d62924db13a0a97de941a9078f6fd01fb5d59dc66ea67b.jpg) + +Makeup and Decoration: + +The face is adorned with paintings and various stickers, including... Additionally, the person has a small silver nose ring on the nostril, adding to the eclectic and creative aesthetic. The eyes are accentuated with dark eyeliner and eyeshadow, giving a dramatic and expressive look. The lips are subtly colored with a natural shade. + +FacePlayGround-240K + +# Grounded Hierarchical Semantic QA + +Referring Segmentation + +Can you segment what occludes her face? + +are, it is [SEG]. The person's face is partially obscured by a bandage on their nose and several stickers on their cheeks + +Grounded Caption + +Describe the makeup and decoration of the face in detail. Please output interleaved segmentation mask + +(Omit pixel grounded face caption showing in left) + +Grounded QA + +What impresses you in this image and where is it evident? Please output interleaved segmentation mask. + +What impresses the most is the playful and whimsical makeup and face decoration style of the individual in the image. The face is adorned....(Omit Pixel grounded face caption showing in left) + +![](images/e9629effa2e43a32ffecb55da1aa1856fe37085e7c1c686cc499291d5f8a0a46.jpg) +Figure 1. We propose FacePlayGround-240K for fine-grained face understanding, which includes meticulously annotated fine-grained face part masks and comprehensive face captions. This dataset supports various downstream face-related tasks, and our proposed facial pixel grounding GroundFace achieves impressive results across multiple tasks, while current open-source models fail. + +Qwen-VL InstructBLIP Grounded Cognition CLaV+1.5 -InternalVL+1.5 AP50 + + +# Abstract + +Multimodal Language Learning Models (MLLMs) have shown remarkable performance in image understanding, generation, and editing, with recent advancements achieving pixel-level grounding with reasoning. However, these models for common objects struggle with fine-grained face understanding. In this work, we introduce the FacePlayGround-240K dataset, the first pioneering largescale, pixel-grounded face caption and question-answer (QA) dataset that includes 240K images, 47 mask categories, 5.4M mask annotations, and 7.3M grounded regions, meticulously curated for alignment pretraining and instruction-tuning. We present the GroundingFace frame + +work, specifically designed to enhance fine-grained face understanding. This framework significantly augments the capabilities of existing grounding models in face part segmentation, face attribute comprehension, while preserving general scene understanding. Comprehensive experiments validate that our approach surpasses current state-of-the-art models in pixel-grounded face captioning/QA and various downstream tasks, including face captioning, referring segmentation, and zero-shot face attribute recognition. + +# 1. Introduction + +Multimodal Language Learning Models (MLLMs) have demonstrated impressive performance in image understanding, generation, and editing. Recently, grounding + +MLLMs [5, 13, 36, 51] have extended the understanding capabilities from the image level to the region level, even achieving pixel-level grounding with reasoning capabilities [24]. However, these methods [24, 36, 44] are designed for common scenarios, and their performance on faces is less than satisfactory. Current MLLMs often 'cannot determine' attributes in response to face-related QA problems. This deficiency in fine-grained face understanding impedes the granularity and generalization of models in subsequent generation and editing tasks. + +Challenges for detailed face understanding lie in both the dataset and the model. We identify several issues in current datasets for image-level captioning and visual question answering (VQA): 1) Insufficient attribute: Current face caption dataset typically consists of short descriptions with a limited set of facial attributes, failing to cover enough aspects. Additionally, there is a lack of semantic hierarchy, resulting in both finer and broader descriptions being overlooked. 2) Absence of inter-attribute relationships: Template-generated captions lead to disconnected attributes, hindering relational reasoning. 3) Lack of face QA data: The community suffers from a deficiency in face QA data, while the scarcity of relational captions further hampers the generation of QA pairs that possess reasoning capabilities and semantic richness. 4) Deficiency in region mask: There is a significant gap between the vocabulary of facial parts contained in captions and mask categories. The current 19 mask categories in face parsing do not adequately support region-text alignment for pixel grounding. + +To address the above deficiencies, we propose a new dataset, termed FacePlayGround-240K, for fine-grained face understanding. The construction pipeline (3) involves four stages: 1) Comprehensive caption generation: Discrete attributes are gathered and conditioned on the large VLM [7] to yield captions balancing both attribute reliability and diversity. Captions include 3 semantic levels, i.e., short, detailed and overall, and 12 subdivided aspects (Sec. 3.2). 2) Fine-grained part mask annotation involves a combination of automatic and manual processes. We automatically generate masks for structural areas and lines, acquire masks for skin details through commercial APIs [11], and manually annotate masks for facial makeup and decorations (Sec. 3.3). 3) Text-mask alignment for grounded caption: The captions and masks obtained from the previous two steps are aligned to obtain the grounded caption (Sec. 3.4). 4) Grounded hierarchical semantic QA for instruction following: We use LLM model [1] to generate QA pairs from grounded captions across three hierarchical levels, i.e., concrete attribute-level, abstract trait-level, and overall impression-level. This procedure yields data for referring segmentation (with single object mask) and grounded QA (with multiple object masks) (Sec. 3.5). Fig. 1 showcases one example. + +With the constructed dataset, several key questions must be thoroughly examined for the model design: 1) Current models struggle with fine-grained attribute understand + +ing and small part segmentation due to the low-resolution global feature and deep grounding feature that loses low-level information. 2) There is a disparity in the quality of the annotation masks and the precision required for segmenting larger facial structures (e.g., forehead) versus smaller facial parts (e.g., wrinkles). How can we design training strategies to fully utilize high-quality manually annotated data and improve the segmentation accuracy of small parts? 3) With single face closed-up images suitable for detailed attribute grounding, can we leverage the scene understanding capabilities of general grounding models in segmenting common objects and distinguishing multiple instances? + +To address these challenges, we propose the GroundingFace framework. For high-resolution face understanding, we reuse the SAM shallow feature for segmentation and introduce a face-prior sampler to effectively extract and compress high-quality face tokens (Sec. 4.3). For high-resolution face part segmentation, we integrate a high-quality adapter into the baseline model for fine-tuning, coupled with a two-stage training strategy. This approach fully utilizes both automatically and manually annotated data to improve fine-grained segmentation accuracy (Sec. 4.4). Additionally, we introduce a LoRA MoE to route high-quality and low-quality tokens to their corresponding two-stage LoRA, preserving the ability to segment common objects and distinguish multiple objects while enhancing the model's fine-grained capabilities (Sec. 4.5). + +In summary, our contributions are threefold: + +- We propose a novel fine-grained face understanding FacePlayGround-240K dataset, the first large-scale, pixel-grounded face caption and question-answer (QA) dataset, specifically designed for alignment pretraining and instruction-tuning. +- We introduce the GroundingFace framework for fine-grained face understanding, enhancing GLaMM's capabilities in face part segmentation, face attribute understanding, and maintaining general scene capabilities. +- Extensive experiments show that our method surpasses current state-of-the-art models in pixel-grounded face caption/QA and downstream tasks like face captioning, segmentation, and zero-shot face attribute recognition. + +# 2. Related Work + +Grounding Multimodal Large Language Models. Grounding MLLMs extends fine-grained image understanding from the image level to the region level. Kosmos-2 [40] and Shikra [5] use coordinates for box representation, while GPT4RoI [51] and RegionGPT [13] utilize pooled region embeddings. Leveraging SAM [22], LISA [24] achieves pixel-level grounding and enhances reasoning capabilities, enabling segmentation based on complex and implicit queries. GLaMM [44] surpasses single-object grounding by generating natural language responses integrated with multiple object segmentation masks. However, these methods, designed for general + +scenarios, perform poorly in facial recognition, which demands extremely fine-grained perception. Therefore, we propose incorporating high-resolution face prior information and a high-precision mask decoding architecture for fine-grained face grounding. + +MLLM datasets. MLLM datasets for common scenarios include visual-text alignment and