Add Batch 914b9152-510c-431c-b06a-7b4fbca15ebe data

.gitattributes

@@ -4829,3 +4829,66 @@ saved_model/**/* filter=lfs diff=lfs merge=lfs -text
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2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_content_list.json

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+    {
+        "type": "text",
+        "text": "Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Chamin Hewa Koneputugodage<sup>1</sup> Yizhak Ben-Shabat<sup>1,2</sup> Dylan Campbell<sup>1</sup> Stephen Gould<sup>1</sup>",
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+    {
+        "type": "text",
+        "text": "<sup>1</sup>The Australian National University <sup>2</sup>Technion Israel Institute of Technology",
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+            800,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "{chamin.hewa, dylan.campbell, stephen.gould}@anu.edu.au sitzikbs@gmail.com",
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+    },
+    {
+        "type": "text",
+        "text": "Abstract",
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+        "text": "A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface reconstruction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sampled from the surface of a shape by a scanner. A major issue occurs when the shape's geometry is very different from the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF values. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme facilitates a deformation from an easy problem to the difficult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging.",
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+    {
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Point cloud reconstruction using a neural signed distance function (SDF) is a popular approach due to its simplicity and flexibility. Such methods show impressive performance improvements for cases with significant noise, outliers, missing regions or misalignment [20]. However, they are still unable to outperform classical methods on clean and relatively dense input data [20, 25], especially when the shape exhibits challenging geometry. For example, thin surfaces near each other (see Fig. 1 bottom) or large concave regions with small openings (see Fig. 1 top).",
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+        "type": "text",
+        "text": "We address the task of reconstruction from raw point clouds, i.e., without ground-truth normal vectors. We observe that the standard loss formulation used for the task",
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+            "Input"
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+        "image_caption": [
+            "SDF Baseline"
+        ],
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+        "img_path": "images/630c853cfb726aa5c3097518dbdad5c801e86ef4e46b0de497bc5180cf3bdb89.jpg",
+        "image_caption": [
+            "Ours",
+            "Figure 1. Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right)."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose",
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+    },
+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+            2,
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+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "<sup>1</sup>To avoid confusion, in this paper we use the term normal direction to refer to vectors in the normalized gradient field of the SDF and descent direction for the negative gradient of the loss function.",
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+    },
+    {
+        "type": "page_number",
+        "text": "21456",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "image",
+        "img_path": "images/e8ebb0b1e94055c8da1407da7f88459c925bf1d73f6ee2fc30e51637f273fde0.jpg",
+        "image_caption": [
+            "No Guidance",
+            "Small Steps (between 2a and 2b)",
+            "Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points  $\\mathcal{X}$  are black, the guiding points  $\\mathcal{V}$  are green, and the network's level sets are drawn as contour lines with the zero level set  $\\mathcal{R}$  in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to  $\\mathcal{X}$ . (1c) The network only makes local changes near  $\\mathcal{X}$ , gradually interpolating  $\\mathcal{X}$  by adding complexity. (1d-e)  $\\mathcal{X}$  is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius  $\\delta_0$ . Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are:",
+        "bbox": [
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "1. a point-guided optimization approach for surface reconstruction from point clouds without normals;",
+            "2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and",
+            "3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches."
+        ],
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            76,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22].",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Our method follows a line of work that attempts to",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "21457",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3. Preliminaries",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Notation and Definitions",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We denote the Euclidean inner product as  $\\langle p,q\\rangle = p^{\\mathsf{T}}q$ , the Euclidean distance as  $d(p,q) = \\| p - q\\| _2$ , a unit vector as  $\\hat{v} = v / \\| v\\|$ , the cosine similarity between two vectors as  $s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle$ , and the distance from a point  $p$  to a set  $A$  by  $d(p,A) = d_A(p) = \\inf_{q\\in A}d(p,q)$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The chamfer distance  $d_{C}$  is a common measure of the distance between two discrete point sets  $P$  and  $Q$ , defined by the average of two one-sided chamfer distances",
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+    {
+        "type": "equation",
+        "text": "\n$$\nd _ {C} (P, Q) = \\frac {1}{2} \\left(d _ {\\vec {C}} (P, Q) + d _ {\\vec {C}} (Q, P)\\right) \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "each averaging the distance over one set to the other set",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nd _ {\\vec {C}} (P, Q) = \\frac {1}{| P |} \\sum_ {p \\in P} d (p, Q). \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The chamfer distance can also be used between two surfaces,  $A$  and  $B$ , in which case the chamfer distance is taken over uniform samplings,  $U_A \\sim U(A)$  and  $U_B \\sim U(B)$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "A signed distance function (SDF)  $F_{\\mathcal{V}}: \\mathcal{D} \\to \\mathbb{R}$  of a bounded, open volume  $\\mathcal{V} \\subset \\mathcal{D}$  is a scalar function defined everywhere on  $\\mathcal{D}$ .  $F_{\\mathcal{V}}(z)$  is the distance from  $z$  to the closest point on the boundary  $\\partial \\mathcal{V}$ , with a negative sign if  $z \\in \\mathcal{V}$",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nF _ {\\mathcal {V}} (z) = (- 1) ^ {[ [ z \\in \\mathcal {V} ] ]} d (z, \\partial \\mathcal {V}) \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the Iverson bracket  $\\llbracket X\\rrbracket$  is 1 if  $X$  is true and 0 otherwise. The level set  $L_{a}$  is the set of points that have a signed distance of  $a$  from  $\\partial \\mathcal{V}$ , i.e.,",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nL _ {a} = \\{z \\in \\mathcal {D} \\mid F _ {\\mathcal {V}} (z) = a \\}. \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The exterior level set  $\\Omega_{a}$  ( $a > 0$ ) is the subset of  $L_{a}$  such that for each  $p \\in L_{a}$  there is a connected path from a point on the boundary of  $\\mathcal{D}$  to  $p$  that only intersects  $L_{a}$  at  $p$ .",
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+    },
+    {
+        "type": "text",
+        "text": "3.2. Problem Formulation",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let  $\\mathcal{X} = \\{x_i\\}_{i\\in I}$  be a point cloud sampled from a surface  $S\\subset \\mathcal{D}$  where  $\\mathcal{D}\\subset \\mathbb{R}^3$  is compact. We often refer to  $S$  as the target shape, and assume that it is watertight, i.e.,  $S = \\partial \\mathcal{V}$  of some open volume  $\\mathcal{V}\\subset \\mathcal{D}$ . We wish to reconstruct  $S$  from the point cloud  $\\mathcal{X} = \\{x_i\\}$ . Note that no per-point surface normals or scanner information is provided.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We choose to represent our reconstructed surface  $\\mathcal{R} \\subset \\mathcal{D}$  using an implicit neural representation  $\\Phi$ . Specifically we define  $\\mathcal{R} = \\{z \\in \\mathcal{D} \\mid \\Phi(z, \\theta) = 0\\}$  where  $\\theta$  are the parameters of the neural network  $\\Phi$ . Thus we want to minimize the chamfer distance between  $\\mathcal{S}$  and  $\\mathcal{R}$ . Since we do not know  $\\mathcal{S}$ , we instead compute the distance to our input points  $d_{C}(\\mathcal{X}, \\mathcal{R}) = d_{C}(\\mathcal{X}, U_{\\mathcal{R}})$ , where  $U_{\\mathcal{R}}$  is a uniform sampling from  $\\mathcal{R}$ . Furthermore we choose to optimize the implicit function  $\\Phi$  to approximate the true signed distance function  $F_{\\mathcal{V}}$  of the volume  $\\mathcal{V}$ . As  $\\mathcal{V}$  is unknown, during optimization we care about ensuring that  $\\Phi$  is a valid SDF to some open volume  $\\mathcal{U}$  for which  $\\mathcal{X}$  is an approximate sampling, i.e.,  $\\Phi \\approx F_{\\mathcal{U}}$  and  $d_{C}(\\mathcal{X}, \\partial \\mathcal{U})$  is small (note  $\\partial \\mathcal{U} = \\mathcal{R}$ ). Thus our overall optimization problem is",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l l} \\operatorname {m i n i m i z e} _ {\\theta} & d _ {C} (\\mathcal {X}, \\partial \\mathcal {U}) \\\\ \\text {s u b j e c t t o} & \\Phi (x, \\theta) = F _ {\\mathcal {U}} (x). \\end{array} \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for  $\\Phi$ , and are fairly smooth (unlike indicator functions). This helps with regularizing  $\\mathcal{R}$  and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27].",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "21458",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.3. Neural SDF Formulation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck).",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {X}) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) | \\tag {6}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {e i k}} (\\theta) = \\sum_ {z \\in \\mathcal {D}} | \\| \\nabla_ {z} \\Phi (z, \\theta) \\| _ {2} - 1 | \\tag {7}\n$$\n",
+        "text_format": "latex",
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| x _ {\\mathcal {R}} ^ {\\star} (z) - x _ {\\mathcal {X}} ^ {\\star} (z) \\| _ {2} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            143,
+            463,
+            468,
+            494
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $x_{\\mathcal{R}}^{\\star}(z) = z - \\Phi(z)\\widehat{\\nabla_z\\Phi(z)}$  and  $x_{\\mathcal{X}}^{\\star}(z) = \\arg \\min_{x\\in \\mathcal{X}}d(z,x)$ . The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss  $\\mathcal{L}_{\\mathrm{ZLS}}$  gives a perfect descent direction to the target SDF values for the points in  $\\mathcal{X}$ . However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss  $\\mathcal{L}_{\\mathrm{eik}}$  guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point  $z\\in \\mathcal{D}$ , if the network's current normal directions in the region around  $z$  is in the opposite direction to what the target SDF normals are around  $z$ , then at  $z$  this loss does not guide towards the target SDF values. The neural pull loss  $\\mathcal{L}_{\\mathrm{pull}}$  has two value-gradient pairs that will minimize its loss (one where the normal points towards  $x_{\\mathcal{X}}^{\\star}$  and one where it points away), so the loss will guide towards the closer one, which may not be the target.",
+        "bbox": [
+            75,
+            503,
+            468,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so  $\\mathcal{L}_{\\mathrm{eik}}$  and  $\\mathcal{L}_{\\mathrm{pull}}$  guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are",
+        "bbox": [
+            75,
+            780,
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+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/010afb844fbfe24e3cf7bb6e4af5c2972544629a95bc1c4aa059ff075d825bc7.jpg",
+        "image_caption": [
+            "Figure 3. Surface  $\\mathcal{S}$  and surrounding surface  $\\mathcal{R}$ , with outward normal directions for some points on  $\\mathcal{S}$  shown, and which ones are SIONs relative to  $\\mathcal{R}$  shown in red."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            602,
+            92,
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+            220
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left).",
+        "bbox": [
+            498,
+            287,
+            890,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Shape Reachability",
+        "text_level": 1,
+        "bbox": [
+            500,
+            358,
+            683,
+            375
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface  $\\mathcal{R}$  surrounding the target shape's surface  $S$ . One way of quantifying whether the normal directions are similar is to determine if points on  $S$  can \"reach\"  $\\mathcal{R}$  by travelling in their outward normal direction (see Fig. 3). If  $S$  has large concavities and the outward surface normal of most points in that concavity does not reach  $\\mathcal{R}$  before it self-intersects, then the current normal directions of the network are likely to be poor.",
+        "bbox": [
+            498,
+            382,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "More formally, if  $P_{\\mathcal{S}}$  and  $P_{\\mathcal{R}}$  are samplings of  $\\mathcal{S}$  and  $\\mathcal{R}$  and for each  $p \\in P_{\\mathcal{S}}$  we have a known outward unit normal  $n_p$ , then for a point  $p \\in P_{\\mathcal{S}}$  we can construct around the outward normal a thin cylinder",
+        "bbox": [
+            498,
+            578,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {C} _ {p} = \\{z \\in \\mathcal {D} \\mid \\| p + t n _ {p} - z \\| \\leq \\varepsilon , \\langle z - p, n _ {p} \\rangle \\geq 0 \\}. \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            506,
+            647,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "By the assumption of  $\\mathcal{R}$  surrounding  $S$  and  $P_{\\mathcal{R}}$  being a dense sampling of  $\\mathcal{R}$ , we note that  $\\mathcal{C}_p \\cap P_{\\mathcal{R}} \\neq \\emptyset$ . Then we consider  $p$  to have a self-intersecting outward normal (SION) with respect to  $P_{\\mathcal{R}}$  if its normal direction intersects its own shape before it intersects  $\\mathcal{R}$ :  $\\exists p' \\in P_{\\mathcal{S}}$  such that  $p' \\in \\mathcal{C}_p$  and  $\\forall q \\in \\mathcal{C} \\cap P_{\\mathcal{R}}$  we have that  $\\| p - p' \\|_2 < \\| p - q \\|$ . We then use the percentage of points in  $p_{\\mathcal{S}}$  that have SIONs with respect to  $P_{\\mathcal{R}}$  as a measure of how dissimilar the geometry of  $S$  is to  $\\mathcal{R}$ , which we denote  $\\mathrm{SION}(S; \\mathcal{R})$ , where a high value indicates dissimilarity.",
+        "bbox": [
+            498,
+            672,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "When  $\\mathcal{R}$  is not specified and  $S$  is clear from context, we will use SION as a shorthand for  $\\mathrm{SION}(S; \\mathcal{R})$ , with  $\\mathcal{R}$  assumed to be any sphere surrounding  $S$ . The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization",
+        "bbox": [
+            498,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "21459",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "from a spherical initialization is likely to be difficult.",
+        "bbox": [
+            76,
+            90,
+            426,
+            106
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Point-Guided SDF",
+        "text_level": 1,
+        "bbox": [
+            76,
+            122,
+            256,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The key idea of our method is to slowly converge the surface of reconstruction  $\\mathcal{R}$  towards the input points  $\\mathcal{X}$  until it interpolates  $\\mathcal{X}$ , while maintaining  $\\Phi$  as a valid SDF to the volume enclosed by  $\\mathcal{R}$  (see Fig. 2). We do this by guiding  $\\mathcal{R}$  towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points  $\\mathcal{Y}$ , which represent the surface  $\\mathcal{R}$ , a small distance towards  $\\mathcal{X}$  (Fig. 4c) and then optimize  $\\Phi$  to interpolate the new  $\\mathcal{Y}$  positions, thus defining the new surface of reconstruction  $\\mathcal{R}$  over which  $\\mathcal{Y}$  is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1.",
+        "bbox": [
+            76,
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+            316
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since each movement of the guiding points is small, the geometry of the moved guiding points  $\\mathcal{V}$  should be similar to the network's current surface  $\\mathcal{R}$ , and  $\\mathrm{SION}(\\mathcal{V};\\mathcal{R})$  should be low. Thus optimizing the network to reconstruct the updated  $\\mathcal{V}$  should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points.",
+        "bbox": [
+            76,
+            316,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In Sec. 4.1 we outline how to move the guiding points  $\\mathcal{Y}$  one step closer to the input points  $\\mathcal{X}$  (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network  $\\Phi$  to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework.",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Preprocessing  $\\mathcal{X}$ . Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius  $\\delta_{\\mathcal{X}}$  conservatively by calculating the distance to the four closest neighbors for each  $x \\in \\mathcal{X}$  and averaging the highest  $5\\%$  of all such distances. We use this radius extensively in our method.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Initialization. We first initialize our network to the exterior level set of radius  $\\delta_{\\mathrm{init}} = 16\\delta_{\\mathcal{X}}$ . We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Moving the Guiding Points",
+        "text_level": 1,
+        "bbox": [
+            76,
+            693,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We now describe how to move the guiding points  $y \\in \\mathcal{V}$  towards the input points  $\\mathcal{X}$ . At a high level, each step we move  $\\mathcal{V}$  closer to an exterior level set of radius  $\\delta$ ,  $\\Omega_{\\delta}$ , and when  $\\mathcal{R}$  has converged to  $\\Omega_{\\delta}$  we reduce  $\\delta$  (see Algorithm 1).",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Since we are moving  $y \\in \\mathcal{V}$  to guide the surface  $\\mathcal{R}$ , we only move each  $y$  in the inwards normal direction of  $\\mathcal{R}$ . Next, since we are moving towards an exterior level set  $\\Omega_{\\delta}$  of  $\\mathcal{X}$ , for each  $y \\in \\mathcal{V}$  we find the closest input point in the inwards normal direction  $x^{\\star}(y) \\in \\mathcal{X}$ , and use this to determine the target point  $\\omega^{\\star}(y)$  on  $\\Omega_{\\delta}$  that we move towards. Finally, since we want to move the surface  $\\mathcal{R}$  slowly, we have a maximum step size for each movement.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Closest point in the inward direction. We first define  $x^{\\star}(y)$  (see Fig. 4a-b). As we are moving in the inward normal direction, i.e.,  $-n_y$  where  $n_y = \\widehat{\\nabla_y\\Phi(y)}$ , we want to move  $y$  based on the closest point  $x \\in \\mathcal{X}$  in the inward normal direction  $-n_y$ . We define the inward normal definition by setting a cosine similarity threshold  $a_y \\geq 0$  to define a cone  $C_y$  supported at  $y$  emanating in the direction  $-n_y$ ,",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nC _ {y} = \\left\\{z \\mid s (- n _ {y}, z - y) \\geq a _ {y} \\right\\}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "However as  $y$  gets very close to points in  $\\mathcal{X}$ , it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball  $H_{y}$  of radius  $2\\delta_{\\mathcal{X}}$  containing points close to  $y$",
+        "bbox": [
+            496,
+            234,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nH _ {y} = \\left\\{z \\mid \\| x - y \\| _ {2} \\leq 2 \\delta_ {\\mathcal {X}} \\wedge s (- n _ {y}, z - y) \\geq 0 \\right\\}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            509,
+            304,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Thus our target point  $x^{\\star}(y)$  is given by",
+        "bbox": [
+            500,
+            329,
+            759,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nx ^ {\\star} (y) = \\underset {x \\in \\mathcal {X} \\cap \\left(C _ {y} \\cup H _ {y}\\right)} {\\arg \\min } \\| x - y \\| _ {2}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            581,
+            354,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Moving towards  $\\Omega_{\\delta}$ . As  $x^{\\star}(y)$  is our closest (inward) point, a reasonable location for a point in  $\\Omega_{\\delta}$  can be computed by moving  $\\delta$  away from  $x^{\\star}$  towards  $y$",
+        "bbox": [
+            496,
+            390,
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+            436
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\omega^ {\\star} (y) = \\left(\\| x ^ {\\star} - y \\| _ {2} - \\delta\\right) \\widehat {\\left(x ^ {\\star} - y\\right)}. \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            445,
+            890,
+            465
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We move towards  $\\omega^{\\star}$  with a maximum step size of  $s_m$  so that the movement step is small and easy to optimize. Thus our final point  $y^\\prime$  (see Fig. 4b) is",
+        "bbox": [
+            496,
+            473,
+            890,
+            518
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ny ^ {\\prime} = y - \\operatorname {c l i p} (\\langle \\omega^ {\\star} (y), - n _ {y} \\rangle , s _ {m}) n _ {y} \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            573,
+            527,
+            890,
+            546
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\operatorname{clip}(a, \\varepsilon)$  projects  $a$  to the interval  $[- \\varepsilon, \\varepsilon]$ .",
+        "bbox": [
+            496,
+            553,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Reducing  $\\delta$ . After initialization, we set  $\\delta = \\delta_0$  as our next target level set. Once  $\\mathcal{V}$  has finished moving towards  $\\Omega_{\\delta}$  and  $\\mathcal{R}$  has converged, we decrease the current  $\\delta$  by half and start moving  $\\mathcal{V}$  towards the new exterior level set. We do this until  $\\delta$  reaches  $\\delta_f$ . We use  $\\delta_0 = 4\\delta_{\\mathcal{X}}$ ,  $\\delta_f = \\delta_{\\mathcal{X}}$ . We then abandon  $\\mathcal{V}$  and optimize directly on  $\\mathcal{X}$ .",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Optimizing the Network",
+        "text_level": 1,
+        "bbox": [
+            500,
+            675,
+            723,
+            691
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We now have the points  $\\mathcal{V}$  to guide where our new surface should be. Furthermore, we have an approximate normal  $n_y$  for each  $y\\in \\mathcal{V}$  given by  $\\Phi$ , whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF",
+        "bbox": [
+            496,
+            698,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\tilde {F} _ {\\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \\geq 0 ]} d (z, y (z)) \\tag {15}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            535,
+            796,
+            890,
+            816
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $y(z) = \\arg \\min_{y\\in \\mathcal{Y}}d(z,y)$  and  $s(p,q) = \\langle \\hat{p},\\hat{q}\\rangle$  is cosine similarity. We guide towards these values using",
+        "bbox": [
+            496,
+            825,
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+            857
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\mathrm {s d f}} (\\theta , \\mathcal {X}) = \\sum_ {z \\in \\mathcal {D}} \\| \\Phi (z, \\theta) - \\tilde {F} _ {\\mathcal {V}} (z) \\| _ {2}. \\tag {16}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            563,
+            864,
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+            897
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "21460",
+        "bbox": [
+            478,
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+            519,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/f50af9a8f7141de56ff4290caeb08665cf3282a23906da5a2ee08e01ce4a8bd3.jpg",
+        "image_caption": [
+            "Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network  $\\Phi$  (the contours) and our guiding points  $\\mathcal{V}$  (the green points), for each  $y\\in \\mathcal{V}$  we calculate a half ball  $H_{y}$  and a cone  $C_y$  in the inside normal direction to find an input points  $x\\in \\mathcal{X}$  (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point  $x^{\\star}(y)\\in \\mathcal{X}$  within  $H_{y}\\cap \\mathcal{C}_{y}$ , and use this to calculate the new position  $y^\\prime$  for each  $y\\in \\mathcal{V}$  (shown for all points). (c) The result after each  $y\\in \\mathcal{V}$  has been moved. (d) The network  $\\Phi$  is optimized on the new guiding points, and  $\\mathcal{V}$  is resampled to densely cover the new zero level set  $\\mathcal{R}$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            88,
+            890,
+            250
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Furthermore, our input points  $\\mathcal{X}$  should be at distance  $\\delta$  from  $\\mathcal{Y}$  and should be inside, so we add a loss term",
+        "bbox": [
+            75,
+            351,
+            470,
+            382
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) = \\sum_ {x \\in \\mathcal {X}} | \\Phi (x, \\theta) + \\delta |. \\tag {17}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            151,
+            388,
+            468,
+            421
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Thus our overall loss term formulation is",
+        "bbox": [
+            76,
+            429,
+            349,
+            444
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} (\\theta , \\mathcal {X}, \\mathcal {Y}, \\delta) = \\mathcal {L} _ {\\mathrm {z l s}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {i n p u t}} (\\theta , \\mathcal {X}, \\delta) + \\mathcal {L} _ {\\mathrm {e i k}} (\\theta) +\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            86,
+            455,
+            459,
+            470
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\mathcal {L} _ {\\mathrm {s d f}}} (\\theta , \\mathcal {Y}) + \\mathcal {L} _ {\\text {p u l l}} (\\theta , \\mathcal {Y}). \\tag {18}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            210,
+            473,
+            468,
+            491
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement.",
+        "bbox": [
+            75,
+            500,
+            468,
+            530
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Finally, we resample  $\\mathcal{V}$  in the new zero level set  $\\mathcal{R}$  (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when  $\\Phi$  has converged for  $\\delta = \\delta_f$ ), we optimize  $\\Phi$  on the input points  $\\mathcal{X}$  using the loss in Eq. (18). Here we do not use the approximate SDF term, as  $\\mathcal{X}$  is likely to have more imperfections that our guiding points.",
+        "bbox": [
+            75,
+            531,
+            468,
+            622
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Point-Guided SDF"
+        ],
+        "code_body": "1: procedure PG-SDF( $\\mathcal{X}$ )  \n2: Center  $\\mathcal{X}$ , scale  $\\mathcal{X}$  and compute sampling radius  $\\delta_{\\mathcal{X}}$   \n3:  $\\mathcal{Y}, \\mathcal{N}_{\\mathcal{Y}}, \\Phi \\gets$  Initialization  $(\\mathcal{X}, \\delta_{\\mathrm{init}})$   \n4:  $\\delta \\gets \\delta_0$   \n5: while  $\\delta \\geq \\delta_f$  do  \n6: Move  $\\mathcal{Y}$  using Eq. (14)  \n7: Optimize  $\\Phi$  to match  $\\mathcal{Y}$   \n8: Resample  $\\mathcal{Y}$  on new  $\\mathcal{R}$   \n9: Query  $\\Phi$  for normals  $\\mathcal{N}_{\\mathcal{Y}}$   \n10: if  $\\Phi$ 's zero level set has not changed then  \n11:  $\\delta \\gets \\frac{1}{2} \\delta$   \n12: end if  \n13: end while  \n14: Optimize  $\\Phi$  on  $\\mathcal{X}$   \n15: return  $\\Phi$   \n16: end procedure",
+        "bbox": [
+            81,
+            655,
+            468,
+            878
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.3. Interpretation as a Homotopy Method",
+        "text_level": 1,
+        "bbox": [
+            500,
+            351,
+            828,
+            368
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem  $M(\\theta) = 0$  for  $\\theta$ , and instead consider the homotopy map  $H(\\theta, t) = tM(\\theta) + (1 - t)N(\\theta)$  where  $N(\\theta) = 0$  is easy to solve and  $t \\in [0,1]$ . This forms a homotopy between the problems  $M(\\theta) = H(\\theta, 1)$  and  $N(\\theta) = H(\\theta, 0)$  as we can now continuously deform one problem into the other by varying  $t$ . By taking small steps along the zero path, the trajectory of points  $(\\theta, t)$  for which  $H(\\theta, t) = 0$ , we can reach the solution to  $M(\\theta)$ .",
+        "bbox": [
+            496,
+            375,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "For our method, we start by solving the easier problem  $\\mathcal{L}(\\theta, \\mathcal{Y}_0) = 0$  where  $\\mathcal{Y}_0$  is our initial set of guiding points. Our goal is to solve the hard problem  $\\mathcal{L}(\\theta, \\mathcal{X}) = 0$ . To see that our method is a homotopy method, note that our guiding points  $\\mathcal{Y}$  are facilitating a topological homotopy from  $\\mathcal{Y}_0$  to our input points  $\\mathcal{X}$ . Thus we can parameterize our zero path using  $\\mathcal{Y}$ . It is given by  $(\\theta(\\mathcal{Y}), t(\\mathcal{Y}))$  where",
+        "bbox": [
+            498,
+            526,
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+            632
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\theta (\\mathcal {Y}) \\text {s a t i s f i e s} \\mathcal {L} (\\theta (\\mathcal {Y}), \\mathcal {Y}) = 0 \\tag {19}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            602,
+            642,
+            890,
+            659
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nt (\\mathcal {Y}) = \\frac {d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right) - d _ {C} \\left(\\mathcal {Y} , \\mathcal {X}\\right)}{d _ {C} \\left(\\mathcal {Y} _ {0} , \\mathcal {X}\\right)}. \\tag {20}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            584,
+            662,
+            890,
+            694
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Note that at initialization  $\\mathcal{V} = \\mathcal{V}_0$  and we have  $t(\\mathcal{V}_0) = 0$ , while at termination  $\\mathcal{V} = \\mathcal{X}$  and we have  $t(\\mathcal{X}) = 1$ . Each time we update  $\\mathcal{V}$ , we are traversing the zero path. If we take  $n$  steps to reach the final exterior level set of radius  $\\delta_{\\mathcal{X}}$ , then we visit  $n + 2$  points along the zero path parameterized by the sequence  $\\mathcal{V}_0, \\mathcal{V}_1, \\ldots, \\mathcal{V}_n, \\mathcal{X}$ .",
+        "bbox": [
+            496,
+            703,
+            890,
+            794
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To see why this works well in practice, we need to show that solving  $H(\\theta(\\mathcal{Y}_{k+1}), t(\\mathcal{Y}_{k+1}))$  for  $\\theta(\\mathcal{Y}_{k+1})$  given  $\\theta(\\mathcal{Y}_k)$  is easy, and solving  $H(\\theta(\\mathcal{Y}_0), t(\\mathcal{Y}_0))$  for  $\\theta(\\mathcal{Y}_0)$  is easy. To see the former, note that we move our guiding points  $\\mathcal{V}$  only a small distance from  $\\mathcal{V}_k$  to  $\\mathcal{V}_{k+1}$ , and that  $\\mathrm{SION}(\\mathcal{Y}_{k+1};\\mathcal{V}_k)$  is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the",
+        "bbox": [
+            496,
+            795,
+            890,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "21461",
+        "bbox": [
+            478,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/3f37c96cba253e0cec25111a07694230dd9d9b2e04f27bb1bdbdf1e1c07d8226.jpg",
+        "image_caption": [
+            "Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets  $\\Omega_{\\delta}$ . Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            93,
+            468,
+            375
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "latter, when  $\\delta_{\\mathrm{init}} \\gg \\delta_{\\mathcal{X}}$  we can estimate good normals for  $\\mathcal{Y}_0$  by taking the displacement from the closest input point. With good normal estimates,  $\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}$  is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement.",
+        "bbox": [
+            75,
+            453,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5. Results",
+        "text_level": 1,
+        "bbox": [
+            76,
+            573,
+            163,
+            588
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement.",
+        "bbox": [
+            75,
+            598,
+            470,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/4716caa984dfd79357e62fdf329a7ebc97edc28374b6f13447499f348c1c706f.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td colspan=\"5\">Squared Chamfer ↓</td><td colspan=\"2\">IoU ↑</td></tr><tr><td>NN nx</td><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>SPSR [22]</td><td>× T</td><td>5.44e-5</td><td>1.97e-5</td><td>5.06e-4</td><td>0.9926</td><td>0.9956</td><td>0.0105</td></tr><tr><td>IGR [15]</td><td>✓ T</td><td>5.12e-4</td><td>1.13e-4</td><td>2.15e-3</td><td>0.8102</td><td>0.8480</td><td>0.1519</td></tr><tr><td>SIREN [41]</td><td>✓ T</td><td>1.03e-4</td><td>5.28e-5</td><td>1.93e-4</td><td>0.8268</td><td>0.9097</td><td>0.2329</td></tr><tr><td>FFN [43]</td><td>✓ T</td><td>9.12e-5</td><td>8.65e-5</td><td>3.36e-5</td><td>0.8218</td><td>0.8396</td><td>0.0989</td></tr><tr><td>NSP [46]</td><td>× T</td><td>5.36e-5</td><td>4.06e-5</td><td>3.64e-5</td><td>0.8973</td><td>0.9230</td><td>0.0871</td></tr><tr><td>DiGS+N [5]</td><td>✓ T</td><td>2.74e-4</td><td>2.32e-5</td><td>9.90e-4</td><td>0.9200</td><td>0.9774</td><td>0.1992</td></tr><tr><td>SDF+N†</td><td>✓ T</td><td>3.97e-5</td><td>2.22e-5</td><td>8.98e-5</td><td>0.9915</td><td>0.9951</td><td>0.0141</td></tr><tr><td>Ours+N</td><td>✓ T</td><td>2.43e-5</td><td>2.15e-5</td><td>1.66e-5</td><td>0.9932</td><td>0.9955</td><td>0.0076</td></tr><tr><td>SPSR [22]</td><td>× E</td><td>3.76e-3</td><td>4.37e-5</td><td>1.14e-2</td><td>0.7187</td><td>0.9761</td><td>0.3767</td></tr><tr><td>SIREN [41]</td><td>✓ ×</td><td>3.08e-4</td><td>2.58e-4</td><td>3.26e-4</td><td>0.3085</td><td>0.2952</td><td>0.2014</td></tr><tr><td>SAL [2]</td><td>✓ ×</td><td>1.14e-3</td><td>2.11e-4</td><td>3.63e-3</td><td>0.4030</td><td>0.3944</td><td>0.2722</td></tr><tr><td>DiGS [5]</td><td>✓ ×</td><td>1.32e-4</td><td>2.55e-5</td><td>4.73e-4</td><td>0.9390</td><td>0.9764</td><td>0.1262</td></tr><tr><td>SAP [39]</td><td>× ×</td><td>4.09e-4</td><td>2.46e-5</td><td>2.60e-3</td><td>0.9118</td><td>0.9923</td><td>0.2002</td></tr><tr><td>OG-S [25]</td><td>✓ ×</td><td>3.75e-5</td><td>2.17e-5</td><td>8.24e-5</td><td>0.9615</td><td>0.9871</td><td>0.1048</td></tr><tr><td>OG-N [25]</td><td>✓ ×</td><td>5.07e-5</td><td>2.57e-5</td><td>9.39e-5</td><td>0.9593</td><td>0.9870</td><td>0.1057</td></tr><tr><td>SDF†</td><td>✓ ×</td><td>1.84e-4</td><td>8.15e-4</td><td>2.95e-3</td><td>0.5490</td><td>0.5245</td><td>0.3572</td></tr><tr><td>SDF+N†</td><td>✓ E</td><td>2.48e-2</td><td>5.89e-5</td><td>5.63e-3</td><td>0.6817</td><td>0.9671</td><td>0.3990</td></tr><tr><td>Ours+N</td><td>✓ E</td><td>2.79e-2</td><td>4.79e-5</td><td>6.79e-2</td><td>0.7017</td><td>0.9721</td><td>0.3876</td></tr><tr><td>Ours</td><td>✓ ×</td><td>3.72e-5</td><td>2.40e-5</td><td>5.39e-5</td><td>0.9729</td><td>0.9896</td><td>0.0676</td></tr></table>",
+        "bbox": [
+            498,
+            88,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network.  $n_x$ : uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation.",
+        "bbox": [
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+            368,
+            893,
+            425
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses  $\\mathcal{L}_{\\mathrm{zls}}$ ,  $\\mathcal{L}_{\\mathrm{eik}}$ , and  $\\mathcal{L}_{\\mathrm{pull}}$  while 'SDF+N' additionally uses  $\\mathcal{L}_{\\widetilde{\\mathrm{sdf}}}$  and  $\\mathcal{L}_{\\mathrm{normal}}$  [15]. We also evaluate our methods with estimated normals (using Open3D [50]).",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.1. Surface Reconstruction on ShapeNet",
+        "text_level": 1,
+        "bbox": [
+            498,
+            542,
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+            558
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.2. Challenging High-SION Shapes",
+        "text_level": 1,
+        "bbox": [
+            498,
+            680,
+            779,
+            696
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "21462",
+        "bbox": [
+            478,
+            944,
+            517,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2629c760daeac6654d94d308a61910968f8fd786c3aadcbf08e3c9b0494a5077.jpg",
+        "image_caption": [
+            "Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            87,
+            464,
+            282
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/14061386cdc55fc9bcba1fcae0414483b5192cbb30307615467d4be380c7f490.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Method</td><td rowspan=\"2\">NN</td><td rowspan=\"2\">\\(n_x\\)</td><td colspan=\"3\">Squared Chamfer ↓</td><td colspan=\"3\">IoU ↑</td></tr><tr><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>SPSR [22]</td><td>×</td><td>T</td><td>3.98e-5</td><td>3.92e-5</td><td>1.80e-5</td><td>0.9798</td><td>0.9848</td><td>0.0222</td></tr><tr><td>DiGS+N [5]</td><td>✓</td><td>T</td><td>2.09e-4</td><td>7.42e-5</td><td>2.91e-4</td><td>0.8160</td><td>0.8764</td><td>0.2119</td></tr><tr><td>\\(\\text{SDF}+\\text{N}^{\\dagger}\\)</td><td>✓</td><td>T</td><td>1.11e-4</td><td>4.84e-5</td><td>1.95e-4</td><td>0.9733</td><td>0.9854</td><td>0.0409</td></tr><tr><td>Ours+N</td><td>✓</td><td>T</td><td>4.16e-5</td><td>3.89e-5</td><td>1.86e-5</td><td>0.9822</td><td>0.9865</td><td>0.0148</td></tr><tr><td>SPSR [22]</td><td>×</td><td>E</td><td>5.83e-3</td><td>1.25e-3</td><td>1.16e-2</td><td>0.3290</td><td>0.1802</td><td>0.3445</td></tr><tr><td>DiGS [5]</td><td>✓</td><td>×</td><td>4.34e-4</td><td>1.71e-4</td><td>5.34e-4</td><td>0.7108</td><td>0.8196</td><td>0.2536</td></tr><tr><td>SAP [39]</td><td>×</td><td>×</td><td>1.28e-4</td><td>5.84e-5</td><td>1.99e-4</td><td>0.7616</td><td>0.8872</td><td>0.2665</td></tr><tr><td>OG-S [25]</td><td>✓</td><td>×</td><td>1.31e-4</td><td>6.50e-5</td><td>1.79e-4</td><td>0.7651</td><td>0.9219</td><td>0.2512</td></tr><tr><td>\\(\\text{SDF}^{\\dagger}\\)</td><td>✓</td><td>×</td><td>1.29e-3</td><td>7.75e -4</td><td>1.43e-3</td><td>0.3413</td><td>0.2617</td><td>0.2292</td></tr><tr><td>\\(\\text{SDF}+\\text{N}^{\\dagger}\\)</td><td>✓</td><td>E</td><td>5.32e-2</td><td>4.51e-3</td><td>7.03e-2</td><td>0.2896</td><td>0.1977</td><td>0.3288</td></tr><tr><td>Ours+N</td><td>✓</td><td>E</td><td>4.89e-2</td><td>7.32e-3</td><td>6.25e-2</td><td>0.3173</td><td>0.2362</td><td>0.3259</td></tr><tr><td>Ours</td><td>✓</td><td>×</td><td>5.51e-5</td><td>4.87e-5</td><td>3.12e-5</td><td>0.9153</td><td>0.9598</td><td>0.0906</td></tr></table>",
+        "bbox": [
+            76,
+            354,
+            468,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/73e3c84f5cfceb9dfee1fbe8d7ed3a35567e845e31f98e5c6c93e66e5c2f59f0.jpg",
+        "table_caption": [
+            "Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network.  $n_x$ : uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Guidance y0 yδ0 δf</td><td colspan=\"3\">Squared Chamfer ↓</td><td colspan=\"3\">IoU ↑</td></tr><tr><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>× × - -</td><td>2.41e-3</td><td>1.18e-3</td><td>2.65e-3</td><td>0.2795</td><td>0.2255</td><td>0.2078</td></tr><tr><td>✓ × - -</td><td>2.63e-4</td><td>1.91e-4</td><td>2.31e-4</td><td>0.5694</td><td>0.6091</td><td>0.2278</td></tr><tr><td>✓ ✓ 4</td><td>2</td><td>9.89e-5</td><td>7.70e-5</td><td>7.95e-5</td><td>0.8657</td><td>0.9163</td></tr><tr><td>✓ ✓ 1</td><td>1</td><td>8.08e-5</td><td>7.52e-5</td><td>5.66e-5</td><td>0.8538</td><td>0.9386</td></tr><tr><td>✓ ✓ 4</td><td>1</td><td>5.51e-5</td><td>4.87e-5</td><td>3.12e-5</td><td>0.9153</td><td>0.9598</td></tr></table>",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablation results on the 20 highest SION ShapeNet shapes.  $\\mathcal{V}_0$ : uses our SDF initialization strategy instead of spherical initialization [15].  $\\mathcal{V}$ : uses our point guidance strategy.  $\\delta_0 / \\delta_f$ : starting and final level set radii, given in multiples of  $\\delta_{\\mathcal{X}}$ .",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.3. Ablation Study and Runtime",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/c1e7de4b29b4865bd25a908524a6750fb0526d66715e27e1961c33cf06a65f65.jpg",
+        "image_caption": [
+            "Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as  $\\times$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            501,
+            85,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when  $\\delta_f = 2\\delta_{\\mathcal{X}}$ ) harms performance, as does guiding straight to the final level set target ( $\\delta_0 = \\delta_{\\mathcal{X}}$ ) without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy.",
+        "bbox": [
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+            340,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid ( $>99\\%$  of the parameters).",
+        "bbox": [
+            496,
+            462,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "6. Discussion and Conclusion",
+        "text_level": 1,
+        "bbox": [
+            500,
+            580,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes.",
+        "bbox": [
+            496,
+            606,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii  $\\delta_{i}$ .",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. We would also like to thank Mingda Xu for discussions about homotopy methods.",
+        "bbox": [
+            496,
+            806,
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+        "page_idx": 7
+    },
+    {
+        "type": "page_number",
+        "text": "21463",
+        "bbox": [
+            478,
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
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2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/688fa8a6-01ab-4bec-bd21-cd592944e2e4_origin.pdf

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2024/Small Steps and Level Sets_ Fitting Neural Surface Models with Point Guidance/full.md