instruction-following datasets [6, 30], featuring subtasks like captioning [6], referring segmentation [37, 41, 50], and grounded captioning [42, 44]. However, these datasets lack fine-grained facial concepts due to the rarity of close-up faces in general scenario images. And their region annotations typically come from detection datasets like COCO [29], Objects365 [45], and SAM [22], which often treat the face as a whole or include only a few categories such as eyes, hair, and ears. Currently, MLLM datasets for faces are limited to caption datasets [22] and lack fine-grained semantic descriptions and pixel-level mask annotations, hindering the development of high-precision face understanding models. To address this limitation, this paper introduces the FacePlayGround-240K dataset to facilitate the training of fine-grained face understanding models. + +Fine-grained face understanding. Facial understanding encompasses a range of fine-grained linguistic perceptions: 1) Static attribute understanding, which includes fine-grained facial attribute recognition [3] like age and gender; 2) Action understanding, which involves expression [27], pose [48], and gaze estimation [52]; 3) Region understanding, which includes landmark detection [23] and face parsing [21]. However, current facial understanding datasets [18, 25, 34] contain a limited number of attribute categories, such as the 40 attributes in the CelebA [34] and 19 semantic areas for CelebAMask-HQ [25]. Consequently, models trained on these datasets are restricted to closed-set categories and cannot generalize to more fine-grained facial understanding. Our FacePlayGround-240K, a large-scale face dataset with fine-grained facial masks and descriptions, which supplies the generalization and fine-grained understanding capabilities of the models trained on it. + +# 3. Pipeline for FacePlayGround-240K + +# 3.1. Acquisition Sources. + +To meet the requirements for fine-grained facial attribute understanding and grounding, the data selection criteria are based on high-resolution, close-up images of individual faces. This includes datasets such as CelebAMask-HQ [25] (30K), FFHQ [19] (70K), and EasyPortrait [18] (40K). To enhance the generalizability of the data, we also supplement with high-resolution individual face images from LAION-Face [53] (98K), which covers a broader range of everyday scenarios. We use high-precision face detectors and aesthetic scoring strategies to exclude low-quality facial data. + +# 3.2. Comprehensive Face Caption Generation. + +In the current dataset, facial captions are primarily generated using grammar templates to organize discrete attributes [34]. This method not only has limitations in the variety of attributes but also, even when rewritten using large language models (LLMs) to enrich expression, the generated descriptions still lack attribute relationships and semantic hierarchy. Additionally, relying solely on large visual language models (VLMs) for annotation faces issues of unreliable attributes due to hallucination effects. To address these problems, we employ a method that combines facial attribute recognition with large visual language models to generate fine-grained descriptions as follows. + +LLM-assisted caption generation. We utilize a commercial high-precision face recognition API by Face++ to obtain quantitative data, including gender, age, emotion intensity, occlusion area, pose/gaze angle, and skin analysis, which supports the generation of detailed fine-grained facial captions. Using a list of discrete attribute values as premises, we prompt InternVL [7] from seven predefined aspects (top part of Fig. 2) to generate initial text responses. While this approach yields detailed and comprehensive answers, it may result in semantic repetition and redundancy. Additionally, using discrete attributes as strict conditions can lead to responses that directly replicate attribute values, causing incoherent expressions. Therefore, we integrate the original texts from all aspects and employ a large language model (LLM) [1] for dedduplication and rewriting. + +# 3.3. Fine-grained Part Mask Annotation + +To achieve face grounding, it is essential to address the discrepancy in the number of face part vocabularies between captions and masks. Therefore, we utilize SpaCy to perform phrase segmentation, noun phrase extraction, and word frequency statistics on the descriptions obtained in Sec. 3.2. From this, we select high-frequency terms related to facial features, merging similar categories to derive 47 new concepts. These concepts are introduced as mask categories and are grouped into six supercategories in Fig. 4. + +Structural area/line. We categorize facial regions from facial structure priors into planar regions (e.g., forehead) and linear regions (e.g., cheekbone). These regions are decomposed using MediaPipe's 478 dense facial landmarks [35], and edge optimization is performed on the parsing masks according to the design logic. + +Skin analysis. Skin details, representing local texture features of the face, are obtained using the commercial skin analysis API [11] for masks of skin issues like wrinkles and spots. We also include one manually annotated class from FFHQ-Wrinkle [38] (1K) and 17 classes from an open-source project [15] (1.45K). + +Hair analysis. Facial hair includes bangs, moustache, and beard. We determine these categories in images based on descriptions and then use GroundingDINO [32] to locate them. To prevent errors, we constrain the locations using + +![](images/e55a0cc3fb22b91a2199ce3a99099f6dff644e9fb89bc60a1759e688216d63d8.jpg) +Figure 2. Construction pipeline of FacePlayGround-240K. The process involves 4 stages: 1) Comprehensive Face Caption Generation (Sec. 3.2); 2) Fine-grained Part Mask Annotation (Sec. 3.3); 3) Text-Mask Alignment for Grounded Caption (Sec. 3.4); and 4) Grounded Hierarchical Semantic QA for Instruction Following (Sec. 3.5). + +![](images/be80003e27bfe498484772e3c4dfed644f54c9c1e502e97088b04eb6eb5a092d.jpg) +Skin Detail + +The individual has combination skin with a very light tone, and at the skin age of 25, the person has slight wrinkles on his forehead, along with mild nasolabial folds and eye lines. The person may have severe crows feet. Notably, the person have existing melasma but no blackheads, freckles, acne, or any form of acne lesions. + +![](images/97faf381ad6388da3114f918be4589535b092fd908700a5ac8e14d297dc3b01e.jpg) +Emotion-Expression Reasoning + +This person appears to be very angry. His eyebrows are furrowed and drawn together, creating deep furrows on his forehead. His eyes are slightly narrowed, with a intense gaze. His mouth is partially open, with the corners turned downwards, suggesting tense jawline. + +![](images/61eabca48f0968169a6a1f28a349ad097db24148175084537b5b605c87724e3d.jpg) +Figure 3. Examples of grounded caption in FacePlayGround-240K. + +The person in the image is a male, likely in his 40s or 50s. He has a broad forehead and slightly furrowed eyebrows, with deep-set eyes and dark lashes. He has a slightly chiseled jawline/enhance his facial structure. His hair is short and graying, with a noticeable receding hairline, further indicating his age group. + +![](images/1ccee89d8b5aef38ad6d7015989089b34a19e790dca028c0e09b6677380c3c76.jpg) +General Appearance +Makeup + +The woman's makeup is meticulously applied, featuring a bold red lipstick that matches the vibrant red flower adorning her hair. The dark, welldefined eyelashes, complemented by long, voluminous lashes, and shiny orange eyelash, giving her a striking appearance. Her cheeks are subtly flushed... + +landmark priors and then provide the bounding boxes to SAM [22] to obtain the corresponding masks. + +Manually-labeled makeup and face decoration. The fuzzy boundaries of makeup make annotation challenging. Therefore, we filter images with heavy makeup through face captions and manually annotate eyeliner, eyeshadow, and eyelashes with clear boundaries, while omitting annotations for makeup areas with fuzzy boundaries such as highlighter and blush. Lipstick and eyebrow shadow are directly annotated using parsing masks. We employed 10 individuals, resulting in 3,745 annotated images. + +# 3.4. Text-Mask Alignment for Grounded Caption + +Phrase decomposition. To align fine-grained masks with local phrases in long texts, we first need to obtain semantically clear phrases. We use SpaCy to decompose the original text and extract phrases and corresponding noun chunks. Text-mask Alignment. The masks for hair, face makeup, and decoration are annotated based on the descriptions in the captions, thus they have a one-to-one correspondence + +and can be directly matched. We only need to match the face structure area, skin mask, and captions. By merging the high-frequency word list, we obtained a synonym list corresponding to the class names. We traverse all noun phrases to determine if they are in the synonym list, allowing for direct matching of noun vocabulary. However, this approach can lead to issues. For example, "lines on the forehead" (corresponding to the forehead wrinkle mask) contains two noun phrases: "line" and "forehead," which may result in one phrase matching multiple class masks. To address this problem, we further use SpaCy to calculate the similarity between class names and phrases, matching the mask class name with the phrase that has a higher similarity above a given threshold. Results are shown in Fig. 3. + +# 3.5. Grounded Hierarchical Semantic QA + +We observe that general-purpose MLLMs tend to generate face captions when answering questions about facial attributes. This tendency is due to the imbalance between the amount of face caption data and detailed attribute question- + +Table 1. Comparison for popular facial datasets from multiple dimensions. FacePlayGround-240K contains a larger volume of data along with detailed pixel-level and textual annotations in multiple granularity. $\checkmark$ Satisfied; $\times$ Unsatisfied. -: Inapplicable. + +