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+# Small Steps and Level Sets: Fitting Neural Surface Models with Point Guidance
+
+Chamin Hewa Koneputugodage<sup>1</sup> Yizhak Ben-Shabat<sup>1,2</sup> Dylan Campbell<sup>1</sup> Stephen Gould<sup>1</sup>
+
+<sup>1</sup>The Australian National University <sup>2</sup>Technion Israel Institute of Technology
+
+{chamin.hewa, dylan.campbell, stephen.gould}@anu.edu.au sitzikbs@gmail.com
+
+# Abstract
+
+A neural signed distance function (SDF) is a convenient shape representation for many tasks, such as surface reconstruction, editing and generation. However, neural SDFs are difficult to fit to raw point clouds, such as those sampled from the surface of a shape by a scanner. A major issue occurs when the shape's geometry is very different from the structural biases implicit in the network's initialization. In this case, we observe that the standard loss formulation does not guide the network towards the correct SDF values. We circumvent this problem by introducing guiding points, and use them to steer the optimization towards the true shape via small incremental changes for which the loss formulation has a good descent direction. We show that this point-guided homotopy-based optimization scheme facilitates a deformation from an easy problem to the difficult reconstruction problem. We also propose a metric to quantify the difference in surface geometry between a target shape and an initial surface, which helps indicate whether the standard loss formulation is guiding towards the target shape. Our method outperforms previous state-of-the-art approaches, with large improvements on shapes identified by this metric as particularly challenging.
+
+# 1. Introduction
+
+Point cloud reconstruction using a neural signed distance function (SDF) is a popular approach due to its simplicity and flexibility. Such methods show impressive performance improvements for cases with significant noise, outliers, missing regions or misalignment [20]. However, they are still unable to outperform classical methods on clean and relatively dense input data [20, 25], especially when the shape exhibits challenging geometry. For example, thin surfaces near each other (see Fig. 1 bottom) or large concave regions with small openings (see Fig. 1 top).
+
+We address the task of reconstruction from raw point clouds, i.e., without ground-truth normal vectors. We observe that the standard loss formulation used for the task
+
+![](images/568962fbab4f03017bee74cb8c54b85aa592cebfe0a129c6eced93b2fd7b8793.jpg)
+
+![](images/314fa1430c52073e9e1807122b3c06b6acf3414afce1c190ba025a80c7b2fce7.jpg)  
+Input
+
+![](images/90ed2fd69971a6d971725560340f526be3dd1c2c5f4ab4f672cfc1cf32bd20ac.jpg)
+
+![](images/d3f655f805eb6267a50b7ba88133c8a0e54bbf7cb9ad1ab81ae84f063b9db526.jpg)  
+SDF Baseline
+
+![](images/0e4e6965f1e6a3fbb171ec5f0f9b0ce132432aa1497383c6454b50f4313c9759.jpg)
+
+![](images/630c853cfb726aa5c3097518dbdad5c801e86ef4e46b0de497bc5180cf3bdb89.jpg)  
+Ours  
+Figure 1. Given a point cloud without ground-truth normals (left), neural SDF optimization for surface fitting frequently gets trapped in local minima (middle). Note that these two shapes have geometry very different to a sphere, which causes the loss right after spherical initialization to not provide a good descent direction towards the target shape (see Sec. 3.3). Our point-guided homotopy-based approach provides a principled way to avoid this issue and improve reconstruction quality (right).
+
+does not give a good descent direction towards the target SDF values, especially when the initialization does not align with the target geometry. Since most methods initialize to a sphere to bias the optimization result towards a bounded shape, and rely on this bias to find a good descent direction, their performance can be poor if the input shape has very different geometry to a sphere (see Fig. 1).
+
+Instead we propose a point-guided SDF (PG-SDF) approach, where we introduce guiding points to represent an intermediate surface for the optimization to target. By incrementally moving the guiding points towards the sampled input and optimizing the network to their new location, we ensure that the loss formulation gives a good descent direction during optimization. We eventually converge the guiding points to the input points, leading the optimization stably towards the target SDF. We also propose
+
+![](images/e8ebb0b1e94055c8da1407da7f88459c925bf1d73f6ee2fc30e51637f273fde0.jpg)  
+No Guidance  
+Small Steps (between 2a and 2b)  
+Figure 2. Reconstructing a 2D surface using a neural SDF, without (1a-e) and with (2a-e,3a-f) our proposed point guidance. Note that our point guidance has two parts, converging to level sets (2) and taking small steps in between (3). The input points  $\mathcal{X}$  are black, the guiding points  $\mathcal{V}$  are green, and the network's level sets are drawn as contour lines with the zero level set  $\mathcal{R}$  in bold. (1a-b) The network deforms from the sphere initialization to one whose zero level set is close to  $\mathcal{X}$ . (1c) The network only makes local changes near  $\mathcal{X}$ , gradually interpolating  $\mathcal{X}$  by adding complexity. (1d-e)  $\mathcal{X}$  is fully interpolated, but the result is unsatisfactory. (2a) Our initialization. (2b-d) Our method after convergence to each intermediate level set. (2e) Our method after optimizing on the input points. (3a-f) The small steps taken by our method while reaching the first intermediate level set of radius  $\delta_0$ . Each row shows a single step, where the guiding points are first moved a short distance (left) and then the network is optimized to match this (right).
+
+a metric—the percentage of self-intersecting outward normals (SION%)—to quantify the difference between the surface geometry of a target shape and that of another surface, such as the sphere initialization. We use this metric to determine which shapes are likely to be difficult for neural SDF methods, and why the optimization steps in our method are robust. Our contributions are:
+
+1. a point-guided optimization approach for surface reconstruction from point clouds without normals;  
+2. a metric to quantify differences between surfaces, which can be used to identify the most challenging shapes to reconstruct; and  
+3. an interpretation of the algorithm as a homotopy method, providing a justification for the design decisions and insight into the failure modes of existing approaches.
+
+# 2. Related Work
+
+Surface reconstruction from point clouds is a fundamental problem in computer vision. We restrict our attention to methods that optimize using generic priors, rather than methods that learn reconstruction priors from a dataset [19, 45] and are sensitive to domain shift.
+
+Early approaches [1, 7, 10, 24] directly triangulated point clouds, with provable guarantees given dense input points with no defects. However, the limitation of vertices being input points make them impractical for even small levels of imperfection [6], and the result is often not watertight. A less restrictive class of approaches is implicit field methods
+
+[9, 22, 23, 32, 34], where an implicit function is defined over the domain to represent the reconstructed surface. Such methods often use a carefully defined set of basis functions, and optimize for an energy function with respect to the basis function parameters. However they usually rely on normal vectors as inputs, allowing efficient optimization with linear solvers, such as Poisson Surface Reconstruction [23] and its screened version [22].
+
+Neural implicit methods, which were popularised by DeepSDF [35] and Occupancy Networks [29], are promising as they provide more modeling and optimization flexibility. Rather than creating basis functions tailored to the input, the network is fixed and can adapt its representational ability through optimization. Furthermore, as they are optimized by gradient descent, they can work with any differentiable loss. This flexibility has led to learned shape spaces that allow for strong learned biases and interpolation [21, 26, 35, 47]. However, while many neural methods are able to perform better than non-neural approaches when the input has defects, they often perform worse when the data is clean and dense [20]. A major issue is that gradient descent optimization is not guaranteed to converge to a global optimum. Furthermore, many methods for the surface reconstruction task [2-4, 15, 41] use losses that are difficult for gradient descent to optimize. As the reason these losses are hard to optimize is fundamental to our method, we examine this issue and related loss formulations in Sec. 3.3.
+
+Our method follows a line of work that attempts to
+
+improve upon these issues for reconstruction from points clouds without normals. There are three major methods that are competitive for this task, DiGS [5], SAP [39] and OG-INR [25]. DiGS and OG-INR are neural SDF methods. In order to avoid the difficulties of SDF optimization, DiGS [5] changes the optimization landscape by adding strong regularization at the start, and slowly annealing the regularization to gently change the optimization landscape back to the correct one. OG-INR [25] avoids local minima by first discretizing the problem and solving for inside-outside labels. It then uses this discrete solution to get an approximate SDF that makes it easier to optimize the original SDF. SAP [39] does not use neural methods or SDFs, and instead minimizes a chamfer loss on points and normals directly. This is related to our approach as we also use points and SDF-derived normals to guide our SDF optimization. However, rather than using a chamfer loss, which we find gets trapped in bad local minima, we use a more nuanced strategy to move our guiding points, outlined in Sec. 4.1.
+
+Another highly related approach is Point2Mesh [17], which deforms an enclosing mesh onto the point cloud. Like SAP, they use a chamfer loss to guide the deformation, however they note that this loss does not easily enter concavities. To address this, they introduce a beam gap loss, which guides mesh vertices towards input points in the inward normal direction if they are not already well matched by chamfer distance. Our deformation strategy, in contrast, is based purely on explicitly matching points in the inward normal direction. Our approach also avoids a major shortcoming of Point2Mesh, the reconstruction output must have the same genus as the initial mesh.
+
+# 3. Preliminaries
+
+# 3.1. Notation and Definitions
+
+We denote the Euclidean inner product as  $\langle p,q\rangle = p^{\mathsf{T}}q$ , the Euclidean distance as  $d(p,q) = \| p - q\| _2$ , a unit vector as  $\hat{v} = v / \| v\|$ , the cosine similarity between two vectors as  $s(p,q) = \langle \hat{p},\hat{q}\rangle$ , and the distance from a point  $p$  to a set  $A$  by  $d(p,A) = d_A(p) = \inf_{q\in A}d(p,q)$ .
+
+The chamfer distance  $d_{C}$  is a common measure of the distance between two discrete point sets  $P$  and  $Q$ , defined by the average of two one-sided chamfer distances
+
+$$
+d _ {C} (P, Q) = \frac {1}{2} \left(d _ {\vec {C}} (P, Q) + d _ {\vec {C}} (Q, P)\right) \tag {1}
+$$
+
+each averaging the distance over one set to the other set
+
+$$
+d _ {\vec {C}} (P, Q) = \frac {1}{| P |} \sum_ {p \in P} d (p, Q). \tag {2}
+$$
+
+The chamfer distance can also be used between two surfaces,  $A$  and  $B$ , in which case the chamfer distance is taken over uniform samplings,  $U_A \sim U(A)$  and  $U_B \sim U(B)$ .
+
+A signed distance function (SDF)  $F_{\mathcal{V}}: \mathcal{D} \to \mathbb{R}$  of a bounded, open volume  $\mathcal{V} \subset \mathcal{D}$  is a scalar function defined everywhere on  $\mathcal{D}$ .  $F_{\mathcal{V}}(z)$  is the distance from  $z$  to the closest point on the boundary  $\partial \mathcal{V}$ , with a negative sign if  $z \in \mathcal{V}$
+
+$$
+F _ {\mathcal {V}} (z) = (- 1) ^ {[ [ z \in \mathcal {V} ] ]} d (z, \partial \mathcal {V}) \tag {3}
+$$
+
+where the Iverson bracket  $\llbracket X\rrbracket$  is 1 if  $X$  is true and 0 otherwise. The level set  $L_{a}$  is the set of points that have a signed distance of  $a$  from  $\partial \mathcal{V}$ , i.e.,
+
+$$
+L _ {a} = \{z \in \mathcal {D} \mid F _ {\mathcal {V}} (z) = a \}. \tag {4}
+$$
+
+The exterior level set  $\Omega_{a}$  ( $a > 0$ ) is the subset of  $L_{a}$  such that for each  $p \in L_{a}$  there is a connected path from a point on the boundary of  $\mathcal{D}$  to  $p$  that only intersects  $L_{a}$  at  $p$ .
+
+# 3.2. Problem Formulation
+
+Let  $\mathcal{X} = \{x_i\}_{i\in I}$  be a point cloud sampled from a surface  $S\subset \mathcal{D}$  where  $\mathcal{D}\subset \mathbb{R}^3$  is compact. We often refer to  $S$  as the target shape, and assume that it is watertight, i.e.,  $S = \partial \mathcal{V}$  of some open volume  $\mathcal{V}\subset \mathcal{D}$ . We wish to reconstruct  $S$  from the point cloud  $\mathcal{X} = \{x_i\}$ . Note that no per-point surface normals or scanner information is provided.
+
+We choose to represent our reconstructed surface  $\mathcal{R} \subset \mathcal{D}$  using an implicit neural representation  $\Phi$ . Specifically we define  $\mathcal{R} = \{z \in \mathcal{D} \mid \Phi(z, \theta) = 0\}$  where  $\theta$  are the parameters of the neural network  $\Phi$ . Thus we want to minimize the chamfer distance between  $\mathcal{S}$  and  $\mathcal{R}$ . Since we do not know  $\mathcal{S}$ , we instead compute the distance to our input points  $d_{C}(\mathcal{X}, \mathcal{R}) = d_{C}(\mathcal{X}, U_{\mathcal{R}})$ , where  $U_{\mathcal{R}}$  is a uniform sampling from  $\mathcal{R}$ . Furthermore we choose to optimize the implicit function  $\Phi$  to approximate the true signed distance function  $F_{\mathcal{V}}$  of the volume  $\mathcal{V}$ . As  $\mathcal{V}$  is unknown, during optimization we care about ensuring that  $\Phi$  is a valid SDF to some open volume  $\mathcal{U}$  for which  $\mathcal{X}$  is an approximate sampling, i.e.,  $\Phi \approx F_{\mathcal{U}}$  and  $d_{C}(\mathcal{X}, \partial \mathcal{U})$  is small (note  $\partial \mathcal{U} = \mathcal{R}$ ). Thus our overall optimization problem is
+
+$$
+\begin{array}{l l} \operatorname {m i n i m i z e} _ {\theta} & d _ {C} (\mathcal {X}, \partial \mathcal {U}) \\ \text {s u b j e c t t o} & \Phi (x, \theta) = F _ {\mathcal {U}} (x). \end{array} \tag {5}
+$$
+
+Why SDFs? We choose SDFs over other popular implicit functions like indicator or occupancy functions [22, 23, 29, 38] or unsigned distance functions (UDFs) [12, 16, 49] for several reasons. First, SDFs and UDFs constrain the possibilities for  $\Phi$ , and are fairly smooth (unlike indicator functions). This helps with regularizing  $\mathcal{R}$  and ensures that they can be represented by neural networks, which are biased to be smooth. Previous works have shown that neural SDFs empirically perform better than neural occupancy functions [51]. Second, SDFs allow for distance and direction to the surface queries, which we make use of in our algorithm. Last, the signed aspect of SDFs guarantee the watertight criteria compared to UDF, and make it easier to mesh using algorithms like marching cubes [27].
+
+# 3.3. Neural SDF Formulation
+
+Since neural SDFs are coordinate networks, each coordinate is processed independently. During gradient descent each coordinate seeks to minimize its loss locally, and is only affected by changes in nearby coordinates due to the network's inherent smoothness bias. Thus information propagation through the domain (from the smoothness bias) is slow, and optimization is only effective if the loss provides clear guidance. Specifically, if the descent direction of the loss with respect to its SDF input value at a coordinate gives an approximate descent direction towards the target SDF value at that coordinate. However whether or not the loss provides a good descent direction depends on whether the geometry of the current state of the network aligns with the geometry of the target shape (see Fig. 2 top left for when they do not align and thus optimization gets stuck).
+
+We now discuss this observation in relation to currently used neural SDF losses. When optimizing neural SDFs for point clouds without normals, the main losses are
+
+$$
+\mathcal {L} _ {\mathrm {z l s}} (\theta , \mathcal {X}) = \sum_ {x \in \mathcal {X}} | \Phi (x, \theta) | \tag {6}
+$$
+
+$$
+\mathcal {L} _ {\mathrm {e i k}} (\theta) = \sum_ {z \in \mathcal {D}} | \| \nabla_ {z} \Phi (z, \theta) \| _ {2} - 1 | \tag {7}
+$$
+
+$$
+\mathcal {L} _ {\text {p u l l}} (\theta , \mathcal {X}) = \sum_ {z \in \mathcal {D}} \| x _ {\mathcal {R}} ^ {\star} (z) - x _ {\mathcal {X}} ^ {\star} (z) \| _ {2} \tag {8}
+$$
+
+where  $x_{\mathcal{R}}^{\star}(z) = z - \Phi(z)\widehat{\nabla_z\Phi(z)}$  and  $x_{\mathcal{X}}^{\star}(z) = \arg \min_{x\in \mathcal{X}}d(z,x)$ . The first two losses were proposed by IGR [15] and the last one was proposed by Neural Pull [4] (further details in the supplement). The zero level set loss  $\mathcal{L}_{\mathrm{ZLS}}$  gives a perfect descent direction to the target SDF values for the points in  $\mathcal{X}$ . However, for other points in the domain, the loss formulation may not give a descent direction towards the target SDF value. The Eikonal loss  $\mathcal{L}_{\mathrm{eik}}$  guides towards scaling the SDF gradient, and does not change its direction unless forced to by the optimization of nearby points. Thus for a point  $z\in \mathcal{D}$ , if the network's current normal directions in the region around  $z$  is in the opposite direction to what the target SDF normals are around  $z$ , then at  $z$  this loss does not guide towards the target SDF values. The neural pull loss  $\mathcal{L}_{\mathrm{pull}}$  has two value-gradient pairs that will minimize its loss (one where the normal points towards  $x_{\mathcal{X}}^{\star}$  and one where it points away), so the loss will guide towards the closer one, which may not be the target.
+
+As a result, an important part of these methods is spherical initialization [2], where the network is initialized roughly to the SDF of a sphere. If the shape's geometry is similar to a sphere, then the initialized normal directions in the network are mostly in the correct direction, so  $\mathcal{L}_{\mathrm{eik}}$  and  $\mathcal{L}_{\mathrm{pull}}$  guide towards the correct SDF value. When the shape's geometry is very different to a sphere resulting in large regions where the initialized normal directions are
+
+![](images/010afb844fbfe24e3cf7bb6e4af5c2972544629a95bc1c4aa059ff075d825bc7.jpg)  
+Figure 3. Surface  $\mathcal{S}$  and surrounding surface  $\mathcal{R}$ , with outward normal directions for some points on  $\mathcal{S}$  shown, and which ones are SIONs relative to  $\mathcal{R}$  shown in red.
+
+very different to the target normal directions, then the loss does not provide a good descent direction in those regions. As a result, optimization often converges to a local minimum close to the initialization, such as in Fig. 2 (top left).
+
+# 3.4. Shape Reachability
+
+From the analysis in the previous subsection, we are interested in whether the current state of a network provides similar normal directions to the SDF of the target shape, so that the loss provides a good descent direction towards the target SDF values. Let us assume that the current state of the network is roughly the SDF to some surface  $\mathcal{R}$  surrounding the target shape's surface  $S$ . One way of quantifying whether the normal directions are similar is to determine if points on  $S$  can "reach"  $\mathcal{R}$  by travelling in their outward normal direction (see Fig. 3). If  $S$  has large concavities and the outward surface normal of most points in that concavity does not reach  $\mathcal{R}$  before it self-intersects, then the current normal directions of the network are likely to be poor.
+
+More formally, if  $P_{\mathcal{S}}$  and  $P_{\mathcal{R}}$  are samplings of  $\mathcal{S}$  and  $\mathcal{R}$  and for each  $p \in P_{\mathcal{S}}$  we have a known outward unit normal  $n_p$ , then for a point  $p \in P_{\mathcal{S}}$  we can construct around the outward normal a thin cylinder
+
+$$
+\mathcal {C} _ {p} = \{z \in \mathcal {D} \mid \| p + t n _ {p} - z \| \leq \varepsilon , \langle z - p, n _ {p} \rangle \geq 0 \}. \tag {9}
+$$
+
+By the assumption of  $\mathcal{R}$  surrounding  $S$  and  $P_{\mathcal{R}}$  being a dense sampling of  $\mathcal{R}$ , we note that  $\mathcal{C}_p \cap P_{\mathcal{R}} \neq \emptyset$ . Then we consider  $p$  to have a self-intersecting outward normal (SION) with respect to  $P_{\mathcal{R}}$  if its normal direction intersects its own shape before it intersects  $\mathcal{R}$ :  $\exists p' \in P_{\mathcal{S}}$  such that  $p' \in \mathcal{C}_p$  and  $\forall q \in \mathcal{C} \cap P_{\mathcal{R}}$  we have that  $\| p - p' \|_2 < \| p - q \|$ . We then use the percentage of points in  $p_{\mathcal{S}}$  that have SIONs with respect to  $P_{\mathcal{R}}$  as a measure of how dissimilar the geometry of  $S$  is to  $\mathcal{R}$ , which we denote  $\mathrm{SION}(S; \mathcal{R})$ , where a high value indicates dissimilarity.
+
+When  $\mathcal{R}$  is not specified and  $S$  is clear from context, we will use SION as a shorthand for  $\mathrm{SION}(S; \mathcal{R})$ , with  $\mathcal{R}$  assumed to be any sphere surrounding  $S$ . The two point clouds in Fig. 1 have a high SION, which indicates that their geometry is very different to a sphere and that optimization
+
+from a spherical initialization is likely to be difficult.
+
+# 4. Point-Guided SDF
+
+The key idea of our method is to slowly converge the surface of reconstruction  $\mathcal{R}$  towards the input points  $\mathcal{X}$  until it interpolates  $\mathcal{X}$ , while maintaining  $\Phi$  as a valid SDF to the volume enclosed by  $\mathcal{R}$  (see Fig. 2). We do this by guiding  $\mathcal{R}$  towards level sets (Fig. 2:2a-e) and taking small steps towards reaching each level set (Fig. 2:3a-f, Fig. 4). At each step we move guiding points  $\mathcal{Y}$ , which represent the surface  $\mathcal{R}$ , a small distance towards  $\mathcal{X}$  (Fig. 4c) and then optimize  $\Phi$  to interpolate the new  $\mathcal{Y}$  positions, thus defining the new surface of reconstruction  $\mathcal{R}$  over which  $\mathcal{Y}$  is resampled (Fig. 4d). Our full algorithm is shown in Algorithm 1.
+
+Since each movement of the guiding points is small, the geometry of the moved guiding points  $\mathcal{V}$  should be similar to the network's current surface  $\mathcal{R}$ , and  $\mathrm{SION}(\mathcal{V};\mathcal{R})$  should be low. Thus optimizing the network to reconstruct the updated  $\mathcal{V}$  should be robust (unlikely to converge to local minima) as the optimization is likely to have a clear descent direction from the loss at most points.
+
+In Sec. 4.1 we outline how to move the guiding points  $\mathcal{Y}$  one step closer to the input points  $\mathcal{X}$  (Fig. 4a-c). In Sec. 4.2 we outline how to optimize the network  $\Phi$  to interpolate the new guiding point locations (Fig. 4d). Finally, in Sec. 4.3 we analyze our method within the homotopy framework.
+
+Preprocessing  $\mathcal{X}$ . Following standard practice, we first center and (isotropically) scale the shape to fit in a centered ball. After scaling, we calculate the point cloud's approximate sampling radius  $\delta_{\mathcal{X}}$  conservatively by calculating the distance to the four closest neighbors for each  $x \in \mathcal{X}$  and averaging the highest  $5\%$  of all such distances. We use this radius extensively in our method.
+
+Initialization. We first initialize our network to the exterior level set of radius  $\delta_{\mathrm{init}} = 16\delta_{\mathcal{X}}$ . We provide intuition into why we can do this robustly in Sec. 4.3, and provide details on how to make this more efficient in the supplement.
+
+# 4.1. Moving the Guiding Points
+
+We now describe how to move the guiding points  $y \in \mathcal{V}$  towards the input points  $\mathcal{X}$ . At a high level, each step we move  $\mathcal{V}$  closer to an exterior level set of radius  $\delta$ ,  $\Omega_{\delta}$ , and when  $\mathcal{R}$  has converged to  $\Omega_{\delta}$  we reduce  $\delta$  (see Algorithm 1).
+
+Since we are moving  $y \in \mathcal{V}$  to guide the surface  $\mathcal{R}$ , we only move each  $y$  in the inwards normal direction of  $\mathcal{R}$ . Next, since we are moving towards an exterior level set  $\Omega_{\delta}$  of  $\mathcal{X}$ , for each  $y \in \mathcal{V}$  we find the closest input point in the inwards normal direction  $x^{\star}(y) \in \mathcal{X}$ , and use this to determine the target point  $\omega^{\star}(y)$  on  $\Omega_{\delta}$  that we move towards. Finally, since we want to move the surface  $\mathcal{R}$  slowly, we have a maximum step size for each movement.
+
+Closest point in the inward direction. We first define  $x^{\star}(y)$  (see Fig. 4a-b). As we are moving in the inward normal direction, i.e.,  $-n_y$  where  $n_y = \widehat{\nabla_y\Phi(y)}$ , we want to move  $y$  based on the closest point  $x \in \mathcal{X}$  in the inward normal direction  $-n_y$ . We define the inward normal definition by setting a cosine similarity threshold  $a_y \geq 0$  to define a cone  $C_y$  supported at  $y$  emanating in the direction  $-n_y$ ,
+
+$$
+C _ {y} = \left\{z \mid s (- n _ {y}, z - y) \geq a _ {y} \right\}. \tag {10}
+$$
+
+However as  $y$  gets very close to points in  $\mathcal{X}$ , it is unlikely that any of those nearby points stay within this cone. Thus we also consider the half ball  $H_{y}$  of radius  $2\delta_{\mathcal{X}}$  containing points close to  $y$
+
+$$
+H _ {y} = \left\{z \mid \| x - y \| _ {2} \leq 2 \delta_ {\mathcal {X}} \wedge s (- n _ {y}, z - y) \geq 0 \right\}. \tag {11}
+$$
+
+Thus our target point  $x^{\star}(y)$  is given by
+
+$$
+x ^ {\star} (y) = \underset {x \in \mathcal {X} \cap \left(C _ {y} \cup H _ {y}\right)} {\arg \min } \| x - y \| _ {2}. \tag {12}
+$$
+
+Moving towards  $\Omega_{\delta}$ . As  $x^{\star}(y)$  is our closest (inward) point, a reasonable location for a point in  $\Omega_{\delta}$  can be computed by moving  $\delta$  away from  $x^{\star}$  towards  $y$
+
+$$
+\omega^ {\star} (y) = \left(\| x ^ {\star} - y \| _ {2} - \delta\right) \widehat {\left(x ^ {\star} - y\right)}. \tag {13}
+$$
+
+We move towards  $\omega^{\star}$  with a maximum step size of  $s_m$  so that the movement step is small and easy to optimize. Thus our final point  $y^\prime$  (see Fig. 4b) is
+
+$$
+y ^ {\prime} = y - \operatorname {c l i p} (\langle \omega^ {\star} (y), - n _ {y} \rangle , s _ {m}) n _ {y} \tag {14}
+$$
+
+where  $\operatorname{clip}(a, \varepsilon)$  projects  $a$  to the interval  $[- \varepsilon, \varepsilon]$ .
+
+Reducing  $\delta$ . After initialization, we set  $\delta = \delta_0$  as our next target level set. Once  $\mathcal{V}$  has finished moving towards  $\Omega_{\delta}$  and  $\mathcal{R}$  has converged, we decrease the current  $\delta$  by half and start moving  $\mathcal{V}$  towards the new exterior level set. We do this until  $\delta$  reaches  $\delta_f$ . We use  $\delta_0 = 4\delta_{\mathcal{X}}$ ,  $\delta_f = \delta_{\mathcal{X}}$ . We then abandon  $\mathcal{V}$  and optimize directly on  $\mathcal{X}$ .
+
+# 4.2. Optimizing the Network
+
+We now have the points  $\mathcal{V}$  to guide where our new surface should be. Furthermore, we have an approximate normal  $n_y$  for each  $y\in \mathcal{V}$  given by  $\Phi$ , whose direction should be useful as the SION between the new position of the points relative to the previous positions is low. We use this to estimate an approximate SDF
+
+$$
+\tilde {F} _ {\mathcal {V}} (z) = (- 1) ^ {[ s (z - y (z), n _ {y (z)}) \geq 0 ]} d (z, y (z)) \tag {15}
+$$
+
+where  $y(z) = \arg \min_{y\in \mathcal{Y}}d(z,y)$  and  $s(p,q) = \langle \hat{p},\hat{q}\rangle$  is cosine similarity. We guide towards these values using
+
+$$
+\mathcal {L} _ {\mathrm {s d f}} (\theta , \mathcal {X}) = \sum_ {z \in \mathcal {D}} \| \Phi (z, \theta) - \tilde {F} _ {\mathcal {V}} (z) \| _ {2}. \tag {16}
+$$
+
+![](images/f50af9a8f7141de56ff4290caeb08665cf3282a23906da5a2ee08e01ce4a8bd3.jpg)  
+Figure 4. One iteration of Algorithm 1, steps 6-8. (a) Given the current value of our network  $\Phi$  (the contours) and our guiding points  $\mathcal{V}$  (the green points), for each  $y\in \mathcal{V}$  we calculate a half ball  $H_{y}$  and a cone  $C_y$  in the inside normal direction to find an input points  $x\in \mathcal{X}$  (black points) to move towards (shown for 3 points, with one highlighted in red). (b) We find the closest input point  $x^{\star}(y)\in \mathcal{X}$  within  $H_{y}\cap \mathcal{C}_{y}$ , and use this to calculate the new position  $y^\prime$  for each  $y\in \mathcal{V}$  (shown for all points). (c) The result after each  $y\in \mathcal{V}$  has been moved. (d) The network  $\Phi$  is optimized on the new guiding points, and  $\mathcal{V}$  is resampled to densely cover the new zero level set  $\mathcal{R}$ .
+
+Furthermore, our input points  $\mathcal{X}$  should be at distance  $\delta$  from  $\mathcal{Y}$  and should be inside, so we add a loss term
+
+$$
+\mathcal {L} _ {\text {i n p u t}} (\theta , \mathcal {X}, \delta) = \sum_ {x \in \mathcal {X}} | \Phi (x, \theta) + \delta |. \tag {17}
+$$
+
+Thus our overall loss term formulation is
+
+$$
+\mathcal {L} (\theta , \mathcal {X}, \mathcal {Y}, \delta) = \mathcal {L} _ {\mathrm {z l s}} (\theta , \mathcal {Y}) + \mathcal {L} _ {\text {i n p u t}} (\theta , \mathcal {X}, \delta) + \mathcal {L} _ {\mathrm {e i k}} (\theta) +
+$$
+
+$$
+\widetilde {\mathcal {L} _ {\mathrm {s d f}}} (\theta , \mathcal {Y}) + \mathcal {L} _ {\text {p u l l}} (\theta , \mathcal {Y}). \tag {18}
+$$
+
+Relevant details (e.g., loss term weightings, domain sampling procedure, optimizer settings) are in the supplement.
+
+Finally, we resample  $\mathcal{V}$  in the new zero level set  $\mathcal{R}$  (Fig. 4f) so that it densely samples it. After this process has finished (i.e., when  $\Phi$  has converged for  $\delta = \delta_f$ ), we optimize  $\Phi$  on the input points  $\mathcal{X}$  using the loss in Eq. (18). Here we do not use the approximate SDF term, as  $\mathcal{X}$  is likely to have more imperfections that our guiding points.
+
+Algorithm 1 Point-Guided SDF  
+1: procedure PG-SDF( $\mathcal{X}$ )  
+2: Center  $\mathcal{X}$ , scale  $\mathcal{X}$  and compute sampling radius  $\delta_{\mathcal{X}}$   
+3:  $\mathcal{Y}, \mathcal{N}_{\mathcal{Y}}, \Phi \gets$  Initialization  $(\mathcal{X}, \delta_{\mathrm{init}})$   
+4:  $\delta \gets \delta_0$   
+5: while  $\delta \geq \delta_f$  do  
+6: Move  $\mathcal{Y}$  using Eq. (14)  
+7: Optimize  $\Phi$  to match  $\mathcal{Y}$   
+8: Resample  $\mathcal{Y}$  on new  $\mathcal{R}$   
+9: Query  $\Phi$  for normals  $\mathcal{N}_{\mathcal{Y}}$   
+10: if  $\Phi$ 's zero level set has not changed then  
+11:  $\delta \gets \frac{1}{2} \delta$   
+12: end if  
+13: end while  
+14: Optimize  $\Phi$  on  $\mathcal{X}$   
+15: return  $\Phi$   
+16: end procedure
+
+# 4.3. Interpretation as a Homotopy Method
+
+One way to analyze this method is in the context of a homotopy method [33]. Here, we wish to solve a difficult problem  $M(\theta) = 0$  for  $\theta$ , and instead consider the homotopy map  $H(\theta, t) = tM(\theta) + (1 - t)N(\theta)$  where  $N(\theta) = 0$  is easy to solve and  $t \in [0,1]$ . This forms a homotopy between the problems  $M(\theta) = H(\theta, 1)$  and  $N(\theta) = H(\theta, 0)$  as we can now continuously deform one problem into the other by varying  $t$ . By taking small steps along the zero path, the trajectory of points  $(\theta, t)$  for which  $H(\theta, t) = 0$ , we can reach the solution to  $M(\theta)$ .
+
+For our method, we start by solving the easier problem  $\mathcal{L}(\theta, \mathcal{Y}_0) = 0$  where  $\mathcal{Y}_0$  is our initial set of guiding points. Our goal is to solve the hard problem  $\mathcal{L}(\theta, \mathcal{X}) = 0$ . To see that our method is a homotopy method, note that our guiding points  $\mathcal{Y}$  are facilitating a topological homotopy from  $\mathcal{Y}_0$  to our input points  $\mathcal{X}$ . Thus we can parameterize our zero path using  $\mathcal{Y}$ . It is given by  $(\theta(\mathcal{Y}), t(\mathcal{Y}))$  where
+
+$$
+\theta (\mathcal {Y}) \text {s a t i s f i e s} \mathcal {L} (\theta (\mathcal {Y}), \mathcal {Y}) = 0 \tag {19}
+$$
+
+$$
+t (\mathcal {Y}) = \frac {d _ {C} \left(\mathcal {Y} _ {0} , \mathcal {X}\right) - d _ {C} \left(\mathcal {Y} , \mathcal {X}\right)}{d _ {C} \left(\mathcal {Y} _ {0} , \mathcal {X}\right)}. \tag {20}
+$$
+
+Note that at initialization  $\mathcal{V} = \mathcal{V}_0$  and we have  $t(\mathcal{V}_0) = 0$ , while at termination  $\mathcal{V} = \mathcal{X}$  and we have  $t(\mathcal{X}) = 1$ . Each time we update  $\mathcal{V}$ , we are traversing the zero path. If we take  $n$  steps to reach the final exterior level set of radius  $\delta_{\mathcal{X}}$ , then we visit  $n + 2$  points along the zero path parameterized by the sequence  $\mathcal{V}_0, \mathcal{V}_1, \ldots, \mathcal{V}_n, \mathcal{X}$ .
+
+To see why this works well in practice, we need to show that solving  $H(\theta(\mathcal{Y}_{k+1}), t(\mathcal{Y}_{k+1}))$  for  $\theta(\mathcal{Y}_{k+1})$  given  $\theta(\mathcal{Y}_k)$  is easy, and solving  $H(\theta(\mathcal{Y}_0), t(\mathcal{Y}_0))$  for  $\theta(\mathcal{Y}_0)$  is easy. To see the former, note that we move our guiding points  $\mathcal{V}$  only a small distance from  $\mathcal{V}_k$  to  $\mathcal{V}_{k+1}$ , and that  $\mathrm{SION}(\mathcal{Y}_{k+1};\mathcal{V}_k)$  is small by construction. Thus, by the analysis in Secs. 3.3 and 3.4, the relative optimization problem is easy. To see the
+
+![](images/3f37c96cba253e0cec25111a07694230dd9d9b2e04f27bb1bdbdf1e1c07d8226.jpg)  
+Figure 5. Qualitative results on ShapeNet. Top: Intermediate results as our method converges to different level sets  $\Omega_{\delta}$ . Bottom: Comparison with other methods, for challenging high SION shapes (0.40 for the car and 0.42 for the lamp).
+
+latter, when  $\delta_{\mathrm{init}} \gg \delta_{\mathcal{X}}$  we can estimate good normals for  $\mathcal{Y}_0$  by taking the displacement from the closest input point. With good normal estimates,  $\mathcal{L}_{\widetilde{\mathrm{sdf}}}$  is very effective, and so optimization is easy. Furthermore, we note that higher radius exterior level sets are less complex, with smaller SION to an enclosing sphere. We formalize and prove this observation in the supplement.
+
+# 5. Results
+
+Dataset. We evaluate the performance of our method on ShapeNet [11], a large dataset of 3D CAD models. In this dataset, there are many shapes with complex geometries that are challenging to reconstruct, including extremely thin surfaces (sometimes string-like), hollow regions (often with small openings), and shapes with high genus. Previous works [5, 25] have shown that many neural methods fail on these shapes, even when using the ground-truth normals. We use the preprocessed watertight subset of Williams et al. [46], which consists of 13 classes with 20 shapes in each class. For each shape, 100k points are uniformly sampled from the surface and ground-truth normals are provided for each point, which are only used for those methods that require normals. We use these points as the input to our method, and for evaluating the squared chamfer metric. An additional 100k points are uniformly sampled within the domain with ground-truth labels that indicate whether the point is inside or outside the shape, allowing for the interior intersection-over-union (IoU) metric to be calculated. Further experimental details are given in the supplement.
+
+<table><tr><td rowspan="2">Method</td><td colspan="5">Squared Chamfer ↓</td><td colspan="2">IoU ↑</td></tr><tr><td>NN nx</td><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>SPSR [22]</td><td>× T</td><td>5.44e-5</td><td>1.97e-5</td><td>5.06e-4</td><td>0.9926</td><td>0.9956</td><td>0.0105</td></tr><tr><td>IGR [15]</td><td>✓ T</td><td>5.12e-4</td><td>1.13e-4</td><td>2.15e-3</td><td>0.8102</td><td>0.8480</td><td>0.1519</td></tr><tr><td>SIREN [41]</td><td>✓ T</td><td>1.03e-4</td><td>5.28e-5</td><td>1.93e-4</td><td>0.8268</td><td>0.9097</td><td>0.2329</td></tr><tr><td>FFN [43]</td><td>✓ T</td><td>9.12e-5</td><td>8.65e-5</td><td>3.36e-5</td><td>0.8218</td><td>0.8396</td><td>0.0989</td></tr><tr><td>NSP [46]</td><td>× T</td><td>5.36e-5</td><td>4.06e-5</td><td>3.64e-5</td><td>0.8973</td><td>0.9230</td><td>0.0871</td></tr><tr><td>DiGS+N [5]</td><td>✓ T</td><td>2.74e-4</td><td>2.32e-5</td><td>9.90e-4</td><td>0.9200</td><td>0.9774</td><td>0.1992</td></tr><tr><td>SDF+N†</td><td>✓ T</td><td>3.97e-5</td><td>2.22e-5</td><td>8.98e-5</td><td>0.9915</td><td>0.9951</td><td>0.0141</td></tr><tr><td>Ours+N</td><td>✓ T</td><td>2.43e-5</td><td>2.15e-5</td><td>1.66e-5</td><td>0.9932</td><td>0.9955</td><td>0.0076</td></tr><tr><td>SPSR [22]</td><td>× E</td><td>3.76e-3</td><td>4.37e-5</td><td>1.14e-2</td><td>0.7187</td><td>0.9761</td><td>0.3767</td></tr><tr><td>SIREN [41]</td><td>✓ ×</td><td>3.08e-4</td><td>2.58e-4</td><td>3.26e-4</td><td>0.3085</td><td>0.2952</td><td>0.2014</td></tr><tr><td>SAL [2]</td><td>✓ ×</td><td>1.14e-3</td><td>2.11e-4</td><td>3.63e-3</td><td>0.4030</td><td>0.3944</td><td>0.2722</td></tr><tr><td>DiGS [5]</td><td>✓ ×</td><td>1.32e-4</td><td>2.55e-5</td><td>4.73e-4</td><td>0.9390</td><td>0.9764</td><td>0.1262</td></tr><tr><td>SAP [39]</td><td>× ×</td><td>4.09e-4</td><td>2.46e-5</td><td>2.60e-3</td><td>0.9118</td><td>0.9923</td><td>0.2002</td></tr><tr><td>OG-S [25]</td><td>✓ ×</td><td>3.75e-5</td><td>2.17e-5</td><td>8.24e-5</td><td>0.9615</td><td>0.9871</td><td>0.1048</td></tr><tr><td>OG-N [25]</td><td>✓ ×</td><td>5.07e-5</td><td>2.57e-5</td><td>9.39e-5</td><td>0.9593</td><td>0.9870</td><td>0.1057</td></tr><tr><td>SDF†</td><td>✓ ×</td><td>1.84e-4</td><td>8.15e-4</td><td>2.95e-3</td><td>0.5490</td><td>0.5245</td><td>0.3572</td></tr><tr><td>SDF+N†</td><td>✓ E</td><td>2.48e-2</td><td>5.89e-5</td><td>5.63e-3</td><td>0.6817</td><td>0.9671</td><td>0.3990</td></tr><tr><td>Ours+N</td><td>✓ E</td><td>2.79e-2</td><td>4.79e-5</td><td>6.79e-2</td><td>0.7017</td><td>0.9721</td><td>0.3876</td></tr><tr><td>Ours</td><td>✓ ×</td><td>3.72e-5</td><td>2.40e-5</td><td>5.39e-5</td><td>0.9729</td><td>0.9896</td><td>0.0676</td></tr></table>
+
+Table 1. Surface reconstruction results on ShapeNet [11]. NN: uses a neural network.  $n_x$ : uses ground-truth (T), estimated (E) or no (×) input surface normals. Suffix ‘+N’ denotes normal information added to the underlying method. † Our implementation.
+
+Implementation and Baselines. Our baseline methods use the same implementation framework as our approach (see full details in the supplement) with standard loss formulations. 'SDF' uses  $\mathcal{L}_{\mathrm{zls}}$ ,  $\mathcal{L}_{\mathrm{eik}}$ , and  $\mathcal{L}_{\mathrm{pull}}$  while 'SDF+N' additionally uses  $\mathcal{L}_{\widetilde{\mathrm{sdf}}}$  and  $\mathcal{L}_{\mathrm{normal}}$  [15]. We also evaluate our methods with estimated normals (using Open3D [50]).
+
+# 5.1. Surface Reconstruction on ShapeNet
+
+Results on the full ShapeNet subset are given in Tab. 1, with qualitative results in Fig. 5. Our proposed method outperforms all prior normal-free methods and even demonstrates improvement when ground-truth normals are available. In particular, our approach gets a significant improvement in mean IoU, with much smaller variance, indicating that our method performs reliably well.
+
+# 5.2. Challenging High-SION Shapes
+
+In this section, we analyze the performance of surface reconstruction methods with respect to the SION metric. Fig. 6 shows that the mean IoU degrades significantly as we progressively consider shapes with higher SION scores. While our method also follows this trend, performance degradation is considerably slower, indicating that our method is much more robust to challenging shapes. We report the reconstruction performance on the subset of 20 shapes with the highest SION in Tab. 2. On these most challenging shapes, our approach has a decisive advantage. This demonstrates that our structured optimization approach is able to achieve good reconstructions of the most difficult shapes, without sacrificing performance on easy shapes.
+
+![](images/2629c760daeac6654d94d308a61910968f8fd786c3aadcbf08e3c9b0494a5077.jpg)  
+Figure 6. Mean IoU for all shapes with a SION higher than a lower bound. The analysis from Secs. 3.3 and 3.4 predicts a significant negative correlation for existing neural SDF methods. Our method weakens this trend considerably.
+
+<table><tr><td rowspan="2">Method</td><td rowspan="2">NN</td><td rowspan="2">\(n_x\)</td><td colspan="3">Squared Chamfer ↓</td><td colspan="3">IoU ↑</td></tr><tr><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>SPSR [22]</td><td>×</td><td>T</td><td>3.98e-5</td><td>3.92e-5</td><td>1.80e-5</td><td>0.9798</td><td>0.9848</td><td>0.0222</td></tr><tr><td>DiGS+N [5]</td><td>✓</td><td>T</td><td>2.09e-4</td><td>7.42e-5</td><td>2.91e-4</td><td>0.8160</td><td>0.8764</td><td>0.2119</td></tr><tr><td>\(\text{SDF}+\text{N}^{\dagger}\)</td><td>✓</td><td>T</td><td>1.11e-4</td><td>4.84e-5</td><td>1.95e-4</td><td>0.9733</td><td>0.9854</td><td>0.0409</td></tr><tr><td>Ours+N</td><td>✓</td><td>T</td><td>4.16e-5</td><td>3.89e-5</td><td>1.86e-5</td><td>0.9822</td><td>0.9865</td><td>0.0148</td></tr><tr><td>SPSR [22]</td><td>×</td><td>E</td><td>5.83e-3</td><td>1.25e-3</td><td>1.16e-2</td><td>0.3290</td><td>0.1802</td><td>0.3445</td></tr><tr><td>DiGS [5]</td><td>✓</td><td>×</td><td>4.34e-4</td><td>1.71e-4</td><td>5.34e-4</td><td>0.7108</td><td>0.8196</td><td>0.2536</td></tr><tr><td>SAP [39]</td><td>×</td><td>×</td><td>1.28e-4</td><td>5.84e-5</td><td>1.99e-4</td><td>0.7616</td><td>0.8872</td><td>0.2665</td></tr><tr><td>OG-S [25]</td><td>✓</td><td>×</td><td>1.31e-4</td><td>6.50e-5</td><td>1.79e-4</td><td>0.7651</td><td>0.9219</td><td>0.2512</td></tr><tr><td>\(\text{SDF}^{\dagger}\)</td><td>✓</td><td>×</td><td>1.29e-3</td><td>7.75e -4</td><td>1.43e-3</td><td>0.3413</td><td>0.2617</td><td>0.2292</td></tr><tr><td>\(\text{SDF}+\text{N}^{\dagger}\)</td><td>✓</td><td>E</td><td>5.32e-2</td><td>4.51e-3</td><td>7.03e-2</td><td>0.2896</td><td>0.1977</td><td>0.3288</td></tr><tr><td>Ours+N</td><td>✓</td><td>E</td><td>4.89e-2</td><td>7.32e-3</td><td>6.25e-2</td><td>0.3173</td><td>0.2362</td><td>0.3259</td></tr><tr><td>Ours</td><td>✓</td><td>×</td><td>5.51e-5</td><td>4.87e-5</td><td>3.12e-5</td><td>0.9153</td><td>0.9598</td><td>0.0906</td></tr></table>
+
+Table 2. Surface reconstruction results on the 20 highest SION ShapeNet shapes. NN: uses a neural network.  $n_x$ : uses ground-truth (T), estimated (E) or no (X) input surface normals. Suffix ‘+N’ denotes adding normal information to the underlying method. † Our implementation.  
+
+<table><tr><td rowspan="2">Guidance y0 yδ0 δf</td><td colspan="3">Squared Chamfer ↓</td><td colspan="3">IoU ↑</td></tr><tr><td>Mean</td><td>Median</td><td>Std</td><td>Mean</td><td>Median</td><td>Std</td></tr><tr><td>× × - -</td><td>2.41e-3</td><td>1.18e-3</td><td>2.65e-3</td><td>0.2795</td><td>0.2255</td><td>0.2078</td></tr><tr><td>✓ × - -</td><td>2.63e-4</td><td>1.91e-4</td><td>2.31e-4</td><td>0.5694</td><td>0.6091</td><td>0.2278</td></tr><tr><td>✓ ✓ 4</td><td>2</td><td>9.89e-5</td><td>7.70e-5</td><td>7.95e-5</td><td>0.8657</td><td>0.9163</td></tr><tr><td>✓ ✓ 1</td><td>1</td><td>8.08e-5</td><td>7.52e-5</td><td>5.66e-5</td><td>0.8538</td><td>0.9386</td></tr><tr><td>✓ ✓ 4</td><td>1</td><td>5.51e-5</td><td>4.87e-5</td><td>3.12e-5</td><td>0.9153</td><td>0.9598</td></tr></table>
+
+Table 3. Ablation results on the 20 highest SION ShapeNet shapes.  $\mathcal{V}_0$ : uses our SDF initialization strategy instead of spherical initialization [15].  $\mathcal{V}$ : uses our point guidance strategy.  $\delta_0 / \delta_f$ : starting and final level set radii, given in multiples of  $\delta_{\mathcal{X}}$ .
+
+# 5.3. Ablation Study and Runtime
+
+An ablation study, on the 20 highest-SION shapes of ShapeNet, is reported in Tab. 3. The performance when using a spherical initialization and optimizing with respect to the input points (row 1) is poor. It improves significantly
+
+![](images/c1e7de4b29b4865bd25a908524a6750fb0526d66715e27e1961c33cf06a65f65.jpg)  
+Figure 7. Runtime vs SION on ShapeNet for our method. Challenging shapes with high SION take more time to optimize. One outlier (82 min) is truncated for clarity and marked as  $\times$ .
+
+when replaced with our high exterior level set initialization (row 2). When point guidance is added (rows 3-5), the performance increases considerably. In particular, stopping point guidance early (when  $\delta_f = 2\delta_{\mathcal{X}}$ ) harms performance, as does guiding straight to the final level set target ( $\delta_0 = \delta_{\mathcal{X}}$ ) without first converging to intermediate level set targets. Our gradual homotopy approach performs best by a significant margin, justifying the strategy.
+
+An unoptimized implementation of our method takes 10 mins on average per ShapeNet shape (a median of 7.4 mins). Convergence time depends strongly on the difficulty of the shape, as shown in Fig. 7. Our implementation has 17.5M parameters: a small neural network with Fourier feature embeddings [43] and parametric embeddings [31, 42] computed using a dense feature grid ( $>99\%$  of the parameters).
+
+# 6. Discussion and Conclusion
+
+In this paper, we proposed a point-guided optimization method for neural SDF reconstruction from raw point clouds. We also examined why neural SDF losses can be detrimental for some shapes, proposed a metric to identify these shapes, and used this analysis to justify our algorithm design. Our method outperforms prior work, with large improvements for the most challenging shapes.
+
+Like many methods, our approach is not robust to high outlier fractions and large noise scales, behaving similarly to the compared methods. In addition, our approach does not handle large occlusions gracefully, since it treats these regions like concavities to be explored. This could be alleviated by defining anisotropic per-point sampling radii  $\delta_{i}$ .
+
+Acknowledgements. Y. Ben-Shabat is supported by the Marie Sklodowska-Curie grant agreement No. 893465 S. Gould is a recipient of an ARC Future Fellowship (proj. no. LP200100421) funded by the Australian Government. We would also like to thank Mingda Xu for discussions about homotopy methods.
+
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+        "type": "text",
+        "text": "<sup>4</sup> Computer Science Department, University of California, Los Angeles",
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+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Despite the significant demand for assistive technology among vulnerable groups (e.g., the elderly, children, and the disabled) in daily tasks, research into advanced AI-driven assistive solutions that genuinely accommodate their diverse needs remains sparse. Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
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+        "type": "text",
+        "text": "All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished",
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+    {
+        "type": "text",
+        "text": "effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as \"special\" or \"disabled\" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement.",
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+        "type": "text",
+        "text": "To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple \"take-over\" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully.",
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+    {
+        "type": "text",
+        "text": "Leveraging AI2-THOR [32], a 3D interactive environ",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "*Indicates equal contribution. Work was conducted during Zhihao Cao and Zidong Wang's internships at BIGAI. Corresponding author: Lifeng Fan (lifengfan@bigai.ai). Our environment, dataset, and codes are available at https://github.com/caozh20/SmartHelp.",
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+    {
+        "type": "page_number",
+        "text": "18091",
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+        "type": "image",
+        "img_path": "images/b3f89d0f07362e36876a4ad1b65cee0413b83274452b376bf38200830c608548.jpg",
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+        "image_caption": [
+            "Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied."
+        ],
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+    {
+        "type": "text",
+        "text": "ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks.",
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+    {
+        "type": "text",
+        "text": "Furthermore, we build a new benchmark model for our",
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+    {
+        "type": "text",
+        "text": "proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies.",
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+    {
+        "type": "text",
+        "text": "Our main contributions can be summarized as follows:",
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+    },
+    {
+        "type": "page_number",
+        "text": "18092",
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+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities.",
+            "- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner.",
+            "- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model."
+        ],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty.",
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+    {
+        "type": "text",
+        "text": "3. The Smart Help Challenge",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "3.1. Problem Formulation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple  $G = < S, A, O, R, T, n, \\gamma >$ .  $S$  represents the state space, including physical states and mental states.  $A$  is the joint action space for  $n$  agents, whose local observations compose observation space  $O$ .  $T(s'|s, a)$  denotes the transition probability.  $R(s, a)$  denotes the shared reward function and  $\\gamma \\in [0, 1)$  is the discount factor. Specifically, there are  $n = 2$  agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously.",
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+    {
+        "type": "text",
+        "text": "In previous work, the reward for the helper agent is:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \\beta R ^ {g _ {m}} (s, a _ {h}), \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where the  $\\beta \\in (0,1)$  is a factor controlling the level of altruism of the helper.  $R^{g_h}(s,a_h)$  is the reward attributed to the successful completion of the helper agent's goal at state  $s$  through action  $a_{h}$ .  $R^{g_m}(s,a_h)$  is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \\tag {2} \\\\ + \\beta \\left(R ^ {g _ {m}} \\left(s, a _ {h}\\right) + \\lambda_ {e} R ^ {e _ {m}} \\left(s, a _ {h}\\right)\\right), \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $R^{e_m}(s, a_h)$  means the reward correlated to the emotions of the main agent when the helper does the action  $a_h$ , and  $\\lambda_e$  is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18093",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "goals. So we omit the term  $R^{g_h}(s, a_h)$  and set  $\\beta = 1$ , leading to the helper's reward as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nR _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \\lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued.",
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+    {
+        "type": "text",
+        "text": "3.2. Challenge Implementation",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps:",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Object State. We define object state of object  $i$  as  $e_i = (type_i, pos_i, w_i, attr_i, pr_i)$ , where:",
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+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- type  $i \\in \\mathbb{N}$  denotes the type of object  $i$  with an index;",
+            "-  $pos_{i} \\in \\mathbb{R}^{3}$  records the position of object  $i$ 's center;",
+            "-  $w_{i} \\in \\mathbb{R}$  represents the weight of object  $i$ ;",
+            "-  $\\text{attr}_i \\in \\{0,1\\}^{4+2}$  denotes the attributes of object  $i$ , including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents;",
+            "-  $pr_i \\in \\mathbb{R}$  signifies the type of the parent receptacle of the object  $i$  through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object."
+        ],
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as  $a_{i} = (predicate_{i}, e_{i}) \\in A$ ; for instance, (PickUp, 3), where",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3 is an object index, representing \"Bread\" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp,  $e_i$ ), (Put,  $pr_i$ ), (ToggleOn,  $e_i$ ), (ToggleOff,  $e_i$ ), (Open,  $e_i$ ), and (Close,  $e_i$ ). In total, there are  $|A| = 373$  possible intentional actions.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent  $i$  is represented as  $\\eta_{i} = (\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})$  where:",
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+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- The maximum height an agent can reach  $\\alpha_{i} \\in [0,1]$  and the maximum weight an agent can lift  $\\beta_{i} \\in [0,1]$  determine whether an agent can execute the action PickUp;",
+            "-  $\\gamma_{i}, \\delta_{i}, \\epsilon_{i}, \\zeta_{i} \\in [0,1]$  respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff."
+        ],
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Agent State. We define the state of agent  $i$  as  $h_i = (\\eta_i, \\text{pos}_i, \\text{rot}_i, e_i, a_i, \\text{suc}_i)$ , wherein:",
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "-  $\\eta_{i} \\in C = [0,1]^{6}$  denotes the capability of agent  $i$ ,",
+            "-  $pos_i, rot_i \\in \\mathbb{R}^3$  represent agent  $i$ 's position and rotation,",
+            "-  $e_i \\in E, a_i \\in A$ , and  $succ_i \\in \\{0,1\\}$  respectively represent the object held by agent  $i$ , the action undertaken by agent  $i$  in the last step, and whether the last action was a success or a failure."
+        ],
+        "bbox": [
+            500,
+            439,
+            890,
+            527
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "World. The world is denoted as  $W = (S, A, T)$ , wherein:",
+        "bbox": [
+            500,
+            529,
+            882,
+            545
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "-  $S = \\{e_i, h_j\\}_{i=1,\\dots,N_o, j=1,2}$  represents the world state, which encompasses the state of  $N_o$  objects and 2 agents;",
+            "-  $A = \\{a_{i}\\}$  denotes the action space;",
+            "-  $T = P(S'|S, A; \\eta_i)$  refers to the transition matrix controlled by agent capability."
+        ],
+        "bbox": [
+            500,
+            545,
+            888,
+            619
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities:  $(\\alpha_{i},\\beta_{i},\\gamma_{i},\\delta_{i},\\epsilon_{i},\\zeta_{i})$  for Cook Potato,  $(\\alpha_{i},\\beta_{i},\\gamma_{i})$  for Arrange Room, and  $(\\alpha_{i},\\beta_{i},\\epsilon_{i},\\zeta_{i})$  for Make Coffee.",
+        "bbox": [
+            496,
+            621,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time  $t$  is represented as:",
+        "bbox": [
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+            787
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\ng ^ {t} = \\left(\\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\\right) \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            797,
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+            816
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., \"(In, Cup, Cabinet)\".",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine",
+        "bbox": [
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+            854,
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+            900
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18094",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/39ab639524dae24ba4b646746370f748b38a8df7440acaf6d8f75b3838e37c91.jpg",
+        "image_caption": [
+            "Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature  $\\xi_{s}$ . This feature is then processed by a feature extractor to derive the capability feature  $\\xi_{\\eta}$  and the goal feature  $\\xi_{g}^{t}$ . The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            87,
+            893,
+            400
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed.",
+        "bbox": [
+            75,
+            546,
+            468,
+            608
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Our Model",
+        "text_level": 1,
+        "bbox": [
+            76,
+            623,
+            194,
+            638
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal  $g^{t}$  and capabilities  $\\eta$  of the main agent). Given the observation  $o^{0:t}$ , the action policy for the helper is formulated as:",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP (a | o ^ {0: t}) = \\sum_ {g ^ {t} \\in G, \\eta \\in C} P (a | g ^ {t}, \\eta , o ^ {0: t}) P (g ^ {t}, \\eta | o ^ {0: t}). \\quad (5)\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            792,
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+            828
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e.,  $P(g^{t}, \\eta | o^{0:t})$ ; and 2) a helping policy module to learn the distribution of",
+        "bbox": [
+            76,
+            839,
+            470,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e.,  $P(a|g^t,\\eta,o^{0:t})$ .",
+        "bbox": [
+            496,
+            546,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. The Opponent Modeling Module",
+        "text_level": 1,
+        "bbox": [
+            498,
+            709,
+            789,
+            727
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary.",
+        "bbox": [
+            496,
+            733,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This",
+        "bbox": [
+            496,
+            854,
+            890,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18095",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have:",
+        "bbox": [
+            75,
+            90,
+            472,
+            183
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nP \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {0: t}\\right) \\approx P \\left(\\eta_ {i}, g ^ {t} \\mid o ^ {t - w: t}\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            158,
+            195,
+            468,
+            213
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "where  $w$  is the window size.",
+        "bbox": [
+            76,
+            219,
+            266,
+            232
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the \"class token\" in [2], we preprocess the sequence of object feature. We follow the usage of \"class token\" [2], and only retain this object token to represent the object feature  $\\xi_{o}^{t}$  after the transformer [54] layer (other tokens are removed). This object feature  $\\xi_{o}^{t}$ , together with the agent feature  $\\xi_{a}^{t}$ , constitute the state feature  $\\xi_{s}^{t}$ . As in Eq. (6), we use a window size of  $w$  and the state features  $\\{\\xi_{s}^{t - w},\\dots ,\\xi_{s}^{t}\\}$  are fed into an MLP layer to obtain the final state feature  $\\xi_{s}$ . Furthermore, a feature extractor is employed to derive the capability feature  $\\xi_{\\eta}$  and the target state feature  $\\xi_{g}^{t}$  of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature  $\\xi_{g}^{t}$ , as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle.",
+        "bbox": [
+            75,
+            233,
+            472,
+            506
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.2. The Helping Policy Module",
+        "text_level": 1,
+        "bbox": [
+            76,
+            513,
+            323,
+            530
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Our helping policy module has an actor-critic [55] architecture. At each time step  $t$ , given the current observation  $o^t$ , together with all the features  $\\xi_{\\eta}$  and  $\\xi_g^t$  from the opponent modeling module, the helper agent needs to learn the helping policy  $\\pi_{\\theta}(a|o^t,\\eta ,g^t)$ . We employ an MLP layer for action selection (the \"Policy MLP\" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the \"Value MLP\" in Fig. 2) is utilized for the value network to estimate the value of the current state.",
+        "bbox": [
+            75,
+            537,
+            468,
+            674
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            686,
+            269,
+            704
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.1. Two-stage Learning",
+        "text_level": 1,
+        "bbox": [
+            76,
+            710,
+            267,
+            728
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature  $\\xi_{\\eta}$ , target state feature, object feature and parent receptacle feature (i.e., the goal feature  $\\xi_g^t$ ) in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of  $1 \\times 10^{-6}$  and a batch size of 32.",
+        "bbox": [
+            75,
+            734,
+            467,
+            854
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features  $\\xi_{\\eta}$  and  $\\xi_g^t$ , and focus",
+        "bbox": [
+            75,
+            854,
+            467,
+            902
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode.",
+        "bbox": [
+            496,
+            90,
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+            210
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of  $5 \\times 10^{-5}$  without weight decay and a batch size of 128, using the reward defined in Eq. (3) with  $\\lambda_{e} = 0.0$ . We find such \"warm-up\" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of  $5 \\times 10^{-7}$  and  $\\lambda_{e} = 1.0$  in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details.",
+        "bbox": [
+            496,
+            212,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.2. Reward",
+        "text_level": 1,
+        "bbox": [
+            500,
+            449,
+            598,
+            464
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "The reward of the helper is influenced by the goal  $g_{m}$  and the capability  $\\eta_{m}$  of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term  $R^{e_{m}}(s,a_{h})$  in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment:  $R^{e_{m}}(s,a_{h}) = -30$ . For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20.",
+        "bbox": [
+            496,
+            472,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "5.3. Baselines",
+        "text_level": 1,
+        "bbox": [
+            500,
+            680,
+            607,
+            695
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To make a fair comparison, the baselines are:",
+        "bbox": [
+            500,
+            704,
+            797,
+            718
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Random. This helper randomly selects an action.",
+            "- End2end- $\\lambda_{e} = 0.0$ . This model generates actions directly from the observation with MLPs, trained with  $\\lambda_{e} = 0.0$  in Eq. (3). We set learning rate to  $5 \\times 10^{-5}$ , batch size to 128. The model is trained for 350 epochs before convergence.",
+            "- End2end- $\\lambda_{e} = 1.0$ . Similar to End2end- $\\lambda_{e} = 0.0$ , but with  $\\lambda_{e} = 1.0$  in Eq. (3).",
+            "- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted"
+        ],
+        "bbox": [
+            500,
+            719,
+            890,
+            898
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "18096",
+        "bbox": [
+            480,
+            944,
+            519,
+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "by the number of steps taken to achieve this result.",
+        "bbox": [
+            89,
+            90,
+            424,
+            104
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability  $p = 0.5$  by chance and  $p = 0.5$  by a rule-based selection of the next action to complete the goal.",
+            "-  $\\mathbf{MCTS_{TG}}$ . This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent.",
+            "-  $\\mathbf{MCTS}_{\\mathbf{RG}}$ . This model is almost the same as  $MCTS_{TG}$  except that it follows a random goal.",
+            "- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details."
+        ],
+        "bbox": [
+            76,
+            106,
+            467,
+            377
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Study",
+        "text_level": 1,
+        "bbox": [
+            76,
+            388,
+            228,
+            402
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To assess the contributions and efficacy of essential components in our method, we derive the following variants:",
+        "bbox": [
+            76,
+            411,
+            467,
+            440
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set  $\\lambda_{e} = 0.0$  in Eq. (3), and train it for 840 epochs.",
+            "- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy.",
+            "- BaseModel- $\\lambda_{e} = 1.0$ . This model is trained with  $\\lambda_{e} = 1.0$  in Eq. (3) for 840 epochs.",
+            "- BaseModel-PL- $\\lambda_{e} = 0.0$ . Here, \"PL\" means the Progressive Learning technique (detailed in Sec. 5.1), but with  $\\lambda_{e} = 0.0$  in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in  $\\lambda_{e} = 0.0$ ).",
+            "- BaseModel-PL- $\\lambda_{e} = 1.0$  (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to  $\\lambda_{e} = 1.0$  in the second phase after warming up the basic skills of the helper model."
+        ],
+        "bbox": [
+            76,
+            441,
+            467,
+            712
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.5. Evaluation Metrics",
+        "text_level": 1,
+        "bbox": [
+            76,
+            723,
+            261,
+            738
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let  $N$  denote the size of the test scenarios, and let each scenario  $i$  be characterized by an initial room state  $s_i^0$  and a goal of transitioning the room to the target state  $s_i^*$ . Assuming that both the main agent and the helper require  $l_i$  steps (with a maximum of 30) to reach the final state  $s_i^l$ , we elaborate on these metrics as follows.",
+        "bbox": [
+            76,
+            746,
+            467,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "- Success Rate (SR and GSR). It includes Task-",
+        "bbox": [
+            76,
+            885,
+            467,
+            898
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as  $SR = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}$ , where  $R_{i}$  is 1 if the task is finished. For task  $i$ , let  $N_{g_i^m}$  denote the effective goals completed by the main agent,  $N_{g_i^h}$  represent the effective goals completed by the helper, and  $N_{g_i^a}$  be all the effective goals of the task. The goal-conditioned success for task  $i$  is:  $GS_{i} = \\frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}}$ . Hence, the overall GSR is defined as  $GSR = \\frac{1}{N}\\sum_{i=1}^{N}GS_{i}$ .  $R_{i} = 1$  if and only if  $GS_{i} = 1$ .",
+        "bbox": [
+            511,
+            90,
+            890,
+            256
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "list",
+        "sub_type": "text",
+        "list_items": [
+            "- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let  $N_{g_{\\mathrm{nec},i}^h}$  denote the necessary goals completed by the helper, the Helping Necessity is then calculated as  $HN = \\frac{1}{N}\\sum_{i=1}^{N}\\frac{N_{g_{\\mathrm{nec},i}^h}}{N_{g_i^h}}R_i$ , where  $R_i = 1$  if the task is completed, otherwise  $R_i = 0$ . This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance.",
+            "- Helping Rate (HR).  $HR$  represents the helper's initiative to help.  $HR = \\frac{N_{\\text{help}}}{N_{\\text{need\\_help}}}$ , reflecting the probability of helping when the main agent needs help.",
+            "- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as:  $EL = \\frac{1}{N}\\sum_{i=1}^{N}l_i$ .",
+            "- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as:  $SPL = \\frac{1}{N}\\sum_{i=1}^{N}R_{i}\\frac{d_{i}}{\\max(d_{i},l_{i})}$ , where  $R_{i} \\in \\{0,1\\}$  denotes whether the task is successfully completed,  $d_{i}$  represents the minimum number of steps to finish the task  $i$ , and  $l_{i}$  is the actual steps."
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+        "type": "text",
+        "text": "Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the  $HN$  and  $HR$ , while simultaneously descending the  $EL$ , as well as keeping the  $SR$ ,  $GSR$ , and  $SPL$  as high as possible.",
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+        "text": "6. Results and Analyses",
+        "text_level": 1,
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+        "text": "Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the  $MCTS_{RG}$  model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest  $EL$ , falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model.",
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+        "type": "page_number",
+        "text": "18097",
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+        "img_path": "images/97a70cd3646284acf0182469e42abd40cab54e69897cb3439b5a2113bceb163a.jpg",
+        "image_caption": [
+            "(a).BaseModel-PL-  $\\lambda_{e} = 0$  (NormalHelp)"
+        ],
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+        "image_caption": [
+            "(b).BaseModel-PL-  $\\lambda_{\\mathrm{e}} = 1$  (Smart Help)",
+            "Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal (\"(In, Potato, Microwave)\", but fails at the goal \" (Open, Microwave)\". (a) The BaseModel-PL-  $\\lambda_{e} = 0.0$  model not only helps the main agent with the bottleneck \"(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL-  $\\lambda_{e} = 1.0$  only offer necessary help with the bottleneck \"(Open, Microwave)\", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent."
+        ],
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+        "img_path": "images/0685dbefc6e918f88d9363091e12dde025dc862ded06672ce3fd140c03c14c29.jpg",
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+    {
+        "type": "text",
+        "text": "However, our model achieves higher scores in  $SR$ ,  $GSR$ ,  $HN$ , and  $HR$ , while maintaining similar values for  $EL$  and  $SPL$ , indicating the effectiveness of its assistive action planning. The  $MCTS_{TG}$  model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in  $HN$ . This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Ablation analysis. Comparing the BaseModel with BaseModel- $\\lambda_{e} = 1.0$ , we find that setting  $\\lambda_{e} = 0.0$  can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL- $\\lambda_{e} = 0.0$  with BaseModel-PL- $\\lambda_{e} = 1.0$ , we find that after the initial \"warm-up\" of the basic skills, setting  $\\lambda_{e} = 1.0$  in the second phase could greatly improve the  $HN$  while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel \"warm-up\" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings.",
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+    {
+        "type": "text",
+        "text": "Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL- $\\lambda_{e} = 0.0$  only learns to",
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+    {
+        "type": "table",
+        "img_path": "images/04513ed2510857058ff6e50ec1af87129d3b385149643d9f030cec61a7f5a4f7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>SR(↑)</td><td>GSR(↑)</td><td>HN(↑)</td><td>HR(↑)</td><td>Reward(↑)</td><td>EL(↓)</td><td>SPL(↑)</td></tr><tr><td>Random</td><td>0.074</td><td>0.364</td><td>0.054</td><td>0.057</td><td>-31.339</td><td>28.567</td><td>0.054</td></tr><tr><td>End2end-λe=0.0</td><td>0.267</td><td>0.441</td><td>0.149</td><td>0.315</td><td>-23.218</td><td>24.343</td><td>0.212</td></tr><tr><td>End2end-λe=1.0</td><td>0.067</td><td>0.372</td><td>0.057</td><td>0.057</td><td>-26.183</td><td>28.726</td><td>0.049</td></tr><tr><td>LLM</td><td>0.345</td><td>0.506</td><td>0.382</td><td>0.381</td><td>/</td><td>22.914</td><td>0.210</td></tr><tr><td>MCTS</td><td>0.178</td><td>0.482</td><td>0.266</td><td>0.328</td><td>/</td><td>26.743</td><td>0.126</td></tr><tr><td>MCTS-heuristic</td><td>0.274</td><td>0.528</td><td>0.355</td><td>0.400</td><td>/</td><td>24.692</td><td>0.199</td></tr><tr><td>MCTSTG</td><td>0.593</td><td>0.804</td><td>0.610</td><td>0.678</td><td>/</td><td>16.271</td><td>0.541</td></tr><tr><td>MCTSRG</td><td>0.043</td><td>0.348</td><td>0.015</td><td>0.015</td><td>/</td><td>28.950</td><td>0.042</td></tr><tr><td>BaseModel</td><td>0.419</td><td>0.515</td><td>0.408</td><td>0.412</td><td>-15.179</td><td>24.945</td><td>0.176</td></tr><tr><td>BaseModel-w/o. Capability</td><td>0.374</td><td>0.504</td><td>0.375</td><td>0.379</td><td>-13.852</td><td>23.748</td><td>0.235</td></tr><tr><td>BaseModel-λe=1.0</td><td>0.181</td><td>0.466</td><td>0.193</td><td>0.200</td><td>-17.185</td><td>27.448</td><td>0.122</td></tr><tr><td>BaseModel-PL-λe=0.0</td><td>0.488</td><td>0.556</td><td>0.455</td><td>0.496</td><td>-10.959</td><td>24.383</td><td>0.198</td></tr><tr><td>BaseModel-PL-λe=1.0 (Ours)</td><td>0.483</td><td>0.548</td><td>0.498</td><td>0.506</td><td>-10.625</td><td>24.650</td><td>0.200</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines.",
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+    {
+        "type": "text",
+        "text": "help all the goals it successfully infers, while our full model BaseModel-PL- $\\lambda_{e} = 1.0$  learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with \" (Open, Microwave)\".",
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+    {
+        "type": "text",
+        "text": "7. Conclusion",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem.",
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+    {
+        "type": "text",
+        "text": "Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). We thank Zhenliang Zhang at BIGAI and Luyao Yuan at META for their helpful discussions.",
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+        "text": "18098",
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+    {
+        "type": "text",
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2024/Smart Help_ Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households/e39ca544-b333-4b15-8b22-bd984a4f8117_origin.pdf

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2024/Smart Help_ Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households/full.md

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+# Smart Help: Strategic Opponent Modeling for Proactive and Adaptive Robot Assistance in Households
+
+Zhihao Cao $^{1,2,*}$ , Zidong Wang $^{1,2,*}$ , Siwen Xie $^{3}$ , Anji Liu $^{4}$ , Lifeng Fan $^{1,\boxtimes}$
+
+$^{1}$  State Key Laboratory of General Artificial Intelligence, Beijing Institute for General Artificial Intelligence (BIGAI)
+
+$^{2}$  Department of Automation, Tsinghua University  $^{3}$  Yuanpei College, Peking University
+
+<sup>4</sup> Computer Science Department, University of California, Los Angeles
+
+# Abstract
+
+Despite the significant demand for assistive technology among vulnerable groups (e.g., the elderly, children, and the disabled) in daily tasks, research into advanced AI-driven assistive solutions that genuinely accommodate their diverse needs remains sparse. Traditional human-machine interaction tasks often require machines to simply help without nuanced consideration of human abilities and feelings, such as their opportunity for practice and learning, sense of self-improvement, and self-esteem. Addressing this gap, we define a pivotal and novel challenge Smart Help, which aims to provide proactive yet adaptive support to human agents with diverse disabilities and dynamic goals in various tasks and environments. To establish this challenge, we leverage AI2-THOR [32] to build a new interactive 3D realistic household environment for the Smart Help task. We introduce an innovative opponent modeling module that provides a nuanced understanding of the main agent's capabilities and goals, in order to optimize the assisting agent's helping policy. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against established baselines. Our findings illustrate the potential of AI-imbued assistive robots in improving the well-being of vulnerable groups.
+
+# 1. Introduction
+
+All of us may find ourselves within vulnerable demographics at some point. Throughout the human life span, we confront an array of challenges, whether originating from physical discomfort [12], emotional turmoil [53], or the inevitable march of aging [22], that can hinder our ability to perform even the simplest tasks that we once accomplished
+
+effortlessly (e.g., lifting a heavy object). This predicament often triggers a complex emotional response. The fear of being labeled as "special" or "disabled" can evoke feelings of diminished self-esteem, reduced self-efficacy and self-sufficiency, and a sense of personal boundary violation [8, 40]. However, previous research in humanrobot interaction has primarily focused on pure cooperation [30, 38, 42, 43, 52, 57], and assistive technologies [4, 7] have been designed to simply take over everything for human users, often disregarding their emotional well-being. Considering the importance of sensitivity and consideration when offering help, we need new assistance technologies with an emphasis not only on the successful completion of the task but also on the recipient's emotional acceptance of the assistance [8, 40]. This introduces a new dimension to the concept of learning to help in AI, extending the boundaries beyond technical proficiency and into the realm of empathetic engagement.
+
+To tackle this issue, we propose a novel and pivotal challenge Smart Help, aiming to provide both proactive and adaptive support to human agents with diverse disabilities and dynamic goals in different tasks and environments. Fig. 1 exemplifies the concept of the Smart Help strategy as applied to an assistive robot aiding a human in a household task. The Basic Helper fails to provide proactive assistance due to its inability to infer the user's goals accurately. The Ordinary Helper successfully infers the user's goals from observations and offers proactive help, but it lacks adaptability to different user needs. Its simple "take-over" helping strategy can cause a feeling of discomfort in the human user. In contrast, the Smart Helper not only infers both the user's goals distribution but also reasons about the user's capability of completing each goal independently. As a result, the Smart Helper can identify critical goals that hinder task completion and provide proactive and adaptive help that selectively addresses those bottlenecks. This approach allows the user to accomplish the task successfully and joyfully.
+
+Leveraging AI2-THOR [32], a 3D interactive environ
+
+![](images/b3f89d0f07362e36876a4ad1b65cee0413b83274452b376bf38200830c608548.jpg)
+
+![](images/7d93d9a87ebe29ebf887feb218a90f501a8f7adc735bc62403b32f47422a122c.jpg)
+
+![](images/f2a6a7f28eb3050cbd9d9ab74c59fcfd911e258ed7fa64d11abfde1ae3b28949.jpg)  
+Figure 1. An example of the Smart Help strategy for an assistive robot. The top left shows the human user's capability distribution across several dimensions (e.g., weight for lifting heavy objects and height for grasping objects from high positions), as well as the current task (e.g., making coffee). The figure illustrates three types of helpers: (1) The Basic Helper merely observes the human user without inferring anything, and thus remains idle and waits until the human user fails the task, leading to frustration. (2) The Ordinary Helper infers the human user's goals through observations and always provides simple and direct assistance for each goal, taking over the entire task. While the task is successfully completed, the human user is left dissatisfied because the robot's helping strategy is overly intrusive, causing discomfort. (3) The Smart Helper infers both the human user's goals and her capability distribution. It reasons about whether the human user is capable of independently accomplishing each goal and thus identifies the bottleneck goal that hinders task completion. The proactive helper then adapts its strategy to assist solely with the bottleneck goal. As a result, the human user successfully completes the task with tailored support, feeling comfortable and satisfied.
+
+ment engineered for realistic home simulations, we demonstrate a concrete realization of the proposed novel challenge Smart Help. We create a multi-agent interactive environment featuring a main agent with diverse capability distributions (representing the vulnerable group) across dimensions, such as toggling, opening, closing, weight, and height. Within this environment, the main agent faces challenges in achieving dynamic goals across various tasks, and an assistive robot is introduced to assist the main agent throughout their endeavors. Unlike previous assistive tasks that were highly specialized and constrained, such as the use of a robotic arm for the disabled [10, 17, 51], our work represents, to the best of our knowledge, the first construction of a 3D home environment designed to assist the vulnerable group with various general daily household tasks.
+
+Furthermore, we build a new benchmark model for our
+
+proposed challenge, which consists of 1) an opponent modeling module that jointly optimizes goal inference and capability estimation, and 2) a helping policy module that reasons about the bottleneck, and learns an optimal Smart Help policy in an online interactive manner. To better evaluate performance in the Smart Help task, we also introduce six assessment metrics. Contrary to traditional evaluation metrics primarily focusing on cumulative reward or task completion, our metrics emphasize the helper's contribution to the task and the essentiality of assistance. Rigorous experiments validate the efficacy of our model components and show the superiority of our holistic approach against baselines. We believe our proposed task, environment, model, and benchmark will contribute to the development of next-generation advanced home assistive robot technologies.
+
+Our main contributions can be summarized as follows:
+
+- We propose a novel Smart Help challenge that aims at learning to provide both proactive and adaptive help to diverse human users (especially vulnerable groups) based on inferred goals and capabilities.  
+- To the best of our knowledge, we contribute the first 3D realistic home environment built upon AI2-THOR, that focuses on assisting the vulnerable group with daily household tasks in an online and interactive manner.  
+- We provide a benchmark model with a joint goal and capability inference, bottleneck reasoning, and helping policy improvement. Strict experiments and the proposed holistic evaluations validate the efficacy of our model.
+
+# 2. Related Work
+
+Assistive Robots. The domain of assistive robots encompasses a broad spectrum of research, focusing on enhancing the life quality for individuals with various needs and spanning diverse applications such as mobility aids [1, 20], companion robots [46], and robotic arms [21]. Feil-Seifer and Mataric [18] underscore that Socially Assistive Robotics entails robots assisting humans through effective interaction in tasks such as food delivery [49], healthcare [27], and other tasks necessitating social interaction. However, many of them only rely on simple rules or programs to achieve social interaction [27, 49]. The deployment of assistive robots has also raised ethical and safety considerations, particularly in terms of user autonomy, privacy, acceptance, trust, etc. [5, 6, 9, 18]. The objective of our work is to devise an effective algorithm for Socially Assistive Robotics to estimate people's goals and capabilities, thereby enabling comfortable and smart assistance.
+
+Embodied Multi-agent Collaboration. A series of embodied collaboration tasks have been developed recently thanks to the development of Embodied AI simulators [13, 14, 32, 33, 41, 47, 48, 50]. However, these tasks always focus on some limited task completion, such as collaborative navigation [34, 56] and collaborative furniture rearrangement [28, 29]. Watch-and-Help [42] and NOPA [43] study the cooperative tasks between two agents with the same capabilities. Our work focuses on the collaboration between agents with different capabilities and study the strategic assistance for the vulnerable group on household tasks.
+
+Opponent Modeling. Opponent modeling [16, 19, 24], a pivotal approach in multi-agent interaction tasks, leverages a variety of methodologies such as Inverse Reinforcement Learning [36], Bayesian methods [25, 26, 45, 52, 60], Deep Q-Networks (DQN) [23, 35], Variational AutoEncoders [39], Markov Decision Process [36], etc. This technique is especially valuable in competitive settings like games and strategic decision-making, where understanding and anticipating an opponent's behavior or unseen traits (e.g., Theory of Mind modeling [44]) can significantly influence the outcome. It enables agents to predict future en
+
+vironmental state transitions and refine their strategies accordingly [58, 59]. Projects like Watch-and-Help [42] and NOPA [43] have explored estimating a main agent's goals to improve coordination. Yet, these initiatives often overlook the capabilities of the main agent, leading to a gap in developing effective support strategies for those in need. Our research addresses this gap by focusing on enhancing the acceptance of AI assistance among users, as emphasized in [9], highlighting the importance of aligning AI functionalities with user needs and preferences. Additionally, we propose to model the capability of the opponent and learn a smart, adaptive, and empathetic helping policy for vulnerable people in a challenging 3D household interactive environment with partial observation and high uncertainty.
+
+# 3. The Smart Help Challenge
+
+# 3.1. Problem Formulation
+
+We model the interaction between the main agent and the helper with a multi-agent Partially Observable Markov Decision Process (POMDP[11]), which is formally defined as a tuple  $G = < S, A, O, R, T, n, \gamma >$ .  $S$  represents the state space, including physical states and mental states.  $A$  is the joint action space for  $n$  agents, whose local observations compose observation space  $O$ .  $T(s'|s, a)$  denotes the transition probability.  $R(s, a)$  denotes the shared reward function and  $\gamma \in [0, 1)$  is the discount factor. Specifically, there are  $n = 2$  agents in our Smart Help Challenge, i.e., a main agent and a helper agent. The objective is to train a helper agent to assist the main agent in achieving goals, considering the emotional state of the main agent simultaneously.
+
+In previous work, the reward for the helper agent is:
+
+$$
+R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) + \beta R ^ {g _ {m}} (s, a _ {h}), \tag {1}
+$$
+
+where the  $\beta \in (0,1)$  is a factor controlling the level of altruism of the helper.  $R^{g_h}(s,a_h)$  is the reward attributed to the successful completion of the helper agent's goal at state  $s$  through action  $a_{h}$ .  $R^{g_m}(s,a_h)$  is the same for the main agent's goal achievement. This formulation assumes equal consideration for both agents when rewarding goal completion. However, when the helper fulfills a goal of the main agent, it triggers emotional responses in the main agent. Integrating this emotional component with Eq. (1), we have:
+
+$$
+\begin{array}{l} R _ {h} (s, a _ {h}) = R ^ {g _ {h}} (s, a _ {h}) \tag {2} \\ + \beta \left(R ^ {g _ {m}} \left(s, a _ {h}\right) + \lambda_ {e} R ^ {e _ {m}} \left(s, a _ {h}\right)\right), \\ \end{array}
+$$
+
+where  $R^{e_m}(s, a_h)$  means the reward correlated to the emotions of the main agent when the helper does the action  $a_h$ , and  $\lambda_e$  is a hyper-parameter that controls the helper's sensitivity to the emotional states of the main agent. In our Smart Help challenge, the helper agent's role is solely to assist the main agent in accomplishing his/her goals, without its own
+
+goals. So we omit the term  $R^{g_h}(s, a_h)$  and set  $\beta = 1$ , leading to the helper's reward as:
+
+$$
+R _ {h} (s, a _ {h}) = R ^ {g _ {m}} (s, a _ {h}) + \lambda_ {e} R ^ {e _ {m}} (s, a _ {h}). \tag {3}
+$$
+
+Indeed, this is what sets smart Help apart from other assistance-related tasks. Through such design, we emphasize that AI agents must possess the capacity to discern not just how to aid humans, but also when their assistance is truly needed and will be valued.
+
+# 3.2. Challenge Implementation
+
+We implement a tangible version of Smart Help in the AI2THOR [32] simulator, which emphasizes adaptive helping policy for individuals with various disabilities, as shown in Fig. 1. Our new environment includes a main agent that simulates human behavior in various assistive household tasks. The main agent, assigned with a new task and a capability distribution at the beginning of each round, attempts to complete the task with an expert planning policy, which utilizes complete information to divide the task into distinct goals and plan intentional actions for the goals. We also implement a low-level planner that translates the intentional action to a sequence of executable actions in the simulator, so as to enable the main agent to reach the target state indicated by the input intentional action. The workflow of the low-level planner is a loop involving the following steps:
+
+1. Navigate to the relevant object by following the shortest path determined by the object's position and the room layout; or be directly teleported to the target position.
+
+2. Interact with the object in accordance with the goal. However, actions taken by the main agent might fail due to certain disabilities or the physical constraints of the scene. Thus, the helper agent, as in Fig. 2, based on its symbolic observations of the world, should infer both the goal and capability of the main agent and provide proactive assistance with the bottleneck for the main agent. We will introduce the detailed environment settings in the following part.
+
+Object State. We define object state of object  $i$  as  $e_i = (type_i, pos_i, w_i, attr_i, pr_i)$ , where:
+
+- type  $i \in \mathbb{N}$  denotes the type of object  $i$  with an index;  
+-  $pos_{i} \in \mathbb{R}^{3}$  records the position of object  $i$ 's center;  
+-  $w_{i} \in \mathbb{R}$  represents the weight of object  $i$ ;  
+-  $\text{attr}_i \in \{0,1\}^{4+2}$  denotes the attributes of object  $i$ , including its 4 status (i.e., whether it is picked up, opened, cooked, and toggled on) and its visibility to the 2 agents;  
+-  $pr_i \in \mathbb{R}$  signifies the type of the parent receptacle of the object  $i$  through an index; here, the parent receptacle means an object that serves as the container or the support for another subordinate object.
+
+Action Space. We employ intentional actions to construct the action space, where intentional actions represent the target state that the agent wants to achieve. It is defined as  $a_{i} = (predicate_{i}, e_{i}) \in A$ ; for instance, (PickUp, 3), where
+
+3 is an object index, representing "Bread" in our environment. There are seven kinds of different intentional actions: (Wait), (PickUp,  $e_i$ ), (Put,  $pr_i$ ), (ToggleOn,  $e_i$ ), (ToggleOff,  $e_i$ ), (Open,  $e_i$ ), and (Close,  $e_i$ ). In total, there are  $|A| = 373$  possible intentional actions.
+
+Agent Capability. The variance of agent capability is manifested in the differences in the transition matrix, which means that different agents will produce different outcomes for the same action at the same state. For example, some agents may be able to pick an object up, while others cannot due to the its weight. Learning the matrix itself is impractical due to the vast size of the space. Instead, we select six parameters to represent the distinct characteristics of different matrices. Therefore, the capability of agent  $i$  is represented as  $\eta_{i} = (\alpha_{i},\beta_{i},\gamma_{i},\delta_{i},\epsilon_{i},\zeta_{i})$  where:
+
+- The maximum height an agent can reach  $\alpha_{i} \in [0,1]$  and the maximum weight an agent can lift  $\beta_{i} \in [0,1]$  determine whether an agent can execute the action PickUp;  
+-  $\gamma_{i}, \delta_{i}, \epsilon_{i}, \zeta_{i} \in [0,1]$  respectively represent the agent's ability to complete the actions Open, Close, ToggleOn and ToggleOff.
+
+Agent State. We define the state of agent  $i$  as  $h_i = (\eta_i, \text{pos}_i, \text{rot}_i, e_i, a_i, \text{suc}_i)$ , wherein:
+
+-  $\eta_{i} \in C = [0,1]^{6}$  denotes the capability of agent  $i$ ,  
+-  $pos_i, rot_i \in \mathbb{R}^3$  represent agent  $i$ 's position and rotation,  
+-  $e_i \in E, a_i \in A$ , and  $succ_i \in \{0,1\}$  respectively represent the object held by agent  $i$ , the action undertaken by agent  $i$  in the last step, and whether the last action was a success or a failure.
+
+World. The world is denoted as  $W = (S, A, T)$ , wherein:
+
+-  $S = \{e_i, h_j\}_{i=1,\dots,N_o, j=1,2}$  represents the world state, which encompasses the state of  $N_o$  objects and 2 agents;  
+-  $A = \{a_{i}\}$  denotes the action space;  
+-  $T = P(S'|S, A; \eta_i)$  refers to the transition matrix controlled by agent capability.
+
+Task. Given our formulation of agent capabilities, we select three everyday tasks for practical implementations of our challenge: Make Breakfast, Arrange Room, and Make Coffee. These tasks respectively involve different capabilities:  $(\alpha_{i},\beta_{i},\gamma_{i},\delta_{i},\epsilon_{i},\zeta_{i})$  for Cook Potato,  $(\alpha_{i},\beta_{i},\gamma_{i})$  for Arrange Room, and  $(\alpha_{i},\beta_{i},\epsilon_{i},\zeta_{i})$  for Make Coffee.
+
+Goal. Upon setting a task, the agent need to identify several key points (goals) that they must achieve. These goals are hidden from the helper, but affect the helper's reward for a particular action. Each goal is defined by the target state of the involved objects. The goal at time  $t$  is represented as:
+
+$$
+g ^ {t} = \left(\text {t a r g e t - s t a t e} ^ {t}, e ^ {t}, p r ^ {t}\right) \tag {4}
+$$
+
+Target state includes Wait, Get, On, In, KeepOpen, KeepClose, KeepOn and KeepOff, e.g., "(In, Cup, Cabinet)".
+
+Observation Space. The proposed environment supports both symbolic and visual observations. This dual-mode observation system enables the helper to acquire and refine
+
+![](images/39ab639524dae24ba4b646746370f748b38a8df7440acaf6d8f75b3838e37c91.jpg)  
+Figure 2. This figure depicts the architecture of our smart help model and its interaction mechanisms with the environment. The model is partitioned into two primary components: an opponent modeling module and a helping policy module. The opponent modeling module is designed to estimate the goal and capability of the main agent. It adopts a sliding window paradigm and utilizes several MLP layers to generate the state feature  $\xi_{s}$ . This feature is then processed by a feature extractor to derive the capability feature  $\xi_{\eta}$  and the goal feature  $\xi_{g}^{t}$ . The helping policy module is composed of two MLP layers to produce action decision and value estimation respectively. During interaction with the environment, the helping model outputs an intentional action, representing the target state it aims to reach. The environment employs a low-level planner to decompose the intentional action into a sequence of executable actions, which are then processed by the AI2THOR simulator, guiding the assistant toward the intended state. Finally, the simulator provides a new observation as feedback, triggering the next cycle of interaction.
+
+helping behaviors in various contexts. Following previous work [42, 43], we use symbolic observations containing physical states of all perceivable objects and agents. Hidden states, like goals and capabilities, can not be observed.
+
+# 4. Our Model
+
+Our objective is to train a helper agent who can effectively adapt to main agents with varying capabilities and goals. There are two main challenges: 1) the challenge posed by the environment (e.g., partial observation and occlusion), and 2) the challenge posed by the task (i.e., how to estimate the current goal  $g^{t}$  and capabilities  $\eta$  of the main agent). Given the observation  $o^{0:t}$ , the action policy for the helper is formulated as:
+
+$$
+P (a | o ^ {0: t}) = \sum_ {g ^ {t} \in G, \eta \in C} P (a | g ^ {t}, \eta , o ^ {0: t}) P (g ^ {t}, \eta | o ^ {0: t}). \quad (5)
+$$
+
+Therefore, as depicted in Fig. 2, our model consists of: 1) an opponent modeling module to estimate the current goal and capabilities of the main agent, i.e.,  $P(g^{t}, \eta | o^{0:t})$ ; and 2) a helping policy module to learn the distribution of
+
+the helper's action conditioned on the predicted goal and capabilities of the main agent, i.e.,  $P(a|g^t,\eta,o^{0:t})$ .
+
+The training of our model has two stages. In the first stage, we train an opponent modeling module using the collected main agent trajectories. This stage is crucial as it enables the helper agent to understand and anticipate the behavior of the main agent effectively. In the second stage, we utilize the pre-trained opponent modeling module to train the helping policy module, which handles dynamic and complex tasks by interacting in our environment.
+
+# 4.1. The Opponent Modeling Module
+
+To train this module, we collect simulated trajectories in our environment with the main agent following an expert policy and the helper moving randomly, where each frame contains the observations of the helper agent and the true labels of the main agent's goals and capabilities. Throughout data collection, we utilize a main agent with various tasks and capabilities and a helper executing random actions in the environment. See more details in the supplementary.
+
+We use a sliding window trick when inferring goals and capabilities from the main agent's trajectory since goals are transient and typically persist for only a few steps. This
+
+method enables examining a segment of the trajectory at any given time, and sliding the window as new actions are taken. It allows the helper agent to make more immediate and relevant inferences about the main agent's current goals and capabilities, enhancing its adaptability and responsiveness. Formally, we have:
+
+$$
+P \left(\eta_ {i}, g ^ {t} \mid o ^ {0: t}\right) \approx P \left(\eta_ {i}, g ^ {t} \mid o ^ {t - w: t}\right), \tag {6}
+$$
+
+where  $w$  is the window size.
+
+We use an object encoder and an agent encoder to extract features from raw observations (details in supplementary). Similar to the "class token" in [2], we preprocess the sequence of object feature. We follow the usage of "class token" [2], and only retain this object token to represent the object feature  $\xi_{o}^{t}$  after the transformer [54] layer (other tokens are removed). This object feature  $\xi_{o}^{t}$ , together with the agent feature  $\xi_{a}^{t}$ , constitute the state feature  $\xi_{s}^{t}$ . As in Eq. (6), we use a window size of  $w$  and the state features  $\{\xi_{s}^{t - w},\dots ,\xi_{s}^{t}\}$  are fed into an MLP layer to obtain the final state feature  $\xi_{s}$ . Furthermore, a feature extractor is employed to derive the capability feature  $\xi_{\eta}$  and the target state feature  $\xi_{g}^{t}$  of the main agent. A transformer layer is utilized for the capability feature. As for the goal feature  $\xi_{g}^{t}$ , as detailed in Eq. (4), one transformer layer is used for the target state feature, and two MLP layers are employed for the features of the related object and its target parent receptacle.
+
+# 4.2. The Helping Policy Module
+
+Our helping policy module has an actor-critic [55] architecture. At each time step  $t$ , given the current observation  $o^t$ , together with all the features  $\xi_{\eta}$  and  $\xi_g^t$  from the opponent modeling module, the helper agent needs to learn the helping policy  $\pi_{\theta}(a|o^t,\eta ,g^t)$ . We employ an MLP layer for action selection (the "Policy MLP" in Fig. 2), coupled with an LSTM network for context memorization. Meanwhile, another MLP (the "Value MLP" in Fig. 2) is utilized for the value network to estimate the value of the current state.
+
+# 5. Experimental Setup
+
+# 5.1. Two-stage Learning
+
+We apply a two-stage training technique to train our model. In the first stage, we use four auxiliary classifiers to respectively train the capability feature  $\xi_{\eta}$ , target state feature, object feature and parent receptacle feature (i.e., the goal feature  $\xi_g^t$ ) in a supervised learning manner. These classifiers are lightweight and efficient, utilizing MLPs, and are trained using cross-entropy loss and the Adam optimizer, with a learning rate of  $1 \times 10^{-6}$  and a batch size of 32.
+
+In the second stage, we remove these four classifiers, keep the pre-trained opponent modeling module frozen, directly use the learnt opponent features  $\xi_{\eta}$  and  $\xi_g^t$ , and focus
+
+on the training of helping policy module. We use 20 kitchen rooms for helping policy training and 10 for evaluation in AI2-THOR [32]. The RLlib [15] framework and PPO [31] algorithm are applied to train our helping policy module. Unless otherwise stated, we use the default settings of RLlib. During training, the scene is randomly initialized with a new room, a new task, and a new capability distribution of the main agent, at each episode.
+
+We apply a progressive learning technique to train the help policy module. Firstly, we train the helper policy module for 840 epochs, with a constant learning rate of  $5 \times 10^{-5}$  without weight decay and a batch size of 128, using the reward defined in Eq. (3) with  $\lambda_{e} = 0.0$ . We find such "warm-up" quite important in helping the helper agent to familiarize itself with basic skills to complete goals and tasks. Secondly, we progressively train the model for 240 epochs with a learning rate of  $5 \times 10^{-7}$  and  $\lambda_{e} = 1.0$  in Eq. (3) to enhance the smart help ability. In the evaluation phase, we test the helper in 10 rooms (never used in training) and with 14 different task-capability pairs, repeating three times with different random seeds. We exclude 7 task-capability pairs as they will enable the main agent to finish the task independently. See supplementary for more details.
+
+# 5.2. Reward
+
+The reward of the helper is influenced by the goal  $g_{m}$  and the capability  $\eta_{m}$  of the main agent. During training, the helper agent will get a reward of 20 after finishing a goal of the main agent, corresponding to the first term in Eq. (3). The second term  $R^{e_{m}}(s,a_{h})$  in Eq. (3) is influenced by the capability of the main agent. Specifically, if the helper finishes a goal that the main agent can handle independently, the helper will get a punishment:  $R^{e_{m}}(s,a_{h}) = -30$ . For every step, the helper agent will get a cost of -0.12 normally and a cost of -0.5 if the action is illegal (e.g., attempting to open something that can not be opened, such as an apple) in the environment. If the task is not finished when the scenario is ended, the helper will receive a punishment of -20.
+
+# 5.3. Baselines
+
+To make a fair comparison, the baselines are:
+
+- Random. This helper randomly selects an action.  
+- End2end- $\lambda_{e} = 0.0$ . This model generates actions directly from the observation with MLPs, trained with  $\lambda_{e} = 0.0$  in Eq. (3). We set learning rate to  $5 \times 10^{-5}$ , batch size to 128. The model is trained for 350 epochs before convergence.  
+- End2end- $\lambda_{e} = 1.0$ . Similar to End2end- $\lambda_{e} = 0.0$ , but with  $\lambda_{e} = 1.0$  in Eq. (3).  
+- MCTS. This model uses a Monte-Carlo Tree Search (MCTS [3]) algorithm to search for an action with the highest value, given a predicted goal from the opponent modeling module. The value of each action is estimated by the status of goal completion after rollout, discounted
+
+by the number of steps taken to achieve this result.
+
+- MCTS-heuristic. This model combines the MCTS model with expert rules for the three selected tasks. Given a predicted goal from the opponent modeling module, it decides on which action to simulate at a probability  $p = 0.5$  by chance and  $p = 0.5$  by a rule-based selection of the next action to complete the goal.  
+-  $\mathbf{MCTS_{TG}}$ . This is an implementation to reproduce the high-level planning policy of Watch-and-Help [42]. This model knows the true goal of the main agent.  
+-  $\mathbf{MCTS}_{\mathbf{RG}}$ . This model is almost the same as  $MCTS_{TG}$  except that it follows a random goal.  
+- LLM. We use Large Language Model, i.e., gpt-3.5-turbo-instruct [37] as the helper. We compose a prompt based on the state observations from the AI2-THOR [32]. The prompt is fed into the LLM at every step. We extract the action decision generated from the LLM and evaluate its actual effectiveness in the AI2-THOR simulator. See supplementary for more details.
+
+# 5.4. Ablation Study
+
+To assess the contributions and efficacy of essential components in our method, we derive the following variants:
+
+- BaseModel. This model is the aforementioned helping policy model with a pre-trained parameter-frozen opponent modeling module. As in Sec. 5.1, we set  $\lambda_{e} = 0.0$  in Eq. (3), and train it for 840 epochs.  
+- BaseModel-w/o. Capability. Here we remove the capability embedding from the training of the helping policy.  
+- BaseModel- $\lambda_{e} = 1.0$ . This model is trained with  $\lambda_{e} = 1.0$  in Eq. (3) for 840 epochs.  
+- BaseModel-PL- $\lambda_{e} = 0.0$ . Here, "PL" means the Progressive Learning technique (detailed in Sec. 5.1), but with  $\lambda_{e} = 0.0$  in the second phase after the first warm-up phase. We simply continue to train the BaseModel with a smaller learning rate for 240 epochs (with no change in  $\lambda_{e} = 0.0$ ).  
+- BaseModel-PL- $\lambda_{e} = 1.0$  (our full model). We use the correct Progressive Learning technique (detailed in Sec. 5.1), and change to  $\lambda_{e} = 1.0$  in the second phase after warming up the basic skills of the helper model.
+
+# 5.5. Evaluation Metrics
+
+To objectively evaluate an agent's performance, we utilize six distinct metrics, where Helping Necessity (HN) and Helping Rate (HR) are first proposed in our work to better assess the Smart Help policy. Let  $N$  denote the size of the test scenarios, and let each scenario  $i$  be characterized by an initial room state  $s_i^0$  and a goal of transitioning the room to the target state  $s_i^*$ . Assuming that both the main agent and the helper require  $l_i$  steps (with a maximum of 30) to reach the final state  $s_i^l$ , we elaborate on these metrics as follows.
+
+- Success Rate (SR and GSR). It includes Task-
+
+conditioned Success Rate (SR) and Goal-conditioned Success Rate (GSR), respectively representing the completion degree of tasks and goals. The SR is defined as  $SR = \frac{1}{N}\sum_{i=1}^{N}R_{i}$ , where  $R_{i}$  is 1 if the task is finished. For task  $i$ , let  $N_{g_i^m}$  denote the effective goals completed by the main agent,  $N_{g_i^h}$  represent the effective goals completed by the helper, and  $N_{g_i^a}$  be all the effective goals of the task. The goal-conditioned success for task  $i$  is:  $GS_{i} = \frac{N_{g_{i}^{m}} + N_{g_{i}^{h}}}{N_{g_{i}^{a}}}$ . Hence, the overall GSR is defined as  $GSR = \frac{1}{N}\sum_{i=1}^{N}GS_{i}$ .  $R_{i} = 1$  if and only if  $GS_{i} = 1$ .
+
+- Helping Necessity (HN). This metric reflects the necessity of the helper's involvement. Only when the capability required to finish the goal exceeds the main agent's capability, the helping is necessary. Let  $N_{g_{\mathrm{nec},i}^h}$  denote the necessary goals completed by the helper, the Helping Necessity is then calculated as  $HN = \frac{1}{N}\sum_{i=1}^{N}\frac{N_{g_{\mathrm{nec},i}^h}}{N_{g_i^h}}R_i$ , where  $R_i = 1$  if the task is completed, otherwise  $R_i = 0$ . This assesses the helper's ability to swiftly identify the main agent's capability and provide necessary assistance.  
+- Helping Rate (HR).  $HR$  represents the helper's initiative to help.  $HR = \frac{N_{\text{help}}}{N_{\text{need\_help}}}$ , reflecting the probability of helping when the main agent needs help.  
+- Episode Length (EL). We record the average episode length to reflect the efficiency of helping policy. It is computed as:  $EL = \frac{1}{N}\sum_{i=1}^{N}l_i$ .  
+- Success-weighted by Path Length (SPL). We also include SPL to have a comprehensive evaluation. It is computed as:  $SPL = \frac{1}{N}\sum_{i=1}^{N}R_{i}\frac{d_{i}}{\max(d_{i},l_{i})}$ , where  $R_{i} \in \{0,1\}$  denotes whether the task is successfully completed,  $d_{i}$  represents the minimum number of steps to finish the task  $i$ , and  $l_{i}$  is the actual steps.
+
+Beyond these key metrics, we also incorporate the average rewards as a metric for evaluation. For the Smart Help challenge, we want to increase the  $HN$  and  $HR$ , while simultaneously descending the  $EL$ , as well as keeping the  $SR$ ,  $GSR$ , and  $SPL$  as high as possible.
+
+# 6. Results and Analyses
+
+Comparison with baselines. As shown in Tab. 1, our full model exhibits superior performance compared with all other baseline models without ground truth knowledge of the main agent. The Random agent, selecting random actions, and the  $MCTS_{RG}$  model, following random goals, both have minimal ability to provide appropriate help. The superiority of our BaseModel compared to the End2End model underscores the value of opponent modeling in the context of assistance tasks. The LLM agent, although has the shortest  $EL$ , falls short on other metrics compared with our model. The MCTS-heuristic model, which incorporates rule-based heuristics, outperforms the pure MCTS model.
+
+![](images/97a70cd3646284acf0182469e42abd40cab54e69897cb3439b5a2113bceb163a.jpg)  
+(a).BaseModel-PL-  $\lambda_{e} = 0$  (NormalHelp)
+
+![](images/dce0e1e3b57125fde9803893f730547577590c1ad02562bcdd16806bffa0b758.jpg)
+
+![](images/9b79d414220b59ace6c85aff8abe7809f99338497f765c95f1075c75c2e26c66.jpg)  
+(b).BaseModel-PL-  $\lambda_{\mathrm{e}} = 1$  (Smart Help)  
+Figure 3. Qualitative results of the learned smart help policy. In this example, the main agent moves directly to finish the goal ("(In, Potato, Microwave)", but fails at the goal " (Open, Microwave)". (a) The BaseModel-PL-  $\lambda_{e} = 0.0$  model not only helps the main agent with the bottleneck "(Open, Microwave), but also continues to help with another goal ((ToggleOff, Microwave)). (b) Our full model BaseModel-PL-  $\lambda_{e} = 1.0$  only offer necessary help with the bottleneck "(Open, Microwave)", and let the main agent to finish the rest goals independently, which helping policy is smarter since it considers the needs and emotional feelings of the main agent.
+
+![](images/0685dbefc6e918f88d9363091e12dde025dc862ded06672ce3fd140c03c14c29.jpg)
+
+However, our model achieves higher scores in  $SR$ ,  $GSR$ ,  $HN$ , and  $HR$ , while maintaining similar values for  $EL$  and  $SPL$ , indicating the effectiveness of its assistive action planning. The  $MCTS_{TG}$  model, knowing the true goal of the main agent, achieves the best performance among all the models, serving as an upper bound for the task. Notably, while it surpasses other models in most metrics, our model demonstrates competitive performance, particularly in  $HN$ . This suggests that our model achieves a balance by providing only necessary assistance and ensuring user comfort. The gap between our model and the upper bound shows potential for future research and further improvement.
+
+Ablation analysis. Comparing the BaseModel with BaseModel- $\lambda_{e} = 1.0$ , we find that setting  $\lambda_{e} = 0.0$  can augment the assisting actions of the helper. When compared with BaseModel-w/o. Capability, we find that the capability module contributes to the learning of the smart helping policy. Comparing the BaseModel-PL- $\lambda_{e} = 0.0$  with BaseModel-PL- $\lambda_{e} = 1.0$ , we find that after the initial "warm-up" of the basic skills, setting  $\lambda_{e} = 1.0$  in the second phase could greatly improve the  $HN$  while maintaining competitive performances across other metrics. Thus, as in Sec. 5.1, for our full model, in the BaseModel "warm-up" training phase, the model learns how to complete the goals and tasks, and the assistive actions are greatly encouraged; while in the second progressive learning phase, our full model focuses on improving the assistance strategy of the helper based on the main agent's needs and feelings.
+
+Qualitative Results. Fig. 3 demonstrates two helping cases with a baseline model and our full model. The two models exhibit exploration behaviors in the scene and finally learn to solve the bottleneck problem of the main agent. In comparison, the BaseModel-PL- $\lambda_{e} = 0.0$  only learns to
+
+<table><tr><td>Method</td><td>SR(↑)</td><td>GSR(↑)</td><td>HN(↑)</td><td>HR(↑)</td><td>Reward(↑)</td><td>EL(↓)</td><td>SPL(↑)</td></tr><tr><td>Random</td><td>0.074</td><td>0.364</td><td>0.054</td><td>0.057</td><td>-31.339</td><td>28.567</td><td>0.054</td></tr><tr><td>End2end-λe=0.0</td><td>0.267</td><td>0.441</td><td>0.149</td><td>0.315</td><td>-23.218</td><td>24.343</td><td>0.212</td></tr><tr><td>End2end-λe=1.0</td><td>0.067</td><td>0.372</td><td>0.057</td><td>0.057</td><td>-26.183</td><td>28.726</td><td>0.049</td></tr><tr><td>LLM</td><td>0.345</td><td>0.506</td><td>0.382</td><td>0.381</td><td>/</td><td>22.914</td><td>0.210</td></tr><tr><td>MCTS</td><td>0.178</td><td>0.482</td><td>0.266</td><td>0.328</td><td>/</td><td>26.743</td><td>0.126</td></tr><tr><td>MCTS-heuristic</td><td>0.274</td><td>0.528</td><td>0.355</td><td>0.400</td><td>/</td><td>24.692</td><td>0.199</td></tr><tr><td>MCTSTG</td><td>0.593</td><td>0.804</td><td>0.610</td><td>0.678</td><td>/</td><td>16.271</td><td>0.541</td></tr><tr><td>MCTSRG</td><td>0.043</td><td>0.348</td><td>0.015</td><td>0.015</td><td>/</td><td>28.950</td><td>0.042</td></tr><tr><td>BaseModel</td><td>0.419</td><td>0.515</td><td>0.408</td><td>0.412</td><td>-15.179</td><td>24.945</td><td>0.176</td></tr><tr><td>BaseModel-w/o. Capability</td><td>0.374</td><td>0.504</td><td>0.375</td><td>0.379</td><td>-13.852</td><td>23.748</td><td>0.235</td></tr><tr><td>BaseModel-λe=1.0</td><td>0.181</td><td>0.466</td><td>0.193</td><td>0.200</td><td>-17.185</td><td>27.448</td><td>0.122</td></tr><tr><td>BaseModel-PL-λe=0.0</td><td>0.488</td><td>0.556</td><td>0.455</td><td>0.496</td><td>-10.959</td><td>24.383</td><td>0.198</td></tr><tr><td>BaseModel-PL-λe=1.0 (Ours)</td><td>0.483</td><td>0.548</td><td>0.498</td><td>0.506</td><td>-10.625</td><td>24.650</td><td>0.200</td></tr></table>
+
+Table 1. The quantitative results of our experiments. The last ten environments in AI2-THOR are reserved for evaluation. The best results are highlighted in bold. Note that we include some oracle baselines and the upper bound performances are highlighted with underlines.
+
+help all the goals it successfully infers, while our full model BaseModel-PL- $\lambda_{e} = 1.0$  learns to decide whether to help based on its inferred goals and capabilities, i.e., only to help with " (Open, Microwave)".
+
+# 7. Conclusion
+
+In this paper, we propose the novel challenge Smart Help and build an environment and model that fosters smarter and more harmonious interaction between humans and artificial agents. We hope our challenge, environment, dataset, model and benchmark results will serve as valuable resources to future studies of this important problem.
+
+Acknowledgement This work is supported by the National Science and Technology Major Project (2022ZD0114900). We thank Zhenliang Zhang at BIGAI and Luyao Yuan at META for their helpful discussions.
+
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+        "text": "SmartEdit: Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models",
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+        "text": "Yuzhou Huang $^{1,2^{*\\#}}$  Liangbin Xie $^{2,3,5^{*\\#}}$  Xintao Wang $^{2,4\\dagger}$  Ziyang Yuan $^{2,7^{\\#}}$  Xiaodong Cun $^{4}$  Yixiao Ge $^{2,4}$  Jiantao Zhou $^{3}$  Chao Dong $^{5,6}$  Rui Huang $^{1}$  Ruimao Zhang $^{1\\dagger}$  Ying Shan $^{2,4}$ $^{1}$ The Chinese University of Hong Kong, Shenzhen (CUHK-SZ)  $^{2}$ ARC Lab, Tencent PCG  $^{3}$ University of Macau  $^{4}$ Tencent AI Lab Shenzhen Institute of Advanced Technology  $^{6}$ Shanghai Artificial Intelligence Laboratory  $^{7}$ Tsinghua University https://github.com/TencentARC/SmartEdit",
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+        "image_caption": [
+            "Figure 1. We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios."
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+        "text": "Abstract",
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+        "text": "Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we",
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+    {
+        "type": "text",
+        "text": "propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing.",
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+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "type": "page_footnote",
+        "text": "* Equal contribution † Corresponding author # Interns in ARC Lab, Tencent PCG",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users.",
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+        "text": "While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios.",
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+        "text": "The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task.",
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+        "type": "text",
+        "text": "While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In",
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+    {
+        "type": "text",
+        "text": "this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios.",
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+        "text": "The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high.",
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+        "type": "text",
+        "text": "In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios.",
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+        "text": "Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods.",
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+        "text": "In summary, our contributions are as follows:",
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+        "list_items": [
+            "1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research.",
+            "2. We leverage MLLMs to better comprehend instructions."
+        ],
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+        "page_idx": 1
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+        "text": "8363",
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+    {
+        "type": "text",
+        "text": "Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features.",
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+        "list_items": [
+            "3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability.",
+            "4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit."
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+    {
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+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1. Image Editing with Diffusion Models.",
+        "text_level": 1,
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "2.2. LLM with Diffusion Models",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models.",
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+    {
+        "type": "text",
+        "text": "3. Preliminary",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The goal of instruction-based image editing is to make specific modifications to an input image  $x$  based on instructions  $c_{T}$ , resulting in the target image  $y$ . InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image  $y$  and an encoder  $\\mathcal{E}$ , the diffusion process introduces noise to the encoded latent  $z = \\mathcal{E}(y)$ , resulting in a noisy latent  $z_{t}$ , with the noise level increasing over timesteps  $t \\in T$ . A UNet  $\\epsilon_{\\delta}$  is then trained to predict the noise added to the noisy latent  $z_{t}$ , given the image condition  $c_{x}$  and text instruction condition  $c_{T}$ , where  $c_{x} = \\mathcal{E}(x)$ . The",
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+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "\"Change the dog in mirror to a lion\"",
+        "bbox": [
+            192,
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+            325,
+            99
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "\"Change the black raspberry to a tangerine\"",
+        "bbox": [
+            334,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "\"Please remove the tool that is used to cut cakes.\"",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
+        "text": "中",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "header",
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+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "8364",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "image condition is incorporated by directly concatenating  $c_{x}$  and  $z_{t}$ . The specific objective of latent diffusion is as follows:",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ], c _ {T}) \\| _ {2} ^ {2} \\tag {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 3
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+    {
+        "type": "text",
+        "text": "where  $\\epsilon$  is the unscaled noise,  $t$  is the sampling step,  $z_{t}$  is latent noise at step  $t$ ,  $\\mathcal{E}(x)$  is the image condition, and  $c_{T}$  is the text instruction condition. The concat corresponds to the concatenation operation.",
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+    {
+        "type": "text",
+        "text": "Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section.",
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+    {
+        "type": "text",
+        "text": "4. Method",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. The Framework of SmartEdit",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Given an image  $x$  and instruction  $c$ , which is tokenized as  $(s_1, \\dots, s_T)$ , our goal is to obtain the target image  $y$  based on  $c$ . As shown in Fig 3, the image  $x$  is first processed by the image encoder and FC layer, resulting in  $v_{\\mu}(x)$ . Then  $v_{\\mu}(x)$  is sent into the LLM along with the token embedding  $(s_1, \\dots, s_T)$ . The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with  $r$  new tokens  $[\\mathrm{IMG}_1], \\dots, [\\mathrm{IMG}_r]$  and append the  $r$  [IMG] tokens to the end of instruction  $c$ . To be specific, we incorporate a trainable matrix  $\\mathbf{E}$  into the embedding matrix of the LLM, which represents the  $r$  [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "generated  $r$  [IMG] tokens, conditioned on tokens that have been generated previously:",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {\\mathrm {L L M}} (c) = - \\sum_ {i = 1} ^ {r} \\log p _ {\\{\\theta \\cup \\mathbf {E} \\}} ([ \\operatorname {I M G} _ {i} ] \\mid v _ {\\mu} (x), \\\\ \\left. s _ {1}, \\dots , s _ {T}, \\left[ \\mathrm {I M G} _ {1} \\right], \\dots , \\left[ \\mathrm {I M G} _ {i - 1} \\right]\\right) \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            550,
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The majority of parameters  $\\theta$  in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states  $h$  corresponding to the  $r$  [IMG] tokens as the input for the next module.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states  $h$  to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer  $Q_{\\beta}$  with 6-layer transformer [33] and  $n$  learnable queries, obtaining feature  $f$ . Subsequently, the image feature  $v$  output by the image encoder  $E_{\\phi}$  interacts with  $f$  through a bidirectional interaction module (BIM), resulting in  $f'$  and  $v'$ . The mentioned process is represented as:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} h = \\operatorname {L L a V A} (x, c), \\\\ \\begin{array}{l} f = Q _ {\\beta} (h), \\\\ F _ {n} (h) \\end{array} \\tag {3} \\\\ v = E _ {\\phi} (x), \\\\ f ^ {\\prime}, v ^ {\\prime} = \\operatorname {B I M} (f, v) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent  $\\mathcal{E}(x)$  and noisy latent  $z_{t}$ . Unlike Instructpix2pix, we use  $f'$  as the key and value in UNet, and combine  $v'$  into the features before entering UNet in a residual manner. The specific process can be formulated as:",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} L _ {\\text {d i f f u s i o n}} = \\mathbb {E} _ {\\mathcal {E} (y), \\mathcal {E} (x), c _ {T}, \\epsilon \\sim \\mathcal {N} (0, 1), t} [ \\| \\epsilon \\\\ - \\epsilon_ {\\delta} (t, \\operatorname {c o n c a t} [ z _ {t}, \\mathcal {E} (x) ] + v ^ {\\prime}, f ^ {\\prime}) \\| _ {2} ^ {2} \\tag {4} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To keep consistency with equation 1, we omit the Conv operation here.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Bidirectional Interaction Module",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output  $f$  from QFormer and the output  $v$  from the image encoder. After bidirectional information interaction between  $f$  and  $v$ , BIM will eventually output  $f'$  and  $v'$ . In BIM, the process begins with  $f$  undergoing a self-attention mechanism. After this,  $f$  serves as a query to interact with the input  $v$ , which acts as both key and value, through a cross-attention block. This interaction results in the generation of  $f'$  via a pointwise MLP. Following the creation of  $f'$ , it then serves as both key and value to interact with  $v$ , which now acts as a query. This second cross-attention interaction leads to the production of  $v'$ .",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "8365",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/f5c1c8473fe030a1883927546fec6f73a704f268f685ddf872dc104c62e009db.jpg",
+        "image_caption": [
+            "Figure 3. The overall framework of SmartEdit. For the instruction, we first append the  $r$  [IMG] tokens to the end of instruction  $c$ . Together with image  $x$ , they will be sent into LLaVA, which can then obtain the hidden states corresponding to these  $r$  [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature  $f$ . Subsequently, the image feature  $v$  output by the image encoder  $E_{\\phi}$  interacts with  $f$  through a bidirectional interaction module (BIM), resulting in  $f'$  and  $v'$ . The  $f'$  and  $v'$  are input into the diffusion models to achieve the instruction-based image editing task."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/ea735c5f999e0935c5452baed4b6ecaf115dbec6013268642a1af6d0f22583d5.jpg",
+        "image_caption": [
+            "Figure 4. The network design of the BIM Module. In this module, the input information  $f$  and  $v$  will undergo bidirectional information interaction through different cross-attention."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3.",
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.3. Dataset Utilization Strategy",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con-",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material.",
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+    {
+        "type": "text",
+        "text": "4.4. Reason-Edit for Better Evaluation",
+        "text_level": 1,
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+        "page_idx": 4
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+    {
+        "type": "text",
+        "text": "To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con",
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+    {
+        "type": "page_number",
+        "text": "8366",
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+    {
+        "type": "text",
+        "text": "sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods.",
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+    {
+        "type": "text",
+        "text": "5. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "5.1. Experimental Setting",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material.",
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+    {
+        "type": "text",
+        "text": "Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer.",
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+    {
+        "type": "text",
+        "text": "Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios.",
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+        "type": "text",
+        "text": "Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results",
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+    {
+        "type": "text",
+        "text": "from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align).",
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+        "type": "text",
+        "text": "5.2. Comparison with State-of-the-Art Methods",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits.",
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+    {
+        "type": "text",
+        "text": "The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA.",
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+        "type": "text",
+        "text": "However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the  $4_{th}$  and  $5_{th}$  rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. Also, when adopting a more powerful MLLM model, SmartEdit-13B performs better than SmartEdit-7B on Ins-align.",
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+        "type": "text",
+        "text": "\"What is the tool that is used to cut fruits. Remove this tool.\"",
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+    {
+        "type": "text",
+        "text": "\"Please replace food contains most vitamin with an orange.\"",
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+        "img_path": "images/d689782519dfd8bcbf9cb55c7207a38c30a65ed3c93b0040db07a4395793a18d.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/0f71668069997a6876f717e88f133d1a0acfd20213f4ced493612ba6c97380cd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/21ec1fa6696e197e1416d4810ebd7d29c7259855ef97dff24c7496e9676aa820.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"Please remove the object that can be used to have meals.\"",
+        "bbox": [
+            328,
+            231,
+            635,
+            242
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4c41a1b423755ec3450c5e042fcd3960f50f6c1dcd0e90c0f0a4a2e906ea1bcf.jpg",
+        "image_caption": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/992e0ba2a22f7f64cf611f72b1146b869ce28e0d48217b1f7d82f4168bcc9d30.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b3b2591e17801606f3a4b142808b6b3ec5aeef8511a7193830f5f8df912a2cac.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8978e8bb43ef97b1a3a6ad9a2df334d2b5fa3085ed0ed1a34e00191e5ed57a5b.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b5b9030de85756f023f6991f4e7c93ff20d28b666b731d4297e77e8c0bfe9742.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
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+    {
+        "type": "image",
+        "img_path": "images/833e91e275be906d8270c274d17a70cb75118ccf78eb2ac42bdfa233625f2d30.jpg",
+        "image_caption": [],
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+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"Change the middle panda to a cat\"",
+        "bbox": [
+            390,
+            306,
+            571,
+            316
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/c0a8d312101054ec2bd2bb8ae127c31450dda66fa6a95eefe28eb2c46f12957c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/711110d5cedae2dfd6e212d647012dbd105bd404131ec578f02f5f2f83128fec.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b4fb6b739a245ba0484ce270e6bf186e768d48d8ef8244388d64fe31ae108ae8.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/5530be603f1f4cd859944bb9a584d8f997e9907f7daf5fe0741434ddbb7a5030.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/36b37f9a4c1d8bacc82c1f2eff34b4ef8d97a97bea0a2c9fe620a2a57fa58c1b.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/ba332000f27e717434765d9db7ce7b88ecf6ca9bee74447f0cd0452ea7530477.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            686,
+            318,
+            784,
+            377
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"Change the cat in mirror to a tiger.\"",
+        "bbox": [
+            385,
+            378,
+            576,
+            388
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/aa8cbbf55762203fed39f44b51cb67c5900f6048c6fdf32f378421ffaefdd07e.jpg",
+        "image_caption": [
+            "Input Image",
+            "Figure 5. Qualitative comparison on Reason-Edit. When compared to several existing instruction editing methods that have undergone further fine-tuning on our synthetic editing dataset, our approach demonstrates superior editing capabilities in complex scenarios."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            181,
+            388,
+            279,
+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/72afc780cb6a3e2710d85b807a95c02ae4ce83078e74e0c2cf5144d429118978.jpg",
+        "image_caption": [
+            "InstructPix2Pix"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            290,
+            388,
+            388,
+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/23bb399c88f20697a58cdc051f4c8aab6dd36a9a3a67bfef0562852dc5041db7.jpg",
+        "image_caption": [
+            "MagicBrush"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            390,
+            388,
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+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b6a359ceb371dec36c97b12252d1148d654c1d22d6133f5c6814fcc79f6ff03b.jpg",
+        "image_caption": [
+            "InstructDiffusion"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/3f03be9e68a14c376f13b0064166210d11bc219cbc794a0a4ed2fe68545383ed.jpg",
+        "image_caption": [
+            "SmartEdit-7B"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            588,
+            388,
+            684,
+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/10505587151f1a37c2aa3705e9aca3f53a3069481b7e95990dd632b46fcf13ba.jpg",
+        "image_caption": [
+            "SmartEdit-13B"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            686,
+            388,
+            784,
+            474
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c707fd32c2bcd98e99975276a98b0594938ca1cd9da486ec7e0bc4cd898dd246.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Methods</td><td colspan=\"5\">Understanding Scenarios</td><td colspan=\"5\">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>InstructPix2Pix</td><td>21.576</td><td>0.721</td><td>0.089</td><td>22.762</td><td>0.537</td><td>24.234</td><td>0.707</td><td>0.083</td><td>19.413</td><td>0.344</td></tr><tr><td>MagicBrush</td><td>18.120</td><td>0.68</td><td>0.143</td><td>22.620</td><td>0.290</td><td>22.101</td><td>0.694</td><td>0.113</td><td>19.755</td><td>0.283</td></tr><tr><td>InstructDiffusion</td><td>23.258</td><td>0.743</td><td>0.067</td><td>23.080</td><td>0.697</td><td>21.453</td><td>0.666</td><td>0.117</td><td>19.523</td><td>0.483</td></tr><tr><td>SmartEdit-7B</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.611</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.950</td><td>0.789</td></tr><tr><td>SmartEdit-13B</td><td>23.596</td><td>0.751</td><td>0.068</td><td>23.536</td><td>0.771</td><td>25.757</td><td>0.747</td><td>0.051</td><td>20.777</td><td>0.817</td></tr></table>",
+        "bbox": [
+            101,
+            530,
+            870,
+            619
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit.",
+        "bbox": [
+            75,
+            621,
+            888,
+            650
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"What is the object that the dog's food should be put into? Remove this object.\"",
+        "bbox": [
+            125,
+            662,
+            421,
+            672
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/b822ded3281a0d80947b525ea25d15bff37f7667c456219b6c2b0d94601e97bb.jpg",
+        "image_caption": [
+            "Figure 6. Demonstration of the effectiveness of the BIM Module."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            112,
+            672,
+            434,
+            820
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "5.3. Ablation Study on BIM",
+        "text_level": 1,
+        "bbox": [
+            76,
+            847,
+            292,
+            863
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct",
+        "bbox": [
+            76,
+            869,
+            468,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"Please replace the animal that is lying on the grass with a fox\"",
+        "bbox": [
+            560,
+            661,
+            830,
+            671
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/8ec6bcbaa0d407c835ef1d35c20cd715362fe7b3e50030d2b27cfcaeb5e99c32.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            671,
+            586,
+            728
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2be4fdc566c0dcaf3d15f1fa675917f6949e1db66b28fcc18b85a0288bd70783.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            728
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/f12255bdd968ef068497398649c39e040706aa377cf9603ddb9e7d83282dcb57.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            660,
+            672,
+            730,
+            727
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7f4d9f98dfe1bd8db79287c372f9acaddf14196de5e933be7d5536a230c0f4dd.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            732,
+            672,
+            803,
+            727
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/08794862aa30241b1998a302b1ebffa25d9475e8ef07138bd812124e064bf0a7.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            805,
+            672,
+            877,
+            727
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "\"Change the red strawberry to a white pumpkin\"",
+        "bbox": [
+            593,
+            732,
+            799,
+            742
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/5cdc4a37c81cf54440b9de80886ba5f1d95246442498591d68cfdb8abdcad7cc.jpg",
+        "image_caption": [
+            "Input Image",
+            "Figure 7. Demonstration of the significance of joint training with multiple datasets."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            514,
+            742,
+            586,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/576c36cdfa99cbc7c29ae4a4740e4d733a565cfff3c4a76ff748c3fa301beaa4.jpg",
+        "image_caption": [
+            "Edit"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            588,
+            742,
+            658,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/dfb36085eba9a4b01687154d71952a07eebdb5985d8efe147afce5863f10708d.jpg",
+        "image_caption": [
+            "Edit+Seg"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            660,
+            742,
+            730,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/fd7eddfa0d375c4c4659189f784d04640aa2afd84e6863fa3dc149d7b5e47bea.jpg",
+        "image_caption": [
+            "Edit+Reason-Edit"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            732,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/937a9798d99aa9d4fe48b25bb9ba17a3ef4926b3d20301e5a3326e1449f1ca41.jpg",
+        "image_caption": [
+            "Total"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            805,
+            742,
+            879,
+            799
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "comparative experiments on the SmartEdit-7B model. The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in",
+        "bbox": [
+            500,
+            854,
+            890,
+            900
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "8368",
+        "bbox": [
+            482,
+            944,
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+            955
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/43ff37a01b8ec83eea3fa3bac6bab82f091d17d2602eb660b2e2cc1df53d2e63.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Exp ID</td><td rowspan=\"2\">Plain</td><td rowspan=\"2\">SimpleCA</td><td rowspan=\"2\">BIM</td><td colspan=\"5\">Understanding Scenarios</td><td colspan=\"5\">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>1</td><td>✓</td><td></td><td></td><td>20.975</td><td>0.713</td><td>0.108</td><td>23.36</td><td>0.695</td><td>23.848</td><td>0.725</td><td>0.074</td><td>20.33</td><td>0.694</td></tr><tr><td>2</td><td></td><td>✓</td><td></td><td>19.557</td><td>0.692</td><td>0.126</td><td>23.66</td><td>0.692</td><td>23.508</td><td>0.716</td><td>0.081</td><td>20.17</td><td>0.722</td></tr><tr><td>3</td><td></td><td></td><td>✓</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.61</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.95</td><td>0.789</td></tr></table>",
+        "bbox": [
+            81,
+            88,
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+            148
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/c113f2fc2ffa062fa9588efcad3f1da18db80bf666a6cbfe2a15495f056ed371.jpg",
+        "table_caption": [
+            "Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Exp ID</td><td rowspan=\"2\">Edit</td><td rowspan=\"2\">Segmentation</td><td rowspan=\"2\">Synthetic editing dataset</td><td colspan=\"5\">Understanding Scenarios</td><td colspan=\"5\">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>1</td><td>✓</td><td></td><td></td><td>17.568</td><td>0.664</td><td>0.171</td><td>22.79</td><td>0.201</td><td>22.400</td><td>0.706</td><td>0.102</td><td>19.22</td><td>0.233</td></tr><tr><td>2</td><td>✓</td><td>✓</td><td></td><td>18.960</td><td>0.690</td><td>0.143</td><td>22.83</td><td>0.361</td><td>21.774</td><td>0.693</td><td>0.116</td><td>19.82</td><td>0.311</td></tr><tr><td>3</td><td>✓</td><td></td><td>✓</td><td>19.562</td><td>0.702</td><td>0.111</td><td>22.32</td><td>0.440</td><td>23.595</td><td>0.715</td><td>0.079</td><td>20.43</td><td>0.567</td></tr><tr><td>4</td><td>✓</td><td>✓</td><td>✓</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.61</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.95</td><td>0.789</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "5.4. Ablation Study on Dataset Usage",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training",
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects.",
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+    },
+    {
+        "type": "text",
+        "text": "6. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing.",
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+    },
+    {
+        "type": "text",
+        "text": "Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen).",
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+    },
+    {
+        "type": "page_number",
+        "text": "8369",
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+    },
+    {
+        "type": "text",
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2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/a4f5fe59-781a-4bca-bc8e-e339b6bcabf9_origin.pdf

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2024/SmartEdit_ Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models/full.md