DatasetData SourceSamplesMaskText
PartLabeling MannerAttributeShort DescriptionDetailed DescriptionOverall EvaluationLabeling Manner
General appearancePose GazeEmotionOcclusionLighting BackgroundSkin detailMakeup Face decorationExpression
FFHQ-Text [19]FFHQ760--162✓XXXXXXXXXmanual
MM-CelebA [47]CelebA-HQ30K19manual40✓XXXXXXXXX-
CelebA-Dialog [17]CelebA-HQ30K--40✓XXXXXXXXX-
CelebV-Text [49]self-collected70K--77✓✓✓X✓✓X✓XXautomatic
LAION-Face [53]self-collected50K-------------automatic
FaceCaption-15M [8]LAION-Face15M--40✓XXXXXXXXXautomatic
EasyPortrait [18]self-collected40k9manual------------
FacePlayGround -240K (Ours)CelebAMask-HQ EasyPortrait, FFHQ LAION-Face, SEWA240K66automatic manualopen-ended✓✓✓✓✓✓✓✓✓✓automatic
+ +![](images/3315d456a1aab5b62e36803606164ca8d903f00f61d781ac5489fa6e6a6e9993.jpg) +(a) Attribute categories and distribution in addition to the original public annotation. + +![](images/a47421efd969ccb2f2c299a7454f87b53d6231e6247ee53094391986d74ebf3a.jpg) + +![](images/b778ef887b1ef0cc11efdaf7f79dcabb614c2e2a120d5ab33a6fd4bcdbb61852.jpg) +(b) Mask number per image + +![](images/43047e0e4e485b666c2bde6177be79d127c32462bfe9cf6690ebbb75af3eb2b1.jpg) +(c) Mask proportion of image + +![](images/45659c9295d9e261f97b44ea761fae208bbd5c9e4c2430d13553d7fc09d6338a.jpg) +(d) Caption length distribution + +![](images/c4129e790cad67be302d2f6a476b3973ab7f5598f1bd1fc55cb41b93e690ef7e.jpg) +(e) Word number per Q/A + +![](images/5d3e124eb9382d831ca6e13e4a238572e007cd6176aa4d7c02f63a3d04cbb246.jpg) +(f) QA pairs per image +Figure 4. Comprehensive statistics of FacePlayGround-240K in several aspects. Zoom in for better viewing. + +answering data available in the community. On the other hand, excessively long captions increase the difficulty of visual-text alignment for the model. Therefore, in pursuit of comprehensiveness, the description of each aspect's details is limited. In contrast, question-answering tasks allow for detailed inquiries into specific aspects, which better facilitates the model's fine-grained understanding of faces. + +Hierarchical semantic QA. There exist different semantic levels and inferential relationships among facial attributes. For instance, age-related attributes include skin condition and hair color, while emotions are closely related to facial expressions. In the descriptions obtained in Sec. 3.2, these associations are already present. We highlight and emphasize these connections through a question-and-answer format. Specifically, we categorize the semantic levels into three: "concrete attribute-level" (e.g., hair color, wrinkles), "abstract trait-level" (e.g., age), and "overall impression-level" (e.g., elderly person). We use contextual prompts to guide the LLM in generating question-and-answer pairs + +from grounded caption for these three semantic levels. + +Data for grounded QA and referring segmentation. The obtained grounded Hierarchical Semantic QA data is used for the grounded QA task. QA pairs that only point to a single object mask are used for the referring segmentation. + +# 3.6. Dataset Analysis + +Comparing with counterpart datasets. The current facial datasets primarily exhibit the following issues: 1) limited data scale; 2) the face part vocabulary is restricted to the 19 categories proposed by CelebAMask-HQ [25]; 3) limited textual attribute annotations; 4) lack of attribute relationships and hierarchical semantic descriptions; 5) insufficient alignment between mask and text annotations; 6) absence of fine-grained understanding and reasoning VQA data. These factors contribute to low accuracy or poor generalization in multimodal fine-grained facial understanding. Our FacePlayGround-240K addresses these issues by expanding the previous parsing dataset [25] with addi + +tional high-resolution FFHQ [19]. Additionally, we have filtered LaionFace [53] based on resolution. Ultimately, through a meticulous multi-level annotation process, the proposed dataset demonstrates significant improvements in data scale, fine-grained and precise attribute diversity, and annotation/alignment, as illustrated in Fig. 2, which highlights the differences compared to related datasets. + +Dataset statistics. Fig. 4 presents a comprehensive statistical analysis of FacePlayGround-240K. In addition to the originally published attribute annotations, Fig. 4(a) shows the distribution of the fine-grained facial attribute categories we provided, as discussed in Sec. 3.3, along with their subattributes in FacePlayGround-240K. Note that each subattribute in the Face Structure and Line category is present in every image, hence they are not listed. Word clouds illustrate the diversity and frequency distribution of text annotations. Fig. 4(b) shows the mask number per image. Fig. 4(c) illustrates the distribution of the relative area occupied by mask annotations, which varies widely and provides diverse pixel-level grounding annotations. Fig. 4(d), (e), and (f) present the distribution of the caption length, word number per question / answer, and QA pair per image. + +# 4. Methodology: GroundingFace + +# 4.1. Research definition. + +This work extends face understanding task to a finer granularity of facial pixel-wise grounding in MLLM. Given a prompt $P$ and a facial image $I$ , the MLLM generates text responses $T$ interleaved with one or multiple face part segmentation masks $M$ . After the training phase, this model can be applied to various downstream tasks, including grounded face captioning, zero-shot face attribute recognition, and face-oriented grounded question answering. We use the general GLaMM framework based on MLLM [44] as the foundation to develop the GroundingFace model for fine-grained face understanding, as illustrated in Fig. 5. + +# 4.2. Motivation of Different Components + +Instance-level vs. Part-level. Typically, MLLM for general object pixel grounding tends to understand inter-instance relationships and perform instance-level segmentation [44]. However, the current global visual encoder, which uses low-resolution input, fails to meet the requirements for understanding fine-grained attributes within instances. Face understanding is particularly sensitive to detailed parts. Additionally, the mask decoder based on SAM is inadequate for fine-grained part segmentation due to the coarse-grained nature of the generated masks. To address these issues, we propose Fine-grained Face Part Segmentation (Sec. 4.3) and Fine-grained Face Attribute Understanding (Sec. 4.4). + +Coarse auto-generated masks vs. Accurate manual-annotated masks. Compared to larger face structure areas (e.g., forehead), smaller facial parts (e.g., wrinkles) demand higher precision in mask edges, requiring different levels of annotation quality. Training all granularity masks together + +can negatively impact the segmentation accuracy of small parts. Therefore, we introduce an additional Stage-2, where we fine-tune the model using high-quality data specifically for small facial parts and manually annotated data. + +Distinguish multiple instances and prevent common object forgetting. To achieve fine-grained face grounding, we utilize a close-up single-face image dataset without multiple-person scenes and common object labeling. However, the general scene base model inherently excels in common object grounding and distinguishing multiple instances. Thus, we incorporate stage-aware LoRA [14] and MoE [16] for efficient fine-tuning to retain the model's general scene understanding capabilities Sec. 4.5. + +# 4.3. Fine-grained Face Part Segmentation + +The vanilla SAM decoder is trained for general instance segmentation without considering the need for high-precision segmentation. Therefore, we introduce HQ-SAM [20] to improve the face-oriented mask decoder in MLLM, referred to as the HQ-SAM Adapter, to achieve fine-grained mask generation. + +High-quality mask decoder. We visualize the features of different ViT layers in Fig. 6 and observe that shallow layer features exhibit finer pixel details, while deep layer features are more oriented towards high-level semantics. Considering that facial understanding requires high detail but small parts are almost invisible in deep-layer features, we introduce shallow-layer features to enhance fine-grained representation. To better utilize fine-grained features, we employ a Shallow-Deep Fusion method to integrate ViT features of different depths. This module is implemented using a combination of naive deconvolution and linear layers. + +# 4.4. Fine-grained Face Attribute Understanding + +To achieve highresolution image understanding, the current mainstream approach in MLLM methods is to adopt a dynamic resolution crop strategy. This method enlarges + +![](images/6ef009ebcaf9857f95e35c17edb8f352c30cbbaa0d0f4d54f4740a5d70401f8e.jpg) +Figure 6. Visualization of different scale (by rows) / depth (by columns) features of CLIP ViT [10, 43]. + +local regions to capture more image details while keeping the visual encoder unchanged, but it results in a significant increase in the number of tokens, thereby increasing the computational cost of the LLM component [13, 51]. Some works focus on adaptive token selection and sampling, but this is unnecessary for faces since their locations can be easily obtained through priors, such as a pretrained face detector. Another approach involves introducing higher resolution visual encoders and multi-stage features, which also significantly increase computational costs. Unlike these methods, we propose reusing the shallow and deep features extracted by SAM, as described in Sec. 4.3, which + +![](images/606a9e78eadd03b1b992abdcd07e1e95b7fffc06d442292d50f6f15abbd80f70.jpg) +Figure 5. Overview: The GroundingFace framework is specifically designed for fine-grained face understanding, which enhances GLaMM's fine-grained facial understanding capabilities on three aspects: 1) Fine-grained Face Part Segmentation (Sec. 4.3) that integrates shallow and deep features for small part mask generation. 