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+# SmartEdit: Exploring Complex Instruction-based Image Editing with Multimodal Large Language Models
+
+Yuzhou Huang $^{1,2^{*\#}}$  Liangbin Xie $^{2,3,5^{*\#}}$  Xintao Wang $^{2,4\dagger}$  Ziyang Yuan $^{2,7^{\#}}$  Xiaodong Cun $^{4}$  Yixiao Ge $^{2,4}$  Jiantao Zhou $^{3}$  Chao Dong $^{5,6}$  Rui Huang $^{1}$  Ruimao Zhang $^{1\dagger}$  Ying Shan $^{2,4}$ $^{1}$ The Chinese University of Hong Kong, Shenzhen (CUHK-SZ)  $^{2}$ ARC Lab, Tencent PCG  $^{3}$ University of Macau  $^{4}$ Tencent AI Lab Shenzhen Institute of Advanced Technology  $^{6}$ Shanghai Artificial Intelligence Laboratory  $^{7}$ Tsinghua University https://github.com/TencentARC/SmartEdit
+
+![](images/0cddff250e1da8feb141963c68da27be358057cf683357a2dbb7f17c5543e8e0.jpg)  
+Figure 1. We propose SmartEdit, an instruction-based image editing model that leverages Multimodal Large Language Models (MLLMs) to enhance the understanding and reasoning capabilities of instruction-based editing methods. With the specialized design, our SmartEdit is capable of handling complex understanding (the instructions that contain various object attributes like location, relative size, color, and in or outside the mirror) and reasoning scenarios.
+
+# Abstract
+
+Current instruction-based image editing methods, such as InstructPix2Pix, often fail to produce satisfactory results in complex scenarios due to their dependence on the simple CLIP text encoder in diffusion models. To rectify this, this paper introduces SmartEdit, a novel approach of instruction-based image editing that leverages Multimodal Large Language Models (MLLMs) to enhance its understanding and reasoning capabilities. However, direct integration of these elements still faces challenges in situations requiring complex reasoning. To mitigate this, we
+
+propose a Bidirectional Interaction Module (BIM) that enables comprehensive bidirectional information interactions between the input image and the MLLM output. During training, we initially incorporate perception data to boost the perception and understanding capabilities of diffusion models. Subsequently, we demonstrate that a small amount of complex instruction editing data can effectively stimulate SmartEdit's editing capabilities for more complex instructions. We further construct a new evaluation dataset, Reason-Edit, specifically tailored for complex instruction-based image editing. Both quantitative and qualitative results on this evaluation dataset indicate that our SmartEdit surpasses previous methods, paving the way for the practical application of complex instruction-based image editing.
+
+# 1. Introduction
+
+Text-to-image synthesis [8, 13, 23, 26, 27, 29] has experienced significant advancements in recent years, thanks to the development of diffusion models. These methods have enabled the generation of images that are not only consistent with natural language descriptions, but also align with human perception and preferences, marking a substantial leap forward in the field. Instruction-based image editing methods [1, 36], represented by InstructPix2Pix, leverage pre-trained text-to-image diffusion models as priors. This allows users to conveniently and effortlessly modify images through natural language instructions for ordinary users.
+
+While existing instruction-based image editing methods can handle simple instructions effectively, they often fall short when dealing with complex scenarios, which require the model to have a more powerful understanding and reasoning capabilities. As depicted in Fig. 1, there are two common types of complex scenarios. The first is when the original image contains multiple objects, and the instruction modifies only one of these objects through certain attributes (such as location, relative size, color, in or outside the mirror). The other is when world knowledge is needed to identify the object to be edited (such as the object that can tell the time). We define these two types as complex understanding scenarios and complex reasoning scenarios, respectively. Handling these two scenarios is crucial for practical instruction editing, but existing instruction-based image editing methods probably fail in these scenarios (as shown in Fig. 2). In this paper, we attempt to identify the reasons why existing instruction-based image editing methods fail in these scenarios, and try to tackle the challenge in these scenarios.
+
+The first reason why existing instruction-based image editing methods fail in these scenarios is that they typically rely on a simple CLIP text encoder [25] in diffusion models (e.g., Stable Diffusion) to process the instructions. Under this circumstance, these models struggle to 1) understand and reason through the instructions, and 2) integrate the image to comprehend the instructions. To address these limitations, we introduce the Multimodal Large Language Models (MLLMs) (e.g., LLaVA) [22, 39] into instruction-based editing models. Our method, SmartEdit, jointly optimizes MLLMs and diffusion models, leveraging the powerful reasoning capabilities of MLLMs to facilitate instruction-based image editing task.
+
+While substituting the CLIP encoder in the diffusion model with MLLMs can alleviate some problems, this approach still falls short when it comes to examples that necessitate complex understanding and reasoning. This is because the input image to edit (original image) is integrated into the UNet of the Stable Diffusion model through a straightforward concatenation, which is further interacted with MLLM outputs through a cross-attention operation. In
+
+this setup, the image features serve as the query, and MLLM outputs act as the key and value. This means that the MLLM outputs unilaterally modulate and interact with the image feature, which affects the results. To alleviate this issue, we further propose a Bidirectional Interaction Module (BIM). This module reuses the image information extracted by the LLaVA's visual encoder from the input image. It also facilitates a comprehensive bidirectional information interaction between this image and the MLLM output, enabling the model to perform better in complex scenarios.
+
+The second reason contributing to the failure of existing instruction-based editing methods is the absence of specific data. When solely training on editing datasets, such as the datasets used in Instructpix2pix [1] and MagicBrush [36], SmartEdit also struggles to handle scenarios requiring complex reasoning and understanding. This is because SmartEdit has not been exposed to data from these scenarios. One straightforward approach is to generate a substantial amount of paired data similar to those scenarios. However, this method is excessively expensive because the cost of generating data for these scenarios is high.
+
+In this paper, we find that there are two keys to compensate the insufficiency of specific editing data. The first is to enhance the perception capabilities of UNet [28], and the second is to stimulate the model capacity in those scenarios with a few high-quality examples. Correspondingly, we 1) incorporate the perception-related data (e.g., segmentation) into the model's training. 2) synthesize a few high-quality paired data with complex instructions to fine-tune our SmartEdit (similar to LISA [19]). In this way, SmartEdit not only reduces the reliance on paired data under complex scenarios but also effectively stimulates its ability to handle these scenarios.
+
+Equipped with both the model designs and the data utilization strategy, SmartEdit can understand complex instructions, surpassing the scope that previous instruction editing methods can do. To better evaluate the understanding and reasoning ability of instruction-based image editing methods, we collect the Reason-Edit dataset, which contains a total of 219 image-text pairs. Note that there is no overlap between the Reason-Edit dataset and the small-amount high-quality synthesized training data pairs. Based on the Reason-Edit dataset, we evaluate existing instruction-based image editing methods comprehensively. Both the quantitative and qualitative results on the ReasonEdit dataset indicate that SmartEdit significantly outperforms previous instruction-based image editing methods.
+
+In summary, our contributions are as follows:
+
+1. We analyze and focus on the performance of instruction-based image editing methods in more complex instructions. These complex scenarios have often been overlooked and less explored in past research.  
+2. We leverage MLLMs to better comprehend instructions.
+
+Figure 2. For more complex instructions or scenarios, InstructPix2Pix fails to follow the instructions.
+
+To further improve the performance, we propose a Bidirectional Interaction Module to facilitate the interaction of information between text and image features.
+
+3. We propose a new dataset utilization strategy to enhance the performance of SmartEdit in complex scenarios. In addition to using conventional editing data, we introduce perception-related data to strengthen the perceptual ability of UNet in the diffusion process. Besides, we also add a small amount of synthetic editing data to further stimulate the model's reasoning ability.  
+4. An evaluation dataset, Reason-Edit, is specifically collected for evaluating the performance of instruction-based image editing tasks in complex scenarios. Both qualitative and quantitative results on Reason-Edit demonstrate the superiority of SmartEdit.
+
+# 2. Related Work
+
+# 2.1. Image Editing with Diffusion Models.
+
+Pretrained text-to-image diffusion models [8, 13, 23, 26, 27, 29] can strongly assist image editing task. Instruction-based image editing task [1, 4, 11, 12, 16, 17, 32, 36, 38] requires users to provide an instruction, which converts the original image to a newly designed image that matches the given instruction. Some methods can achieve this by utilizing a tuning-free approach. For example, Prompt-to-Prompt [12] suggests modifying the cross-attention maps by comparing the original input caption with the revised caption. MasaCtrl [4] converts existing self-attention in diffusion models into mutual self-attention, which can help query correlated local contents and textures from source images for consistency. In addition, due to the scarcity of paired image-instruction editing datasets, the pioneering work InstructPix2Pix [1] introduces a large-scale vision-language image editing datasets created by fine-tuned GPT-3 [2] and Prompt-to-Prompt with stable diffusion, and further finetunes the UNet [28], which can edit images by providing a simple instruction. To enhance the editing effect of InstructPix2Pix on real images, MagicBrush [36] further provides a large-scale and manually annotated dataset for instruction-guided real image editing.
+
+The recent work, InstructDiffusion [11], also adopts the network design of InstructPix2Pix and focuses on unifying vision tasks in a joint training manner. By taking advantage of multiple different datasets, it can handle a variety of vision tasks, including understanding tasks (such as segmen
+
+tation and keypoint detection) and generative tasks (such as editing and enhancement). Compared with InstructDiffusion, our primary focus is on the field of instruction-based image editing, especially for complex understanding and reasoning scenarios. In these scenarios, InstructDiffusion typically generates inferior results.
+
+# 2.2. LLM with Diffusion Models
+
+The exceptional open-sourced LLaMA [6, 31] significantly enhances the performance of vision tasks with the aid of Large Language Models (LLMs). Pioneering works such as LLaVA and MiniGPT-4 have improved image-text alignment through instruction-tuning. While numerous MLLM-based [7, 22, 24, 39] studies have demonstrated their robust capabilities across a variety of tasks, primarily those reliant on text generation (e.g., human-robot interaction, complex reasoning, science question answering, etc.), GILL [18] serves as a bridge between MLLMs and diffusion models. It learns to process images with LLMs and is capable of generating coherent images based on the input texts. SEED [9] presents an innovative image tokenizer to enable LLM to process and generate images and text concurrently. SEED-2 [10] further refines the tokenizer by aligning the generation embedding with the image embedding of unCLIP-SD, which allows for better preservation of rich visual semantics and reconstruction of more realistic images. Emu [30] can be characterized as a multimodal generalist, trained with the next-token-prediction objective. CM3Leon [35] proposes a multi-modal language model that is capable of executing text-to-image and image-to-text generation. It employs the CM3 multi-modal architecture that is fine-tuned on diverse instruction-style data, and utilizes a training method adapted from text-only language models.
+
+# 3. Preliminary
+
+The goal of instruction-based image editing is to make specific modifications to an input image  $x$  based on instructions  $c_{T}$ , resulting in the target image  $y$ . InstructPix2Pix, which is based on latent diffusion, is a seminal work in this field. For the target image  $y$  and an encoder  $\mathcal{E}$ , the diffusion process introduces noise to the encoded latent  $z = \mathcal{E}(y)$ , resulting in a noisy latent  $z_{t}$ , with the noise level increasing over timesteps  $t \in T$ . A UNet  $\epsilon_{\delta}$  is then trained to predict the noise added to the noisy latent  $z_{t}$ , given the image condition  $c_{x}$  and text instruction condition  $c_{T}$ , where  $c_{x} = \mathcal{E}(x)$ . The
+
+image condition is incorporated by directly concatenating  $c_{x}$  and  $z_{t}$ . The specific objective of latent diffusion is as follows:
+
+$$
+\begin{array}{l} L _ {\text {d i f f u s i o n}} = \mathbb {E} _ {\mathcal {E} (y), \mathcal {E} (x), c _ {T}, \epsilon \sim \mathcal {N} (0, 1), t} [ \| \epsilon \\ - \epsilon_ {\delta} (t, \operatorname {c o n c a t} [ z _ {t}, \mathcal {E} (x) ], c _ {T}) \| _ {2} ^ {2} \tag {1} \\ \end{array}
+$$
+
+where  $\epsilon$  is the unscaled noise,  $t$  is the sampling step,  $z_{t}$  is latent noise at step  $t$ ,  $\mathcal{E}(x)$  is the image condition, and  $c_{T}$  is the text instruction condition. The concat corresponds to the concatenation operation.
+
+Although InstructPix2Pix has some effectiveness in instruction editing, its performance is limited when dealing with complex understanding and reasoning scenarios. To address this issue, we introduce a Multimodal Large Language Model (MLLM) into the network architecture and propose a Bidirectional Interaction Module (BIM) to implement bidirectional information interaction between the MLLM output and image information. In addition, we also explore the data utilization strategy and find that perception-related data and a small amount of complex editing data are crucial for enhancing model's performance. We provide detailed descriptions of these aspects in the next section.
+
+# 4. Method
+
+In this paper, we introduce SmartEdit, specifically designed to handle complex instruction editing scenarios. In this section, we first provide a detailed overview of the framework of SmartEdit (Section 4.1). Then, we delve into the Bidirectional Interaction Module (Section 4.2). In Section 4.3, we discuss how to enhance the perception and understanding capabilities of UNet in the diffusion model and stimulate the ability of MLLMs to handle complex scenarios. Finally, We introduce Reason-Edit, which is primarily used to evaluate the ability of instruction-based image editing methods toward complex scenarios. (Section 4.4).
+
+# 4.1. The Framework of SmartEdit
+
+Given an image  $x$  and instruction  $c$ , which is tokenized as  $(s_1, \dots, s_T)$ , our goal is to obtain the target image  $y$  based on  $c$ . As shown in Fig 3, the image  $x$  is first processed by the image encoder and FC layer, resulting in  $v_{\mu}(x)$ . Then  $v_{\mu}(x)$  is sent into the LLM along with the token embedding  $(s_1, \dots, s_T)$ . The output of the LLM is discrete tokens, which cannot be used as the input for subsequent modules. Therefore, we take the hidden states corresponding to these discrete tokens as the input for the following modules. To jointly optimize LLaVA and the diffusion model, following GILL [18], we expand the original LLM vocabulary with  $r$  new tokens  $[\mathrm{IMG}_1], \dots, [\mathrm{IMG}_r]$  and append the  $r$  [IMG] tokens to the end of instruction  $c$ . To be specific, we incorporate a trainable matrix  $\mathbf{E}$  into the embedding matrix of the LLM, which represents the  $r$  [IMG] token embeddings. Subsequently, we minimize the negative log-likelihood of
+
+generated  $r$  [IMG] tokens, conditioned on tokens that have been generated previously:
+
+$$
+\begin{array}{l} L _ {\mathrm {L L M}} (c) = - \sum_ {i = 1} ^ {r} \log p _ {\{\theta \cup \mathbf {E} \}} ([ \operatorname {I M G} _ {i} ] \mid v _ {\mu} (x), \\ \left. s _ {1}, \dots , s _ {T}, \left[ \mathrm {I M G} _ {1} \right], \dots , \left[ \mathrm {I M G} _ {i - 1} \right]\right) \tag {2} \\ \end{array}
+$$
+
+The majority of parameters  $\theta$  in the LLM are kept frozen and we utilize LoRA [15] to carry out efficient fine-tuning. We take the hidden states  $h$  corresponding to the  $r$  [IMG] tokens as the input for the next module.
+
+Considering the discrepancy between the feature spaces of the hidden states in the LLM and the clip text encoder, we need to align the hidden states  $h$  to the clip text encoder space. Inspired by BLIP2 [20] and DETR [5], we adopt the QFormer  $Q_{\beta}$  with 6-layer transformer [33] and  $n$  learnable queries, obtaining feature  $f$ . Subsequently, the image feature  $v$  output by the image encoder  $E_{\phi}$  interacts with  $f$  through a bidirectional interaction module (BIM), resulting in  $f'$  and  $v'$ . The mentioned process is represented as:
+
+$$
+\begin{array}{l} h = \operatorname {L L a V A} (x, c), \\ \begin{array}{l} f = Q _ {\beta} (h), \\ F _ {n} (h) \end{array} \tag {3} \\ v = E _ {\phi} (x), \\ f ^ {\prime}, v ^ {\prime} = \operatorname {B I M} (f, v) \\ \end{array}
+$$
+
+For the diffusion model, following the design of Instructpix2pix, we concat the encoded image latent  $\mathcal{E}(x)$  and noisy latent  $z_{t}$ . Unlike Instructpix2pix, we use  $f'$  as the key and value in UNet, and combine  $v'$  into the features before entering UNet in a residual manner. The specific process can be formulated as:
+
+$$
+\begin{array}{l} L _ {\text {d i f f u s i o n}} = \mathbb {E} _ {\mathcal {E} (y), \mathcal {E} (x), c _ {T}, \epsilon \sim \mathcal {N} (0, 1), t} [ \| \epsilon \\ - \epsilon_ {\delta} (t, \operatorname {c o n c a t} [ z _ {t}, \mathcal {E} (x) ] + v ^ {\prime}, f ^ {\prime}) \| _ {2} ^ {2} \tag {4} \\ \end{array}
+$$
+
+To keep consistency with equation 1, we omit the Conv operation here.
+
+# 4.2. Bidirectional Interaction Module
+
+The design of BIM is depicted in Fig 4. It includes a self-attention block, two cross-attention blocks, and an MLP layer. The two inputs of BIM are the output  $f$  from QFormer and the output  $v$  from the image encoder. After bidirectional information interaction between  $f$  and  $v$ , BIM will eventually output  $f'$  and  $v'$ . In BIM, the process begins with  $f$  undergoing a self-attention mechanism. After this,  $f$  serves as a query to interact with the input  $v$ , which acts as both key and value, through a cross-attention block. This interaction results in the generation of  $f'$  via a pointwise MLP. Following the creation of  $f'$ , it then serves as both key and value to interact with  $v$ , which now acts as a query. This second cross-attention interaction leads to the production of  $v'$ .
+
+![](images/f5c1c8473fe030a1883927546fec6f73a704f268f685ddf872dc104c62e009db.jpg)  
+Figure 3. The overall framework of SmartEdit. For the instruction, we first append the  $r$  [IMG] tokens to the end of instruction  $c$ . Together with image  $x$ , they will be sent into LLaVA, which can then obtain the hidden states corresponding to these  $r$  [IMG] tokens. Then the hidden state is sent into the QFormer and gets feature  $f$ . Subsequently, the image feature  $v$  output by the image encoder  $E_{\phi}$  interacts with  $f$  through a bidirectional interaction module (BIM), resulting in  $f'$  and  $v'$ . The  $f'$  and  $v'$  are input into the diffusion models to achieve the instruction-based image editing task.
+
+![](images/ea735c5f999e0935c5452baed4b6ecaf115dbec6013268642a1af6d0f22583d5.jpg)  
+Figure 4. The network design of the BIM Module. In this module, the input information  $f$  and  $v$  will undergo bidirectional information interaction through different cross-attention.
+
+As discussed in the introduction, the proposed BIM module reuses the image feature and inputs it as supplementary information into UNet. The implementation of two cross-attention blocks in this module facilitates a robust bidirectional information interaction between the image feature and the text feature. Compared to not adopting the BIM module or only fusing the image feature and text feature in one direction, SmartEdit which is equipped with the BIM module yields better results. The experimental comparison of different designs is shown in Section 5.3.
+
+# 4.3. Dataset Utilization Strategy
+
+During the training process of SmartEdit, two primary challenges emerge when solely utilizing datasets gathered from InstructPix2Pix and MagicBrush as the training set. The first challenge is that SmartEdit has a poor perception of position and concept. The second challenge is that, despite being equipped with MLLM, SmartEdit still has limited capability in scenarios that require reasoning. In summary, the effectiveness of SmartEdit in handling complex scenarios is limited if it is only trained on conventional editing datasets. After analysis, we have identified the causes of these issues. The first issue stems from the UNet in the diffusion model which lacks an understanding of perception and concepts, leading to SmartEdit's poor perception of position and con-
+
+cept. The second issue is that SmartEdit has limited exposure to editing data that requires reasoning abilities, which in turn limits its reasoning capabilities.
+
+To tackle the first issue, we incorporate the segmentation data into the training set. Such modifications significantly enhanced the perception capabilities of the SmartEdit model. Regarding the second issue, we take inspiration from LISA [19] that a minimal amount of reasoning segmentation data can efficiently activate MLLM's reasoning capacity. Guided by this insight, we establish a data production pipeline and synthesize 476 paired data (each sample contains original image, instruction, and synthetic target image) as a supplement to the training data. This synthetic editing dataset includes two major types of scenarios: complex understanding and reasoning scenarios. For complex understanding scenarios, the original image contains multiple objects and the corresponding instruction modifies the specific object based on various attributes (i.e., location, color, relative size, and in or outside the mirror). We specifically consider the mirror attribute because it is a typical example that requires a strong understanding of the scene (both inside and outside the mirror) to perform well. For reasoning scenarios, we involve complex reasoning cases that need world knowledge to identify the specific object. The effectiveness of this synthetic editing dataset and the impact of different datasets on the model's performance are detailed in Section 5.4. The details of the data production pipeline and some visual examples are described in the supplementary material.
+
+# 4.4. Reason-Edit for Better Evaluation
+
+To better evaluate existing instruction editing methods and SmartEdit's capabilities in complex understanding and reasoning scenarios, we collect an evaluation dataset, ReasonEdit. Reason-Edit consists of 219 image-text pairs. Con
+
+sistent with the synthetic training data pairs, Reason-Edit is also categorized in the same manner. Note that there is no overlap between the data in Reason-Edit and the synthetic training set. With Reason-Edit, we can thoroughly test the performance of instruction-based image editing models in terms of understanding and reasoning scenarios. We hope more researchers will pay attention to the capabilities of instruction-based image editing models from these perspectives, thereby fostering the practical application of instruction-based image editing methods.
+
+# 5. Experiments
+
+# 5.1. Experimental Setting
+
+Training Process and Implementation Details. The training process and implementation details of SmartEdit can be found in the supplementary material.
+
+Network Architecture. For the Large Language Model with visual input (e.g., LLaVA), we choose LLaVA-1.1-7b and LLaVA-1.1-13b as the base model. During training, the weights of LLaVA are frozen and we add LoRA for efficient fine-tuning. In LoRA, the values of the two parameters, dim and alpha, are 16 and 27, respectively. We expand the original LLM vocabulary with 32 new tokens. The QFormer is composed of 6-layer transformer [33] and 77 learnable query tokens. In the BIM module, there is a self-attention block, two cross-attention blocks, and an MLP layer.
+
+Training Datasets. For the training process of SmartEdit, the training data can be divided into 4 categories: (1) segmentation datasets, which include COCOStuff [3], RefCOCO [34], GRefCOCO [21], and the reasoning segmentation dataset from LISA [19]; (2) editing datasets, which involve InstructPix2Pix and MagicBrush; (3) visual question answering (VQA) dataset, which is the LLaVA-Instruct-150k dataset [22]; (4) synthetic editing dataset, where we collect a total of 476 paired data for complex understanding and reasoning scenarios.
+
+Evaluation Metrics. As we hope to only change the foreground of the image while keeping the background unchanged for editing, we adopt three metrics for the background area: PSNR, SSIM, and LPIPS [14, 37]. For the foreground area, we calculate CLIP Score [25] between the foreground area of the edited image and the GT label. The GT label is annotated manually. Among these four metrics, except for LPIPS where lower is better, the other three metrics are higher the better. While these metrics can reflect the performance to a certain extent, they are not entirely accurate. To provide a more accurate evaluation of the effects of edited images, we propose a metric for assessing editing accuracy. Specifically, we hire four workers to manually evaluate the results of these different methods on Reason-Edit. The evaluation criterion is whether the edited image aligns with the instruction. After obtaining the evaluation results
+
+from each worker, we average all the results to get the final metric result, which is Instruction-Alignment (Ins-align).
+
+# 5.2. Comparison with State-of-the-Art Methods
+
+We compare SmartEdit with existing SOTA instruction-based image editing methods, namely InstructPix2Pix, MagicBrush, and InstructDiffusion. Considering that these released models are trained on specific datasets, they would inevitably perform poorly if directly evaluated on ReasonEdit. To ensure a fair comparison, we fine-tune these methods on the same training set used by SmartEdit, and evaluate the fine-tuned models on Reason-Edit. The experimental results are shown in Tab. 1. From the quantitative results of the reasoning scenarios in the table, it can be observed that when we replace the clip text encoder in the diffusion model with LLaVA and adopt the proposed BIM module, both SmartEdit-7B and SmartEdit-13B achieve better results on these five metrics. This suggests that in scenarios requiring reasoning from instructions, a simple clip text encoder may struggle to understand the meaning of the instructions. However, the MLLM can fully utilize its powerful reasoning ability and world knowledge to correctly identify the corresponding objects and perform edits.
+
+The qualitative results further illustrate this point. As shown in Fig. 5, the first three examples are reasoning scenarios. In the first example, both SmartEdit-7B and SmartEdit-13B successfully identify the tool used for cutting fruit (knife) and remove it, while keeping the rest of the background unchanged. The second example can also be handled well by both of them. However, in the third example, we observe a difference in performance. Only SmartEdit-13B can accurately locate the object and perform the corresponding edits without altering other background areas. This suggests that in instruction-based image editing tasks that require reasoning, a more powerful MLLM model can effectively generalize its reasoning ability to this task. This observation aligns with the findings from LISA.
+
+However, for understanding scenarios, we observe a difference in performance between SmartEdit-7B and SmartEdit-13B when compared to InstructDiffusion on PSNR/SSIM/LPIPS. Specifically, SmartEdit-7B performs worse than InstructDiffusion, while SmartEdit-13B outperforms InstructDiffusion on these metrics. Upon further analysis of the qualitative results, as shown in the  $4_{th}$  and  $5_{th}$  rows of Fig. 5, we find that from a visual perspective, both SmartEdit-7B and SmartEdit-13B appear superior to InstructDiffusion. This suggests that the three metrics do not always align with human visual perception. We confirm this phenomenon in the supplementary material. From the result of the Ins-align metric, it can be observed that SmartEdit shows a significant improvement compared to previous instruction-based image editing methods. Also, when adopting a more powerful MLLM model, SmartEdit-13B performs better than SmartEdit-7B on Ins-align.
+
+"What is the tool that is used to cut fruits. Remove this tool."
+
+![](images/6bc85be1f86c219aba6e3151188cda4a67ea4be65a7debd04e9f34ab0188cda4.jpg)
+
+![](images/6e3589d589ebb96025d134f94b508cb62cf34b72e4da5bcc44bf2f6922e02286.jpg)
+
+![](images/e7d960d7226904cfbbaaf543777d81e3b6077efc3c0b044645854aa10a2cb8f0.jpg)
+
+![](images/a50b8238129b0a03ceab42d0e57ca8fb04caa4e2f9d251f3af614c81584c94d1.jpg)
+
+![](images/19d204169620e369a8e8718e561eee41c5be01cdfaf0d896acd98329528b8c81.jpg)
+
+![](images/7ff9e27bfcda6d1a644cd1d02cf9db3249b5e4e9b201b509ebd6304f7738c136.jpg)
+
+"Please replace food contains most vitamin with an orange."
+
+![](images/0f774d92aaa7abdff996f16194a2362b9f51a6a2d3cbb5d919997507fd845591.jpg)
+
+![](images/0d3c838fcf97c70e6113ecbad7cb13776d10669f95acbf5b9853c7c5684382c7.jpg)
+
+![](images/f4578766e3262c5022e76eadbcac7ce8494874e8df2aebc2e4cb82d63b4ff8c2.jpg)
+
+![](images/d689782519dfd8bcbf9cb55c7207a38c30a65ed3c93b0040db07a4395793a18d.jpg)
+
+![](images/0f71668069997a6876f717e88f133d1a0acfd20213f4ced493612ba6c97380cd.jpg)
+
+![](images/21ec1fa6696e197e1416d4810ebd7d29c7259855ef97dff24c7496e9676aa820.jpg)
+
+"Please remove the object that can be used to have meals."
+
+![](images/4c41a1b423755ec3450c5e042fcd3960f50f6c1dcd0e90c0f0a4a2e906ea1bcf.jpg)
+
+![](images/992e0ba2a22f7f64cf611f72b1146b869ce28e0d48217b1f7d82f4168bcc9d30.jpg)
+
+![](images/b3b2591e17801606f3a4b142808b6b3ec5aeef8511a7193830f5f8df912a2cac.jpg)
+
+![](images/8978e8bb43ef97b1a3a6ad9a2df334d2b5fa3085ed0ed1a34e00191e5ed57a5b.jpg)
+
+![](images/b5b9030de85756f023f6991f4e7c93ff20d28b666b731d4297e77e8c0bfe9742.jpg)
+
+![](images/833e91e275be906d8270c274d17a70cb75118ccf78eb2ac42bdfa233625f2d30.jpg)
+
+"Change the middle panda to a cat"
+
+![](images/c0a8d312101054ec2bd2bb8ae127c31450dda66fa6a95eefe28eb2c46f12957c.jpg)
+
+![](images/711110d5cedae2dfd6e212d647012dbd105bd404131ec578f02f5f2f83128fec.jpg)
+
+![](images/b4fb6b739a245ba0484ce270e6bf186e768d48d8ef8244388d64fe31ae108ae8.jpg)
+
+![](images/5530be603f1f4cd859944bb9a584d8f997e9907f7daf5fe0741434ddbb7a5030.jpg)
+
+![](images/36b37f9a4c1d8bacc82c1f2eff34b4ef8d97a97bea0a2c9fe620a2a57fa58c1b.jpg)
+
+![](images/ba332000f27e717434765d9db7ce7b88ecf6ca9bee74447f0cd0452ea7530477.jpg)
+
+"Change the cat in mirror to a tiger."
+
+![](images/aa8cbbf55762203fed39f44b51cb67c5900f6048c6fdf32f378421ffaefdd07e.jpg)  
+Input Image  
+Figure 5. Qualitative comparison on Reason-Edit. When compared to several existing instruction editing methods that have undergone further fine-tuning on our synthetic editing dataset, our approach demonstrates superior editing capabilities in complex scenarios.
+
+![](images/72afc780cb6a3e2710d85b807a95c02ae4ce83078e74e0c2cf5144d429118978.jpg)  
+InstructPix2Pix
+
+![](images/23bb399c88f20697a58cdc051f4c8aab6dd36a9a3a67bfef0562852dc5041db7.jpg)  
+MagicBrush
+
+![](images/b6a359ceb371dec36c97b12252d1148d654c1d22d6133f5c6814fcc79f6ff03b.jpg)  
+InstructDiffusion
+
+![](images/3f03be9e68a14c376f13b0064166210d11bc219cbc794a0a4ed2fe68545383ed.jpg)  
+SmartEdit-7B
+
+![](images/10505587151f1a37c2aa3705e9aca3f53a3069481b7e95990dd632b46fcf13ba.jpg)  
+SmartEdit-13B
+
+<table><tr><td rowspan="2">Methods</td><td colspan="5">Understanding Scenarios</td><td colspan="5">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>InstructPix2Pix</td><td>21.576</td><td>0.721</td><td>0.089</td><td>22.762</td><td>0.537</td><td>24.234</td><td>0.707</td><td>0.083</td><td>19.413</td><td>0.344</td></tr><tr><td>MagicBrush</td><td>18.120</td><td>0.68</td><td>0.143</td><td>22.620</td><td>0.290</td><td>22.101</td><td>0.694</td><td>0.113</td><td>19.755</td><td>0.283</td></tr><tr><td>InstructDiffusion</td><td>23.258</td><td>0.743</td><td>0.067</td><td>23.080</td><td>0.697</td><td>21.453</td><td>0.666</td><td>0.117</td><td>19.523</td><td>0.483</td></tr><tr><td>SmartEdit-7B</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.611</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.950</td><td>0.789</td></tr><tr><td>SmartEdit-13B</td><td>23.596</td><td>0.751</td><td>0.068</td><td>23.536</td><td>0.771</td><td>25.757</td><td>0.747</td><td>0.051</td><td>20.777</td><td>0.817</td></tr></table>
+
+Table 1. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. All the methods we compared have been fine-tuned using the same training data as that used by SmartEdit.
+
+"What is the object that the dog's food should be put into? Remove this object."
+
+![](images/b822ded3281a0d80947b525ea25d15bff37f7667c456219b6c2b0d94601e97bb.jpg)  
+Figure 6. Demonstration of the effectiveness of the BIM Module.
+
+# 5.3. Ablation Study on BIM
+
+To validate the effectiveness of the bidirectional information interaction in our proposed BIM module, we conduct
+
+"Please replace the animal that is lying on the grass with a fox"
+
+![](images/8ec6bcbaa0d407c835ef1d35c20cd715362fe7b3e50030d2b27cfcaeb5e99c32.jpg)
+
+![](images/2be4fdc566c0dcaf3d15f1fa675917f6949e1db66b28fcc18b85a0288bd70783.jpg)
+
+![](images/f12255bdd968ef068497398649c39e040706aa377cf9603ddb9e7d83282dcb57.jpg)
+
+![](images/7f4d9f98dfe1bd8db79287c372f9acaddf14196de5e933be7d5536a230c0f4dd.jpg)
+
+![](images/08794862aa30241b1998a302b1ebffa25d9475e8ef07138bd812124e064bf0a7.jpg)
+
+"Change the red strawberry to a white pumpkin"
+
+![](images/5cdc4a37c81cf54440b9de80886ba5f1d95246442498591d68cfdb8abdcad7cc.jpg)  
+Input Image  
+Figure 7. Demonstration of the significance of joint training with multiple datasets.
+
+![](images/576c36cdfa99cbc7c29ae4a4740e4d733a565cfff3c4a76ff748c3fa301beaa4.jpg)  
+Edit
+
+![](images/dfb36085eba9a4b01687154d71952a07eebdb5985d8efe147afce5863f10708d.jpg)  
+Edit+Seg
+
+![](images/fd7eddfa0d375c4c4659189f784d04640aa2afd84e6863fa3dc149d7b5e47bea.jpg)  
+Edit+Reason-Edit
+
+![](images/937a9798d99aa9d4fe48b25bb9ba17a3ef4926b3d20301e5a3326e1449f1ca41.jpg)  
+Total
+
+comparative experiments on the SmartEdit-7B model. The details are presented in Tab. 2. The first experiment, denoted as Exp 1, aims to verify the necessity of the information in
+
+<table><tr><td rowspan="2">Exp ID</td><td rowspan="2">Plain</td><td rowspan="2">SimpleCA</td><td rowspan="2">BIM</td><td colspan="5">Understanding Scenarios</td><td colspan="5">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>1</td><td>✓</td><td></td><td></td><td>20.975</td><td>0.713</td><td>0.108</td><td>23.36</td><td>0.695</td><td>23.848</td><td>0.725</td><td>0.074</td><td>20.33</td><td>0.694</td></tr><tr><td>2</td><td></td><td>✓</td><td></td><td>19.557</td><td>0.692</td><td>0.126</td><td>23.66</td><td>0.692</td><td>23.508</td><td>0.716</td><td>0.081</td><td>20.17</td><td>0.722</td></tr><tr><td>3</td><td></td><td></td><td>✓</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.61</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.95</td><td>0.789</td></tr></table>
+
+Table 2. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B.  
+
+<table><tr><td rowspan="2">Exp ID</td><td rowspan="2">Edit</td><td rowspan="2">Segmentation</td><td rowspan="2">Synthetic editing dataset</td><td colspan="5">Understanding Scenarios</td><td colspan="5">Reasoning Scenarios</td></tr><tr><td>PSNR(dB)↑</td><td>SSIM↑</td><td>LPIPS↓</td><td>CLIP Score↑</td><td>Ins-align↑</td><td>PSNR(dB)</td><td>SSIM</td><td>LPIPS</td><td>CLIP Score</td><td>Ins-align↑</td></tr><tr><td>1</td><td>✓</td><td></td><td></td><td>17.568</td><td>0.664</td><td>0.171</td><td>22.79</td><td>0.201</td><td>22.400</td><td>0.706</td><td>0.102</td><td>19.22</td><td>0.233</td></tr><tr><td>2</td><td>✓</td><td>✓</td><td></td><td>18.960</td><td>0.690</td><td>0.143</td><td>22.83</td><td>0.361</td><td>21.774</td><td>0.693</td><td>0.116</td><td>19.82</td><td>0.311</td></tr><tr><td>3</td><td>✓</td><td></td><td>✓</td><td>19.562</td><td>0.702</td><td>0.111</td><td>22.32</td><td>0.440</td><td>23.595</td><td>0.715</td><td>0.079</td><td>20.43</td><td>0.567</td></tr><tr><td>4</td><td>✓</td><td>✓</td><td>✓</td><td>22.049</td><td>0.731</td><td>0.087</td><td>23.61</td><td>0.712</td><td>25.258</td><td>0.742</td><td>0.055</td><td>20.95</td><td>0.789</td></tr></table>
+
+Table 3. Quantitative comparison (PSNR↑/SSIM↑/LPIPS↓/CLIP Score↑(ViT-L/14)/Ins-align↑) on Reason-Edit. These comparative experiments are conducted based on the SmartEdit-7B.
+
+teraction proposed in the BIM module. In this experiment, we remove the BIM module from the SmartEdit-7B model and directly apply the text feature output from QFormer to the diffusion model. The second experiment, denoted as Exp 2, aims to verify the necessity of the bidirectional information interaction proposed in the BIM module. Specifically, all blocks are discarded except for the cross-attention block on the image feature branch. Therefore, the information from the text feature of QFormer is unidirectionally applied to the image feature. These two experiments are designed to test the impact of removing or altering the BIM module on the performance of SmartEdit-7B in complex understanding and reasoning scenarios. As shown in Tab. 2, if the BIM module is removed, there is a significant decline in all metrics for both understanding and reasoning scenarios. When the BIM module is replaced with the SimpleCA module, we observe a noticeable decline in all metrics, except for the clip score in understanding scenarios. Further comparison of the qualitative results in Fig. 6 confirms that the introduction of the BIM indeed enhances SmartEdit's instruction editing performance. To be specific, when we do not use the BIM module (i.e., plain), the dog bowl (first row) turns into other objects (marked with a red circle), and the fork (second row) does not change at all. After using SimpleCA, it can be found that the dog bowl and fork have been partially removed. When SmartEdit is equipped with BIM, the dog bowl and fork can be well removed.
+
+# 5.4. Ablation Study on Dataset Usage
+
+In Section 4.3, we explore an efficient strategy for data utilization, aiming to enhance SmartEdit's capabilities in handling complex understanding and reasoning scenarios. During the training process of SmartEdit, we employ the common editing dataset, segmentation dataset, and the synthetic editing dataset. To validate the significance of these different data types in boosting SmartEdit's performance, we conduct a series of ablation studies, as detailed in Tab. 3. These experiments are based on the SmartEdit-7B model. In Exp 1, we train the model using only the editing data. In Exp 2, we incorporate segmentation data into the training
+
+process, building upon Exp 1. In Exp 3, we further add the synthetic editing data to the basis established in Exp 1. The quantitative results of these experiments reveal that segmentation data and synthetic editing data play complementary roles in enhancing the model's performance. This is further corroborated by the visual comparison in Fig. 7. For reasoning scenarios, when adopting only the editing dataset or combining the editing dataset and the segmentation dataset, the performance of SmartEdit is inferior. When the synthetic editing data is incorporated into the editing dataset, SmartEdit can accurately locate the specific objects. However, the output of SmartEdit is also mediocre (the generated fox has obvious artifacts, and two pumpkins are generated). When all these datasets are combined as the training set, the results generated by SmartEdit have a further significant improvement in visual effects.
+
+# 6. Conclusion
+
+In conclusion, this paper presents SmartEdit, a novel approach to instruction-based image editing that enhances understanding and reasoning capabilities by incorporating the LLMs with visual inputs. By introducing the Bidirectional Interaction Module (BIM), we have overcome challenges associated with the direct integration of LLMs and diffusion models in complex reasoning scenarios. Our data utilization strategy, which incorporates perception data and complex instruction editing data, effectively enhances SmartEdit's capabilities in handling complex understanding and reasoning scenarios. Evaluation on our newly constructed dataset, Reason-Edit, shows that SmartEdit outperforms previous methods, marking a significant step towards practical applications of complex instruction-based image editing.
+
+Acknowledgement. The work is partially supported by the Young Scientists Fund of the National Natural Science Foundation of China under grant No. 62106154, the Natural Science Foundation of Guangdong Province, China (General Program) under grant No.2022A1515011524, Shenzhen Science and Technology Program JCYJ20220818103001002 and JCYJ20220818103006012, and the Guangdong Provincial Key Laboratory of Big Data Computing, The Chinese University of Hong Kong (Shenzhen).
+
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+# SmartMask: Context Aware High-Fidelity Mask Generation for Fine-grained Object Insertion and Layout Control
+
+Jaskirat Singh $^{1,2}$
+
+Jianming Zhang
+
+Qing Liu<sup>1</sup>
+
+Cameron Smith<sup>1</sup>
+
+Zhe Lin
+
+Liang Zheng<sup>2</sup>
+
+1 Adobe Research
+
+2Australian National University
+
+https://smartmask-gen.github.io
+
+Inputs
+
+Conventional Inpainting
+
+![](images/5edad89bc8a0c19452c825749f632f1cf619c964c9406c5ccca98b73422491f5.jpg)  
+Image Input
+
+![](images/0ad97216176c879a3fd03279d618fb86905d73d0e7503453b20ec38365784ce5.jpg)  
+Image Input + Mask
+
+![](images/203ac10b40edbd4620f2a88796c2100fa03fe9df45c77ac99f1f087e9c0d9aaa.jpg)  
+SD - Impaint
+
+![](images/bfab34a4539904c20c62a55f32d6afbe45bab18f90d513028026495f6e86d81c.jpg)  
+Blended Latent Diff.
+
+![](images/078afec3fe31d0fdd55cfc394104e399c2891b698f053ae950822d3169d392a7.jpg)  
+Adobe SmartBrush
+
+![](images/30625f7b6cfc65d344ddc80fd4283fdd68fc85a13dcfc3fd53a542e8f704ddbc.jpg)  
+Adobe Gen-Fill
+
+![](images/70c87662f173dfa99ef1554f4cbafc030409602de8c2bdb6fcf15a427148a149.jpg)  
+SmartMask Prediction
+
+![](images/82c22c36a5354ba73c94f98bedf2201e3e9039b1b6600af1ea1338457b89a9fc.jpg)  
+Output (Ours)
+
+(a) SmartMask for performing object insertion ("bride") with better background preservation.
+
+![](images/eebb3be1459bb9d86a403cb6b9a746700505f87b988bbd874b0e97892695e519.jpg)  
+Input Image
+
+![](images/9ec704501ee31c21e5d4f6790c7f297d5b0cff38ffeca97c2048454e9050d640.jpg)  
+SmartMask Outputs for "woman beside a river in mountains"
+
+![](images/82f0004ba92a745e6a71b57217acddc2245668e971ccdeab17d7fa00f3b02ef4.jpg)
+
+![](images/a3ef05fb4e7af95cebc55d17c80b2ed7811e8c46d7688f074924d8934540a831.jpg)
+
+![](images/4dfd1e5a81bea99d21aabd238b639017a058f72749930c407ecdb90067c0c2f4.jpg)
+
+![](images/c3b5419350751a7157f6d64bd620cc4279d0e3d14dcecd673197cd73a52e2ad5.jpg)  
+SmartMask Outputs for "woman in a living room"
+
+![](images/aa73bd545b74a30678fa3c8c3e13f89c79d1b27772e0d3d46814fe7461812b8f.jpg)
+
+![](images/99fad521d354666b955ec2f3c9f79f196ffb2c74b17c5442343c61ea411092e4.jpg)
+
+(b) SmartMask for mask-free object insertion where it provides diverse suggestions without user bounding box input.
+
+Input Prompt: Two children sitting in front of a cardboard tree
+
+![](images/091f5ea1c6e9ee821bb8bf9614b89d3570f558daad5d13b20834476d0f3e1c6a.jpg)  
+User Scribbles
+
+![](images/b1f585ffc0402011e47b71bcd8c9e7486f79e092a028d4e47876138ebce86bcd.jpg)  
+Scribble + Controlnet
+
+![](images/397d362fd1b3b280b339ec52515f9ca06a01a283d6ab4c6f762cd73e69caff81.jpg)  
+Scribble + PwW
+
+![](images/4c23cfd7e669319effb9926b929d7e5c3c7eca4f4d3b1625d4d3f91dbaede64e.jpg)  
+Scribble + DenseDiff
+
+![](images/e717a482810ff85feb8996198ac3573252e7d85472b888840d73223c0485bc30.jpg)  
+Fine-grain Layout Generation (Ours)  
+Figure 1. Overview. We introduce SmartMask which allows a novice user to generate high-fidelity masks for fine-grained object insertion and layout control. The proposed approach can be used for object insertion (a-b) where it not only allows for image inpainting with better background preservation (a) but also provides diverse suggestions for mask-free object insertion at different positions and scales. We also find that when used iteratively SmartMask can be used for fine-grained layout design (c) for better quality semantic-to-image generation.
+
+![](images/98b856e4064d94ac354783dbcb0b80aeee56b1c6408a95fc6aafb048651d6e46.jpg)  
+Ours + Controlnet
+
+(c) SmartMask for fine-grain layout design for layout to image generation.
+
+# Abstract
+
+The field of generative image inpainting and object insertion has made significant progress with the recent advent of latent diffusion models. Utilizing a precise object mask can greatly enhance these applications. However, due to the challenges users encounter in creating high-fidelity masks, there is a tendency for these methods to rely on more coarse masks (e.g., bounding box) for these applications. This results in limited control and compromised background content preservation. To overcome these limitations, we introduce SmartMask, which allows any novice user to create detailed masks for precise object insertion. Combined with a ControlNet-Inpaint model, our experiments demonstrate that SmartMask achieves superior object insertion qual
+
+ity, preserving the background content more effectively than previous methods. Notably, unlike prior works the proposed approach can also be used even without user-mask guidance, which allows it to perform mask-free object insertion at diverse positions and scales. Furthermore, we find that when used iteratively with a novel instruction-tuning based planning model, SmartMask can be used to design detailed layouts from scratch. As compared with user-scribble based layout design, we observe that SmartMask allows for better quality outputs with layout-to-image generation methods.
+
+# 1. Introduction
+
+Multi-modal object inpainting and insertion has gained widespread public attention with the recent advent of large-
+
+scale language-image (LLI) models [1-3, 19, 24, 27, 30, 37, 38]. A novice user can gain significant control over the inserted object details by combining text-based conditioning with additional guidance from a coarse bounding box or user-scribble mask. The text prompt can be used to describe the object semantics, while the coarse mask provides control over the position and scale of the generated object.
+
+While convenient, the use of a coarse mask for object insertion suffers from two main limitations. 1) First, the use of a coarse mask can often be undesirable as it tends to also modify the background regions surrounding the inserted object [30, 37] (refer Fig. 1a). In order to minimize the background artifacts, recent works [37, 40] also explore the use of user-scribble based free-form mask instead of a bounding-box input. However, while feasible for describing coarse objects (e.g., mountains, teddy bear etc.), the generation of accurate free-form masks for objects with a number of fine-grain features (e.g., humans) can be quite challenging especially when limited to coarse user-scribbles. 2) Furthermore, generating variations in position and scale of the inserted object can also be troublesome as it requires the user to provide a new scene-aware free-form mask to satisfy the geometric constraints at the new scene location.
+
+To address these drawbacks, we introduce SmartMask, a context-aware diffusion model which allows a novice user to directly generate fine-grained mask suggestions for precise object insertion. In particular, given a semantic object description (e.g. kid) and the overall scene context, SmartMask generates scene-aware precise object masks which can then be used as input to a ControlNet-inpaint model [36, 41] to perform object insertion while preserving the contents of background image. As compared with coarse-mask based inpainting methods, we find that SmartMask provides a highly convenient and controllable method for object insertion and can be used 1) with user-inputs (bounding box, scribbles etc.): where the user can specify location and shape for the target object, or 2) in a mask-free manner: where the model automatically generates diverse suggestions for object insertion at diverse positions and scales.
+
+In addition to object insertion, we also find that SmartMask can be used for fine-grain layout design. Existing segmentation-to-image (S2I) generation methods (e.g. ControlNet [41]) enable the generation of controllable image outputs from user-scribble based semantic segmentation maps. However, generating a good quality semantic layout can be quite challenging if the user wants to generate a scene with objects that require fine-grain details for best description (e.g., humans, chairs etc.). To address this challenge, we show that SmartMask when used with a novel instruction-tuning [34] based planning model allows the user to iteratively generate the desired scene layout from scratch. As compared with scribble based layout generation, we find that the proposed approach allows the users to
+
+better leverage existing S2I generation methods (e.g. ControlNet [41]) for higher quality output generation.
+
+The main contributions of the paper are: 1) We propose SmartMask which allows any novice user to generate precise object masks for finegrained object insertion with better background preservation. 2) We show that unlike prior works, the proposed approach can also be used for mask-free object insertion. 3) Finally, we demonstrate that SmartMask can be used iteratively to generate detailed semantic layouts, which allows users to better leverage existing S2I generation methods for higher quality output generation.
+
+# 2. Related Work
+
+Diffusion based multi-modal image inpainting [1-3, 19, 24, 27, 30, 37, 38] has gained widespread attention with advent of text-conditioned diffusion models [24, 29, 30, 32, 39]. Despite their efficacy, these methods use coarse bounding box or user-scribble based masks for object inpainting which leads to poor background preservation around the inserted object. In contrast, SmartMask directly allows user to generate precise masks for the target object, which can then be combined with ControlNet-Inpaint [30, 41] to insert the target object while better preserving background contents.
+
+Mask-free object placement has been studied in the context of image compositing methods [9, 20, 22, 25, 35, 42, 44, 46], where given a cropped RGB object instance and a target image, the goal is to suggest different positions for the target object. In contrast, we study the problem of mask-free object insertion using text-only guidance. Lee et al. [18] propose a GAN-based approach to directly model a distribution of potential object locations. However, the learned distribution is w.r.t to a specific object class (e.g., cars) which limits its generalizability for diverse use-cases.
+
+Semantic layout to image generation methods have been explored to enable controllable image synthesis from user-scribble based semantic segmentation maps [8, 12, 17, 23, 26, 33, 45]. Recently, [4, 6, 14, 31] propose a cross-attention based training-free approach for controlling the overall scene layout from coarse user-scribbles using text-conditioned diffusion models. Zhang et al. [41] propose a versatile ControlNet model which allows the users to control the output layout on a more fine-grained level through an input semantic map. While effective, generating desired semantic layout with scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g., humans). SmartMask helps address this problem by allowing users to generate more fine-grained layouts to facilitate better quality S2I generation.
+
+# 3. Our Method
+
+Given an input image  $\mathcal{I}$ , object semantic label  $\mathcal{T}_{obj}$  and a textual description  $\mathcal{T}_{context}$  describing the final scene con
+
+![](images/bd575b2128bacfd093658cc193c7561b56e9d51632f8ab78253519898067144a.jpg)  
+Figure 2. Method Overview. A key idea behind SmartMask is to leverage semantic amodal segmentation data [28, 47] in order to obtain high-quality paired training annotations for mask-free single or multi-step object insertion. During training (top), given a training image  $\mathcal{I}$  with caption  $C$ , we stack  $k$  ordered instance maps  $\{A_1, A_2, \ldots, A_k\}$  to obtain an intermediate semantic map  $S_k$ . The diffusion model is then trained to predict the instance map  $A_{k+1}$ , conditional on the semantic map  $S_k$ ,  $\mathcal{T}_{obj} \gets \mathcal{O}_{k+1}$  and scene context  $\mathcal{T}_{context} \gets C$ . During inference (bottom), given a real image  $\mathcal{I}$ , we first use a panoptic segmentation model to compute semantic map  $S_I$ . The generated semantic layout is then directly used as input to the trained diffusion model in order to predict the fine-grained mask for the inserted object.
+
+text, our goal is predict a fine-grained mask  $\mathcal{M}_{obj}$  for the target object. The object mask  $\mathcal{M}_{obj}$  could then be used as input to a ControlNet-Inpaint model for fine-grained object insertion (Sec. 4.1) or used to design detailed semantic layouts from scratch (Sec. 4.3). For instance, SmartMask could be used for single object insertion, where given an image  $\mathcal{I}$  depicting a man on a bench,  $\{\mathcal{T}_{obj} : \text{"woman'}\}$  and  $\{\mathcal{T}_{\text{context}} : \text{"a couple sitting on a bench'}\}$ , our goal is to predict fine-grain binary mask  $\mathcal{M}_{woman}$  which places the 'woman' in a manner such that the resulting scene aligns with overall scene context of a 'a couple sitting on a bench'.
+
+Similarly, SmartMask could also be used for multiple object insertion. For instance, given an image  $\mathcal{I}$  depicting a wedding, the user may wish to add multiple objects \{'man', 'woman' and 'kid'\} such that the final scene aligns with the  $\{\mathcal{T}_{\text {context }}: \text { 'a family posing for a picture at a wedding }\}$ . Unlike prior image inpainting methods which are limited independently adding each object to the scene, the goal of the smartmask model is to add each object in a manner such the generated 'man', 'woman' and 'kid' appear to be 'a family posing for a picture at a wedding'. (refer Fig. 2a).
+
+In the next sections, we describe the key SmartMask components in detail. In particular, in Sec. 3.1 we discuss how SmartMask can leverage semantic amodal segmentation data in order to obtain high-quality paired annotations for mask-free object insertion. We then discuss a simple
+
+data-adaptation strategy which allows the user to also control the position, shape of the inserted object using coarse inputs (bounding-box, scribbles) in Sec. 3.2. Finally, in Sec. 3.3 we propose a visual-instruction tuning [21] based planning model which when used with SmartMask, allows for generation of detailed semantic layouts from scratch.
+
+# 3.1. SmartMask for Mask-Free Object Insertion
+
+Semantic-Space Task Formulation. Directly learning a model for our task in pixel space can be quite challenging, as it would require large-scale collection of training data for single or multi-step object insertion while maintaining background preservation. To address this key challenge, a core idea of our approach is to propose an equivalent task formulation which allows us to leverage large-scale semantic amodal segmentation data [28, 47] for generating high-quality paired training data in the semantic space (Fig. 2).
+
+SmartMask Training. In particular during training, given an image  $\mathcal{I}$ , with a sequence of ordered amodal semantic instance maps  $\{A_1, A_2 \ldots A_n\}$  and corresponding semantic object labels  $\{\mathcal{O}_1, \mathcal{O}_2 \ldots \mathcal{O}_n\}$ , we first compute an intermediate layer semantic map as,
+
+$$
+S _ {k} = f _ {\text {l a y e r}} \left(\left\{A _ {1}, A _ {2} \dots A _ {k} \right\}\right) \quad \text {w h e r e} k \in [ 1, n ]. \tag {1}
+$$
+
+where  $k$  is randomly chosen from  $[1, n]$  and  $f_{layer}$  is a layering operation which stacks the amodal semantic segmentation maps from  $i \in [1, k]$  in an ordered manner (Fig. 2).
+
+We next train a diffusion-based mask prediction model  $\mathcal{D}_{\theta}$  which takes as input the above computed intermediate semantic layer map  $S_{k}$ , textual description for next object  $\mathcal{T}_{obj} \gets \mathcal{O}_{k+1}$ , overall caption  $\mathcal{T}_{context} \gets C_{\mathcal{I}}$  (for image  $\mathcal{I}$ ) and learns to predict the binary mask  $\{A_{k+1}\}$  for the next object. To this end, we first pass the intermediate semantic map  $S_{k}$  through a learnable encoder  $\mathcal{E}_{\phi}$  to obtain the encoded features  $\mathcal{E}_{\phi}(S_{k})$ . At any timestep  $t$  of the reverse diffusion process, the denoising noise prediction  $\epsilon_{t}$  is then computed conditional jointly on previous noise latent  $\mathbf{z}_{t}$ , and model inputs  $\{\mathcal{E}_{\theta}(S_{k}), \mathcal{T}_{obj}, \mathcal{T}_{context}\}$  as,
+
+$$
+\tilde {\epsilon} _ {p r e d} (t) = \mathcal {U} _ {\theta} (\mathbf {z} _ {t}, \mathcal {E} _ {\phi} (S _ {k}), \mathcal {T} _ {o b j}, \mathcal {T} _ {\text {c o n t e x t}}, t), \tag {2}
+$$
+
+where  $\mathcal{U}_{\theta}$  represents the U-Net of the diffusion model  $\mathcal{D}$ .
+
+The overall diffusion model  $\mathcal{D}$  is then trained to predict the next layer  $A_{k + 1}$  using the following diffusion loss,
+
+$$
+\mathcal {L} _ {t} (\theta , \phi) = \mathbf {E} _ {t \sim [ 1, T ], S _ {k}, A _ {k + 1}, \epsilon_ {t}} \left[ \| \epsilon_ {t} - \tilde {\epsilon} _ {p r e d} (t) \| ^ {2} \right], \tag {3}
+$$
+
+where  $T$  is total number of reverse diffusion steps,  $\epsilon_t\sim \mathcal{N}(0,I)$  is sampled from a normal distribution and  $A_{k + 1}$  represents ground truth binary mask for next object  $\mathcal{O}_{k + 1}$ .
+
+SmartMask Inference. During inference, given an input image  $\mathcal{I}$ , semantic object category  $\mathcal{T}_{obj}$  and a textual description  $\mathcal{T}_{\text {context }}$  describing the final scene context, we first use a panoptic semantic segmentation model [15] to obtain the corresponding semantic layout map  $\mathcal{S}_{\mathcal{I}}$ . The generated semantic layout  $\mathcal{S}_{\mathcal{I}}$  is then directly used as input to the above trained diffusion model  $\mathcal{D}_{\theta}$  in order to predict the fine-grained mask  $\mathcal{M}_{obj}$  for the target object,
+
+$$
+\mathcal {M} _ {o b j} = \mathcal {D} _ {\theta} \left(\mathcal {E} _ {\phi} \left(\mathcal {S} _ {I}\right), \mathcal {T} _ {o b j}, \mathcal {T} _ {\text {c o n t e x t}}\right). \tag {4}
+$$
+
+# 3.2. Data Adaptation for Precise Mask Control
+
+While the diffusion model trained in Sec. 3.1, allows the user to perform mask-free object insertion at diverse positions and scales, the user may also wish to obtain more direct control over the spatial location and details of the inserted object. To this end, we propose a simple train-time data adaptation strategy which allows smartmask to be easily adapted to diverse forms of user control (Fig. 4). In particular, given the intermediate layer map  $S_{k}$  computed using Eq. 1 and ground truth mask  $A_{k + 1}$  for the next object, we replace the input  $S_{k}$  to the diffusion model as,
+
+$$
+\tilde {S} _ {k} = g \left(S _ {k}, G _ {o b j}\right) = S _ {k} \odot \left(1 - \alpha G _ {o b j}\right) + \alpha G _ {o b j}, \tag {5}
+$$
+
+where  $G_{obj}$  is the additional guidance input (e.g., bounding box mask, coarse scribbles etc.) provided by the user and  $\alpha = 0.7$  helps add additional guidance while still preserving the content of the original input  $S_{k}$  after data adaptation.
+
+Training. In this paper, we mainly consider four main guidance inputs  $G_{obj}$  for additional mask control for adapting SmartMask. 1) Mask-free guidance: in absence of any
+
+additional user inputs, we use  $G_{obj} = \mathbf{0}^{H,W}$  which prompts the model to suggest fine-grained masks for object insertion at diverse positions and scales. 2) Bounding-box guidance: we set  $G_{obj}$  as a binary mask corresponding to ground truth object mask  $A_{k+1}$ . 3) Coarse Spatial Guidance: Expecting the user to provide precise bounding box for object insertion is not always convenient and can lead to errors if bounding box is not correct. We therefore introduce a coarse spatial control where user may provide a coarse spatial location and the model learns to infer the best placement of the object around the suggested region (Fig. 4c). During training, the same is achieved by setting  $G_{obj}$  as a coarse gaussian blob centered at the ground truth object mask  $A_{k+1}$ . 4) User scribbles: Finally, we also allow the user to describe target object using free-form coarse scribbles, by setting  $G_{obj}$  as the dilated mask output of ground-truth object mask  $A_{k+1}$ .
+
+Inference. At inference time, the additional guidance input  $G_{obj}$  (e.g. bounding box mask, coarse scribbles etc.) is directly provided by the user. Given an input image  $\mathcal{I}$  with semantic layout  $S_{\mathcal{I}}$ , we then use transformation from Eq. 5 as input to the adapted SmartMask model in order to generate object insertion suggestions with additional control.
+
+# 3.3. Global Planning for Multi-Step Inference
+
+While the original SmartMask model allows the user to generate fine-grained masks for single object insertion, we would also like to use SmartMask for iterative use cases such as multiple object insertion (Sec. A.1) or designing a fine-grained layout from scratch with large number  $(>10)$  of scene elements. Such an iterative use of SmartMask would require the model to carefully plan the spatial location of each inserted object to allow for the final scene to be consistent with the final scene context description  $\mathcal{T}_{\text{context}}$ .
+
+To achieve this, we train a visual-instruction tuning [21] based planning model which given the input semantic layout  $S_{I}$ , learns to plan the positioning of different scene elements over long sequences. Given a semantic object description  $T_{obj}$  and final scene context  $T_{context}$ , the global planning model provides several bounding box suggestions for object insertion. SmartMask model then uses the above predictions as coarse spatial guidance input  $G_{obj}$  to provide fine-grained mask suggestions for the next object. The above process can then be repeated in an iterative manner until all objects have been added to the scene (refer Fig. 7a).
+
+The global planning model is trained in two stages. 1) Feature Alignment. Typical instruction tuning models are often trained on real images. In contrast, as discussed in Sec. 3.1 we would like to model our problem in semantic space as it allows us to leverage amodal segmentation data for training. To address this domain gap, we first finetune an existing LLaVA model [21] to understand the semantic inputs. To do this, given an intermediate semantic map  $S_{k}$  computed using Eq. 1, we finetune the projection matrix  $\mathbf{W}$
+
+![](images/c845681feea1a94c6197d1c87a541ea6826a41236c4c81c83bb0db580470cb5f.jpg)  
+Figure 3. Qualitative Results for Image Inpainting. We observe that as compared to with state-of-the-art image inpainting [1, 2, 30, 37] methods, SmartMask allows the user to perform object insertion while better preserving the background around the inserted object.
+
+of the LLaVA model [21]  $\mathcal{H}$  to predict the semantic object labels  $\{\mathcal{O}_1,\mathcal{O}_2\ldots \mathcal{O}_k\}$  described in the current scene as,
+
+$$
+\mathcal {L} _ {\text {a l i g n}} (\mathbf {W}) = \mathcal {L} _ {C E} (<   \mathcal {O} _ {1}, \mathcal {O} _ {2} \dots \mathcal {O} _ {k} >, \mathcal {H} (S _ {k})). \tag {6}
+$$
+
+2) Instruction-Tuning. Finally, keeping the visual encoder weights for LLaVA model fixed, we next finetune both project matrix  $\mathbf{W}$  and LLM weights  $\Phi$  [43] for global object planning. In particular, given an intermediate semantic map  $S_{k}$ , we first compute the bounding box coordinates  $\mathcal{B}_{k+1} = \{x_{min}, y_{min}, x_{max}, y_{max}\}$  for the next object  $\mathcal{T}_{obj} = \mathcal{O}_{k+1}$  using ground truth object mask  $\mathcal{A}_{k+1}$ . The LLaVA based planning model  $\mathcal{H}$  is then trained as,
+
+$$
+\mathcal {L} _ {\text {i n s t r u c t}} (\mathbf {W}, \Phi) = \mathcal {L} _ {C E} \left(\mathcal {B} _ {k + 1}, \mathcal {H} \left(S _ {k}, \mathcal {T} _ {\text {o b j}}, C\right)\right), \tag {7}
+$$
+
+where  $C$  represents the caption for the final scene (obtained using ground-truth image  $\mathcal{I}$ ) and provides the model context for placing different scene elements in the image.
+
+# 4. Experiments
+
+Training Data Collection. As discussed in Sec. 3, we note that a key idea behind SmartMask is to model the object insertion problem in semantic space (instead of pixel space), which allows us to leverage semantic amodal segmentation data to obtain large-scale paired training annotations for single or multiple object insertions. However, traditional datasets for semantic amodal segmentations such as COCOA [47] (2,500 images, 22,163 instances) and KINS [28]
+
+(7,517 images, 92,492 instances) though containing fine-grained amodal segmentation annotations may lack sufficient diversity to generalize across different use-cases.
+
+To address this, we curate a new large-scale dataset consisting of fine-grain amodal segmentation masks for different objects in an input image. The overall dataset consists of 32785 diverse real world images and a total of 725897 object instances across more than 500 different semantic classes (e.g. man, woman, trees, furniture etc.). Each image  $\mathcal{I}$  in the dataset consists of a variable number of object instances  $\{A_1, A_2, \ldots, A_n\}$ ,  $n \in [2, 50]$  and is annotated with an ordered sequence of semantic amodal segmentation maps  $\{S_1, S_2, \ldots, S_n\}$ . The detailed descriptions  $C_I$  for each image are obtained using the InstructBLIP [7] model.
+
+SmartMask Training. In order to leverage the rich generalizable prior of T2I diffusion models, we use the weights from publicly available Stable-Diffusion-v1.5 model [30] in order to initialize the weights of the SmartMask U-Net model trained in Sec. 3.1. Similar to [5], we modify the architecture of the U-Net model to also condition the output mask predictions on segmentation layout  $S_{I}$ . The SmartMask model is trained for a total of 100k iterations with a batch size of 192 and learning rate  $1e - 5$  using 8 Nvidia-A100 GPUs. During inference, a panoptic semantic segmentation model finetuned on the dataset in Sec. 4 is used for converting real image  $\mathcal{L}$  to its semantic layout  $S_{I}$ . ControlNet model trained with SDXL backbone was used to perform precise object insertion with SmartMask outputs. Please refer the supp. material for further training details.
+
+![](images/1541e367e0ddb99394b602a3e451e55245b1a75949436b7951887e38463e48ff.jpg)
+
+![](images/cc25d52d8bc78c5c9b741c3ce4a0ee0f8c1f2ce428235dead328f6181c3d5efb.jpg)
+
+![](images/eb859377da04b062180ddd715fda3d717138552a742497afdd2d256ac4e1ca86.jpg)
+
+![](images/c1e77d73c40fbb5db1ae36e87d9f31b7fa661ef3f5ac2a254e4bb8bad2e79c47.jpg)
+
+![](images/3042c0e9452c4474ff54170db29cb210b24dbbabb8f9ecdfb5c8ba8c4ced6bfc.jpg)  
+Image Input
+
+![](images/a7b3321d03121ca3e7dbd48b2383c6b317bda3785a1c41dc2ef12efb8a7ed94a.jpg)  
+SmartMask Outputs
+
+![](images/7cca24f4f08be3af5a9aeaccb9c7a298a503a89cf6e19d39de0a7101641de4ee.jpg)
+
+![](images/d4eea0a9d7fb22feaaf6eee5cc1dfb82c8d94704240b746d5b5237e9a5a2aa7a.jpg)
+
+![](images/af922d360658972d19853bf32c07845ff73d0614336a09dd52f0aaeab2d583bd.jpg)
+
+![](images/e9966b8b42b03b4dc14f33bf6bab8e18fdee1b4eebc7867b9626dc0d665b90d6.jpg)
+
+![](images/a22667328a345a39fdb788a827863c8004f33b300e43b2a5b9f3f37b25eed146.jpg)
+
+![](images/203e45e0b6477d3323c2de30afef4688aa58b3e19099f8570a98264d864b9602.jpg)
+
+![](images/2cca947d733e9fa0e17b992cdd05753155595d06d57d93a646029ef144a96aea.jpg)  
+Image Input
+
+![](images/0f177d283ca250dd1a99e5d7f4de447cf9194bca2e377ac281b3989705b03ce0.jpg)  
+SmartMask Outputs
+
+![](images/9ddb99fdeb7a0a078fc27535fe4ef8ddc08be3f93b639af43b115bcafbf4608c.jpg)
+
+![](images/2bb685ea4685a640b3a7e09abfbf4cebb8c7b955220a6e96a2239c5bb0956840.jpg)
+
+![](images/2b050e7dc75fac17cbd6fde107de344a7640e7e10a31ef8a949136423caa6f16.jpg)  
+(a) Mask-free object insertion
+
+![](images/d5abdb25e3ffdc8ef40393ee48b5baad47bfab48ebef1abb319f5550e7d3dc1b.jpg)
+
+![](images/3286d89a27bd30c7be2da56fa92707f52547285588415474886e7d10074a1faa.jpg)
+
+![](images/e5df1655e0040e04db85e6136905bead5107740ace2e3dbd2855090c5a6c7fd4.jpg)
+
+![](images/9abad4c2de77fabd5f67c7bf325216ac6459a93f71251026d97daa77cac60c7b.jpg)  
+(c) Coarse-spatial guidance for mask generation
+
+![](images/ee767df46b45577aad1d8b8566db68eb0e520ce2315ef284b7d26d0a5f899359.jpg)  
+Figure 4. Diverse User Controls. SmartMask is easily adaptable to diverse user-controls for precise mask generation for the target object.
+
+![](images/c536381eaf88f8b706a7f9d3b44fa0d9dd09afc80218f134d6d028d7145265f0.jpg)
+
+![](images/d203fa9e54c436037dc166536aa14b39fc9c42c1c27d30d02b596062ee68eee6.jpg)
+
+![](images/43f5155cf43a7f4e16c2fca1c04f6b1e97bbda9f6da518218bb87fbc4125596d.jpg)  
+(b) Bounding-box guidance for mask generation
+
+![](images/3d2eda6e7647c2c890e6e6e6ad3707fdf848033f26727366b47ff4923a13bbeb.jpg)
+
+![](images/df8b1f1beb4bda91833a976dd18b578e0d7aebc7193204591369aa3c246a2862.jpg)
+
+![](images/b7971ae117e80ca52b74fabac87b02e4cee6c23e14fcdd4367354c42aae8a29d.jpg)
+
+![](images/51b224e66510246178c91a6c9855216e8ed0b74134436504637d2d9e537215ef.jpg)
+
+![](images/5316f72cb0b4ca50ecdf754f8a0c715346e1126edcb0d7e2fd97c67eaaeca5d9.jpg)  
+(d) Scribble-based object insertion
+
+![](images/b6672613038cc9524e177291009597b7ede8d577ddab4666a43e925328624ba8.jpg)
+
+![](images/20b1b3bf833f8b8b4796f01e2f266375969cb76447c156a7a8450701f6ca7095.jpg)
+
+![](images/e6b82c159d332af5c48118df2f718beabc4ad5baae34faf1f1929ac61feeecd7.jpg)
+
+# 4.1. SmartMask for Object Insertion
+
+Baselines. We compare the performance of our approach on object-insertion with prior works on performing multimodal image-inpainting using a textual description and coarse bounding box mask. In particular we show comparisons with SD-Inpaint [30], SDXL-Inpaint [27], Blended-Latent Diffusion [30], and Adobe SmartBrush [37]. We also compare the performance of our approach with state-of-the-art commercial inpainting tools by reporting results on recently released Generative-Fill from Adobe Firefly [1].
+
+Evaluation Metrics. Following [37], we report the results for object insertion using 1) Local-FID [11] which measures the realism of the generated objects, 2) CLIP-Score [10] which measures the alignment between the textual description and the generated object, and 3) Norm. L2-BG: which reports the normalized L2 difference in the background regions before and after insertion, and helps capture the degree to which the background was preserved.
+
+Qualitative Results. Results are shown in Fig. 3. We observe that when performing objectn insertion using a coarse bounding box mask, traditional inpainting methods usually lead to a lot of changes in the background regions around the inserted object (e.g. living room details in row-1&2, mountains in row-4 etc.). Adobe SmartBrush [37] which is trained to allow better background preservation, shows better performance, however, still suffers from notable changes to background regions. In contrast, by directly predicting a high-fidelity mask for the target object, the proposed approach allows the user to add new objects on the scene with
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">Evaluation Criteria</td></tr><tr><td>Local-FID ↓</td><td>CLIP-Score ↑</td><td>Norm. L2-BG ↓</td></tr><tr><td>SD Inpaint [30]</td><td>22.31</td><td>0.249</td><td>0.374</td></tr><tr><td>SDXL Inpaint [27]</td><td>21.84</td><td>0.235</td><td>0.623</td></tr><tr><td>Blended L-Diffusion [2]</td><td>39.77</td><td>0.253</td><td>0.451</td></tr><tr><td>Adobe SmartBrush [37]</td><td>17.94</td><td>0.262</td><td>0.304</td></tr><tr><td>Adobe Gen-Fill* [1]</td><td>N/A</td><td>0.268</td><td>0.289</td></tr><tr><td>Smartmask (Ours)</td><td>19.21</td><td>0.261</td><td>0.098</td></tr></table>
+
+Table 1. Quantitative results for image inpainting. We observe that in comparison with state-of-art image inpainting methods, our approach leads to better preservation of background regions.
+
+minimal changes to the background image. Furthermore we observe that target object masks are generated in a scene-aware manner, which helps us add new objects while interacting with already existing ones. For instance, when adding 'a man to a couch with table in front' (Fig. 3), prior works typically replace the couch and table to insert the target object ('man'). In contrast, smartmask places the 'man sitting on the couch with his leg on the table', and provides a more natural way for inserting objects in complex scenes.
+
+Quantitative Results. In addition to qualitative results, we also report the performance of our approach quantitatively in Tab. 1. We find that similar to results in Fig. 3, the proposed approach shows better background preservation (Norm. L2-BG ↓) while performing comparably in terms of image quality (local-FID) and text-alignment (CLIP-Score).
+
+# 4.2. Evaluating Mask Controllability and Quality
+
+A key advantage of SmartMask is the ability to generate high-quality masks for target object in a controllable man
+
+![](images/5afad3b15493e52d50f73742b4494c974ea3dc4b540204e1f077c5f1349d7ea0.jpg)  
+Figure 5. Comparing output mask quality with different Inpaint + HQSAM (middle) methods and SmartBrush mask output (right).
+
+![](images/d1bdff23c45e9ac1d093535aeb24ccf1e869f294a72052c458f942bb7a4ef9b3.jpg)  
+Figure 6. Limitation of Inpaint + HQSAM. In addition to poor mask quality errors (Fig. 5), we observe that Inpaint+HQSAM can lead to scene-unaware masks (e.g. mask for woman sitting in air)
+
+ner. In this section, we evaluate the performance of SmartMask in terms of 1) user control, & 2) output mask quality.
+
+1) User Control. As shown in Fig. 4, we observe that SmartMask allows the user to control the output object mask in four main ways. 1) Mask-free insertion: where the model automatically suggests diverse positions and scales for the target object (e.g., table, woman in Fig. 4a). 2) Bounding-box guidance: which allows user to specify the exact bounding box for object insertion (potted plant, motorbike in Fig. 4b). 3) Coarse spatial guidance: (Fig. 4c) providing a precise bounding box can be challenging for cases with complex object insertions e.g., dog with owner. SmartMask allows the user to only specify a coarse location for the target object, and the model automatically adjusts the object placement (i.e. dog with head near woman's hand) to capture object interactions. 3) User-scribbles: Finally, the user may also control the output shape by providing coarse scribbles. The smartmask model can use this as guidance to automatically predict the more finegrain-masks for the target object (e.g., palm-tree, gaming chair in Fig. 4d).
+
+2) Output Mask Quality. We also report results on the quality of generated masks by showing comparisons with the mask-prediction head of the SmartBrush model [37]. Furthermore, we also show comparisons combining standard inpainting methods with HQSAM [13, 16]. To this end, we first use the provided bounding-box mask to inpaint the target object. The user-provided bounding-box and the inpainted output are then used as input to the HQSAM model [13] to obtain target object-mask predictions.
+
+<table><tr><td rowspan="2">Method</td><td colspan="3">User Study Results</td></tr><tr><td>Win ↑</td><td>Draw</td><td>Lose ↓</td></tr><tr><td>SDInpaint + HQSAM [13, 30]</td><td>92.04%</td><td>5.12%</td><td>2.84%</td></tr><tr><td>Blended L-Diff + HQSAM [2, 13]</td><td>88.91%</td><td>8.33%</td><td>2.75%</td></tr><tr><td>SmartBrush + HQSAM [13, 37]</td><td>63.89%</td><td>27.78%</td><td>8.34%</td></tr><tr><td>SmartBrush Mask [37]</td><td>91.67%</td><td>2.78%</td><td>5.56%</td></tr></table>
+
+Table 2. User study results. For evaluating generated mask quality. We observe that SmartMask generates higher quality masks as compared to SmartBrush and various Inpaint+HQSAM methods.
+
+Results are shown in Fig. 5. We observe that as compared to outputs of SmartBrush [37] mask-prediction head, SmartMask generates higher-quality masks with fewer artifacts. Similarly, while using HQSAM on inpainting outputs helps achieve good mask quality for some examples (e.g. child in row-2), the HQSAM generated masks (or the inpainted image) often have accompanying artifacts which limits the quality of the output masks. In addition to poor mask quality errors, we also observe that Inpaint+HQSAM can lead to scene-unaware masks (Fig. 6). This occurs because prior inpainting methods typically add additional objects in the background when performing object insertion. For instance, when inserting woman in a living room in Fig. 6), we observe that Adobe Gen-Fill [1] adds an additional chair on which the woman is sitting. Extracting only the object mask for such inpainted outputs can lead to scene-unaware masks where 'the woman appears floating in the air' as the chair was not present in the original image.
+
+The above findings are also reflected in a quantitative user study (Tab. 2), where human subjects are shown a pair of object mask suggestions (ours vs baselines discussed above), and asked to the select the mask suggestion with the higher quality. As shown in Tab. 2, we observe that SmartMask outputs are preferred by majority of human subjects over SmartBrush mask [37] and Inpaint + HQSAM outputs.
+
+# 4.3. SmartMask for Semantic Layout Design
+
+In addition to object insertion, we also find that when used iteratively along with the visual-instruction tuning based planning model from Sec. 3.3, SmartMask forms a convenient approach for designing detailed semantic layouts with a large number of fine-grain objects (e.g. humans, furniture etc.). Results are shown in Fig. 7a. We observe that given a sequence of user provided scene elements (e.g. painting, sofa, chair etc.), SmartMask generates the entire scene layout from scratch. Furthermore, unlike static layouts generated by a panoptic segmentation model, SmartMask generated layouts allow the user greater control over the details of each scene element. Since each object in the final layout is represented by a distinct object mask, the final layouts are highly controllable and allow for a range of custom operations such as adding, removing, modifying or moving objects through simple layer manipulations. (refer Fig. 7b).
+
+Controllable S2I Generation. Layout to image gener
+
+Input Prompt: A living room with a couch, chair and table.
+
+![](images/9a46b4685407607a3a4dd885a0e476304736ef7b91251dbbf99eed3c20f367fc.jpg)
+
+![](images/42401609e3a49356bb558be9ce6cc3711ef81e043ea513177c806c87f88e4a2e.jpg)
+
+![](images/feb372a54979f3e4ddef475b45b15a2e9d2812af9905091833fd158bb8786ee7.jpg)
+
+![](images/cb4df6409925b628bf3fce0d6bffc1e98563e92ac99b5ab2bc98b09cd21e6cc8.jpg)
+
+![](images/498d06a6c97e6831fd9241436f9544aa6fe8228d52129524dd4d4baf56a01291.jpg)
+
+![](images/0c24cf0bf4e50977f1e5dca77f1b201a94687281f4a03df5f84fa4087608996d.jpg)
+
+![](images/f1465f37731e52fa4f55f8c816274ced944d7e646d294ba0280d7169074fb3d5.jpg)
+
+![](images/65a8d9d495c409fa221330d86a8a077ae9152a9cf2780a5ca36c65a75aa4ad36.jpg)
+
+![](images/1cc3854ddd4e16a081d4e85d7756644bccfd00cc6c0efee08d579f32131b4825.jpg)
+
+![](images/691ec8b0fe874d7100da9ec24c916e8eea1cc54327a63ed1089b56da64e20156.jpg)  
+(a) SmartMask for designing very detailed semantic layouts from scratch.
+
+![](images/33cac393520128e3b2a5adf5523e423e6deb9fb6a25f574683258155bc2b548c.jpg)
+
+![](images/393471f832fe7b182306381cb8959634fcd3009536702fd1cf711d6569caca68.jpg)
+
+![](images/3bd3f724decfdb3b96c4d5c8a80b646b3126c83ab7557bbdd67d2d45d2645a7e.jpg)
+
+![](images/5f759e0b747b87796ad5e54703f6dcee2e0fd585616212aa8b84f802a07d9916.jpg)
+
+![](images/fc64b9d0fc9ac011c04406610b6e3281727e87b035a9d3d5a59b79d307c5b34c.jpg)
+
+![](images/a8e501849aa4a30b58c93be9302a797729fe59b796b976100fffb59ea4932c81.jpg)
+
+![](images/fd9c13250aa29a6e5c95a11d759323ac9786ecd6e3c0f37d8d54efb60ab3703f.jpg)  
+Add new objects at different layers
+
+![](images/82442166caec084566d6368ec4ac446e284c12a2bcf4e01bf1bc8c8e63444e1a.jpg)  
+Remove objects at different layers  
+(b) Analyzing controllability of the layouts generated with SmartMask.
+
+![](images/f3a420db952460cda33210094ffec638cf362064923df695146d864f4caf0a9e.jpg)  
+Modify objects at different layers
+
+![](images/3e4ea7cf2e425134cbf8ad24cd6f04369daf06cfb41a8a10fa0392804105f318.jpg)  
+Move objects at different layers
+
+![](images/f1d2439fcd2e54c94b35bde05278a7aa0772da3c0848760bd826b8997dfcf9cc.jpg)
+
+![](images/d21a5ce8b9462d97115f12075c63124749d16aa921d3bff122829e0272994068.jpg)
+
+![](images/a6eed146a8db20079a85b0e61b436f4d353d968fe91d62e7e294afb6aac8e678.jpg)  
+Input Prompt: Two children sitting in front of a building
+
+![](images/81c98acd29d02f877801ff8cadbd02d094c51a931f6f71ff8e7c33d993a02696.jpg)
+
+![](images/153b7a968c523f4262be3138bfcbcce0c3c42e0f2dbda5b91d280f15956125e3.jpg)
+
+![](images/c8a7fa196d600ccd2909b9d0870f393b0a59a69fcbf79ac0bd1147679050d706.jpg)
+
+![](images/772a083b73e522ba74e3119bc3d9d3c79be3546c3d573bc44e4caf424919097d.jpg)
+
+![](images/c0729db918085758d6b08988f2146748ae325de7fa138f59d8b8f80b768c38f2.jpg)
+
+![](images/dd8849f499a6dd8f7f33a6470413f4eb4599ad1986a168d8c12b74f168d82a84.jpg)  
+User Scribble  
+Scribble + Controlnet  
+Figure 7. Fine-grained layout design. We observe that SmartMask when used iteratively, allows the user to generate very detailed layouts from scratch (a). The generated layouts are highly controllable and allow for custom variations through simple layer manipulations (b).
+
+![](images/849c41d3cabe8ec5505da94aa55177f996fb1fe134e24a778d84f8e38b82f8bb.jpg)
+
+![](images/a0cbaeea35788f6ddc3e83aaabc566909c79c153926d24d479448fb55b9e3fc8.jpg)
+
+![](images/bd49d37d6cf74a2fcb9c459c40f6cc3dbbf893cf63f42a755bc88b67a1ec2efc.jpg)  
+Input Prompt: a woman walking with two children on the beach  
+Scribble  $^+$  PwW  
+(c) Using SmartMask generated layouts for better quality layout-to-image generation.
+
+![](images/0dc9473c3ef4c219d05398331353f6c2b00a169885c0b3aa6d7a6757a6a1f6af.jpg)  
+Scribble + DenseDiff
+
+![](images/02a845fdbc6348c31c153bf41f477e14d1d022f7f1aa9b50f739e97459b9f259.jpg)  
+Fine-g  
+Fine-grain Layout Generation (Ours)
+
+![](images/6e1b08b835353c919c58970dd5de2b0ef4c55ccc9a084e2af9872909d8e46cce.jpg)
+
+![](images/fbb9453edf6597213a3d0183eba7aa4cfc355b0a75e769a600234353ebd66f5c.jpg)
+
+![](images/b6351bafcf23570078b24480b0535b58ec2cb18f1aa29b3e045f5a050a566574.jpg)  
+Ours + Controlnet
+
+ation methods e.g., ControlNet [41] enable the generation of controllable image outputs from user-scribble based semantic segmentation maps or layouts. However, generating the user-desired layouts with coarse scribbles can itself be quite challenging for scenes with objects that require fine-grain details for best description (e.g. humans, chairs etc.). As shown in Fig. 7c, we find that this can lead to image outputs with either deformity artifacts (child in row-1) or incorrect description (woman and children in row-2) when using ControlNet [41]. A similar problem is also observed in other coarse-scribble based S2I methods such as DenseDiffusion [14] and Paint-with-Words (PwW) [4], which provide coarse control over object position but are unable to control finegrain details such as pose, action etc. of the target object. SmartMask helps address this problem by allowing any novice user to generate controllable (Fig. 7b) fine-grain layouts from scratch, which can allow users to better leverage existing S2I methods [41] for higher quality layout-to-image generation (refer Fig. 7c).
+
+# 5. Conclusion
+
+In this paper, we present SmartMask which allows a novice user to generate scene-aware precision masks for object insertion and finegrained layout design. Existing methods for object insertion typically rely on a coarse bounding box or user-scribble input which can lead to poor background preservation around the inserted object. To address this, we propose a novel diffusion based framework which leverages semantic amodal segmentation data in order to learn to generate fine-grained masks for precise object insertion. When used along with a ControlNet-Inpaint model, we show that the proposed approach achieves superior object-insertion performance, preserving background content more effectively than previous methods. Additionally, we show that SmartMask provides a highly controllable approach for designing detailed layouts from scratch. As compared with user-scribble based layout design, we observe that the proposed approach can allow users to better leverage existing S2I methods for higher quality layout-to-image generation.
+
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2024/SmartMask_ Context Aware High-Fidelity Mask Generation for Fine-grained Object Insertion and Layout Control/images.zip