2) Fine-grained Face Attribute Understanding (Sec. 4.4) that reuses SAM features and employs a face prior sampler to efficiently inject facial information. 3) Training Recipe (Sec. 4.5) introduces MoE and LoRA to maintain the model's general scene capabilities while incorporating fine-grained facial concept understanding. + +![](images/0aa860024436a76e6f93980e87c5d4cd894d9b08853bd706d5781409130f4cef.jpg) +Figure 7. Two-stage training recipe for GroundingFace. + +contain rich detailed features. + +High resolution facial tokens sampler. Directly using SAM features reduces the computational cost of feature extraction, but it still retains a large number of tokens to maintain detailed features. We propose to sample the high-resolution feature tokens corresponding to the facial region in the first stage feature using a face prior sampler: 1) First, determine that the target size of the $64 \times 64$ SAM features after sampling is $48 \times 48$ . Compute the affine transformation matrix using a 1024-resolution SAM image input and a 768-resolution standard five-point facial landmark. By applying the matrix and transforming the features, we obtain the cropped and aligned facial region tokens. This approach increases the proportion of the facial region while reducing the feature space resolution, effectively compressing the number of tokens with minimal loss. Subsequently, we further downsample and compress the tokens using pixel unshuffle [46] and learnable linear layers. Since these high-resolution facial tokens are not spatially aligned with the original image, and the SAM features and Global Visual Encoder features are not in the same feature space, we introduce an additional projector for feature alignment. + +# 4.5. Training Recipe + +Efficient Adaption with LoRA. We introduce a two-stage training strategy, as shown in Fig. 7, to preserve the pretrained knowledge of the baseline GLaMM and enhance + +the understanding and segmentation of small parts. In the first stage, we fine-tune using both general data and facial data: we freeze the base model's LoRA1 and fine-tune the trainable LoRA2, Projector1, and mask decoder. This step primarily aims to integrate the newly introduced facial concepts with the general scene knowledge. In the second stage, we freeze Projector1, LoRA1/2, and the Mask Decoder, and fine-tune LoRA3, Projector2, and the HQ Adapter on a high-quality hand-labeled dataset and a fine-grained part mask subset. This approach allows the model to learn fine-grained understanding and segmentation while keeping the previous weights unchanged to retain the general knowledge as much as possible. + +Boosting Fine-grained Understanding with MoE. Although the high-quality data subset has been filtered, it only increases the proportion of high-quality hand-labeled masks in the data. There are still coarse masks present in the grounded caption and VQA data. The model needs to decide whether to use coarse LoRA2 or fine-grained LoRA3 based on the input. Therefore, we introduce a MoE [16] to address this issue. Inspired by MOELoRA [12, 26, 31], we employ a Top-K (K=1) router to assign HQ and LQ token to the corresponding LoRA expert of two training stages. Specifically, it computes the probability $S^l$ of the input token $x$ being routed to an expert with trainable parameters $W_r$ in layer $l$ . The whole process is denoted as follows: + +$$ +S ^ {l} (x) = \operatorname {T o p - 1} \left(\operatorname {S o f t m a x} \left(W _ {r} ^ {l} x\right)\right), +$$ + +$$ +h ^ {l} = W _ {0} ^ {l} x + S ^ {l} (x) A ^ {l} B ^ {l} x, +$$ + +$$ +A ^ {l} B ^ {l} = \left\{ \begin{array}{l l} A _ {H Q} ^ {l} B _ {H Q} ^ {l} & \text {i f} S ^ {l} (x) = S _ {H Q} ^ {l} (x) \\ A _ {L Q} ^ {l} B _ {L Q} ^ {l} & \text {i f} S ^ {l} (x) = S _ {L Q} ^ {l} (x) \end{array} \right., +$$ + +$h^l$ is the output embedding, $W_0^l \in \mathbb{R}^{d_q \times d_p}$ is pretrained weight matrix, and $A^l, B^l$ are the low-rank matrices, where $A^l \in \mathbb{R}^{d_q \times r}, B^l \in \mathbb{R}^{r \times d_p}$ , and $r \ll \min(d_q, d_p)$ . Following [16], we apply load balancing loss to mitigate the + +Describe the emotion and expression of person in detail. Please output with interleaved mask. + +The emotion of the person is one of discomfort or pain. The facial expression, characterized by tightly closed eyes, furrowed brows, and pressed lips, reveals a range of wrinkles, contribute to the overall look of distress. + +![](images/17ec42549693dea93da8a6591d4626f0e921efccd75ecbcfb7aeee414ce05073.jpg) +Figure 8. Quantitative capability demonstration across different downstream grounded caption / VQA and referring segmentation tasks. + +Can you segment the mole on her face? + +![](images/7ae3b41d252f1f73c8f4e30c844c80f0104188622a8c5cecbcec9bd99153220c.jpg) + +What makes her looks unapproachable? + +Her lips are pressed into a straight line, and her eyes are slightly narrowed, giving her a stern look. The luxurious fur collar exudes opulence and power, evoking a sense of confidence and pride, while the large, ornate earrings add a touch of sophistication. Together, these elements enhance her unapproachable demeanor. + +Can you segment the eyeshadow of the person with darker skin tones? + +![](images/a01fec085a9940afda52e64ce145953f595c32a4221ca885d1c91fa54bcab928.jpg) + +What occludes her face? Please output with interleaved mask. + +The person is holding a tennis. +racket, which obscures nearly +half of the face. + +![](images/73867ae48050b054ade360b4847b128b56aba5b016fe3a7d5f3dc56938095859.jpg) + +unbalanced load for experts when training. + +# 5. Experiments + +Benchmarking setting. We conduct a quantitative evaluation of GroundingFace on four benchmarks: 1) Pixel Grounded Face Caption, 2) Face Referring Segmentation, 3) Face-oriented Grounded Caption and Question Answering, and 4) Zero-shot Face Attribute Recognition. + +Dataset and evaluation criteria. We split the FacePlayGround-240K into training, validation, and test sets comprising 232.5K, 2.5K, and 5K images, respectively. For each model, we evaluate three key aspects: 1) dense caption quality, 2) mask quality, and 3) phrase-mask correspondence accuracy. We include METEOR [4] for captions, class-agnostic mask AP for grounding, and mask IoU for segmentation. We select the currently most powerful and related GLaMM [44] as our baseline since there are no prior pixel grounding works for the face field. + +# 5.1. Experimental Results + +Pixel Grounded Face Caption Tab. 2 shows that GLaMM, trained on general scenario data, performs poorly on the fine-grained face grounding task (Idx.1). However, finetuning GLaMM on FacePlayGround-240K significantly improves its performance (Idx.2). Additionally, Grounding-Face demonstrates enhanced performance compared to the baseline, as well as obtaining consistent conclusion on pixel grounded face caption and VQA Tab. 3. Qualitative results are presented in Fig. 8. + +Face Referring Segmentation. Given explicit and implicit user instructions, the model outputs a segmentation mask for the specified single target. Qualitative results in Tab. 2 and quantitative cases in Fig. 8 demonstrate our superiority. + +Zero-shot Face Attribute Recognition We compare our method with general state-of-the-art MLLMs by reorganizing widely-used face attribute recognition benchmarks into question-answer pairs. Our method demonstrates a significant advantage, as shown in Tab. 4. + +Ablation Analysis To more clearly observe the capabilities of GroundingFace in face understanding and segmentation, we conduct ablation studies on the face captioning and referring segmentation tasks, as shown in Tab. 2. ① Key + +Table 2. Results on face caption (METEOR) and referring segmentation (gIoU). Our full model achieves obvious improvement over GLaMM baseline. The effect of each component is ablated. + +
Idx.MethodHQ-SAM Adapter HQ Facial TokensMoEMETEORgIoU
Sec. 4.3Sec. 4.4Sec. 4.5
1GLaMMXXX1.16.6
2Stage-1XXX18.283.6
3Stage-1✓✓X20.686.2
4Stage-2✓X✓17.587.1
5Stage-2X✓✓22.385.3
6Stage-2✓✓X21.388.2
7Full Model✓✓✓23.188.9
86/12/18/24th Feats.✓✓✓22.388.1
+ +Table 3. Results on pixel grounded face caption and VQA. + +
MethodGrounded CaptionGrounded VQA
METEORAP50mIoUMETEORAP50mIoU
GLaMM0.90.027.01.65.05.4
Stage-119.830.648.618.352.173.2
Ours21.932.952.020.653.776.9