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2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_content_list.json

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+[
+    {
+        "type": "text",
+        "text": "SmartRefine: A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Yang Zhou $^{1*}$  Hao Shao $^{1,2*}$  Letian Wang $^{3}$   \nven L. Waslander $^{3}$  Hongsheng Li $^{2,4,5}$  Yu Liu $^{1,5}$",
+        "bbox": [
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+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "$^{1}$ SenseTime Research  $^{2}$ CUHK MMLab  $^{3}$ University of Toronto  $^{4}$ CPII under InnoHK  $^{5}$ Shanghai Artificial Intelligence Laboratory",
+        "bbox": [
+            220,
+            243,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+            315,
+            316,
+            330
+        ],
+        "page_idx": 0
+    },
+    {
+        "type": "text",
+        "text": "Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission<sup>1</sup>. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving.",
+        "bbox": [
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+        "page_idx": 0
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+    {
+        "type": "text",
+        "text": "By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved.",
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+        "text": "While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
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+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_footnote",
+        "text": "* Equal contribution,  $\\boxtimes$  Corresponding author.",
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+    },
+    {
+        "type": "page_footnote",
+        "text": "1 November 2023.",
+        "bbox": [
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+    {
+        "type": "page_number",
+        "text": "15281",
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+    {
+        "type": "text",
+        "text": "ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement.",
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+        "text": "To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency.",
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+        "text": "It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both.",
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+        "type": "text",
+        "text": "To summarize, the contributions of this work are threefold:",
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+        "list_items": [
+            "- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation.",
+            "- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research.",
+            "- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi"
+        ],
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+    {
+        "type": "table",
+        "img_path": "images/9acac4aa2a2e5a45881e39d8a4d4cabc47513a8ec18c7f8501a299de7829e8df.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Refine</td><td colspan=\"3\">Context Selection/Encoding</td><td colspan=\"3\">Refinement Iteration</td></tr><tr><td>All</td><td>Fixed Strategy</td><td>Adaptive Strategy</td><td>Single</td><td>Multiple</td><td>Scenario Adaptive</td></tr><tr><td>TNT [38]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GoalNet [37]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GANet [32]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ProphNet [33]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DCMS [36]</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>QCNet [40]</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>R-Pred [5]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>MTR [25]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>SmartRefine (ours)</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations.",
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+        "type": "text",
+        "text": "ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+        "type": "text",
+        "text": "2.1. Goal-Conditioned Trajectory Prediction",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con",
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+    {
+        "type": "page_number",
+        "text": "15282",
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+    {
+        "type": "text",
+        "text": "text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information.",
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+    {
+        "type": "text",
+        "text": "2.2. Refinement: Two-Stage Trajectory Prediction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation.",
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+    {
+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+        "type": "text",
+        "text": "SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework.",
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+    {
+        "type": "text",
+        "text": "3.1. Problem formulation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Given the observed states of the target agent  $\\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \\dots, s_0]$  in the historic  $T_h$  steps, we aim at",
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+        "type": "text",
+        "text": "predicting its future states  $\\mathbf{s}_f = [s_1,s_2,\\dots ,s_{T_f}]$  of  $T_{f}$  steps and associated probabilities  $\\mathbf{p}$ . Naturally, the target agent will interact with the context  $\\mathbf{c} = (\\mathbf{o}_h,\\mathbf{m})$ , including historic states of surrounding agents  $\\mathbf{o}_h$ , and the HD map  $\\mathbf{m}$ . For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as  $(\\mathbf{s}_f,\\mathbf{p}) = f(\\mathbf{s}_h,\\mathbf{c})$ , where  $f$  denotes the prediction model.",
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+        "text": "In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model  $f_{b}$  generating initial trajectories  $\\mathbf{s}_f^0$  and trajectory features  $\\mathbf{h}_f^0$ , as typical prediction methods  $(\\mathbf{s}_f^0, \\mathbf{h}_f^0, \\mathbf{p}) = f_b(\\mathbf{s}_h, \\mathbf{c})$ . The initial predicted trajectory  $\\mathbf{s}_f^0$  is then used to select anchors  $\\mathbf{a}^0$  and retrieve critical context elements  $\\mathbf{c}^0$ , which are then passed along with the trajectory features  $\\mathbf{h}_f^0$  into the refinement model  $f_{r}$  for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the  $i$ -th iteration is formulated as  $(\\delta \\mathbf{s}_f^i, \\mathbf{h}_f^i, \\mathbf{p}) = f_r(\\mathbf{h}_f^{i-1}, \\mathbf{s}_f^{i-1}, \\mathbf{c}^{i-1})$ . The generated offset  $\\delta \\mathbf{s}_f^i$  is added to the input trajectory  $\\mathbf{s}_f^{i-1}$  for refinement.",
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+        "text": "3.2. Scenario-Adaptive Refinement",
+        "text_level": 1,
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+        "type": "text",
+        "text": "3.2.1 Adaptive Anchor/Context Selection",
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+        "type": "text",
+        "text": "Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1).",
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+        "text": "Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all  $T_{f}$  waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into  $N < T_{f}$  segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments  $N$  is designed to adapt to the prediction horizon.",
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+        "type": "text",
+        "text": "Context Retrieval. When retrieving context information  $\\mathbf{c}$  around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal",
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+        "text": "15283",
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+    {
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+        "img_path": "images/b7e67582f0dceddbaadbd8e0f4748f83f0e1af21a7a6e14c5b4014683a942acb.jpg",
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+    {
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+        "image_caption": [
+            "Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models."
+        ],
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+    {
+        "type": "text",
+        "text": "especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration  $i$ , because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed  $v$  around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range  $R$  varies by the refinement iterations  $i$  and the agent's average velocity  $v$  around the anchor:  $R_{i,v} = \\mathcal{F}(i)\\cdot v$ .  $\\mathcal{F}(i)$  can be any monotonically decreasing function of the refinement iteration  $i$ , to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function  $\\mathcal{F}(i) = \\beta (\\frac{1}{2})^{i - 1}$ , where  $\\beta$  denotes a constant. The retrieval range is also constrained within a permissible range  $[R_{\\mathrm{min}},R_{\\mathrm{max}}]$  to ensure computational stability and efficiency.",
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+    {
+        "type": "text",
+        "text": "3.2.2 Anchor-Centric Context Encoding",
+        "text_level": 1,
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+        "type": "text",
+        "text": "With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations  $i$ , these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor  $a$ , generating a set of context embeddings  $\\mathbf{z}_a$ .",
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+        "type": "page_number",
+        "text": "15284",
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+    {
+        "type": "text",
+        "text": "3.2.3 Recurrent and Multi-Iteration Refinement",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into  $N$  segments, and refine the trajectory  $N$  times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here  $N$  equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all  $N$  segments finishes one iteration of refinement, and we will conduct multiple refinement iterations.",
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+    {
+        "type": "text",
+        "text": "Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings  $\\mathbf{z}_a$  around the segment's corresponding anchor  $a$ , and the target agent's future trajectory embeddings  $\\mathbf{h}_f$ . We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings  $\\mathbf{z}_a$ . The fused trajectory embeddings will be used to predict  $\\delta s$ , the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all  $N$  steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction.",
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+    {
+        "type": "text",
+        "text": "Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another  $N$  recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss.",
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+    {
+        "type": "text",
+        "text": "3.2.4 Adaptive Number of Refinement Iterations",
+        "text_level": 1,
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+        "type": "text",
+        "text": "As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di",
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+    {
+        "type": "code",
+        "sub_type": "algorithm",
+        "code_caption": [
+            "Algorithm 1 Adaptive Inference with SmartRefine"
+        ],
+        "code_body": "Input: Backbone model  $f_{b}$ , refinement model  $f_{r}$ , quality score decoder  $f_{d}$ , agents history trajectories  $\\mathbf{s}_{h}$ , scene context  $\\mathbf{c}$ , and score threshold  $\\bar{q}$ , maximum refinement iteration at inference  $I'$ .  \nOutput: Target agent's future trajectories  $\\mathbf{s}_{f}$  and corresponding probabilities  $\\mathbf{p}$ .  \n1:  $\\mathbf{s}_{f}^{0}, \\mathbf{h}_{f}^{0}, \\mathbf{p}^{0} = f_{b}(\\mathbf{s}_{f}^{0}, \\mathbf{c})$   \n2:  $q^{0} = f_{d}(\\mathbf{h}_{f}^{0})$   \n3: if  $q^{0} > \\bar{q}$  then  \n4: Return  $\\mathbf{s}_{f}^{0}, \\mathbf{p}^{0}$   \n5: for  $i = 1, 2, \\ldots, I'$  do  \n6: Adaptively select anchors and contexts  \n7: Adaptatively encode contexts  $\\mathbf{c}^{i-1}$  (anchor-centric)  \n8: Multi-segment recurrent refinement:  \n $\\delta \\mathbf{s}_{f}^{i}, \\mathbf{h}_{f}^{i}, \\mathbf{p}^{i}, q^{i} = f_{r}(\\mathbf{s}_{f}^{i-1}, \\mathbf{h}_{f}^{i-1}, \\mathbf{c}^{i-1})$ $\\mathbf{s}_{f}^{i} = \\mathbf{s}_{f}^{i-1} + \\delta \\mathbf{s}_{f}^{i}$   \n9: if  $q^{i} < q^{i-1}$  then  \n10: Return  $\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}$   \n11: Return  $\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}$   \n% Reach max refinement iteration",
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+    {
+        "type": "text",
+        "text": "minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality.",
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+        "text": "Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration  $i$  is  $d_{max} - d_i$ , where  $d_{max}$  denotes the largest predicted error among all iterations. A small  $d_i$  means that the current prediction has already been improved from the largest prediction error  $d_{max}$ , and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize  $d_{max} - d_i$  with  $d_{max} - d_{min}$ , where  $d_{min}$  denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as",
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+    {
+        "type": "equation",
+        "text": "\n$$\nq _ {i} = \\frac {d _ {\\text {m a x}} - d _ {i}}{d _ {\\text {m a x}} - d _ {\\text {m i n}}} \\tag {1}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score.",
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+    {
+        "type": "page_number",
+        "text": "15285",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency.",
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+    {
+        "type": "text",
+        "text": "3.3. Training Loss",
+        "text_level": 1,
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+        "type": "text",
+        "text": "The training of our model considers three loss terms, and uses hyper-parameter  $\\alpha$  to balance them:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c l s}} + \\mathcal {L} _ {\\mathrm {r e g}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {s c o r e}} \\tag {2}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{\\mathrm{cls}}$  denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss  $\\mathcal{L}_{\\mathrm{reg}}$ , as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss  $\\mathcal{L}_{\\mathrm{score}}$ , in the training stage, we fix the refinement iteration as  $I$  and each iteration will output a quality score. Thus for each iteration  $i$ , we calculate the  $\\ell_1$  loss between the predicted quality score  $\\hat{q}_i$  and labeled quality score  $q_i$  (see Sec 3.2.4), and average the loss over all iterations:",
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+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {s c o r e}} = \\frac {1}{I + 1} \\sum_ {i = 0} ^ {I} \\| \\hat {q} _ {i} - q _ {i} \\| _ {1} \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Similarly, the score loss also only considers the modal closest to the ground truth.",
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+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency.",
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+    {
+        "type": "text",
+        "text": "4.1. Experimental Settings",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at  $10\\mathrm{Hz}$ . Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at  $10\\mathrm{Hz}$ . The data is split into 200k, 25k, and 25k for training, validation, and test respectively.",
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+    {
+        "type": "text",
+        "text": "Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics.",
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+    {
+        "type": "text",
+        "text": "Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material.",
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+    {
+        "type": "text",
+        "text": "4.2. Quantitative Result",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by  $6.0\\%$ ,  $3.7\\%$ ,  $5.4\\%$ ,  $4.3\\%$ ,  $3.5\\%$  respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-",
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+    {
+        "type": "page_number",
+        "text": "15286",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8e0fffe301820899b0c2aa9203a23b941033347f606712e911a5797e2c24b84a.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td><td>#Param.(M) ↓</td><td>Flops(G) ↓</td><td>Latency(ms) ↓</td></tr><tr><td rowspan=\"6\">Argoverse</td><td>HiVT [39]</td><td>0.969</td><td>0.661</td><td>0.092</td><td>2.5</td><td>2.6</td><td>54±4.0</td></tr><tr><td>HiVT w/ Ours</td><td>0.911</td><td>0.646</td><td>0.083</td><td>2.7</td><td>2.7</td><td>67±8.4</td></tr><tr><td>Prophnet* [33]</td><td>1.004</td><td>0.687</td><td>0.093</td><td>15.2</td><td>7.8</td><td>59±1.7</td></tr><tr><td>Prophnet w/ Ours</td><td>0.967</td><td>0.675</td><td>0.092</td><td>15.4</td><td>7.9</td><td>71±6.2</td></tr><tr><td>mmTransformer [14]</td><td>1.081</td><td>0.709</td><td>0.102</td><td>2.6</td><td>1.2</td><td>15±4.8</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.023</td><td>0.692</td><td>0.094</td><td>2.8</td><td>1.3</td><td>27±9.7</td></tr><tr><td rowspan=\"6\">Argoverse 2</td><td>DenseTNT [10]</td><td>1.624</td><td>0.964</td><td>0.233</td><td>1.6</td><td>3.6</td><td>1,075±199</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.553</td><td>0.834</td><td>0.221</td><td>1.9</td><td>4.0</td><td>1,099±212</td></tr><tr><td>QCNet (no ref)</td><td>1.304</td><td>0.729</td><td>0.164</td><td>5.5</td><td>47.0</td><td>338±53</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.258</td><td>0.718</td><td>0.157</td><td>5.8</td><td>47.4</td><td>363±67</td></tr><tr><td>QCNet [40]</td><td>1.253</td><td>0.720</td><td>0.157</td><td>7.7</td><td>55.8</td><td>392±54</td></tr><tr><td>QCNet w/ Ours</td><td>1.240</td><td>0.716</td><td>0.156</td><td>8.0</td><td>56.2</td><td>418±68</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "eters, flops, and latency.",
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+    {
+        "type": "text",
+        "text": "Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by  $3.4\\%$ ,  $6.9\\%$ ,  $7.5\\%$ ,  $4.2\\%$ ,  $3.9\\%$  respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation.",
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+    {
+        "type": "text",
+        "text": "4.3. Ablation studies",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds  $\\bar{q}$  for adaptive refinement, while a higher threshold leads to better accuracy, we find  $\\bar{q} = 0.5$  achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve.",
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+    {
+        "type": "text",
+        "text": "Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger",
+        "bbox": [
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+    },
+    {
+        "type": "table",
+        "img_path": "images/bb0b3e90fc8ba4370093c10861cfdb446fd2766901a490858b5afa06ee324599.jpg",
+        "table_caption": [
+            "Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td></tr><tr><td rowspan=\"6\">Argoverse</td><td>HiVT [39]</td><td>1.17</td><td>0.77</td><td>0.13</td></tr><tr><td>HiVT w/ Ours</td><td>1.13</td><td>0.77</td><td>0.12</td></tr><tr><td>ProphNet* [33]</td><td>1.30</td><td>0.85</td><td>0.14</td></tr><tr><td>Prophnet* w/ Ours</td><td>1.21</td><td>0.81</td><td>0.13</td></tr><tr><td>mmTransformer [14]</td><td>1.34</td><td>0.84</td><td>0.15</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.24</td><td>0.81</td><td>0.14</td></tr><tr><td rowspan=\"6\">Argoverse 2</td><td>DenseTNT [10]</td><td>1.66</td><td>0.99</td><td>0.23</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.59</td><td>0.85</td><td>0.22</td></tr><tr><td>QCNet (no ref)</td><td>1.29</td><td>0.65</td><td>0.16</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet [40]</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet w/ Ours</td><td>1.23</td><td>0.63</td><td>0.15</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set.",
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+        "image_caption": [
+            "Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds  $\\bar{q}$  mentioned in Algorithm 1."
+        ],
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+    {
+        "type": "text",
+        "text": "model parameters with the same or slightly worse accuracy.",
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+    {
+        "type": "text",
+        "text": "Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding.",
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+        "type": "page_number",
+        "text": "15287",
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+        "image_caption": [
+            "Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions."
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+    {
+        "type": "text",
+        "text": "Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay.",
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+    {
+        "type": "text",
+        "text": "4.4. Discussion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about  $56\\%$  of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about  $44\\%$  trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the \"blue\" and \"orange\" trajectories change. Two phenomenons are observed:",
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+    {
+        "type": "text",
+        "text": "- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score \"blue\" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score \"orange\" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can",
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+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>#Anchor numbers</td><td>minFDE</td><td>#Param.</td></tr><tr><td>1</td><td>0.928</td><td>134K</td></tr><tr><td>2</td><td>0.911</td><td>207K</td></tr><tr><td>3</td><td>0.911</td><td>280K</td></tr><tr><td>5</td><td>0.915</td><td>433K</td></tr><tr><td>6</td><td>0.916</td><td>509K</td></tr></table>",
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+        "table_caption": [
+            "Table 4. Ablation study on the number of anchors."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Context Encoding</td><td>minFDE</td></tr><tr><td>Agent-Centric</td><td>0.941</td></tr><tr><td>Anchor-Centric</td><td>0.911</td></tr></table>",
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+        "img_path": "images/a8625216a2f0975765aec214f4b5de886ca7b6cd54cb690c225a25f3b3491b27.jpg",
+        "table_caption": [
+            "Table 5. Ablation study on how the contexts are encoded."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Retrieval Radius</td><td>minFDE</td><td>Flops (M)</td></tr><tr><td rowspan=\"4\">Fixed Radius</td><td>50</td><td>0.926</td><td>2,297</td></tr><tr><td>20</td><td>0.923</td><td>722</td></tr><tr><td>10</td><td>0.921</td><td>325</td></tr><tr><td>2</td><td>0.930</td><td>58</td></tr><tr><td rowspan=\"2\">Adaptive Radius</td><td>Rmax=10, Rmin=2, linear</td><td>0.911</td><td>245</td></tr><tr><td>Rmax=10, Rmin=2, exp</td><td>0.911</td><td>130</td></tr></table>",
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+    },
+    {
+        "type": "text",
+        "text": "Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius.",
+        "bbox": [
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+        "page_idx": 7
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+    {
+        "type": "text",
+        "text": "hardly be further improved, or even be pushed away from the ground truth due to over-refinement.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance.",
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+        "text": "These results show the necessity of adaptive refinement.",
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+    {
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+        "text": "5. Conclusion",
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+        "type": "text",
+        "text": "In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings.",
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+    {
+        "type": "text",
+        "text": "References",
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+        "bbox": [
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+        "page_idx": 8
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+    {
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2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_model.json

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+            "content": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore."
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+            "content": "Yang Zhou\\(^{1*}\\) Hao Shao\\(^{1,2*}\\) Letian Wang\\(^{3}\\)  \nven L. Waslander\\(^{3}\\) Hongsheng Li\\(^{2,4,5}\\) Yu Liu\\(^{1,5}\\)"
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+            "content": "\\(^{1}\\)SenseTime Research \\(^{2}\\)CUHK MMLab \\(^{3}\\)University of Toronto \\(^{4}\\)CPII under InnoHK \\(^{5}\\)Shanghai Artificial Intelligence Laboratory"
+        },
+        {
+            "type": "title",
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+            "content": "Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission<sup>1</sup>. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage."
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+            "content": "1. Introduction"
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+            "content": "Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently"
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+            ],
+            "angle": 0,
+            "content": "make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.602,
+                0.892,
+                0.827
+            ],
+            "angle": 0,
+            "content": "By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.827,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em"
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.1,
+                0.875,
+                0.35,
+                0.888
+            ],
+            "angle": 0,
+            "content": "* Equal contribution, \\( \\boxtimes \\) Corresponding author."
+        },
+        {
+            "type": "page_footnote",
+            "bbox": [
+                0.1,
+                0.888,
+                0.203,
+                0.899
+            ],
+            "angle": 0,
+            "content": "1 November 2023."
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.1,
+                0.875,
+                0.35,
+                0.899
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.518,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15281"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.475,
+                0.211
+            ],
+            "angle": 0,
+            "content": "ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.212,
+                0.476,
+                0.555
+            ],
+            "angle": 0,
+            "content": "To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.556,
+                0.476,
+                0.705
+            ],
+            "angle": 0,
+            "content": "It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.706,
+                0.468,
+                0.72
+            ],
+            "angle": 0,
+            "content": "To summarize, the contributions of this work are threefold:"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.722,
+                0.475,
+                0.796
+            ],
+            "angle": 0,
+            "content": "- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.797,
+                0.475,
+                0.855
+            ],
+            "angle": 0,
+            "content": "- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.078,
+                0.856,
+                0.475,
+                0.901
+            ],
+            "angle": 0,
+            "content": "- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi"
+        },
+        {
+            "type": "list",
+            "bbox": [
+                0.078,
+                0.722,
+                0.475,
+                0.901
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Refine</td><td colspan=\"3\">Context Selection/Encoding</td><td colspan=\"3\">Refinement Iteration</td></tr><tr><td>All</td><td>Fixed Strategy</td><td>Adaptive Strategy</td><td>Single</td><td>Multiple</td><td>Scenario Adaptive</td></tr><tr><td>TNT [38]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GoalNet [37]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GANet [32]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ProphNet [33]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DCMS [36]</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>QCNet [40]</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>R-Pred [5]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>MTR [25]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>SmartRefine (ours)</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.493,
+                0.237,
+                0.892,
+                0.293
+            ],
+            "angle": 0,
+            "content": "Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.506,
+                0.323,
+                0.892,
+                0.428
+            ],
+            "angle": 0,
+            "content": "ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.446,
+                0.635,
+                0.461
+            ],
+            "angle": 0,
+            "content": "2. Related Work"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.472,
+                0.836,
+                0.489
+            ],
+            "angle": 0,
+            "content": "2.1. Goal-Conditioned Trajectory Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.491,
+                0.497,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.956
+            ],
+            "angle": 0,
+            "content": "15282"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.092,
+                0.477,
+                0.226
+            ],
+            "angle": 0,
+            "content": "text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.235,
+                0.465,
+                0.251
+            ],
+            "angle": 0,
+            "content": "2.2. Refinement: Two-Stage Trajectory Prediction"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.256,
+                0.478,
+                0.66
+            ],
+            "angle": 0,
+            "content": "Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.675,
+                0.169,
+                0.69
+            ],
+            "angle": 0,
+            "content": "3. Method"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.701,
+                0.476,
+                0.835
+            ],
+            "angle": 0,
+            "content": "SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.847,
+                0.276,
+                0.862
+            ],
+            "angle": 0,
+            "content": "3.1. Problem formulation"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.871,
+                0.476,
+                0.903
+            ],
+            "angle": 0,
+            "content": "Given the observed states of the target agent \\( \\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \\dots, s_0] \\) in the historic \\( T_h \\) steps, we aim at"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.092,
+                0.892,
+                0.24
+            ],
+            "angle": 0,
+            "content": "predicting its future states \\(\\mathbf{s}_f = [s_1,s_2,\\dots ,s_{T_f}]\\) of \\(T_{f}\\) steps and associated probabilities \\(\\mathbf{p}\\). Naturally, the target agent will interact with the context \\(\\mathbf{c} = (\\mathbf{o}_h,\\mathbf{m})\\), including historic states of surrounding agents \\(\\mathbf{o}_h\\), and the HD map \\(\\mathbf{m}\\). For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as \\((\\mathbf{s}_f,\\mathbf{p}) = f(\\mathbf{s}_h,\\mathbf{c})\\), where \\(f\\) denotes the prediction model."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.242,
+                0.892,
+                0.432
+            ],
+            "angle": 0,
+            "content": "In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model \\( f_{b} \\) generating initial trajectories \\( \\mathbf{s}_f^0 \\) and trajectory features \\( \\mathbf{h}_f^0 \\), as typical prediction methods \\( (\\mathbf{s}_f^0, \\mathbf{h}_f^0, \\mathbf{p}) = f_b(\\mathbf{s}_h, \\mathbf{c}) \\). The initial predicted trajectory \\( \\mathbf{s}_f^0 \\) is then used to select anchors \\( \\mathbf{a}^0 \\) and retrieve critical context elements \\( \\mathbf{c}^0 \\), which are then passed along with the trajectory features \\( \\mathbf{h}_f^0 \\) into the refinement model \\( f_{r} \\) for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the \\( i \\)-th iteration is formulated as \\( (\\delta \\mathbf{s}_f^i, \\mathbf{h}_f^i, \\mathbf{p}) = f_r(\\mathbf{h}_f^{i-1}, \\mathbf{s}_f^{i-1}, \\mathbf{c}^{i-1}) \\). The generated offset \\( \\delta \\mathbf{s}_f^i \\) is added to the input trajectory \\( \\mathbf{s}_f^{i-1} \\) for refinement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.441,
+                0.766,
+                0.456
+            ],
+            "angle": 0,
+            "content": "3.2. Scenario-Adaptive Refinement"
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.465,
+                0.794,
+                0.48
+            ],
+            "angle": 0,
+            "content": "3.2.1 Adaptive Anchor/Context Selection"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.489,
+                0.892,
+                0.579
+            ],
+            "angle": 0,
+            "content": "Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1)."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.583,
+                0.892,
+                0.822
+            ],
+            "angle": 0,
+            "content": "Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all \\( T_{f} \\) waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into \\( N < T_{f} \\) segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments \\( N \\) is designed to adapt to the prediction horizon."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.826,
+                0.894,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Context Retrieval. When retrieving context information \\( \\mathbf{c} \\) around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15283"
+        }
+    ],
+    [
+        {
+            "type": "image",
+            "bbox": [
+                0.09,
+                0.092,
+                0.885,
+                0.254
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.091,
+                0.256,
+                0.874,
+                0.453
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
+                0.463,
+                0.896,
+                0.561
+            ],
+            "angle": 0,
+            "content": "Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.578,
+                0.479,
+                0.863
+            ],
+            "angle": 0,
+            "content": "especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration \\( i \\), because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed \\( v \\) around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range \\( R \\) varies by the refinement iterations \\( i \\) and the agent's average velocity \\( v \\) around the anchor: \\( R_{i,v} = \\mathcal{F}(i)\\cdot v \\). \\( \\mathcal{F}(i) \\) can be any monotonically decreasing function of the refinement iteration \\( i \\), to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function \\( \\mathcal{F}(i) = \\beta (\\frac{1}{2})^{i - 1} \\), where \\( \\beta \\) denotes a constant. The retrieval range is also constrained within a permissible range \\( [R_{\\mathrm{min}},R_{\\mathrm{max}}] \\) to ensure computational stability and efficiency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.493,
+                0.578,
+                0.789,
+                0.593
+            ],
+            "angle": 0,
+            "content": "3.2.2 Anchor-Centric Context Encoding"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.491,
+                0.602,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations \\( i \\), these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor \\( a \\), generating a set of context embeddings \\( \\mathbf{z}_a \\)."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.52,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15284"
+        }
+    ],
+    [
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.092,
+                0.427,
+                0.106
+            ],
+            "angle": 0,
+            "content": "3.2.3 Recurrent and Multi-Iteration Refinement"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.116,
+                0.477,
+                0.355
+            ],
+            "angle": 0,
+            "content": "The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into \\(N\\) segments, and refine the trajectory \\(N\\) times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here \\(N\\) equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all \\(N\\) segments finishes one iteration of refinement, and we will conduct multiple refinement iterations."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.358,
+                0.478,
+                0.612
+            ],
+            "angle": 0,
+            "content": "Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings \\(\\mathbf{z}_a\\) around the segment's corresponding anchor \\(a\\), and the target agent's future trajectory embeddings \\(\\mathbf{h}_f\\). We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings \\(\\mathbf{z}_a\\). The fused trajectory embeddings will be used to predict \\(\\delta s\\), the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all \\(N\\) steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.615,
+                0.478,
+                0.81
+            ],
+            "angle": 0,
+            "content": "Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another \\( N \\) recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.831,
+                0.431,
+                0.847
+            ],
+            "angle": 0,
+            "content": "3.2.4 Adaptive Number of Refinement Iterations"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.856,
+                0.476,
+                0.901
+            ],
+            "angle": 0,
+            "content": "As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di"
+        },
+        {
+            "type": "code_caption",
+            "bbox": [
+                0.495,
+                0.091,
+                0.832,
+                0.107
+            ],
+            "angle": 0,
+            "content": "Algorithm 1 Adaptive Inference with SmartRefine"
+        },
+        {
+            "type": "algorithm",
+            "bbox": [
+                0.494,
+                0.11,
+                0.892,
+                0.422
+            ],
+            "angle": 0,
+            "content": "Input: Backbone model \\(f_{b}\\), refinement model \\(f_{r}\\), quality score decoder \\(f_{d}\\), agents history trajectories \\(\\mathbf{s}_{h}\\), scene context \\(\\mathbf{c}\\), and score threshold \\(\\bar{q}\\), maximum refinement iteration at inference \\(I'\\).  \nOutput: Target agent's future trajectories \\(\\mathbf{s}_{f}\\) and corresponding probabilities \\(\\mathbf{p}\\).  \n1: \\(\\mathbf{s}_{f}^{0}, \\mathbf{h}_{f}^{0}, \\mathbf{p}^{0} = f_{b}(\\mathbf{s}_{f}^{0}, \\mathbf{c})\\)  \n2: \\(q^{0} = f_{d}(\\mathbf{h}_{f}^{0})\\)  \n3: if \\(q^{0} > \\bar{q}\\) then  \n4: Return \\(\\mathbf{s}_{f}^{0}, \\mathbf{p}^{0}\\)  \n5: for \\(i = 1, 2, \\ldots, I'\\) do  \n6: Adaptively select anchors and contexts  \n7: Adaptatively encode contexts \\(\\mathbf{c}^{i-1}\\) (anchor-centric)  \n8: Multi-segment recurrent refinement:  \n\\(\\delta \\mathbf{s}_{f}^{i}, \\mathbf{h}_{f}^{i}, \\mathbf{p}^{i}, q^{i} = f_{r}(\\mathbf{s}_{f}^{i-1}, \\mathbf{h}_{f}^{i-1}, \\mathbf{c}^{i-1})\\)  \n\\(\\mathbf{s}_{f}^{i} = \\mathbf{s}_{f}^{i-1} + \\delta \\mathbf{s}_{f}^{i}\\)  \n9: if \\(q^{i} < q^{i-1}\\) then  \n10: Return \\(\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}\\)  \n11: Return \\(\\mathbf{s}_{f}^{i}, \\mathbf{p}^{i}\\)  \n% Reach max refinement iteration"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.45,
+                0.892,
+                0.556
+            ],
+            "angle": 0,
+            "content": "minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.56,
+                0.892,
+                0.754
+            ],
+            "angle": 0,
+            "content": "Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration \\( i \\) is \\( d_{max} - d_i \\), where \\( d_{max} \\) denotes the largest predicted error among all iterations. A small \\( d_i \\) means that the current prediction has already been improved from the largest prediction error \\( d_{max} \\), and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize \\( d_{max} - d_i \\) with \\( d_{max} - d_{min} \\), where \\( d_{min} \\) denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.625,
+                0.767,
+                0.892,
+                0.8
+            ],
+            "angle": 0,
+            "content": "\\[\nq _ {i} = \\frac {d _ {\\text {m a x}} - d _ {i}}{d _ {\\text {m a x}} - d _ {\\text {m i n}}} \\tag {1}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.812,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score."
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15285"
+        }
+    ],
+    [
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.091,
+                0.477,
+                0.391
+            ],
+            "angle": 0,
+            "content": "Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.401,
+                0.221,
+                0.417
+            ],
+            "angle": 0,
+            "content": "3.3. Training Loss"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.425,
+                0.476,
+                0.455
+            ],
+            "angle": 0,
+            "content": "The training of our model considers three loss terms, and uses hyper-parameter \\(\\alpha\\) to balance them:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.182,
+                0.468,
+                0.476,
+                0.485
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} = \\mathcal {L} _ {\\mathrm {c l s}} + \\mathcal {L} _ {\\mathrm {r e g}} + \\alpha \\cdot \\mathcal {L} _ {\\mathrm {s c o r e}} \\tag {2}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.496,
+                0.477,
+                0.692
+            ],
+            "angle": 0,
+            "content": "where \\(\\mathcal{L}_{\\mathrm{cls}}\\) denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss \\(\\mathcal{L}_{\\mathrm{reg}}\\), as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss \\(\\mathcal{L}_{\\mathrm{score}}\\), in the training stage, we fix the refinement iteration as \\(I\\) and each iteration will output a quality score. Thus for each iteration \\(i\\), we calculate the \\(\\ell_1\\) loss between the predicted quality score \\(\\hat{q}_i\\) and labeled quality score \\(q_i\\) (see Sec 3.2.4), and average the loss over all iterations:"
+        },
+        {
+            "type": "equation",
+            "bbox": [
+                0.175,
+                0.703,
+                0.476,
+                0.745
+            ],
+            "angle": 0,
+            "content": "\\[\n\\mathcal {L} _ {\\text {s c o r e}} = \\frac {1}{I + 1} \\sum_ {i = 0} ^ {I} \\| \\hat {q} _ {i} - q _ {i} \\| _ {1} \\tag {3}\n\\]"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.756,
+                0.476,
+                0.786
+            ],
+            "angle": 0,
+            "content": "Similarly, the score loss also only considers the modal closest to the ground truth."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.078,
+                0.801,
+                0.21,
+                0.817
+            ],
+            "angle": 0,
+            "content": "4. Experiments"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.826,
+                0.476,
+                0.902
+            ],
+            "angle": 0,
+            "content": "We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.091,
+                0.7,
+                0.108
+            ],
+            "angle": 0,
+            "content": "4.1. Experimental Settings"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.114,
+                0.892,
+                0.309
+            ],
+            "angle": 0,
+            "content": "Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at \\(10\\mathrm{Hz}\\). Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at \\(10\\mathrm{Hz}\\). The data is split into 200k, 25k, and 25k for training, validation, and test respectively."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.312,
+                0.892,
+                0.431
+            ],
+            "angle": 0,
+            "content": "Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.435,
+                0.892,
+                0.63
+            ],
+            "angle": 0,
+            "content": "Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.494,
+                0.639,
+                0.681,
+                0.654
+            ],
+            "angle": 0,
+            "content": "4.2. Quantitative Result"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.662,
+                0.892,
+                0.901
+            ],
+            "angle": 0,
+            "content": "Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by \\(6.0\\%\\), \\(3.7\\%\\), \\(5.4\\%\\), \\(4.3\\%\\), \\(3.5\\%\\) respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-"
+        },
+        {
+            "type": "page_number",
+            "bbox": [
+                0.481,
+                0.945,
+                0.519,
+                0.957
+            ],
+            "angle": 0,
+            "content": "15286"
+        }
+    ],
+    [
+        {
+            "type": "table",
+            "bbox": [
+                0.182,
+                0.078,
+                0.787,
+                0.263
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td><td>#Param.(M) ↓</td><td>Flops(G) ↓</td><td>Latency(ms) ↓</td></tr><tr><td rowspan=\"6\">Argoverse</td><td>HiVT [39]</td><td>0.969</td><td>0.661</td><td>0.092</td><td>2.5</td><td>2.6</td><td>54±4.0</td></tr><tr><td>HiVT w/ Ours</td><td>0.911</td><td>0.646</td><td>0.083</td><td>2.7</td><td>2.7</td><td>67±8.4</td></tr><tr><td>Prophnet* [33]</td><td>1.004</td><td>0.687</td><td>0.093</td><td>15.2</td><td>7.8</td><td>59±1.7</td></tr><tr><td>Prophnet w/ Ours</td><td>0.967</td><td>0.675</td><td>0.092</td><td>15.4</td><td>7.9</td><td>71±6.2</td></tr><tr><td>mmTransformer [14]</td><td>1.081</td><td>0.709</td><td>0.102</td><td>2.6</td><td>1.2</td><td>15±4.8</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.023</td><td>0.692</td><td>0.094</td><td>2.8</td><td>1.3</td><td>27±9.7</td></tr><tr><td rowspan=\"6\">Argoverse 2</td><td>DenseTNT [10]</td><td>1.624</td><td>0.964</td><td>0.233</td><td>1.6</td><td>3.6</td><td>1,075±199</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.553</td><td>0.834</td><td>0.221</td><td>1.9</td><td>4.0</td><td>1,099±212</td></tr><tr><td>QCNet (no ref)</td><td>1.304</td><td>0.729</td><td>0.164</td><td>5.5</td><td>47.0</td><td>338±53</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.258</td><td>0.718</td><td>0.157</td><td>5.8</td><td>47.4</td><td>363±67</td></tr><tr><td>QCNet [40]</td><td>1.253</td><td>0.720</td><td>0.157</td><td>7.7</td><td>55.8</td><td>392±54</td></tr><tr><td>QCNet w/ Ours</td><td>1.240</td><td>0.716</td><td>0.156</td><td>8.0</td><td>56.2</td><td>418±68</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.076,
+                0.265,
+                0.895,
+                0.308
+            ],
+            "angle": 0,
+            "content": "Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.077,
+                0.334,
+                0.24,
+                0.349
+            ],
+            "angle": 0,
+            "content": "eters, flops, and latency."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.352,
+                0.477,
+                0.517
+            ],
+            "angle": 0,
+            "content": "Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by \\(3.4\\%\\), \\(6.9\\%\\), \\(7.5\\%\\), \\(4.2\\%\\), \\(3.9\\%\\) respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.077,
+                0.526,
+                0.24,
+                0.541
+            ],
+            "angle": 0,
+            "content": "4.3. Ablation studies"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.549,
+                0.476,
+                0.626
+            ],
+            "angle": 0,
+            "content": "We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.628,
+                0.476,
+                0.837
+            ],
+            "angle": 0,
+            "content": "Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds \\(\\bar{q}\\) for adaptive refinement, while a higher threshold leads to better accuracy, we find \\(\\bar{q} = 0.5\\) achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.841,
+                0.476,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger"
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.498,
+                0.32,
+                0.89,
+                0.504
+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td></tr><tr><td rowspan=\"6\">Argoverse</td><td>HiVT [39]</td><td>1.17</td><td>0.77</td><td>0.13</td></tr><tr><td>HiVT w/ Ours</td><td>1.13</td><td>0.77</td><td>0.12</td></tr><tr><td>ProphNet* [33]</td><td>1.30</td><td>0.85</td><td>0.14</td></tr><tr><td>Prophnet* w/ Ours</td><td>1.21</td><td>0.81</td><td>0.13</td></tr><tr><td>mmTransformer [14]</td><td>1.34</td><td>0.84</td><td>0.15</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.24</td><td>0.81</td><td>0.14</td></tr><tr><td rowspan=\"6\">Argoverse 2</td><td>DenseTNT [10]</td><td>1.66</td><td>0.99</td><td>0.23</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.59</td><td>0.85</td><td>0.22</td></tr><tr><td>QCNet (no ref)</td><td>1.29</td><td>0.65</td><td>0.16</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet [40]</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet w/ Ours</td><td>1.23</td><td>0.63</td><td>0.15</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.492,
+                0.507,
+                0.892,
+                0.576
+            ],
+            "angle": 0,
+            "content": "Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set."
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.497,
+                0.596,
+                0.691,
+                0.728
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image",
+            "bbox": [
+                0.693,
+                0.597,
+                0.887,
+                0.728
+            ],
+            "angle": 0,
+            "content": null
+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.492,
+                0.73,
+                0.895,
+                0.772
+            ],
+            "angle": 0,
+            "content": "Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds \\( \\bar{q} \\) mentioned in Algorithm 1."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.492,
+                0.79,
+                0.888,
+                0.807
+            ],
+            "angle": 0,
+            "content": "model parameters with the same or slightly worse accuracy."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.491,
+                0.811,
+                0.892,
+                0.902
+            ],
+            "angle": 0,
+            "content": "Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding."
+        },
+        {
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+        {
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+            "angle": 0,
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+        },
+        {
+            "type": "image_caption",
+            "bbox": [
+                0.076,
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+            "angle": 0,
+            "content": "Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.076,
+                0.253,
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+            ],
+            "angle": 0,
+            "content": "Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay."
+        },
+        {
+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "4.4. Discussion"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about \\(56\\%\\) of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about \\(44\\%\\) trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the \"blue\" and \"orange\" trajectories change. Two phenomenons are observed:"
+        },
+        {
+            "type": "text",
+            "bbox": [
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+            "angle": 0,
+            "content": "- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score \"blue\" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score \"orange\" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can"
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            "angle": 0,
+            "content": "<table><tr><td>#Anchor numbers</td><td>minFDE</td><td>#Param.</td></tr><tr><td>1</td><td>0.928</td><td>134K</td></tr><tr><td>2</td><td>0.911</td><td>207K</td></tr><tr><td>3</td><td>0.911</td><td>280K</td></tr><tr><td>5</td><td>0.915</td><td>433K</td></tr><tr><td>6</td><td>0.916</td><td>509K</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
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+                0.32,
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+                0.345
+            ],
+            "angle": 0,
+            "content": "Table 4. Ablation study on the number of anchors."
+        },
+        {
+            "type": "table",
+            "bbox": [
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td>Context Encoding</td><td>minFDE</td></tr><tr><td>Agent-Centric</td><td>0.941</td></tr><tr><td>Anchor-Centric</td><td>0.911</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.699,
+                0.306,
+                0.891,
+                0.332
+            ],
+            "angle": 0,
+            "content": "Table 5. Ablation study on how the contexts are encoded."
+        },
+        {
+            "type": "table",
+            "bbox": [
+                0.534,
+                0.349,
+                0.849,
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+            ],
+            "angle": 0,
+            "content": "<table><tr><td></td><td>Retrieval Radius</td><td>minFDE</td><td>Flops (M)</td></tr><tr><td rowspan=\"4\">Fixed Radius</td><td>50</td><td>0.926</td><td>2,297</td></tr><tr><td>20</td><td>0.923</td><td>722</td></tr><tr><td>10</td><td>0.921</td><td>325</td></tr><tr><td>2</td><td>0.930</td><td>58</td></tr><tr><td rowspan=\"2\">Adaptive Radius</td><td>Rmax=10, Rmin=2, linear</td><td>0.911</td><td>245</td></tr><tr><td>Rmax=10, Rmin=2, exp</td><td>0.911</td><td>130</td></tr></table>"
+        },
+        {
+            "type": "table_caption",
+            "bbox": [
+                0.493,
+                0.433,
+                0.892,
+                0.46
+            ],
+            "angle": 0,
+            "content": "Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.505,
+                0.487,
+                0.891,
+                0.516
+            ],
+            "angle": 0,
+            "content": "hardly be further improved, or even be pushed away from the ground truth due to over-refinement."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.493,
+                0.517,
+                0.892,
+                0.591
+            ],
+            "angle": 0,
+            "content": "- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance."
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.493,
+                0.594,
+                0.863,
+                0.608
+            ],
+            "angle": 0,
+            "content": "These results show the necessity of adaptive refinement."
+        },
+        {
+            "type": "title",
+            "bbox": [
+                0.493,
+                0.622,
+                0.612,
+                0.637
+            ],
+            "angle": 0,
+            "content": "5. Conclusion"
+        },
+        {
+            "type": "text",
+            "bbox": [
+                0.491,
+                0.647,
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+            ],
+            "angle": 0,
+            "content": "In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings."
+        },
+        {
+            "type": "page_number",
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+        }
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+    [
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+            "type": "title",
+            "bbox": [
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+            "angle": 0,
+            "content": "References"
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2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/f7e9eb16-11f4-4de8-b800-9a022b980e5e_origin.pdf

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2024/SmartRefine_ A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction/full.md