+ +Table 4. Performance of GroundingFace in zero shot face attribute recognition. Our method perform best in all datasets. + +
MethodParams.RAF-DB [28]LFWA [33]AgeDB [39]
Emotion↑Attribute↑Gender↑Age↓
Qwen-VL [2]7B42.90.093.911.44
InstructBLIP [9]7B27.949.571.99.97
LLaVA-v1.5 [30]7B55.458.398.510.22
InternVL-v1.5 [7]26B67.261.194.419.26
Ours7B91.773.198.56.92
+ +components in GroundingFace. As shown in Tab. 2-Idx.4/5/6/7, each key component contributes to the model's final performance. $②$ Different depth SAM features. By default, we use the 6th and 24th SAM features. We explore the impact of using additional 6th, 12th, 18th, and 24th SAM features on the model and find that it leads to a performance drop despite the increased computational cost, as shown in Tab. 2-Idx.7/8. $③$ Fine-tuning stages. The two-stage training strategy significantly outperforms the one-stage approach (Idx.3/6 in Tab. 2). + +# 6. Conclusion + +We introduce a novel FacePlayGround-240K dataset, the first large-scale, pixel-grounded face caption and question-answer (QA) dataset designed for alignment pretraining and instruction-tuning, which provides comprehensive captions and QA data rich in attribute relationships. Additionally, we propose the GroundingFace framework, enhancing fine-grained facial understanding through improved face part segmentation and attribute understanding. + +Acknowledgement. This work is supported by the State Key Laboratory of Industrial Control Technology, China (Grant No. ICT2024A09). + +# References + +[1] Marah Abdin, Jyoti Aneja, Hany Awadalla, Ahmed Awadallah, Ammar Ahmad Awan, Nguyen Bach, Amit Bahree, Arash Bakhtiari, Jianmin Bao, Harkirat Behl, et al. Phi-3 technical report: A highly capable language model locally on your phone. arXiv preprint arXiv:2404.14219, 2024. 2, 3 +[2] Jinze Bai, Shuai Bai, Yunfei Chu, Zeyu Cui, Kai Dang, Xiaodong Deng, Yang Fan, Wenbin Ge, Yu Han, Fei Huang, et al. Qwen technical report. arXiv preprint arXiv:2309.16609, 2023.8 +[3] Tadas Baltrusaitis, Peter Robinson, and Louis-Philippe Morency. Openface: an open source facial behavior analysis toolkit. In WACV, 2016. 3 +[4] Satanjeev Banerjee and Alon Lavie. 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However, purely SSM-based models face critical challenges related to stability and achieving state-of-the-art performance in computer vision tasks. Our paper addresses the challenges of scaling SSM-based models for computer vision, particularly the instability and inefficiency of large model sizes. We introduce a parameter-efficient modulated group mamba layer that divides the input channels into four groups and applies our proposed SSM-based efficient Visual Single Selective Scanning (VSSS) block independently to each group, with each VSSS block scanning in one of the four spatial directions. The Modulated Group Mamba layer also wraps the four VSSS blocks into a channel modulation operator to improve cross-channel communication. Furthermore, we introduce a distillation-based training objective to stabilize the training of large models, leading to consistent performance gains. Our comprehensive experiments demonstrate the merits of the proposed contributions, leading to superior performance over existing methods for image classification on ImageNet-1K, object detection, instance segmentation on MS-COCO, and semantic segmentation on ADE20K. Our tiny variant with 23M parameters achieves state-of-the-art performance with a classification top-1 accuracy of $83.3\%$ on ImageNet-1K, while being $26\%$ efficient in terms of parameters, compared to the best existing Mamba design of same model size. Code and models are available at: https://github.com/Amshaker/GroupMamba + +# 1. Introduction + +Various context modeling methods have emerged in the domains of language and vision understanding. These include Convolution [21, 66], Attention [60], and, more recently, State Space Models [16, 17]. Transformers with their multi- + +![](images/6571034e94e1d9dbf7d5a9d05c3b5bdfff0806839e7517109fb25dab6f12e97d.jpg) +Figure 1. Comparison in terms of Parameters vs. Top-1 Accuracy on ImageNet-1k [9]. Our GroupMamba-B achieves superior top-1 classification accuracy while reducing parameters by $36\%$ compared to VMamba [35]. + +headed self-attention mechanism [60] have been central to both language models such as GPT-3 [2] and vision models such as Vision Transformers [10, 36]. However, challenges arose due to the quadratic computational complexity of attention mechanisms particularly for longer sequences, leading to the recent emergence of State Space models such as S4 [17]. + +While being effective in handling extended input sequences due to their linear complexity in terms of sequence lengths, S4 [17] encountered limitations in global context processing in information-dense data, especially in domains like computer vision due to the data-independent nature of the model. Alternatively, approaches such as global convolutions-based state space models [14] and Liquid S4 [20] have been proposed to mitigate the aforementioned limitations. The recent Mamba [16] introduces the S6 architecture which aims to enhance the ability of statespace models to handle long-range dependencies efficiently. + +The selective-scan algorithm introduced by Mamba uses input-dependent state-space parameters, which allow for better in-context learning while still being computationally efficient compared to self-attention. + +However, Mamba, specifically the S6 algorithm, is known to be unstable for e.g., image classification, especially when scaled to large sizes [46]. Additionally, the Mamba model variant used in image classification, generally called the VSS (Visual State Space) block, can be more efficient in terms of parameters and compute requirements based on the number of channels. The VSS block includes extensive input and output projections along with depth-wise convolutions, whose parameters and compute complexities are directly proportional to the number of channels in the input. To address this issue, we propose a hierarchical-based Modulated Group Mamba layer that mitigates the aforementioned issues in a computation and parameter-efficient manner. The main contributions of our paper are: + +1. We introduce a Modulated Group Mamba layer, inspired by Group Convolutions, which enhances computational efficiency and interaction in state-space models by using a multi-direction scanning method for comprehensive spatial coverage and effective modeling of local and global information. +2. We introduce a Channel Affinity Modulation (CAM) operator, which enhances communication across channels to improve feature aggregation, addressing the limited interaction inherent in the grouping operation. +3. To address the instability issue in the SSM-based architecture, we introduce a distillation-based training objective designed to stabilize models with a large number of parameters, leading to better performance and a smooth loss convergence trend. +4. We build a series of parameter-efficient generic classification models called "GroupMamba", based on the proposed Modulated Group Mamba layer. Our tiny variant achieves $83.3\%$ top-1 accuracy on ImageNet-1k [9] with $23M$ parameters and $4.5G$ FLOPs. Additionally, our base variant achieves top-1 accuracy of $84.5\%$ with $57M$ parameters and $14G$ FLOPs, outperforming all recent SSM methods (see Fig. 1). + +# 2. Related Work + +Convolutional Neural Networks (ConvNets) have been the popular choice for computer vision tasks since the introduction of AlexNet [30]. The field has rapidly evolved with several landmark ConvNet architectures [21, 25, 52, 56, 57]. Alongside these architectural advances, significant efforts have been made to refine individual convolution layers, including depthwise convolution [65], group convolution [7], and deformable convolution [8]. Recently, ConvNeXt variants [37, 63] have taken concrete steps towards modernizing + +traditional 2D ConvNets by incorporating macro designs with advanced settings and training recipes to achieve on-par performance with the state-of-the-art models. + +In recent years, the pioneering Vision Transformer (ViT) [10] has significantly impacted the computer vision field, including tasks such as image classification [12, 36, 38, 58], object detection [3, 44, 68, 71], and segmentation [5, 28, 51]. ViT [10] introduces a monolithic design that approaches an image as a series of flattened 2D patches without image-specific inductive bias. The remarkable performance of ViT for computer vision tasks, along with its scalability, has inspired numerous subsequent endeavors to design better architectures. The early ViT-based models usually require large-scale datasets (e.g., JFT-300M [55]) for pretraining. Later, DeiT [58] proposes advanced training techniques in addition to integrating a distillation token into the architecture, enabling effective training on smaller datasets (e.g., ImageNet-1K [9]). Since then, subsequent studies have designed hierarchical and hybrid architectures by combining CNN and ViT modules to improve performance on different vision tasks [11, 12, 41, 50, 54]. Another line of work is to mitigate the quadratic complexity inherent in self-attention, a primary bottleneck of ViTs. This effort has led to significant improvements and more efficient and approximated variants [6, 29, 43, 45, 50, 59, 62], offering reduced complexity while maintaining effectiveness. + +Recently, State Space Models (SSMs) have emerged as an alternative to ViTs [60], capturing the intricate dynamics and inter-dependencies within language sequences [17]. One notable method in this area is the structured state-space sequence model (S4) [17], designed to tackle long-range dependencies while maintaining linear complexity. Following this direction, several models have been proposed, including S5 [53], H3 [13], and GSS [42]. More recently, Mamba [16] introduces an input-dependent SSM layer and leverages a parallel selective scan mechanism (S6). + +In the visual domain, various works have applied SSMs to different tasks. In particular for image classification, VMamba [35] uses Mamba with bidirectional scans across both spatial dimensions in a hierarchical Swin-Transformer [36] style design to build a global receptive field efficiently. A concurrent work, Vision Mamba (Vim) [70], instead proposed a monolithic design with a single bidirectional scan for the entire image, outperforming traditional vision transformers like DeiT. LocalVMamba [27] addresses the challenge of capturing detailed local information by introducing a scanning methodology within distinct windows (inspired from SwinTransformer [36]), coupled with dynamic scanning directions across network layers. EfficientVMamba [47] integrates atrous-based selective scanning and dual-pathway modules for efficient global and local feature extraction, achieving competitive results with reduced computational + +complexity. These models have been applied for image classification, as well as image segmentation [15, 34, 40, 49], video understanding [4, 31, 67], and various other tasks [18, 19, 23, 32, 61]. Their wide applicability shows the effectiveness of SSMs [13, 17, 42, 53], and in particular Mamba [16], in the visual domain. In this paper, we propose a Modulated Group Mamba layer that mitigates the drawbacks of the default vision Mamba block, such as lack of stability [46] and the increased number of parameters with respect to the number of channels. + +# 3. Method + +Motivation: Our method is motivated based on the observations with respect to the limitations of existing Visual State-Space models. + +- Lack of Stability for Larger Models: We observe from [46] that Mamba [16] based image classification models with an MLP channel mixer are unstable when scaled to a large number of parameters. This instability can be seen in SiMBA-L (MLP) [46], which leads to suboptimal classification results of $49\%$ accuracy. We mitigate this issue by introducing a Modulated Group Mamba design alongside a distillation objective (as presented in Sec. 3.4) that stabilizes the Mamba SSM training without modifying the channel mixer. +- Efficient Improved Interaction: Given the computational impact of Mamba-based design on the number of channels, the proposed Modulated Group Mamba layer is computationally inexpensive and parameter efficient than the default Mamba and able to model both local and global information from the input tokens through multidirection scanning. An additional Channel Affinity Modulation operator is proposed in this work to compensate for the limited channel interaction due to the grouped operation and enhance their interactions. + +# 3.1. Preliminaries + +State-Space Models: State-space models (SSMs) like S4 [17] and Mamba [16] are structured sequence architectures inspired by a combination of recurrent neural networks (RNNs) and convolutional neural networks (CNNs), with linear or near-linear scaling in sequence length. Derived from continuous systems, SSMs define and 1D function-to-function map for an input $x(t) \in \mathbb{R}^L \to y(t) \in \mathbb{R}^L$ via a hidden state $h(t) \in \mathbb{R}^N$ . More formally, SSMs are described by the continuous time Ordinary Differential Equation (ODE) in Eq. 1. + +$$ +\begin{array}{l} h ^ {\prime} (t) = \mathbf {A} h (t) + \mathbf {B} x (t), \\ \quad (t) = \mathbf {G} _ {1} (t). \end{array} \tag {1} +$$ + +$$ +y (t) = \mathbf {C} h (t), +$$ + +where $h(t)$ is the current hidden state, $h'(t)$ is the updated hidden state, $x(t)$ is the current input, $y(t)$ is the + +output, $\mathbf{A} \in \mathbb{R}^{N \times N}$ is SSM's evolution matrix, and $\mathbf{B} \in \mathbb{R}^{1 \times N}$ , $\mathbf{C} \in \mathbb{R}^{1 \times N}$ are the input and output projection matrices, respectively. + +Discrete State-Space Models: To allow these models to be used in sequence modeling tasks in deep learning, they need to be discretized, converting the SSM from a continuous time function-to-function map into a discrete-time sequence-to-sequence map. S4 [17] and Mamba [16] are among the discrete adaptations of the continuous system, incorporating a timescale parameter $\Delta$ to convert the continuous parameters $\mathbf{A},\mathbf{B}$ into their discrete equivalents $\overline{\mathbf{A}},\overline{\mathbf{B}}$ . This discretization is typically done through the Zero-Order Hold (ZOH) method given in Eq. 2. + +$$ +\overline {{\mathbf {A}}} = \exp (\Delta \mathbf {A}), +$$ + +$$ +\overline {{\mathbf {B}}} = \begin{array}{c} (\boldsymbol {\Delta} \mathbf {A}) ^ {- 1} (\exp (\boldsymbol {\Delta} \mathbf {A}) - \mathbf {I}) \cdot \boldsymbol {\Delta} \mathbf {B} \\ - \end{array} \tag {2} +$$ + +$$ +h _ {t} = \overline {{\mathbf {A}}} h _ {t - 1} + \overline {{\mathbf {B}}} x _ {t}, +$$ + +$$ +y _ {t} = \mathbf {C} h _ {t}. +$$ + +While both S4 [17] and Mamba [16] utilize a similar discretization step as stated above in Eq. 2, Mamba differentiates itself from S4 by conditioning the parameters $\pmb{\Delta} \in \mathbb{R}^{B \times L \times D}$ , $\mathbf{B} \in \mathbb{R}^{B \times L \times N}$ and $\mathbf{C} \in \mathbb{R}^{B \times L \times N}$ , on the input $x \in \mathbb{R}^{B \times L \times D}$ , through the S6 Selective Scan Mechanism, where $B$ is the batch size, $L$ is the sequence length, and $D$ is the feature dimension. + +# 3.2. Overall Architecture + +As shown in Fig. 2 (a), our model uses a hierarchical architecture, similar to Swin-Transformer [36], with four stages to efficiently process images at varying resolutions. Assuming an input image, $\mathbf{I} \in \mathbb{R}^{H \times W \times 3}$ , we first apply a Patch Embedding layer to divide the image into non-overlapping patches of size $4 \times 4$ and embed each patch into a $C_1$ -dimensional feature vector. The patch embedding layer is implemented using two $3 \times 3$ convolutions with a stride of 2. This produces features maps of size $\frac{H}{4} \times \frac{W}{4} \times C_1$ at the first stage. These feature maps are passed through $N_1$ blocks of our Modulated Grouped Mamba (as detailed in Sec. 3.3). In each subsequent stage, a down-sampling layer merges patches in a $2 \times 2$ region, followed by another $N$ blocks of our Modulated Grouped Mamba layer. Hence, feature size at stages two, three and four are $\frac{H}{8} \times \frac{W}{8} \times C_2$ , $\frac{H}{16} \times \frac{W}{16} \times C_3$ , and $\frac{H}{32} \times \frac{W}{32} \times C_4$ , respectively. + +# 3.3. Modulated Group Mamba Layer + +We present the overall operations of the proposed Modulated Group Mamba layer (Fig. 2 (b)) for an input sequence $\mathbf{X}_{\mathrm{in}}$ , with dimensions $(B, H, W, C)$ , where $B$ is the batch size, $C$ is the number of input channels and $H/W$ are the + +![](images/6d90da731d799f6e0f9f709d2ba8e949614e9aa24242486e34311fa8f871c34e.jpg) +(a) Overall Architecture of GroupMamba + +![](images/ec27c2c0f0d996debddd178641380208168e51145b9c914427f8ff683ef51c04.jpg) +(b) The proposed Modulated Group Mamba Layer + +![](images/c2cd3dab0d4978e3cd6cf9a67911eb2bec54025eecdaaa5ce97bf99114e022d6.jpg) +(c) VSSS Block +Figure 2. Overview of the proposed method. Top Row: The overall architecture of our framework with a consistent hierarchical design comprising four stages. Bottom Row: We present (b) The design of the modulated group mamba layer. The input channels are divided into four groups with a single scanning direction for each VSSS block. This significantly reduces the computational complexity compared to the standard mamba layer, with similar performance. Channel Affinity Modulation mechanism is introduced to address the limited interactions within the VSSS blocks. (c) The design of VSSS block. It consists of Mamba block with 1D Selective Scanning block followed by FFN. (d) The four scanning directions used for the four VSSS blocks are illustrated. + +![](images/8313cddb125e8d86850842039b66013a3257e096765ee607e933eb1eee43d2b5.jpg) +(d) Scanning Directions + +width and height of the feature map, in Eq. 3. + +$$ +\mathbf {X} _ {\mathrm {G M}} = \text {G r o u p e d M a m b a} (\mathbf {X} _ {\text {i n}}, \Theta) +$$ + +$$ +\mathbf {X} _ {\text {C A M}} = \operatorname {C A M} \left(\mathbf {X} _ {\mathrm {G M}}, \text {A f f i n i t y} \left(\mathbf {X} _ {\text {i n}}\right)\right) \tag {3} +$$ + +$$ +\mathbf {X} _ {\text {o u t}} = \mathbf {X} _ {\text {i n}} + \operatorname {F F N} (\operatorname {L N} (\mathbf {X} _ {\text {C A M}})) +$$ + +Here, $\mathbf{X}_{\mathrm{GM}}$ is the output of Eq. 6, $\mathbf{X}_{\mathrm{CAM}}$ is the output of Eq. 9, LN is the Layer Normalization [1] operation, FFN is the Feed-Forward Network as described by Eq. 5, and $\mathbf{X}_{\mathrm{out}}$ is the final output of the Modulated Group Mamba block. The individual operations, namely the GroupedMamba operator, the VSSS block used inside the GroupedMamba operator, and the CAM operator, are presented in Sec. 3.3.1, Sec. 3.3.2 and Sec. 3.3.3, respectively. + +# 3.3.1. Visual Single Selective Scan (VSSS) Block + +The VSSS block (Fig. 2 (c)) is a token and channel mixer based on the Mamba operator, comprising of a Mamba block followed by a Feed-Forward Network, each with a LayerNorm before it. Mathematically, for an input token sequence $\mathbf{Z}_{\mathrm{in}}$ , the VSSS block performs the operations as described in Eq. 4. + +$$ +\begin{array}{l} \mathbf {Z} _ {\text {o u t}} ^ {\prime} = \mathbf {Z} _ {\text {i n}} + \text {M a m b a} (\mathrm {L N} (\mathbf {Z} _ {\text {i n}})) \\ \overline {{\mathbf {Z}}} _ {\text {i n}} = \overline {{\mathbf {Z}}} _ {\text {i n}} ^ {\prime} = \overline {{\mathbf {F N}}} (\mathrm {L N} (\mathbf {Z} _ {\text {i n}} ^ {\prime})) \end{array} \tag {4} +$$ + +$$ +\mathbf {Z} _ {\text {o u t}} = \mathbf {Z} _ {\text {o u t}} ^ {\prime} + \text {F F N} (\ln (\mathbf {Z} _ {\text {o u t}} ^ {\prime})) +$$ + +Where $\mathbf{Z}_{\mathrm{out}}$ is the output sequence, Mamba is the discretized Mamba SSM operator as described in Eq. 2. + +$$ +\operatorname {F F N} \left(\operatorname {L N} \left(\mathbf {Z} _ {\text {o u t}} ^ {\prime}\right)\right) = \operatorname {G E L U} \left(\operatorname {L N} \left(\mathbf {Z} _ {\text {o u t}} ^ {\prime}\right) \mathbf {W} _ {1} + \mathbf {b} _ {1}\right) \mathbf {W} _ {2} + \mathbf {b} _ {2} \tag {5} +$$ + +Where GELU [24] is the activation function and $\mathbf{W}_1$ , $\mathbf{W}_2$ , $\mathbf{b}_1$ , and $\mathbf{b}_2$ are weights and biases for the linear projections. + +# 3.3.2. Grouped Mamba Operator + +Considering the motivation presented earlier in Sec. 3, we aim to design a variant of the Mamba [16] that is both computationally efficient and can effectively model the spatial dependencies of the input sequence. Given that Mamba is computationally inefficient on large number of channels $C$ in the input sequence, we propose a grouped variant of the operator, inspired by Grouped Convolutions. The Grouped Mamba operation is a variant of the VSSS block presented in Sec. 3.3.1, where the input channels are divided into groups, and the VSSS operator is applied separately to each group. Specifically, we divide the input channels into four groups, each of size $\frac{C}{4}$ , and an independent VSSS block is applied to each group. Hence, the proposed grouped mamba operator enhances the model efficiency by splitting channels into smaller groups. To better model spatial dependencies in the input, each of the four groups scans in one of + +four directions across the input: left-to-right, right-to-left, bottom-to-top, and top-to-bottom as outlined in Fig. 2 (d). + +Let $G = 4$ be the number of groups representing four scanning directions: left-to-right, right-to-left, top-to-bottom, and bottom-to-top. We form four sequences from the input sequence $\mathbf{X}_{\mathrm{in}}$ , namely $\mathbf{X}_{\mathrm{LR}}$ , $\mathbf{X}_{\mathrm{RL}}$ , $\mathbf{X}_{\mathrm{TB}}$ , and $\mathbf{X}_{\mathrm{BT}}$ , each of shape $(B, H, W, \frac{C}{4})$ , representing one of the four directions specified earlier. These are then flattened to form a single token sequence of shape $(B, N, \frac{C}{4})$ , where $N = W \times H$ is the number of tokens in the sequence. The parameters for each of the four groups can be specified by $\theta_{\mathrm{LR}}$ , $\theta_{\mathrm{RL}}$ , $\theta_{\mathrm{TB}}$ , and $\theta_{\mathrm{BT}}$ , respectively, for each of the four groups, representing the parameters for the VSSS blocks. + +Given the above definitions, the overall relation for the Grouped Mamba operator can be written as shown in Eq. 6. + +$$ +\begin{array}{l} \mathbf {X} _ {\mathrm {G M}} = \text {G r o u p e d M a m b a} (\mathbf {X} _ {\text {i n}}, \Theta) = \text {C o n c a t} ( \\ \mathrm {V S S S} \left(\mathbf {X} _ {\mathrm {L R}}, \Theta_ {\mathrm {L R}}\right), \mathrm {V S S S} \left(\mathbf {X} _ {\mathrm {R L}}, \Theta_ {\mathrm {R L}}\right), \tag {6} \\ \operatorname {V S S S} \left(\mathbf {X} _ {\mathrm {T B}}, \Theta_ {\mathrm {T B}}\right), \operatorname {V S S S} \left(\mathbf {X} _ {\mathrm {B T}}, \Theta_ {\mathrm {B T}}\right)) \\ \end{array} +$$ + +Where: + +- $\mathbf{X}_{\mathrm{LR}}$ , $\mathbf{X}_{\mathrm{RL}}$ , $\mathbf{X}_{\mathrm{TB}}$ , and $\mathbf{X}_{\mathrm{BT}}$ represent the input tensors scanned in the respective directions. +- $\Theta_{\mathrm{LR}}$ , $\Theta_{\mathrm{RL}}$ , $\Theta_{\mathrm{TB}}$ , and $\Theta_{\mathrm{BT}}$ represents the parameters of the VSSS block for each direction. +- The output of each Mamba operator is reshaped again to $(B, H, W, \frac{C}{4})$ , and concatenated back to form the token sequence $\mathbf{X}_{\mathrm{GM}}$ , again of the size $(B, H, W, C)$ . + +# 3.3.3. Channel Affinity Modulation (CAM) + +On its own, the Grouped Mamba operator may have a disadvantage in the form of limited information exchange across channels, given the fact that each operator in the group only operates over $\frac{C}{4}$ channels. To encourage the exchange of information across channels, we propose a Channel Affinity Modulation operator, which recalibrates channel-wise feature responses to enhance the representation power of the network. In this block, we first average pool the input to calculate the channel statistics as shown in Eq. 7. + +$$ +\operatorname {C h a n n e l S t a t} \left(\mathbf {X} _ {\text {i n}}\right) = \operatorname {A v g P o o l} \left(\mathbf {X} _ {\text {i n}}\right) \tag {7} +$$ + +where $\mathbf{X}_{\mathrm{in}}$ is the input tensor, and AvgPool represents the global average pooling operation. Next comes the affinity calculation operation as shown in Eq. 8. + +$$ +\operatorname {A f f i n i t y} \left(\mathbf {X} _ {\text {i n}}\right) = \sigma \left(W _ {2} \delta \left(W _ {1} \text {C h a n n e l S t a t} \left(\mathbf {X} _ {\text {i n}}\right)\right)\right) \tag {8} +$$ + +where $\delta$ and $\sigma$ represent non-linearity functions, and $W_{1}$ and $W_{2}$ are learnable weights. The role of $\sigma$ is to assign an importance weight to each channel to compute the affinity. The result of the affinity calculation is used to recalibrate the output of the Grouped Mamba operator, as shown in Eq. 9. + +$$ +\mathbf {X} _ {\mathrm {C A M}} = \operatorname {C A M} \left(\mathbf {X} _ {\mathrm {G M}}, \text {A f f i n i t y} \left(\mathbf {X} _ {\mathrm {i n}}\right)\right) = \mathbf {X} _ {\mathrm {G M}} \cdot \text {A f f i n i t y} \left(\mathbf {X} _ {\mathrm {i n}}\right) \tag {9} +$$ + +where $\mathbf{X}_{\mathrm{CAM}}$ is the recalibrated output, $\mathbf{X}_{\mathrm{GM}}$ is the concatenated output of the four VSSS groups from Eq. 6, $\mathbf{X}_{\mathrm{in}}$ is the input tensor, and Affinity $(\mathbf{X}_{\mathrm{in}})$ are the channel-wise attention scores obtained from the channel affinity calculation operation in Eq. 8. + +While the average pooling and affinity procedure employed by the CAM module resembles the Squeeze-and-Excitation (SE) block [26], it introduces a distinct mechanism tailored explicitly for cross-channel attention within multi-group transformations. Specifically, CAM allows inter-group information exchange to overcome the inherent limitations of the "Grouped Mamba Operator," which inherently restricts interactions within individual groups. In contrast, SE blocks typically focus on recalibrating a single feature group and have not yet been investigated within the context of Mamba-based architectures. + +# 3.4. Distilled Loss Function + +As mentioned earlier in the motivation in Sec. 3, the Mamba training is unstable when scaled to large models [46]. To mitigate this issue, we propose to utilize a distillation objective alongside the standard cross-entropy objective. Knowledge distillation involves training a student model to learn from a teacher model's behavior by minimizing a combination of the classification loss and distillation loss. The distillation loss is computed using the cross-entropy objective between the logits of the teacher and student models. Given the logits $(Z_{s})$ from the student model, logits $(Z_{t})$ from a teacher model (RegNetY-16G [48] in our case), the ground truth label $y$ , and the hard decision of the teacher $y_{\mathrm{t}} = \operatorname{argmax}_{c} Z_{\mathrm{t}}(c)$ , the joint loss function is defined as shown in Eq. 10. + +$$ +\mathcal {L} _ {\text {t o t a l}} = \alpha \mathcal {L} _ {\mathrm {C E}} \left(Z _ {s}, y\right) + (1 - \alpha) \mathcal {L} _ {\mathrm {C E}} \left(Z _ {s}, y _ {\mathrm {t}}\right). \tag {10} +$$ + +where $\mathcal{L}_{\mathrm{CE}}$ is the cross-entropy objective and $\alpha$ is the weighting parameter. We demonstrate in the supplementary material that incorporating the distilled loss enhances training stability, resulting in consistent performance improvements for larger model variants. + +# 4. Experiments + +# 4.1. Image Classification + +Settings: The image classification experiments are based on ImageNet-1K [9], which comprising of over 1.28 million training images and 50K validation images, spanning 1,000 categories. Following [38], we train our models for using the AdamW [39] optimizer and a cosine decay learning rate scheduler for 300 epochs, including a 20 epoch warm-up. The total batch size is set to 1024, with models trained on 8x A100 GPUs, each with 80GB of CUDA memory. Optimizer betas are set to (0.9, 0.999); momentum is set to 0.9, and + +
MethodToken mixingImage size#Param.FLOPsTop-1 acc.
RegNetY-8G [48]Conv224239M8.0G81.7
RegNetY-16G [48]Conv224284M16.0G82.9
EffNet-B4 [57]Conv380219M4.2G82.9
EffNet-B5 [57]Conv456230M9.9G83.6
DeiT-S [58]Attention224222M4.6G79.8
DeiT-B [58]Attention224286M17.5G81.8
DeiT-B [58]Attention384286M55.4G83.1
ConvNeXt-T [37]Conv224229M4.5G82.1
ConvNeXt-S [37]Conv224250M8.7G83.1
ConvNeXt-B [37]Conv224289M15.4G83.8
Swin-T [36]Attention224228M4.6G81.3
Swin-S [36]Attention224250M8.7G83.0
Swin-B [36]Attention224288M15.4G83.5
ViM-S [70]SSM224226M-80.5
VMamba-T [35]SSM224231M4.9G82.5
VMamba-S [35]SSM224250M8.7G83.6
VMamba-B [35]SSM224289M15.4G83.9
LocalVMamba-T [27]SSM224226M5.7G82.7
LocalVMamba-S [27]SSM224250M11.4G83.7
EfficientVMamba-B [47]SSM224233M4.0G81.8
GroupMamba-TSSM224223M4.5G83.3
GroupMamba-SSSM224234M7.0G83.9
GroupMamba-BSSM224257M14G84.5
+ +Table 1. Performance comparison of GroupMamba models with state-of-the-art convolution-based, attention-based, and SSM-based models on ImageNet-1K [9]. Our models demonstrate better trade-off between accuracy and parameters. + +an initial learning rate of $1 \times 10^{-3}$ is used with a weight decay of 0.05. Label smoothing of 0.1 is used alongside the distillation objective (see Sec. 3.4). + +Results: Tab. 1 presents a comparison of our proposed GroupMamba models (T, S, B) with various state-of-the-art methods. The GroupMamba models exhibit a notable balance of accuracy and computational efficiency. GroupMamba-T achieves a top-1 accuracy of $83.3\%$ with 23 million parameters and 4.5 GFLOPs, outperforming ConvNeXt-T [37] and Swin-T [36] by $1.2\%$ and $2.0\%$ , respectively, with fewer parameters. Additionally, GroupMamba-T surpasses the recently introduced SSM models, outperforming VMamba-T [35] and LocalVMamba-T [27] by $0.8\%$ and $0.6\%$ , respectively, while using $26\%$ fewer parameters than VMamba-T. GroupMamba-S, with 34 million parameters and 7.0 GFLOPs, achieves an accuracy of $83.9\%$ , surpassing VMamba-S [35], Swin-S [36], and EfficientVMamba-B [47]. The performance is better than LocalVMamba-S [27] by $0.2\%$ with $32\%$ fewer parameters. Further + +more, GroupMamba-B achieves an accuracy of $84.5\%$ with only 57 million parameters and 14 GFLOPs, exceeding VMamba-B [35] by $0.6\%$ while using $36\%$ fewer parameters. + +# 4.2. Object Detection and Instance Segmentation + +Settings: We evaluate the performance of GroupMamba-T for object detection on the MS-COCO 2017 dataset [33]. Our method is based on the Mask R-CNN $1 \times$ schedule [22] detector with the hyperparameters as used for Swin [36]. We use the AdamW [39] optimizer and train Mask-RCNN with GroupMamba-T backbone for 12 epochs. The backbone is initialized and fine-tuned from the ImageNet-1K [9]. We use an initial learning rate of $1 \times 10^{-4}$ and decay by a factor of 10 at epochs 9 and 11. FLOPs are computed for an input dimension of $1280 \times 800$ . + +Results: Tab. 2 shows the results of GroupMamba-T, comparing it against various state-of-the-art models for object detection and instance segmentation using the Mask R-CNN framework on the MS-COCO dataset. Our model + +
Detection & Instance SegmentationSemantic Segmentation
Backbone\(AP^b\)\(AP_{50}^b\)\(AP_{75}^b\)\(AP^m\)\(AP_{50}^m\)\(AP_{75}^m\)#param.FLOPsmIoU (SS)mIoU (MS)
ResNet-50 [21]38.258.841.434.755.737.244M260G42.142.8
Swin-T [36]42.765.246.839.362.242.248M267G44.445.8
ConvNeXt-T [37]44.266.648.340.163.342.848M262G46.046.7
VMamba-T [35]47.469.552.042.766.346.050M270G48.348.6
LocalVMamba-T [27]46.768.750.842.265.745.545M291G47.949.1
GroupMamba-T47.669.852.142.966.546.340M279G48.649.2
+ +Table 2. Comparison of model performance on dense prediction tasks: Object detection and instance segmentation results on MS-COCO [33] using Mask R-CNN $1 \times$ schedule [22], and semantic segmentation results on ADE20K [69] using UperNet [64]. 'SS' and 'MS' denote single-scale and multi-scale evaluations, respectively. $AP^b$ and $AP^m$ represent box and mask AP. + +achieves box AP $(\mathrm{AP}^{\mathrm{b}})$ of 47.6 and mask AP $(\mathrm{AP}^{\mathrm{m}})$ of 42.9. It surpasses ResNet-50 [21], Swin-T [38], ConvNeXt-T [37]. In addition, GroupMamba-T has competitive performance compared to VMamba-T [35] and LocalVMamba-T [27], with less $20\%$ parameters compared to VMamba-T. Fig. 3 (first row) displays qualitative examples of object detection and instance segmentation. GroupMamba-T accurately detects and segments the targets in various scenes. More qualitative examples are presented in the supplementary material. + +# 4.3. Semantic Segmentation + +Settings: We also evaluate the performance of GroupMamba-T for semantic segmentation on the ADE20K [69] dataset. The framework is based on the UperNet [64] architecture, and we follow the same hyperparameters as used for the Swin [36] backbone. More specifically, we use the AdamW [39] optimizer for a total of $160k$ iterations with an initial learning rate of $6 \times 10^{-5}$ . The default resolution in our experiments is $512 \times 512$ . + +Results: The GroupMamba-T model demonstrates favorable performance in semantic segmentation compared to various state-of-the-art methods, as presented in Tab. 2. GroupMamba-T achieves a mIoU of 48.6 in single-scale and 49.2 in multi-scale evaluation. This outperforms ResNet-50 [21], Swin-T [36], and ConvNeXt-T [37]. Additionally, GroupMamba-T exceeds the performance of the recent SSM methods, including ViM-S [70], VMamba-T [35], and LocalVMamba [27]. Fig. 3 (second row) shows qualitative examples of GroupMamba-T. These examples demonstrate our model's ability to accurately segment various classes for indoor and outdoor scenes. More qualitative examples are presented in the supplementary material. + +# 4.4. Ablation Study + +Fig. 4 shows the impact of each proposed contribution in terms of top-1 accuracy, number of parameters, and throughput, compared to other SSM-based methods. GroupMamba-T with 4-D scanning, comprising 22M pa + +rameters, achieves a top-1 accuracy of $82.30\%$ and a throughput of 803. By applying a unidirectional 1D scan across $N / 4$ channels in four directions—left-to-right, right-to-left, top-to-bottom, and bottom-to-top instead of the full 4-D scanning across all $N$ channels, the throughput significantly increased from 803 to 1125, with only $0.1\%$ drop in accuracy and the same number of parameters. + +The integration of the CAM module further elevates the top-1 accuracy from $82.20\%$ to $82.50\%$ , with a minor reduction in throughput (from 1125 to 1069). Finally, incorporating the proposed distillation-based loss pushes the top-1 accuracy to $83.30\%$ , while preserving the throughput at 1069. Compared to Vim-S [70], GroupMamba-T demonstrates a more efficient design, achieving a $2.8\%$ improvement in top-1 accuracy with $1.5 \times$ higher throughput, all while utilizing fewer parameters. Compared to LocalVMamba-T [27], GroupMamba-T has a $0.6\%$ higher accuracy in top-1 accuracy, with $3 \times$ faster and smaller number of parameters. Regarding VMamba-T V1 [35], our model achieves a $1.1\%$ gain in top-1 accuracy with a comparable number of parameters while being faster by $2.5 \times$ . Likewise, when compared to VMamba-T V2 [35], GroupMamba-T shows marginally faster throughput, an increase of $0.8\%$ in top-1 accuracy, and a $26\%$ improvement in parameter efficiency. + +# 5. Conclusion and Future Work + +In this paper, we tackle the computational inefficiencies and stability challenges associated with visual SSMs for computer vision tasks by introducing a novel layer called Modulated Group Mamba. We also propose a multi-directional scanning method that improves parameter efficiency by scanning in four spatial directions and leveraging Channel Affinity Modulation (CAM) operator to enhance feature aggregation across channels. To stabilize training, especially for larger models, we employ a distillation-based training objective. Our experiments demonstrate that the proposed GroupMamba models outperform recent SSMs while being more efficient in terms of parameters and throughput. + +![](images/09b62771340ec4d4030353f603514516fdfbe5387746140dd9d4122e29ce54d2.jpg) + +![](images/da2a316358c6c2d53adab810a1b1ec4cc7fc6e5db43558b1e5930baa0da64e0d.jpg) + +![](images/d8a213e6b0d90ee246b24517e02f6ead2e2688e20ea24a5ef30a07c3efe7cd4b.jpg) + +![](images/725e975a5183ff536345f942bf1202b9dab271f0a583a5b83db82235b4ced26b.jpg) + +![](images/7abdf0fe15b45fd586572fd678ad348894fccfc7bf4419eb3d4ec9f05b71bfdd.jpg) +Figure 3. Qualitative results of GroupMamba-T for object detection and instance segmentation (first row) on the MS-COCO val. set and semantic segmentation (second row) on ADE20k val. set. + +![](images/35fd1a1b27a8983c307e7da1ca4177e2fabef60722f752e6901ee90b8b52e27a.jpg) + +![](images/2688256e5287a06e5bff1f4982f4048e5b125befe6956b0e46c2f26cdb675263.jpg) + +![](images/532b405f8ab83e9501f66695fa6f89285f02c17f1359011dd4bccb58be324608.jpg) + +![](images/068dae68919f292af74b8db9cac5893173bd5ecf4a417d7ce8e94b46f8a81f0a.jpg) +Figure 4. Comparison of GroupMamba variants and SSM-based methods in top-1 accuracy on ImageNet-1k [9] and computational efficiency in terms of throughput and number of parameters. The throughput (number of predicted samples per second) is measured using a single NVIDIA A100 GPU with a batch size of 128 for all methods. + +Our research has focused on image classification, object detection, and segmentation. To further validate and extend the generalization ability of our method, we aim to explore additional downstream tasks, such as video recogni + +tion and time-series data applications. Evaluating the Modulated Group Mamba layer in these contexts will help to uncover its potential benefits and limitations, providing deeper insights and guiding further improvements. + +# 6. Acknowledgments + +Syed Talal Wasim and Juergen Gall have been supported by the Federal Ministry of Education and Research (BMBF) under grant no. 01IS22094A WEST-AI and the ERC Consolidator Grant FORHUE (101044724). + +# References + +[1] Jimmy Lei Ba, Jamie Ryan Kiros, and Geoffrey E. Hinton. Layer normalization. arxiv preprint, arXiv:1607.06450, 2016. 4 +[2] Tom Brown, Benjamin Mann, Nick Ryder, et al. Language models are few-shot learners. In NeurIPS, 2020. 1 +[3] Nicolas Carion, Francisco Massa, Gabriel Synnaeve, Nicolas Usunier, Alexander Kirillov, and Sergey Zagoruyko. 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