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+# SmartRefine: A Scenario-Adaptive Refinement Framework for Efficient Motion Prediction
+
+Yang Zhou $^{1*}$  Hao Shao $^{1,2*}$  Letian Wang $^{3}$   
+ven L. Waslander $^{3}$  Hongsheng Li $^{2,4,5}$  Yu Liu $^{1,5}$
+
+$^{1}$ SenseTime Research  $^{2}$ CUHK MMLab  $^{3}$ University of Toronto  $^{4}$ CPII under InnoHK  $^{5}$ Shanghai Artificial Intelligence Laboratory
+
+# Abstract
+
+Predicting the future motion of surrounding agents is essential for autonomous vehicles (AVs) to operate safely in dynamic, human-robot-mixed environments. Context information, such as road maps and surrounding agents' states, provides crucial geometric and semantic information for motion behavior prediction. To this end, recent works explore two-stage prediction frameworks where coarse trajectories are first proposed, and then used to select critical context information for trajectory refinement. However, they either incur a large amount of computation or bring limited improvement, if not both. In this paper, we introduce a novel scenario-adaptive refinement strategy, named SmartRefine, to refine prediction with minimal additional computation. Specifically, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly chooses the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. SmartRefine is designed as a generic and flexible approach that can be seamlessly integrated into most state-of-the-art motion prediction models. Experiments on Argoverse (1 & 2) show that our method consistently improves the prediction accuracy of multiple state-of-the-art prediction models. Specifically, by adding SmartRefine to QCNet, we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at submission<sup>1</sup>. Comprehensive studies are also conducted to ablate design choices and explore the mechanism behind multi-iteration refinement. Codes are available at our webpage.
+
+# 1. Introduction
+
+Predicting the future motion of surrounding agents (e.g., vehicle, cyclist, pedestrian) is crucial for autonomous driving frameworks [11, 22-24, 31] to safely and efficiently
+
+make decisions in a dynamic and human-robot-mixed environment. Context information, such as high-definition maps (HD maps) and surrounding agents' states, provides crucial geometric and semantic information for motion behavior, as agents' behaviors are highly dependent on the map topology and impacted by interaction with surrounding agents. For instance, vehicles usually move in drivable areas and follow the direction of lanes, and agents' interactive cues such as yielding would inform other agent's decision-making. As a result, recent motion prediction models are shown to significantly benefit from delicate context representation designs [2, 9, 13, 30] and context encodings [16, 21, 26]. However, complicated context encodings usually come at a high computational cost and high memory footprint. Since vehicles are high-speed robots and minimal delay could result in catastrophic accidents, recent advanced state-of-the-art methods could have low applicability due to limitations in mobile computation capacity and the hard real-time requirements of autonomous driving.
+
+By contrast, human drivers can easily predict surrounding agents' future behaviors, even if they confront a daunting amount of context information. As implied by neuroscience, humans' efficient reasoning capabilities benefit from their selective attention mechanism [17, 19], which identifies compact context information critical to the task for efficient reasoning. Similarly, motion prediction models are shown to be able to produce high-quality predictions with only a few critical context elements provided, such as only giving the ground-truth future reference lanes and conducting prediction in the relative coordinates [28, 29, 35]. Therefore, if we can identify the critical context elements, and aggregate more information from these critical inputs to further refine the predictions, both the computational efficiency and prediction performance can be significantly improved.
+
+While multiple refinement strategies have been proposed, the proper design of refinement is non-trivial. [36, 40] apply a prediction backbone to generate trajectory proposals, which are then used as anchor trajectories for refinement. While accuracy improvement is observed, the refinement still em
+
+ploys all context information without selection, which leads to high computation costs. [5, 25] propose pooling and grouping methods to select context features via fixed manual rules and refine trajectory for fixed iterations. However, the mechanism of refinement is still under-studied, and only fixed refinement strategies are applied, where many iterations of refinement usually exchange a large amount of computation for limited performance improvement.
+
+To this end, we therefore propose a scenario-adaptive refinement strategy, SmartRefine, which improves prediction accuracy with minimal additional computation for a wide variety of prediction models. Our key insight is that, while motion prediction models confront various driving scenarios, the prediction quality and refinement potential in different scenarios are not uniform: though some scenarios can benefit from intense refinement, some scenarios can be insensitive to refinement or even pushed away from ground truth due to over-refinement. Further, different scenarios may require different refinement configurations (i.e. how to select and encode context), while previous methods typically apply fixed refinement configurations to all scenarios (as shown in Table 1). To address these issues, the proposed SmartRefine can adapt the anchor/context selection and context encoding according to each scenario's properties, and can select the number of refinement iterations by introducing a quality score to measure the prediction quality and remaining refinement potential of each scenario. Thus, our method can allocate computation resources to those scenarios that require refinement, and terminate the refinement of the other scenarios to avoid worse prediction and wasted computation, achieving a better trade-off between accuracy and efficiency.
+
+It is worth noting that SmartRefine is not only lightweight, but also designed as a general and flexible framework that is decoupled from the primary prediction model backbone, and only requires a generic interface to the model backbone (predicted trajectories and trajectory features). Therefore, SmartRefine can be easily integrated into most state-of-the-art motion prediction models. This distinguishes our method from previous refinement methods [5, 25, 36, 40] which are either computationally heavy, or highly coupled with a particular backbone, if not both.
+
+To summarize, the contributions of this work are threefold:
+
+- We introduce SmartRefine, a scenario-adaptive refinement method that considers comprehensive design choices and configurations for refinement and adapts them to each scenario, to effectively enhance prediction accuracy with limited additional computation.  
+- We propose a generic and flexible refinement framework, which can be easily integrated into most state-of-the-art motion prediction models to enhance performance. Codes are released to facilitate further research.  
+- We conduct extensive experiments on Argoverse and Argoverse 2 datasets (both the validation set and test set), where we evaluate SmartRefine by applying it to multi
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Refine</td><td colspan="3">Context Selection/Encoding</td><td colspan="3">Refinement Iteration</td></tr><tr><td>All</td><td>Fixed Strategy</td><td>Adaptive Strategy</td><td>Single</td><td>Multiple</td><td>Scenario Adaptive</td></tr><tr><td>TNT [38]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GoalNet [37]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>GANet [32]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>ProphNet [33]</td><td>X</td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>DCMS [36]</td><td>✓</td><td>X</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>QCNet [40]</td><td>✓</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>R-Pred [5]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td></tr><tr><td>MTR [25]</td><td>✓</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td></tr><tr><td>SmartRefine (ours)</td><td>✓</td><td>X</td><td>X</td><td>✓</td><td>X</td><td>X</td><td>✓</td></tr></table>
+
+Table 1. A comparison between the proposed SmartRefine framework and previous methods in terms of 1) whether refinement is conducted; 2) how the context selection and encoding is conducted; 3) how to determine the number of refinement iterations.
+
+ple state-of-the-art motion prediction models. We show that SmartRefine improves the accuracy of all considered motion prediction models with little additional computation. Specifically, by adding SmartRefine to QCNet [40], we outperform all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission.
+
+# 2. Related Work
+
+# 2.1. Goal-Conditioned Trajectory Prediction
+
+Trajectory prediction typically takes the road map, agent history states, and semantic type as inputs and outputs future agent states. To encode scene context (road map, surround agents) around the target agents, early works [2, 6] rasterize them into a bird-eye-view image and process it with convolutional neural networks. To encourage relationship reasoning and reduce computation, recent works adopt vector-based encoding schemes, where each scene context is represented as a vector, and encoded with permutation-invariant operators such as pooling [26], graph convolution [7], and attention mechanism [8, 12, 33]. Inspired by human hierarchical decision-making where the motion intention determines the specific trajectory, goal-conditional prediction, which first predicts or predefines goal candidates, and then predicts trajectory conditioned on them, is shown to be effective and has been widely adopted in state-of-the-art methods. Multipath [2] predefines a set of anchor trajectories by clustering and predicts offset for the trajectories. TNT [38] predicts goal points that offset from a lane centerline. GoalNet [37] uses lane segments as trajectory anchors. we predict the lane that a vehicle will pass in the future. FRM [18] predicts the occupancy of each waypoint on the lanes, and then predicts the fine-grained trajectory. GANet [32] proposes a goal area-based framework for predicting goal areas and fusing crucial distant map features. MTR [25] pre-defines a set of goal points as queries by clustering the trajectory data of each agent type, and adopts attention layers to aggregate con
+
+text information based on the queries. Prophet [33] uses trajectory proposals as learnable anchors to enable the attention layers to encode goal-oriented scene contexts. However, while these methods exploit goal-conditioned prediction, they only leverage goal-conditioned contexts once. In this paper, we utilize trajectory anchors as goals in an iterative manner, where the predicted trajectory at one iteration can benefit the next iteration by specifying more precise anchors as goals to extract more relevant map information.
+
+# 2.2. Refinement: Two-Stage Trajectory Prediction
+
+Inspired by refinement networks [1, 20] in computer vision, refinement strategies have been introduced to the trajectory prediction community. Trajectory refinement typically takes proposed trajectories in the first stage as inputs, and outputs the offset and probability for each proposed trajectory. DCMS [36] takes the output of the first stage as anchor trajectories and conducts refinement to predict the offset. QC-Net [40] uses a small GRU to embed the proposed trajectories in the first stage and predict the offset of the trajectories by fusing the same scene context. R-Pred [5] proposes tubequery scene attention layers to refine based on local contexts, and interaction attention layers to refine based on agents' interactions. MTR [25] uses the predicted trajectory as anchors to retrieve contexts along the trajectory for refinement. The refinement is conducted for multiple iterations. However, existing methods typically employ a relatively large refinement network or utilize fixed refinement strategies (e.g. retrieval range, context encodings, and refinement iterations), which leads to sub-optimal performance in various scenarios. By contrast, SmartRefine can comprehensively adapt refinement configurations based on each scenario's properties, and smartly choose the number of refinement iterations. Besides, SmartRefine is designed as a lightweight and flexible approach that can be seamlessly integrated into state-of-the-art motion prediction. We will show through experiments how our method can refine prediction with minimal additional computation.
+
+# 3. Method
+
+SmartRefine is a scenario-adaptive refinement method to enhance the performance of motion prediction models with limited additional computation by adaptively iterating between retrieving critical context information and predicting more accurate trajectories. The overall structure is illustrated in Fig. 1 and Algorithm 1. In Sec. 3.1, we introduce the formulation of the problem. In Sec. 3.2, we elaborate on the proposed methodologies. In Sec. 3.3, we introduce the training details of our framework.
+
+# 3.1. Problem formulation
+
+Given the observed states of the target agent  $\mathbf{s}_h = [s_{-T_h}, s_{-T_h + 1}, \dots, s_0]$  in the historic  $T_h$  steps, we aim at
+
+predicting its future states  $\mathbf{s}_f = [s_1,s_2,\dots ,s_{T_f}]$  of  $T_{f}$  steps and associated probabilities  $\mathbf{p}$ . Naturally, the target agent will interact with the context  $\mathbf{c} = (\mathbf{o}_h,\mathbf{m})$ , including historic states of surrounding agents  $\mathbf{o}_h$ , and the HD map  $\mathbf{m}$ . For the HD map, we adopt the vectorized representation [9, 13], where each lane is defined as a sequence of points along its centerline. Each point is represented by the coordinates and semantic information. Thus typical motion prediction task is formulated as  $(\mathbf{s}_f,\mathbf{p}) = f(\mathbf{s}_h,\mathbf{c})$ , where  $f$  denotes the prediction model.
+
+In this work, the introduced refinement strategy will slightly modifies problem formulation. As in Fig. 1, we first have a backbone model  $f_{b}$  generating initial trajectories  $\mathbf{s}_f^0$  and trajectory features  $\mathbf{h}_f^0$ , as typical prediction methods  $(\mathbf{s}_f^0, \mathbf{h}_f^0, \mathbf{p}) = f_b(\mathbf{s}_h, \mathbf{c})$ . The initial predicted trajectory  $\mathbf{s}_f^0$  is then used to select anchors  $\mathbf{a}^0$  and retrieve critical context elements  $\mathbf{c}^0$ , which are then passed along with the trajectory features  $\mathbf{h}_f^0$  into the refinement model  $f_{r}$  for trajectory refinement. Note that the refinement can be multi-iteration, thus refinement of the  $i$ -th iteration is formulated as  $(\delta \mathbf{s}_f^i, \mathbf{h}_f^i, \mathbf{p}) = f_r(\mathbf{h}_f^{i-1}, \mathbf{s}_f^{i-1}, \mathbf{c}^{i-1})$ . The generated offset  $\delta \mathbf{s}_f^i$  is added to the input trajectory  $\mathbf{s}_f^{i-1}$  for refinement.
+
+# 3.2. Scenario-Adaptive Refinement
+
+# 3.2.1 Adaptive Anchor/Context Selection
+
+Trajectory refinement necessitates informative anchor selection and context retrieval. After the backbone generates the initial trajectories and trajectory features, SmartRefine first selects an adaptive number of anchors along the trajectories, and then retrieves contexts near the anchors with adaptive radius (illustrated in the bottom left in Fig. 1).
+
+Anchor Selection. To select anchors along the trajectory, an intuitive option is to choose the last waypoint of the trajectory as the anchor for long-term context retrieval, as in goal-based predictions [32, 38]. However, relying exclusively on the endpoint as an anchor often misses the intermediate evolution and progression of the trajectory, resulting in deviations and oscillations. On the other extreme, selecting all  $T_{f}$  waypoints as anchors will lead to large but unnecessary computations. To balance between context richness and computation efficiency, we adopt an adaptive approach, where the trajectory is divided into  $N < T_{f}$  segments and each segment's endpoint is selected as an anchor. Note that motion prediction benchmarks typically consider varied prediction horizon lengths. To depress the cumulative error in long-horizon prediction, the number of segments  $N$  is designed to adapt to the prediction horizon.
+
+Context Retrieval. When retrieving context information  $\mathbf{c}$  around the anchors, previous methods usually employ a fixed radius or rectangle around the anchor to extract local contexts (e.g. map and nearby agents) [5, 25]. Such fixed retrieval strategies, though straightforward, can be sub-optimal
+
+![](images/b7e67582f0dceddbaadbd8e0f4748f83f0e1af21a7a6e14c5b4014683a942acb.jpg)
+
+![](images/c2b3b37b594d19f69e01cea0fae890585627d07023ec4c013811f998ab0c3e22.jpg)  
+Figure 1. Overview of our framework. The top section concisely illustrates the full pipeline, while the lower section introduces details of three core modules. We first pass HD map and agent information to a prediction model backbone, generating initial trajectories and trajectory features. The initial predicted trajectory is then used to adaptively select anchors and retrieve critical context elements (bottom left). The contexts retrieved by each anchor are transformed to the coordinate frame centered at the corresponding anchors (bottom middle). The encoded contexts are then utilized to refine each trajectory segment by generating the offset of each trajectory segment (bottom right). Our model will predict a quality score measuring the prediction quality, and adaptively decide the number of refinement iterations (upper right). Our method is lightweight and can be seamlessly integrated with most existing motion prediction models.
+
+especially when applied across diverse datasets and scenarios which could require different retrieval ranges. To address this issue, our idea is that, the retrieval range of one anchor should depend on 1) the refinement iteration  $i$ , because only fine-grained context information is needed in later refinement iterations, where the trajectories are more accurate compared to early iterations. 2) the target agent's speed  $v$  around the anchor, since large speed requires a far and long-term vision of the environment context. Thus we introduce an adaptive retrieval strategy, where each anchor's retrieval range  $R$  varies by the refinement iterations  $i$  and the agent's average velocity  $v$  around the anchor:  $R_{i,v} = \mathcal{F}(i)\cdot v$ .  $\mathcal{F}(i)$  can be any monotonically decreasing function of the refinement iteration  $i$ , to reduce the retrieval range as the trajectory becomes more precise. We instantiate it with an exponential decay function  $\mathcal{F}(i) = \beta (\frac{1}{2})^{i - 1}$ , where  $\beta$  denotes a constant. The retrieval range is also constrained within a permissible range  $[R_{\mathrm{min}},R_{\mathrm{max}}]$  to ensure computational stability and efficiency.
+
+# 3.2.2 Anchor-Centric Context Encoding
+
+With the retrieved context elements, most existing methods directly use their embeddings generated by the prediction backbone for further refinement [40]. However, these context embeddings from the backbone are typically encoded in the coordinate frame centered at the target agent's current position. While this agent-centric embedding emphasizes the context details around the target agent, the refinement process instead desires the context nuances along the future trajectories. To address this issue, we propose an anchor-centric context encoding approach, to better capture future trajectory details. (illustrated in the bottom middle in Fig. 1) This is achieved by transforming the context features into the coordinate frame centered and aligned with the anchor, and then encoding the features to generate anchor-centric context embeddings for refinement. Note that as the positions and orientations of anchors are dynamically changing across different refinement iterations  $i$ , these anchor-centric context features could also vary. This encoding process is applied to every context element retrieved around the anchor  $a$ , generating a set of context embeddings  $\mathbf{z}_a$ .
+
+# 3.2.3 Recurrent and Multi-Iteration Refinement
+
+The anchor-centric context embeddings introduced in the previous section are then fused with the trajectory embeddings to refine predictions. To this end, previous methods usually fuse all embeddings once and refine the trajectory of the whole future horizon, which suffers from long-term cumulative error. To mitigate this issue, we adopt a recurrent refinement strategy where we divide the trajectory into  $N$  segments, and refine the trajectory  $N$  times, one trajectory segment each time (illustrated in the bottom right in Fig. 1). Note that here  $N$  equals the number of anchors, which means each trajectory segment corresponds to one anchor. For each trajectory segment, we refine it only using the context retrieved by the corresponding anchor to enhance local context fusion. Besides, refining all  $N$  segments finishes one iteration of refinement, and we will conduct multiple refinement iterations.
+
+Recurrent Refinement. Specifically, in each recurrent refinement step, we refine one trajectory segment, with a set of scene context embeddings  $\mathbf{z}_a$  around the segment's corresponding anchor  $a$ , and the target agent's future trajectory embeddings  $\mathbf{h}_f$ . We adopt the cross attention mechanism [27] to fuse them, where the trajectory embeddings are used as queries to attend to the keys/values from the context embeddings  $\mathbf{z}_a$ . The fused trajectory embeddings will be used to predict  $\delta s$ , the offset of waypoints in the trajectory segment, to subtly adjust the original trajectory segment. The updated trajectory embeddings will also be leveraged as new queries to refine the next segment. After all  $N$  steps within one iteration, the whole trajectory will be adjusted, and the trajectory embeddings will also be updated with rich context information. Note that we predict multiple possible predictions, thus the trajectory embeddings will also be used to predict the probability of each prediction.
+
+Multi-Iteration Refinement. After one iteration terminates, the updated trajectory and trajectory embeddings will be used to start another refinement iteration. We first repeat the adaptive anchor selection and context retrieval mentioned in Sec. 3.2.1, and then conduct another  $N$  recurrent refinement steps. Thus in the multi-iteration refinement, the trajectory and trajectory embeddings used in one iteration can come from either the backbone (for the first iteration) or the previous refinement iteration (for the later iterations). Note that in the first refinement iteration, we employ a compressor network to reduce the hidden dimension of the trajectory embedding from the backbone for efficient refinement, which we found brings little performance loss.
+
+# 3.2.4 Adaptive Number of Refinement Iterations
+
+As mentioned in the previous section, the refinement is multi-iteration. As we get into later iterations, the predicted trajectory becomes more accurate. Nonetheless, there's a di
+
+Algorithm 1 Adaptive Inference with SmartRefine  
+Input: Backbone model  $f_{b}$ , refinement model  $f_{r}$ , quality score decoder  $f_{d}$ , agents history trajectories  $\mathbf{s}_{h}$ , scene context  $\mathbf{c}$ , and score threshold  $\bar{q}$ , maximum refinement iteration at inference  $I'$ .  
+Output: Target agent's future trajectories  $\mathbf{s}_{f}$  and corresponding probabilities  $\mathbf{p}$ .  
+1:  $\mathbf{s}_{f}^{0}, \mathbf{h}_{f}^{0}, \mathbf{p}^{0} = f_{b}(\mathbf{s}_{f}^{0}, \mathbf{c})$   
+2:  $q^{0} = f_{d}(\mathbf{h}_{f}^{0})$   
+3: if  $q^{0} > \bar{q}$  then  
+4: Return  $\mathbf{s}_{f}^{0}, \mathbf{p}^{0}$   
+5: for  $i = 1, 2, \ldots, I'$  do  
+6: Adaptively select anchors and contexts  
+7: Adaptatively encode contexts  $\mathbf{c}^{i-1}$  (anchor-centric)  
+8: Multi-segment recurrent refinement:  
+ $\delta \mathbf{s}_{f}^{i}, \mathbf{h}_{f}^{i}, \mathbf{p}^{i}, q^{i} = f_{r}(\mathbf{s}_{f}^{i-1}, \mathbf{h}_{f}^{i-1}, \mathbf{c}^{i-1})$ $\mathbf{s}_{f}^{i} = \mathbf{s}_{f}^{i-1} + \delta \mathbf{s}_{f}^{i}$   
+9: if  $q^{i} < q^{i-1}$  then  
+10: Return  $\mathbf{s}_{f}^{i}, \mathbf{p}^{i}$   
+11: Return  $\mathbf{s}_{f}^{i}, \mathbf{p}^{i}$   
+% Reach max refinement iteration
+
+minishing return as we utilize more refinement iterations. To trade-off between performance gain and additional computation, we propose an adaptive refinement strategy where the number of refinement iterations is dynamically adapted according to the current prediction quality and remaining potential refinement improvement. Specifically, we propose a quality score to quantify current prediction quality.
+
+Quality Score Design. At the training stage, since we have access to the ground-truth trajectory and predicted trajectory of all refinement iterations, an intuitive measure for the quality of the predicted trajectory in iteration  $i$  is  $d_{max} - d_i$ , where  $d_{max}$  denotes the largest predicted error among all iterations. A small  $d_i$  means that the current prediction has already been improved from the largest prediction error  $d_{max}$ , and thus of high quality. However, this design as the quality score can be unstable as it lies in a big range and can vary a lot in different scenarios. We then normalize  $d_{max} - d_i$  with  $d_{max} - d_{min}$ , where  $d_{min}$  denotes the smallest predicted error among all iterations. Thus the final quality score lies in between [0,1] and is designed as
+
+$$
+q _ {i} = \frac {d _ {\text {m a x}} - d _ {i}}{d _ {\text {m a x}} - d _ {\text {m i n}}} \tag {1}
+$$
+
+To enable the model to predict the quality score, we first employ a GRU [4] to recurrently process the trajectory embeddings of all previous iterations, and then use an MLP to generate the quality score. Thus our model will generate three types of output: the predicted trajectories, the probabilities of the trajectories, and the quality score.
+
+Adaptive Refinement Iteration. The contents above introduce how to design and generate the quality score at the training stage. At the inference stage, the initial trajectory features from the backbone will be appended with the quality score decoder to predict an initial quality score. Our model will also predict the quality score at each refinement iteration. Thus we propose a simple yet effective strategy to dynamically decide whether another refinement iteration is needed. As outlined in Algorithm 1, the adaptive strategy includes three major criteria: 1) an initial quality score threshold is set, and we only conduct refinement if the initial predicted quality score is below the threshold, which means the current prediction is not good enough and need refinement; 2) at any of the later refinement iterations, if the quality score stops growing compared to previous iterations, we terminate the refinement as this indicates that we are close to ideal performance, and further refinement will only bring diminishing returns or negative effects due to over-refinement; 3) a maximum refinement iteration is set, which is a hyper-parameter to balance performance and efficiency.
+
+# 3.3. Training Loss
+
+The training of our model considers three loss terms, and uses hyper-parameter  $\alpha$  to balance them:
+
+$$
+\mathcal {L} = \mathcal {L} _ {\mathrm {c l s}} + \mathcal {L} _ {\mathrm {r e g}} + \alpha \cdot \mathcal {L} _ {\mathrm {s c o r e}} \tag {2}
+$$
+
+where  $\mathcal{L}_{\mathrm{cls}}$  denotes the cross-entropy classification loss for predicting the probability of the multi-modal trajectories. For the regression loss  $\mathcal{L}_{\mathrm{reg}}$ , as our model predicts a Laplace distribution for each time step's waypoint, we calculate the negative log-likelihood of the ground-truth trajectory in the predicted distribution. Note that among all predicted multimodal trajectories, only the modal closest to the ground truth is considered for the regression loss. For the quality score loss  $\mathcal{L}_{\mathrm{score}}$ , in the training stage, we fix the refinement iteration as  $I$  and each iteration will output a quality score. Thus for each iteration  $i$ , we calculate the  $\ell_1$  loss between the predicted quality score  $\hat{q}_i$  and labeled quality score  $q_i$  (see Sec 3.2.4), and average the loss over all iterations:
+
+$$
+\mathcal {L} _ {\text {s c o r e}} = \frac {1}{I + 1} \sum_ {i = 0} ^ {I} \| \hat {q} _ {i} - q _ {i} \| _ {1} \tag {3}
+$$
+
+Similarly, the score loss also only considers the modal closest to the ground truth.
+
+# 4. Experiments
+
+We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency.
+
+# 4.1. Experimental Settings
+
+Dataset. We train and evaluate our method on two large-scale motion forecasting datasets: Argoverse [3] and Argoverse 2 [34]. Argoverse contains 333k scenarios collected from interactive and dense traffic. Each scenario provides the HD map and 2 seconds of history trajectory data, to predict the trajectory for future 3 seconds, sampled at  $10\mathrm{Hz}$ . Following the official guide, we split the training, validation, and test set to 205k, 39k, 78k scenarios respectively. Argoverse 2 upgrades the previous dataset to include 250K sequences with higher prediction complexity. It extends the historic and prediction horizon to 5 seconds and 6 seconds respectively, sampled at  $10\mathrm{Hz}$ . The data is split into 200k, 25k, and 25k for training, validation, and test respectively.
+
+Metrics. Following the official dataset settings, we evaluate our model on the standard metrics for motion prediction, including minimum Average Displacement Error (minADE), minimum Final Displacement Error (minFDE), and Miss Rate (MR). These metrics allow models to forecast up to 6 trajectories for each agent and define the one that has the minimum endpoint error as the best trajectory to calculate the above metrics.
+
+Baselines. As mentioned earlier, our SmartRefine can be seamlessly integrated into most existing trajectory prediction methods to improve accuracy with limited additional computation. In our experiment, we consider five popular and state-of-the-art methods as the prediction backbone to evaluate how our SmartRefine further improves the performance: HiVT [39], Prophnet [33], mmTransformer [14], DenseTNT [10] and QCNet [40]. Note that, since QCNet includes a refinement module itself, we introduce another baseline QCNet (no refinement) which removes the original refinement module from the QCNet. For implementation and computation details of our methods, please refer to the supplementary material.
+
+# 4.2. Quantitative Result
+
+Performance on Val Set. We first report the prediction accuracy and computation cost on the validation set of the two datasets. As shown in Table 2, SmartRefine can consistently improve the prediction accuracy of all considered state-of-the-art methods with limited added parameters, Flops, and latency. For instance, our method can reduce the minFDE of Prophnet, mmTransformer, HiVT, DenseTNT, and QCNet (no ref) by  $6.0\%$ ,  $3.7\%$ ,  $5.4\%$ ,  $4.3\%$ ,  $3.5\%$  respectively. Besides, our refinement model only added Flops by 130M on Argoverse and 408M on Argoverse 2, and thus is much smaller than the Flops of the backbone which range from 1.2G to 55.8G. Our method benefits QCNet less than other methods, because QCNet itself incorporates a relatively large refinement network that has 2,200K parameters. However, if we replace the refinement module in QCNet with ours, we can achieve competitive results with much less added param-
+
+<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td><td>#Param.(M) ↓</td><td>Flops(G) ↓</td><td>Latency(ms) ↓</td></tr><tr><td rowspan="6">Argoverse</td><td>HiVT [39]</td><td>0.969</td><td>0.661</td><td>0.092</td><td>2.5</td><td>2.6</td><td>54±4.0</td></tr><tr><td>HiVT w/ Ours</td><td>0.911</td><td>0.646</td><td>0.083</td><td>2.7</td><td>2.7</td><td>67±8.4</td></tr><tr><td>Prophnet* [33]</td><td>1.004</td><td>0.687</td><td>0.093</td><td>15.2</td><td>7.8</td><td>59±1.7</td></tr><tr><td>Prophnet w/ Ours</td><td>0.967</td><td>0.675</td><td>0.092</td><td>15.4</td><td>7.9</td><td>71±6.2</td></tr><tr><td>mmTransformer [14]</td><td>1.081</td><td>0.709</td><td>0.102</td><td>2.6</td><td>1.2</td><td>15±4.8</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.023</td><td>0.692</td><td>0.094</td><td>2.8</td><td>1.3</td><td>27±9.7</td></tr><tr><td rowspan="6">Argoverse 2</td><td>DenseTNT [10]</td><td>1.624</td><td>0.964</td><td>0.233</td><td>1.6</td><td>3.6</td><td>1,075±199</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.553</td><td>0.834</td><td>0.221</td><td>1.9</td><td>4.0</td><td>1,099±212</td></tr><tr><td>QCNet (no ref)</td><td>1.304</td><td>0.729</td><td>0.164</td><td>5.5</td><td>47.0</td><td>338±53</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.258</td><td>0.718</td><td>0.157</td><td>5.8</td><td>47.4</td><td>363±67</td></tr><tr><td>QCNet [40]</td><td>1.253</td><td>0.720</td><td>0.157</td><td>7.7</td><td>55.8</td><td>392±54</td></tr><tr><td>QCNet w/ Ours</td><td>1.240</td><td>0.716</td><td>0.156</td><td>8.0</td><td>56.2</td><td>418±68</td></tr></table>
+
+eters, flops, and latency.
+
+Performance on Test Set. We also submit our method to Argoverse and Argoverse 2 test set and the results are shown in Table 3. Again, SmartRefine consistently improves the prediction accuracy of all considered methods. For instance, SmartRefine reduces the minFDE of HiVT, Prophnet, mmTransformer, DenseTNT, and QCNet (no ref) by  $3.4\%$ ,  $6.9\%$ ,  $7.5\%$ ,  $4.2\%$ ,  $3.9\%$  respectively. Specifically, our SmartRefine based on QCNet outperforms all published ensemble-free works on the Argoverse 2 leaderboard (single agent track) at the time of the paper submission. See Sec. C for a more detailed explanation.
+
+# 4.3. Ablation studies
+
+We conducted comprehensive ablation studies on the effect of each component in our proposed method, on the Argov- erse validation set. We show the performance when we add SmartRefine on top of HiVT, and the results based on other backbones can be found in the supplementary material.
+
+Adaptive Refinement Iterations. Fig. 2 ablates the effect of adaptive refinement iterations. When we use a fixed number of iterations (blue curve), the prediction accuracy improves with more refinement iterations, but diminishing or zero improvements are witnessed in later iterations. In comparison, when we adopt the adaptive refinement iteration proposed by SmartRefine, we can achieve higher accuracy with a smaller number of refinement iterations. Note that we studied different quality score thresholds  $\bar{q}$  for adaptive refinement, while a higher threshold leads to better accuracy, we find  $\bar{q} = 0.5$  achieves an ideal performance and higher thresholds perform similarly. Besides, for each threshold, we ablate different limits for maximum refinement iteration, resulting in 5 points for each curve.
+
+Anchor Numbers. Table 4 ablates the effect of anchor numbers. We can see that increasing the anchor number from 1 to 2 reduces the minFDE. However, excessively increasing the number of anchors is ineffective, as it brings much larger
+
+Table 2. Performance and computation efficiency on Argoverse and Argoverse 2 val set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. QCNet (no ref) denotes the version where we remove the original refinement module in the QCNet. SmartRefine consistently improves the accuracy of all considered state-of-the-art methods with limited added computation and latency.  
+
+<table><tr><td>Dataset</td><td>Method</td><td>minFDE ↓</td><td>minADE ↓</td><td>MR ↓</td></tr><tr><td rowspan="6">Argoverse</td><td>HiVT [39]</td><td>1.17</td><td>0.77</td><td>0.13</td></tr><tr><td>HiVT w/ Ours</td><td>1.13</td><td>0.77</td><td>0.12</td></tr><tr><td>ProphNet* [33]</td><td>1.30</td><td>0.85</td><td>0.14</td></tr><tr><td>Prophnet* w/ Ours</td><td>1.21</td><td>0.81</td><td>0.13</td></tr><tr><td>mmTransformer [14]</td><td>1.34</td><td>0.84</td><td>0.15</td></tr><tr><td>mmTransformer w/ Ours</td><td>1.24</td><td>0.81</td><td>0.14</td></tr><tr><td rowspan="6">Argoverse 2</td><td>DenseTNT [10]</td><td>1.66</td><td>0.99</td><td>0.23</td></tr><tr><td>DenseTNT w/ Ours</td><td>1.59</td><td>0.85</td><td>0.22</td></tr><tr><td>QCNet (no ref)</td><td>1.29</td><td>0.65</td><td>0.16</td></tr><tr><td>QCNet (no ref) w/ Ours</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet [40]</td><td>1.24</td><td>0.64</td><td>0.15</td></tr><tr><td>QCNet w/ Ours</td><td>1.23</td><td>0.63</td><td>0.15</td></tr></table>
+
+Table 3. Performance on Argoverse (1&2) test set. Methods that are not open-source and reproduced by us are marked with the symbol “*”. The original DenseTNT and QCNet (no ref) did not report results in the test set, thus we train them to match the validation set and submit them to the test set.
+
+![](images/9496fb08086673546e98ca71b8e2033a6c91889faf7340ffde38fbadb692c7ff.jpg)  
+Figure 2. Comparison between the fixed and adaptive number of refinement iterations. For the adaptive methods, We tested different quality score thresholds  $\bar{q}$  mentioned in Algorithm 1.
+
+![](images/6d3196a1d87945dd9b252629e27b1afd460b55245cad9a5d7d732a02fc9e1491.jpg)
+
+model parameters with the same or slightly worse accuracy.
+
+Context Representation. In Table 5, we compare the performance when we employ the fixed agent-centric context embeddings or the adaptive anchor-centric context embeddings (see details in Sec 3.2.2). We can see our adaptive anchor-centric encoding effectively outperforms the fixed agent-centric context encoding.
+
+![](images/d30db22a5732690fa15161f3217c5fe39fb9dc20c8dab479a2a01db9371b9947.jpg)  
+Figure 3. A study to understand the mechanism behind the refinement. Specifically, We mark the quality score distribution of the predictive trajectory before refinement, and track how the quality score changes along the multi-iteration refinement. We can see while the overall performance is improved, not every trajectory benefits from refinement, which implies the necessity of adaptive refinement. See Sec. 4.4 for detailed discussions.
+
+![](images/009efeb68911d1f475b6bd134b314208f8691127e9ce85a6ae778744b70e72e4.jpg)
+
+![](images/5613082faf5562bee17e6cb1e1261da00189c9503db82692e030d4c00634aa66.jpg)
+
+![](images/48b8669549bf53d061ae1a8eca62b12c1b8e6d3b4513b88482b80d15f4fff7b7.jpg)
+
+![](images/fc6bdcd919f5e8c6d7a30e223de2663ba9bd480136b85475c82c1d121d73266a.jpg)
+
+![](images/0c47feb96f45286ccb1809164c0eddd48c09e9dc95feec5062a2754e885ffdf0.jpg)
+
+Retrieval Radius. Table 6 studies the effect of the radius used to retrieve contexts. We can see a fixed retrieval radius from 50 to 2 can be sub-optimal, as a large retrieval radius might lead to redundant or unrelavant context information, while a small radius might not provide sufficient context for refinement. In comparison, our SmartRefine adapts the radius to each agent's velocity, and decays the radius with the number of refinement iterations (see details in Sec 3.2.1). Here we consider two strategies for radius decay: linear decay and exponential decay. Both methods lead to lower minFDE compared to the fixed radius, and the exponential decay has lower Flops compared to linear decay.
+
+# 4.4. Discussion
+
+While many previous works have explored various refinement strategies, few of them explain how exactly the refinement works and what limitations it has. For example, it remains unclear whether every trajectory is improved by the refinement. In this section, we take a step forward to study the mechanism behind the refinement. Specifically, for each predicted trajectory, we measure its accuracy using the quality score proposed earlier. We will track how the quality score changes along the multi-iteration refinements. As shown in Fig. 3, before the refinement, the quality score of the trajectories most fall in two categories: about  $56\%$  of the trajectories have a low quality score between 0 and 0.2 (marked as blue), and about  $44\%$  trajectories have a high quality score between 0.8 and 1 (marked as orange). We then conduct multi-iteration refinement and track how the quality score of the "blue" and "orange" trajectories change. Two phenomenons are observed:
+
+- Not every trajectory benefits from refinement: as the refinement goes, we can see that the initially low-score "blue" trajectories gradually move to the right, which means they become more accurate. However, the initially high-score "orange" trajectories gradually move to the left, which means they become less accurate. In fact, we can see that initially low-score blue trajectories and initially high-score orange trajectories switched their quality score at the final iteration. We hypothesize that this is because while inaccurate trajectories can get much improvement from refinement, the accurate trajectories are good enough and can
+
+<table><tr><td>#Anchor numbers</td><td>minFDE</td><td>#Param.</td></tr><tr><td>1</td><td>0.928</td><td>134K</td></tr><tr><td>2</td><td>0.911</td><td>207K</td></tr><tr><td>3</td><td>0.911</td><td>280K</td></tr><tr><td>5</td><td>0.915</td><td>433K</td></tr><tr><td>6</td><td>0.916</td><td>509K</td></tr></table>
+
+Table 4. Ablation study on the number of anchors.  
+
+<table><tr><td>Context Encoding</td><td>minFDE</td></tr><tr><td>Agent-Centric</td><td>0.941</td></tr><tr><td>Anchor-Centric</td><td>0.911</td></tr></table>
+
+Table 5. Ablation study on how the contexts are encoded.  
+
+<table><tr><td></td><td>Retrieval Radius</td><td>minFDE</td><td>Flops (M)</td></tr><tr><td rowspan="4">Fixed Radius</td><td>50</td><td>0.926</td><td>2,297</td></tr><tr><td>20</td><td>0.923</td><td>722</td></tr><tr><td>10</td><td>0.921</td><td>325</td></tr><tr><td>2</td><td>0.930</td><td>58</td></tr><tr><td rowspan="2">Adaptive Radius</td><td>Rmax=10, Rmin=2, linear</td><td>0.911</td><td>245</td></tr><tr><td>Rmax=10, Rmin=2, exp</td><td>0.911</td><td>130</td></tr></table>
+
+Table 6. Ablation study on the context retrieval radius. Linear and exp denote different ways to decay the radius.
+
+hardly be further improved, or even be pushed away from the ground truth due to over-refinement.
+
+- The overall performance is better: though the initially accurate and inaccurate trajectories switch their quality scores at the final iteration, we see the final iteration has a higher percentage of high-score trajectories. This is why our refinement can lead to a higher overall performance.
+
+These results show the necessity of adaptive refinement.
+
+# 5. Conclusion
+
+In this paper, we introduce SmartRefine, a scenario-adaptive refinement framework for efficient refinement of motion prediction models. Our method adopts adaptive strategies anchor selection, retrieval radius, and context encoding to conduct refinement that better suits each scenario. We then propose the quality score to indicate current prediction quality and potential refinement improvement, and adaptively decide how many refinement iterations are needed for each scenario. Our SmartRefine is not only lightweight, but can also be seamlessly plugged into most existing motion prediction models as it is decoupled from the prediction backbone and only relies on a generic interface between the backbone. Extensive experiments demonstrate the effectiveness of our approach in terms of both prediction accuracy and computation efficiency. We also study the mechanism behind multi-iteration refinement. In the future, we will further extend our framework to multi-agent joint prediction settings.
+
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+        "type": "text",
+        "text": "Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models",
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+        "text": "Jiayi Guo $^{1,2*}$ , Xingqian Xu $^{1,3*}$ , Yifan Pu $^{2}$ , Zanlin Ni $^{2}$ , Chaofei Wang $^{2}$ , Manushree Vasu $^{1}$ , Shiji Song $^{2}$ , Gao Huang $^{2\\dagger}$ , Humphrey Shi $^{1,3\\dagger}$",
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+        "text": "<sup>1</sup>SHI Labs @ Georgia Tech & UIUC <sup>2</sup>Tsinghua University <sup>3</sup>Picsart AI Research (PAIR)",
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+            "Task 2: Image Inversion and Reconstruction \"A train going back to its course filled with people",
+            "\"A mouse is next to a keyboard on a desk\""
+        ],
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+        "image_caption": [
+            "Figure 1. Smooth Diffusion for downstream image synthesis tasks. Our method formally introduces latent space smoothness to diffusion models like Stable Diffusion [62]. This smoothness dramatically aids various tasks in: 1) improving continuity of transitions in image interpolation, 2) reducing approximation errors in image inversion, & 3) better preserving unedited contents in image editing."
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+            "Task 3: Image Editing Replace Item: \"rabbit\"  $\\rightarrow$  \"cat\"",
+            "Transfer Style: \"watercolor style\""
+        ],
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+        "image_caption": [
+            "Add Item: + \"bacon\"",
+            "Drag Point"
+        ],
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+        "type": "text",
+        "text": "Abstract",
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+        "text": "Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a",
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+    },
+    {
+        "type": "text",
+        "text": "new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.",
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+        "text": "CVF",
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+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
+        "bbox": [
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+    {
+        "type": "page_footnote",
+        "text": "*Equal contribution.",
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+    {
+        "type": "page_footnote",
+        "text": "† Corresponding authors.",
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+    },
+    {
+        "type": "page_number",
+        "text": "7548",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
+        "bbox": [
+            78,
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as \"cartoonization\" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations  $\\Delta \\epsilon$  on a latent noise  $\\epsilon$  should produce smooth visual changes  $\\Delta \\widehat{x_0}$  on the",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "synthetic image  $\\widehat{\\pmb{x}_0}$ , rounded to a constant ratio  $C$ . Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" instead of the entire  $T$ -step diffusion process.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation  $\\Delta \\widehat{\\pmb{x}_0}$  given a fixed-size change  $\\Delta \\pmb{x}_t$  in input  $\\pmb{x}_t$  at an arbitrary step  $t$ . The rationale of the reformulation is intuitive: If  $\\pmb{x}_t$  and  $\\widehat{\\pmb{x}_0}$  exhibit smooth changes at any  $t$ , then the relation between the latent noise  $\\epsilon$  (i.e.  $\\pmb{x}_T$ ) and  $\\widehat{\\pmb{x}_0}$  is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks.",
+        "bbox": [
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality.",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Smooth latent space was one of the prominent proper",
+        "bbox": [
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+        ],
+        "page_idx": 1
+    },
+    {
+        "type": "page_number",
+        "text": "7549",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "3. Methodology",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3).",
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+    {
+        "type": "text",
+        "text": "3.1. Preliminaries",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Diffusion process [24] is a kind of Markov chain that gradually adds random noise  $\\epsilon_t \\sim N(0, I)$  to ground truth signal  $\\pmb{x}_0 \\sim p(\\pmb{x}_0)$ , making  $\\pmb{x}_T$  in a total of  $T$  steps. At each step, The noisy data  $\\pmb{x}_t$  is computed as:",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\boldsymbol {x} _ {t} = \\sqrt {1 - \\beta_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {\\beta_ {t}} \\boldsymbol {\\epsilon} _ {t}, \\quad t = 1, 2, \\dots , T, \\tag {1}\n$$\n",
+        "text_format": "latex",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "where  $\\beta_{t}$  is the preset diffusion rate at step  $t$ . By making  $\\alpha_{t} = 1 - \\beta_{t}, \\overline{\\alpha_{t}} = \\prod_{t=1}^{T} \\alpha_{t}$  and  $\\epsilon \\sim N(\\mathbf{0}, \\mathbf{I})$ , we have the following equivalents:",
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\boldsymbol {x} _ {t} = \\sqrt {\\alpha_ {t}} \\boldsymbol {x} _ {t - 1} + \\sqrt {1 - \\alpha_ {t}} \\boldsymbol {\\epsilon} _ {t} \\tag {2} \\\\ = \\sqrt {\\bar {\\alpha} _ {t}} \\boldsymbol {x} _ {0} + \\sqrt {1 - \\bar {\\alpha} _ {t}} \\boldsymbol {\\epsilon}, \\quad t = 1, 2, \\dots , T. \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "A diffusion model  $\\epsilon_{\\theta}(\\pmb{x}_t, t)$  is then trained to estimate  $\\pmb{\\epsilon}_t$  from  $\\pmb{x}_t$ , by which one can predict the original signal  $\\pmb{x}_0$  by gradually remove noise from the degraded  $\\pmb{x}_T$  [71]. This is commonly known as the backward diffusion process:",
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+        "type": "equation",
+        "text": "\n$$\n\\widehat {\\boldsymbol {x} _ {t - 1}} = \\sqrt {\\frac {\\alpha_ {t - 1}}{\\alpha_ {t}}} \\widehat {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t - 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t - 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\tag {3}\n$$\n",
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+    {
+        "type": "text",
+        "text": "Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e.  $\\widehat{\\pmb{x}_t},\\epsilon_\\theta (\\widehat{\\pmb{x}_t},t),t = 1,\\dots,T)$  from a known final prediction  $\\widehat{\\pmb{x_0}}$  . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation:",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\widetilde {\\boldsymbol {x} _ {t + 1}} = \\sqrt {\\frac {\\alpha_ {t + 1}}{\\alpha_ {t}}} \\widetilde {\\boldsymbol {x} _ {t}} + \\sqrt {\\alpha_ {t + 1}} \\left(\\sqrt {\\frac {1}{\\alpha_ {t + 1}} - 1} - \\sqrt {\\frac {1}{\\alpha_ {t}} - 1}\\right) \\cdot \\epsilon_ {\\theta} (\\widetilde {\\boldsymbol {x} _ {t}}, t), \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            498,
+            98,
+            962,
+            151
+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\widetilde{\\boldsymbol{x}_t}$  represent the estimated  $\\widehat{\\boldsymbol{x}}_t$  at time  $t$ . However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings  $\\{\\varnothing_t\\}_{t=1}^T$  for each step  $t$ , simulating the backward process with  $\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\xi,\\varnothing_t)$ , where  $\\xi$  is the input text embedding. The predicted null-text  $\\varnothing_t$  is the null input of the classifier-free guidance [23] with a guidance scale  $w$ :",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi , \\varnothing_ {t}\\right) = w \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\xi\\right) + (1 - w) \\cdot \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\varnothing_ {t}\\right). \\tag {5}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            500,
+            287,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight  $W_0 \\in \\mathbb{R}^{d \\times k}$ , its updated weight  $\\Delta W$  is expressed as a low rank decomposition:",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nW _ {0} + \\Delta W = W _ {0} + B A, \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            414,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $B \\in \\mathbb{R}^{d \\times r}$ ,  $A \\in \\mathbb{R}^{r \\times k}$  and  $r \\ll \\min(d, k)$ . During adaptation,  $W_0$  is frozen, while  $B$  and  $A$  are trainable.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.2. Smooth Diffusion",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness.",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a  $T$  steps procedure that transforms the random noise  $\\epsilon$  (i.e.,  $\\pmb{x}_T$ ) to the prediction  $\\widehat{\\pmb{x}_0}$ . The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change  $\\Delta \\epsilon$  on  $\\epsilon$  (i.e.,  $\\Delta \\pmb{x}_T$  on  $\\pmb{x}_T$ ) will finally lead to a non-zero, fixed-size change  $\\Delta \\widehat{\\pmb{x}_0}$  on  $\\widehat{\\pmb{x}_0}$ , up to a constant ratio  $C$ :",
+        "bbox": [
+            496,
+            657,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\widehat {\\boldsymbol {x} _ {t}}, t\\right). \\quad \\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {T} \\| _ {2} = C \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            473,
+            781,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Notice that by definition,  $\\pmb{x}_T$  is the initial input of the backward diffusion loop in Eq. 3. Since  $\\pmb{x}_T$  is close to  $\\epsilon \\sim N(\\mathbf{0},\\mathbf{1})$ , for simplicity, we make them equivalent in all the following equations.",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train-",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "7550",
+        "bbox": [
+            482,
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/dbb434c32f3441287b89912a156f2fe21d026268eb991c3a1f5e99f730510003.jpg",
+        "image_caption": [
+            "(a) Inference-time Diffusion:"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            148,
+            88,
+            395,
+            157
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/cb32d12ab776eed89c972d5c62bdcd8662fcc44433dcfb5de8bc64ffbb9b07af.jpg",
+        "image_caption": [
+            "(b) Training-time Diffusion:",
+            "Denoising prediction at a single step  $t$"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            465,
+            99,
+            828,
+            157
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/eb89a8343410e614f5db8e7109f04876fcf987f2919e0e6370dbec8346e03c9c.jpg",
+        "image_caption": [
+            "Denoising prediction through  $T$  steps",
+            "(c) Inference-time Smooth Diffusion:",
+            "Variation constraint through  $T$  steps"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            117,
+            202,
+            411,
+            299
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/abbdeec74ef59c411237cf34463eb3e831cd71f2230127b59f9e9af621458a9d.jpg",
+        "image_caption": [
+            "(d) Training-time Smooth Diffusion:",
+            "Variation constraint at a single step  $t$",
+            "Figure 2. Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent  $(\\|\\Delta \\epsilon\\|_2$  or  $\\|\\Delta x_T\\|_2)$  and the variation of the output prediction  $(\\|\\Delta \\widehat{x_0}\\|_2)$  is a constant  $C$ . Training-time Diffusion (b) optimizes a \"t-step snapshot\" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a \"t-step snapshot\" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            428,
+            218,
+            846,
+            300
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a \"t-step snapshot\" of the diffusion process (Fig. 2b), where  $t$  is uniformly sampled from 1 to  $T$ . Hence, the proposed \"global\" objective (Eq. 7) for the entire  $T$ -step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function:",
+        "bbox": [
+            75,
+            409,
+            468,
+            545
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} \\Leftrightarrow C \\| \\Delta \\boldsymbol {x} _ {t} \\| _ {2} = C \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}, \\forall \\boldsymbol {\\epsilon}, \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            102,
+            551,
+            468,
+            569
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $C$  is a non-zero constant. This step-wise objective indicates that at each training step, variations  $\\Delta \\epsilon$  on  $\\epsilon$  should imply variations  $\\Delta x_{t}$  on  $\\pmb{x}_{t}$  with a ratio proportional to  $\\sqrt{1 - \\overline{\\alpha_t}}$ . The rationale of Eq. 8 is intuitive: If  $\\pmb{x}_t$  and  $\\widehat{\\pmb{x_0}}$  show smooth changes at any  $t$ , then the relation between the latent noise  $\\epsilon$  (i.e.  $\\pmb{x}_T$ ) and  $\\widehat{\\pmb{x_0}}$  is just the accumulation of smooth variations and thus can be smooth as well.",
+        "bbox": [
+            75,
+            575,
+            468,
+            681
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.3. Step-wise Variation Regularization",
+        "text_level": 1,
+        "bbox": [
+            76,
+            699,
+            382,
+            715
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training.",
+        "bbox": [
+            75,
+            724,
+            468,
+            801
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix  $\\mathbf{J}_{\\epsilon} = \\partial \\widehat{\\pmb{x}_0} / \\partial \\pmb{\\epsilon}$  of the diffusion system by minimizing the following regularization loss at any  $\\pmb{x}_0, \\pmb{\\epsilon}$ , and step  $t$ :",
+        "bbox": [
+            75,
+            803,
+            468,
+            878
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} _ {\\text {r e g}} = \\mathbb {E} _ {\\Delta \\widehat {\\boldsymbol {x} _ {0}}, \\epsilon} \\left(\\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} - a\\right) ^ {2}, \\tag {9}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            122,
+            883,
+            468,
+            902
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\Delta \\widehat{\\mathbf{x}_0}$  is the normally sampled pixel intensities normalized to unit length,  $\\epsilon$  is a normally sampled noise in Eq. 2, and  $a$  is the exponential moving average of  $\\sqrt{1 - \\overline{\\alpha_t}}\\| \\mathbf{J}_{\\epsilon}^{\\mathrm{T}}\\Delta \\widehat{\\mathbf{x}_0}\\| _2$  computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity:",
+        "bbox": [
+            496,
+            409,
+            892,
+            500
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\| \\nabla_ {\\epsilon} (\\sqrt {1 - \\bar {\\alpha} _ {t}} \\widehat {\\boldsymbol {x} _ {0}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}}) \\| _ {2}. \\tag {10}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            511,
+            503,
+            890,
+            523
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "The identity holds since  $\\Delta \\widehat{\\pmb{x}_0}$  is independently sampled, and uncorrelated with  $\\epsilon$ .",
+        "bbox": [
+            496,
+            527,
+            890,
+            556
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when  $\\mathbf{J}_{\\epsilon}$  is orthogonal at any  $\\epsilon$  up to a global scaling factor  $\\mathcal{K}$  (i.e.  $\\mathbf{J}_{\\epsilon} \\cdot \\mathbf{J}_{\\epsilon}^{\\mathrm{T}} = \\mathcal{K} \\cdot \\mathbf{I}$ ). By applying the orthogonality of  $\\mathbf{J}_{\\epsilon}$ , we have the following:",
+        "bbox": [
+            496,
+            558,
+            890,
+            648
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\mathbf {J} _ {\\epsilon} ^ {- 1} \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\frac {\\partial \\boldsymbol {\\epsilon}}{\\partial \\widehat {\\boldsymbol {x} _ {0}}} \\cdot \\Delta \\widehat {\\boldsymbol {x} _ {0}} = \\mathcal {K} \\Delta \\boldsymbol {\\epsilon}. \\tag {11}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            519,
+            654,
+            890,
+            684
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "When  $\\mathcal{L}_{\\mathrm{reg}}$  in Eq. 9 reaches its optimal, we then have:",
+        "bbox": [
+            500,
+            686,
+            857,
+            703
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\na = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\mathbf {J} _ {\\epsilon} ^ {\\mathrm {T}} \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\| _ {2} = \\sqrt {1 - \\bar {\\alpha} _ {t}} \\mathcal {K} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2}. \\tag {12}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            526,
+            707,
+            890,
+            724
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Notice that  $a = a\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2$  , since  $\\| \\Delta \\widehat{\\pmb{x}_0}\\| _2 = 1$  is the aforementioned random unit length vector. Hence, we can finally reformulate the expression:",
+        "bbox": [
+            496,
+            729,
+            890,
+            775
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\left\\| \\Delta \\widehat {\\boldsymbol {x} _ {0}} \\right\\| _ {2} = \\frac {\\mathcal {K}}{a} \\sqrt {1 - \\overline {{\\alpha_ {t}}}} \\| \\Delta \\boldsymbol {\\epsilon} \\| _ {2} \\tag {13} \\\\ = \\mathcal {C} \\sqrt {1 - \\bar {\\alpha} _ {t}} \\| \\Delta \\epsilon \\| _ {2}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            594,
+            780,
+            890,
+            829
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which exactly matches our proposed objective in Eq. 8.",
+        "bbox": [
+            498,
+            834,
+            864,
+            848
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To summarize, during training, the Smooth Diffusion objective encompasses a combination of  $\\mathcal{L}_{\\mathrm{base}}$  and  $\\mathcal{L}_{\\mathrm{reg}}$ :",
+        "bbox": [
+            496,
+            849,
+            890,
+            880
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\mathcal {L} _ {\\text {b a s e}} + \\lambda \\mathcal {L} _ {\\text {r e g}}, \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            625,
+            885,
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+            901
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "7551",
+        "bbox": [
+            482,
+            944,
+            513,
+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/ae97956fef2e9c401807af508e6c4a441f9a97fb1e0044d0ca44e4ed01668be8.jpg",
+        "image_caption": [
+            "Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            124,
+            92,
+            848,
+            349
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathcal{L}_{\\mathrm{base}}$  denotes the basic training objective of a diffusion model and  $\\lambda$  represents a ratio parameter controlling the intensity of Step-wise Variation Regularization.",
+        "bbox": [
+            75,
+            426,
+            470,
+            472
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            482,
+            209,
+            500
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.1. Experimental Setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            508,
+            266,
+            523
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69].",
+        "bbox": [
+            75,
+            530,
+            468,
+            712
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics  $6.5+$  as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of  $1 \\times 10^{-4}$  and a weight decay of  $1 \\times 10^{-4}$ .",
+        "bbox": [
+            75,
+            719,
+            470,
+            901
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "The ratio parameter  $\\lambda$  in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5.",
+        "bbox": [
+            496,
+            426,
+            890,
+            472
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability.",
+        "bbox": [
+            496,
+            479,
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+            797
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4.2. Latent Space Interpolation",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa",
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+    {
+        "type": "page_number",
+        "text": "7552",
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+    {
+        "type": "text",
+        "text": "isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises  $\\boldsymbol{x}_T$ , sharing the same  $\\{\\varnothing_t\\}_{t=1}^T$ . We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures.",
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+    {
+        "type": "text",
+        "text": "Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory.",
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+    {
+        "type": "table",
+        "img_path": "images/db48c92c2e65abcef8e21fa658644696fea28e654345394485913daf74b7f049.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>Stable Diffusion</td><td>38.63</td><td>12.70</td><td>31.46</td></tr><tr><td>Smooth Diffusion</td><td>16.54</td><td>12.10</td><td>31.54</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the",
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+    {
+        "type": "text",
+        "text": "\"A man using his laptop computer while a cat sits on his lap\"",
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/f5539feab45d8d5b4e8001fbed5189398141e688cec7f9e65a71b6d475cd7a2b.jpg",
+        "image_caption": [
+            "\"A large tower that has a big clock at top"
+        ],
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+        ],
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+    {
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+        "img_path": "images/2b1f88ee370d4360c76f1e4dda4efdd708aa893003f2298ab26feecaf588a3cb.jpg",
+        "image_caption": [
+            "\"A room with a couch, table set with dinnerware and a television\""
+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/f1c57bc4847e375c6325958b4c4898f8036a149dcefe514e90e4d9c5a51f855d.jpg",
+        "image_caption": [
+            "Source",
+            "Smooth Diff. +NTI (Ours)",
+            "able Diff.",
+            "+NTI",
+            "Smooth Diff",
+            "+DDIM (Ours)",
+            "able Diff",
+            "+DDIM",
+            "Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5)."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/5c89efb59942b5e912a76895a8b43de3bc0f359ed4f737e87bfbf88a76d5f79f.jpg",
+        "table_caption": [
+            "Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Method</td><td>MSE (↓)</td><td>LPIPS (↓)</td><td>SSIM (↑)</td><td>PSNR (↑)</td></tr><tr><td>Stable Diff. + DDIM</td><td>0.1756</td><td>0.5385</td><td>0.2662</td><td>13.97</td></tr><tr><td>Smooth Diff. + DDIM</td><td>0.1086</td><td>0.4326</td><td>0.3418</td><td>16.17</td></tr><tr><td>Stable Diff. + NTI</td><td>0.0156</td><td>0.1656</td><td>0.6068</td><td>25.63</td></tr><tr><td>Smooth Diff. + NTI</td><td>0.0153</td><td>0.1635</td><td>0.6102</td><td>25.74</td></tr><tr><td>VAE Reconstruction</td><td>0.0148</td><td>0.1590</td><td>0.6136</td><td>25.98</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values.",
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+    {
+        "type": "text",
+        "text": "enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio.",
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+        "type": "text",
+        "text": "4.3. Image Inversion and Reconstruction",
+        "text_level": 1,
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+        "text": "Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38].",
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+        "text": "As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc",
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+        "image_caption": [
+            "\"A banana on the table\"  $\\rightarrow$  \"A banana and an apple on the table\""
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+    {
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+        "img_path": "images/944e58bc83b2afae72b0453b571b40c6a0d6063a883edb47e00b324a7d2026f9.jpg",
+        "image_caption": [
+            "Global Edit (Transfer Style)",
+            "Source",
+            "Figure 5. Text-based image editing comparison results. We compare Smooth Diffusion and Stable Diffusion [62] (column 2 & 3), considering both local and global edits through the straightforward pipeline described in Sec. 4.4. Additionally, we present results from SOTA approaches, including SDEdit [42], P2P [21], PnP [75], Disentangle [82], Pix2Pix-Zero [55], and Cycle Diffusion [81], as references."
+        ],
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+    {
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+        "image_caption": [
+            "Smooth Diff."
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+        "img_path": "images/6cbc0586d92939d164632d92b370a05673ebe898fa5f4a48e3b411539729f1bd.jpg",
+        "image_caption": [
+            "Stable Diff."
+        ],
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+        "image_caption": [
+            "SDEdit"
+        ],
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+        "img_path": "images/5857ecb9ed067d76cb4f302193b84cf7cd7f7b70f5898e88c014defd997006ab.jpg",
+        "image_caption": [
+            "P2P"
+        ],
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+    {
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+        "img_path": "images/387db9a95a751af37d265786cee3e6694163edfa2f435d758988c598cbe9bf64.jpg",
+        "image_caption": [
+            "PnP"
+        ],
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+    {
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+        "img_path": "images/114420e81f7e92fc91caa8f3fbc0c1d904043243ff42f026b457604ead82f656.jpg",
+        "image_caption": [
+            "Disentangle"
+        ],
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+        ],
+        "page_idx": 6
+    },
+    {
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+        "img_path": "images/222c2426f6793dd5ebe32cb66fcef44f26a3c2a153d754e3c011f5ee263e9b33.jpg",
+        "image_caption": [
+            "Pix2Pix-Zero"
+        ],
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+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/7d345b38d77f69a0f2eb74c8d793a31b4e5c35fab636f790727b5b7cec086f6b.jpg",
+        "image_caption": [
+            "Cycle Diff."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "tion of room layouts. This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4.",
+        "bbox": [
+            75,
+            349,
+            468,
+            516
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, \"Smooth Diffusion + NTI\" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.4. Image Editing",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro",
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+        "type": "text",
+        "text": "cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original  $\\epsilon_{\\theta}(\\boldsymbol{x}_t,t,\\mathcal{C},\\varnothing_t)$  in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with:",
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+        "type": "equation",
+        "text": "\n$$\n\\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C}, \\varnothing_ {t}\\right) = \\left\\{ \\begin{array}{l} \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {s r c}}, \\varnothing_ {t}\\right), t > T \\times r, \\\\ \\epsilon_ {\\theta} \\left(\\boldsymbol {x} _ {t}, t, \\mathcal {C} _ {\\text {t r g}}, \\varnothing_ {t}\\right), t \\leq T \\times r, \\end{array} \\right. \\tag {15}\n$$\n",
+        "text_format": "latex",
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+        "type": "text",
+        "text": "where  $\\mathcal{C}_{\\mathrm{src}}$  represents the source text prompt for inversion, while  $\\mathcal{C}_{\\mathrm{trg}}$  corresponds to the target text prompt for editing. The parameter  $r$  serves as a threshold, determining when to switch from  $\\mathcal{C}_{\\mathrm{src}}$  to  $\\mathcal{C}_{\\mathrm{trg}}$ . In practice,  $r$  is typically chosen within  $\\{0.6, 0.7, 0.8, 0.9\\}$ , with the exact value depending on the specific input images and target visual effects.",
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+        "type": "text",
+        "text": "Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing \"cream\" to \"strawberries\") and adding items (e.g., \"apple\"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a \"cartoon style\". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases.",
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+        "type": "page_number",
+        "text": "7554",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/7841f881951452a64d3834f27f00765f86b6308cf1d148483b0328cbbd5aeaea.jpg",
+        "image_caption": [
+            "Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space.",
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+    {
+        "type": "text",
+        "text": "4.5. Ablation Studies",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Regularization ratio. In Tab. 3, we examine the impact of different strength ratios  $\\lambda$  in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g.,  $\\lambda = 0.1$ ), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g.,  $\\lambda = 10$ ) leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for  $\\lambda$  becomes crucial based on the specific experimental settings. In our default setting, we find that  $\\lambda = 1$  serves as a suitable value.",
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+    {
+        "type": "text",
+        "text": "LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range",
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+    {
+        "type": "table",
+        "img_path": "images/ce5c0e13f6a3e63ef2da5e690c8df5274a83585e05526010b63597da914c3699.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Ratio</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>0.1</td><td>24.23</td><td>12.15</td><td>31.56</td></tr><tr><td>1 (default)</td><td>16.54</td><td>12.11</td><td>31.49</td></tr><tr><td>10</td><td>11.51</td><td>17.44</td><td>31.41</td></tr></table>",
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+    {
+        "type": "text",
+        "text": "of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as \"full,\" which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations.",
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+    },
+    {
+        "type": "table",
+        "img_path": "images/8e9e24e6f7fe5ca536eab5aa5b7c741eeff0a904405349225cc554009ea7b65e.jpg",
+        "table_caption": [
+            "Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td>Rank</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>4</td><td>16.76</td><td>12.36</td><td>31.49</td></tr><tr><td>8 (default)</td><td>16.54</td><td>12.11</td><td>31.54</td></tr><tr><td>16</td><td>16.65</td><td>11.49</td><td>31.61</td></tr><tr><td>full</td><td>11.52</td><td>27.27</td><td>28.86</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined.",
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+    {
+        "type": "text",
+        "text": "5. Conclusion",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. We believe that Smooth Diffusion will become a valuable solution for other challenging tasks, such as video generation, in the future.",
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+    {
+        "type": "text",
+        "text": "Acknowledgements",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This work is supported in part by the ML Center at Georgia Tech, NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education. Huang is in part supported by the National Key R&D Program (#2021ZD0140407) and NSFC (62321005 & 42327901).",
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+        "type": "page_number",
+        "text": "7555",
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+    {
+        "type": "text",
+        "text": "References",
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+        ],
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2024/Smooth Diffusion_ Crafting Smooth Latent Spaces in Diffusion Models/88a5ba4c-516f-44e9-b601-18a2cbb929d6_origin.pdf

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2024/Smooth Diffusion_ Crafting Smooth Latent Spaces in Diffusion Models/full.md

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+# Smooth Diffusion: Crafting Smooth Latent Spaces in Diffusion Models
+
+Jiayi Guo $^{1,2*}$ , Xingqian Xu $^{1,3*}$ , Yifan Pu $^{2}$ , Zanlin Ni $^{2}$ , Chaofei Wang $^{2}$ , Manushree Vasu $^{1}$ , Shiji Song $^{2}$ , Gao Huang $^{2\dagger}$ , Humphrey Shi $^{1,3\dagger}$
+
+<sup>1</sup>SHI Labs @ Georgia Tech & UIUC <sup>2</sup>Tsinghua University <sup>3</sup>Picsart AI Research (PAIR)
+
+https://github.com/SHI-Labs/Smooth-Diffusion
+
+![](images/c58bb6caaef4d90e82c90b483b9ec4f1161b14513a5458675026d2d00887ed51.jpg)
+
+![](images/77167fe2269aba28f7f569ee883a8d7e9e0ed77ed5a413d26bba31d5ddf6b533.jpg)  
+Task 2: Image Inversion and Reconstruction "A train going back to its course filled with people  
+"A mouse is next to a keyboard on a desk"
+
+![](images/6ff1a46c05fcaf841ee8277f1106cd9f3eda6139d5585dd216d0afd092424b3d.jpg)  
+Figure 1. Smooth Diffusion for downstream image synthesis tasks. Our method formally introduces latent space smoothness to diffusion models like Stable Diffusion [62]. This smoothness dramatically aids various tasks in: 1) improving continuity of transitions in image interpolation, 2) reducing approximation errors in image inversion, & 3) better preserving unedited contents in image editing.
+
+![](images/3b1bc098b1eaea86206c1aff1084cc919555c753ad317d7468975e7318140be3.jpg)  
+Task 3: Image Editing Replace Item: "rabbit"  $\rightarrow$  "cat"  
+Transfer Style: "watercolor style"
+
+![](images/244b9ba54ed011299b14b60bc28a751ea897ec537851415a71d2cd4e4fec6b42.jpg)
+
+![](images/f8390b4e94aea599d7843c44f8bcf0cf58f62d8064b98c3b8b72ac5b56f27540.jpg)  
+Add Item: + "bacon"  
+Drag Point
+
+![](images/94bf0431562377f821bc77bc9b712a4a7cb6dee9d8862d2cf70d41f4a74de779.jpg)
+
+# Abstract
+
+Recently, diffusion models have made remarkable progress in text-to-image (T2I) generation, synthesizing images with high fidelity and diverse contents. Despite this advancement, latent space smoothness within diffusion models remains largely unexplored. Smooth latent spaces ensure that a perturbation on an input latent corresponds to a steady change in the output image. This property proves beneficial in downstream tasks, including image interpolation, inversion, and editing. In this work, we expose the non-smoothness of diffusion latent spaces by observing noticeable visual fluctuations resulting from minor latent variations. To tackle this issue, we propose Smooth Diffusion, a
+
+new category of diffusion models that can be simultaneously high-performing and smooth. Specifically, we introduce Step-wise Variation Regularization to enforce the proportion between the variations of an arbitrary input latent and that of the output image is a constant at any diffusion training step. In addition, we devise an interpolation standard deviation (ISTD) metric to effectively assess the latent space smoothness of a diffusion model. Extensive quantitative and qualitative experiments demonstrate that Smooth Diffusion stands out as a more desirable solution not only in T2I generation but also across various downstream tasks. Smooth Diffusion is implemented as a plug-and-play Smooth-LoRA to work with various community models. Code is available at https://github.com/SHI-Labs/Smooth-Diffusion.
+
+# 1. Introduction
+
+In recent years, diffusion models [12, 24, 62] have rapidly grown into very powerful tools for generative AI, particularly for text-to-image generation. The remarkable ability of diffusion models, generating high-quality photorealistic images from open-book contexts, has been highlighted in many research and commercial products. Such success has also inspired various diffusion-based downstream tasks, including image interpolation [29, 78], inversion [13, 44, 54, 71, 77], editing [21, 42, 45, 55, 69, 75, 81, 82], etc.
+
+Despite the great success in the generation field, diffusion models occasionally produce low-quality results with undesirable and unpredictable behaviors. Specifically speaking, for image interpolation, the Stable Diffusion Walk (SDW) [29] test examines latent space with spherical linear interpolations, usually resulting in highly fluctuated outputs with unpredictable visual appearance. Examples can be found in Fig. 1 Task 1, in which such interpolation exhibits undesired sharp changes as well as "cartoonization" on photorealistic dog images, highlighted in the red box. For the image inversion task shown in Fig. 1 Task 2, a naive application of DDIM inversion [71] cannot reconstruct images faithfully from the sources. Instead, it generates incorrect colors and object orientations, and misinterprets the computer mouse as an animal mouse. For the image editing task shown in Fig. 1 Task 3, one may notice that only minor text prompt editing can lead to major updates on image contents and layouts, in which the object (i.e. the cat's pose, the horse's location, the shape of the pizza) can be wildly and incorrectly altered. Moreover, current diffusion models are unsuited to drag-based editing [69] because a fine-engineered drag method still has a noticeably large chance of breaking objects' shape and semantics.
+
+In this work, we step into an important but under-explored area: to improve the latent space smoothness of diffusion models. Our motivation to enhance latent smoothness comes from the real-world demand to improve the output qualities of the aforementioned downstream tasks. A smooth latent space implies a robust visual variation under a minor latent change. Therefore, enhancing such smoothness could help improve the continuity of image interpolation, expand the capacity of image inversion, and maintain correct semantics in image editing. Notably, prior works in GANs [32, 33, 68] have demonstrated that the smooth latent space of the generator can significantly improve downstream tasks' quality, offering additional evidence of the importance of this area.
+
+To achieve our goal, we propose Smooth Diffusion, a new category of diffusion models that can be simultaneously high-performing and smooth. We start our exploration by first formalizing the objective for Smooth Diffusion, in which fixed-size perturbations  $\Delta \epsilon$  on a latent noise  $\epsilon$  should produce smooth visual changes  $\Delta \widehat{x_0}$  on the
+
+synthetic image  $\widehat{\pmb{x}_0}$ , rounded to a constant ratio  $C$ . Although one may think that according to the formulation, the smoothness constraint could be an accessible train-time loss. Actually, there is no direct application of such regularization from inference to training, and the challenge lies in the fact that in each training iteration (i.e., back-propagation), diffusion models optimize only a "t-step snapshot" instead of the entire  $T$ -step diffusion process.
+
+Therefore, we introduce Step-wise Variation Regularization, a novel regularization that seamlessly incorporates our Smooth Diffusion's inference-time objective to training. This regularization aims to bound the 2-norm of output variation  $\Delta \widehat{\pmb{x}_0}$  given a fixed-size change  $\Delta \pmb{x}_t$  in input  $\pmb{x}_t$  at an arbitrary step  $t$ . The rationale of the reformulation is intuitive: If  $\pmb{x}_t$  and  $\widehat{\pmb{x}_0}$  exhibit smooth changes at any  $t$ , then the relation between the latent noise  $\epsilon$  (i.e.  $\pmb{x}_T$ ) and  $\widehat{\pmb{x}_0}$  is just the accumulation of smooth variations and thus can be smooth as well. More details can be found in Sec. 3.
+
+In practice, our Smooth Diffusion is trained on top of a well-known text-to-image model: Stable Diffusion [62]. We examine and demonstrate that Smooth Diffusion dramatically improves the latent space smoothness over its baseline. Meanwhile, we conduct extensive research across numerous downstream tasks, including but not limited to image interpolation, inversion, editing, etc. Both qualitative and quantitative results support our conclusion that Smooth Diffusion can be the next-gen high-performing generative model not only for the baseline text-to-image task but across various downstream tasks.
+
+# 2. Related Work
+
+Diffusion models are initiated from a family of prior works including but not limited to [8, 66, 70, 76]. Since then, DDPM [24] introduced an image-based noise prediction model, becoming one of the most popular image generation research. Later works [12, 48, 71] extended DDPM, demonstrating that diffusion models perform on-par and even surpass GAN-based methods [15, 30-33]. Recently, generating images from text prompts (T2I) become an emerging field [11, 19, 28, 47, 62], among which diffusion models [16, 49, 59, 62, 64] have become quite visible to the public. For example, Stable Diffusion (SD) [62] consists of VAE [36] and CLIP [58], diffuses latent space, and yields an outstanding balance between quality and speed. Following SD [62], researchers also explored diffusion approaches for controls such as ControlNet [14, 26, 46, 57, 80, 85, 86, 89-91, 95] and multimodal such as Versatile Diffusion [6, 41, 73, 88]. Works from a different track reduce diffusion steps to improve speed [5, 34, 39, 43, 65, 72, 92, 96], or restrict data and domain for few-shot learning [20, 25, 40, 63], all had successfully maintained a high output quality.
+
+Smooth latent space was one of the prominent proper
+
+ties of SOTA GAN works [9, 31-33], while exploring such property went through the decade-long GAN research [3, 15], whose goals were mainly robust training. Ideas such as Wasserstein GAN [4, 17] had proved to be effective, which enforced the Lipschitz continuity on discriminator via gradient penalties. Another technique, namely path length regularization, related to the Jacobian clamping in [51], was adapted in StyleGAN2 [32] and later became a standard setting for GAN-based generators [10, 37, 87, 94]. Benefiting from the smoothness property, researchers managed to manipulate latent space in many downstream research projects. Works such as [7, 50, 68, 83] explored latent space disentanglement. GAN-inverse [1, 2, 52, 84] had also proved to be feasible, along with a family of image editing approaches [18, 53, 56, 60, 61, 74, 97]. As aforementioned, our work aims to investigate the latent space smoothness for diffusion models, which by far remains unexplored.
+
+# 3. Methodology
+
+In this section, we first introduce preliminaries of our method, including diffusion process [24], diffusion inversion [12, 44, 71] and low-rank adaptation [25] (Sec. 3.1). Then Smooth Diffusion is proposed with its definition, objective (Sec. 3.2) and regularization function (Sec. 3.3).
+
+# 3.1. Preliminaries
+
+Diffusion process [24] is a kind of Markov chain that gradually adds random noise  $\epsilon_t \sim N(0, I)$  to ground truth signal  $\pmb{x}_0 \sim p(\pmb{x}_0)$ , making  $\pmb{x}_T$  in a total of  $T$  steps. At each step, The noisy data  $\pmb{x}_t$  is computed as:
+
+$$
+\boldsymbol {x} _ {t} = \sqrt {1 - \beta_ {t}} \boldsymbol {x} _ {t - 1} + \sqrt {\beta_ {t}} \boldsymbol {\epsilon} _ {t}, \quad t = 1, 2, \dots , T, \tag {1}
+$$
+
+where  $\beta_{t}$  is the preset diffusion rate at step  $t$ . By making  $\alpha_{t} = 1 - \beta_{t}, \overline{\alpha_{t}} = \prod_{t=1}^{T} \alpha_{t}$  and  $\epsilon \sim N(\mathbf{0}, \mathbf{I})$ , we have the following equivalents:
+
+$$
+\begin{array}{l} \boldsymbol {x} _ {t} = \sqrt {\alpha_ {t}} \boldsymbol {x} _ {t - 1} + \sqrt {1 - \alpha_ {t}} \boldsymbol {\epsilon} _ {t} \tag {2} \\ = \sqrt {\bar {\alpha} _ {t}} \boldsymbol {x} _ {0} + \sqrt {1 - \bar {\alpha} _ {t}} \boldsymbol {\epsilon}, \quad t = 1, 2, \dots , T. \\ \end{array}
+$$
+
+A diffusion model  $\epsilon_{\theta}(\pmb{x}_t, t)$  is then trained to estimate  $\pmb{\epsilon}_t$  from  $\pmb{x}_t$ , by which one can predict the original signal  $\pmb{x}_0$  by gradually remove noise from the degraded  $\pmb{x}_T$  [71]. This is commonly known as the backward diffusion process:
+
+$$
+\widehat {\boldsymbol {x} _ {t - 1}} = \sqrt {\frac {\alpha_ {t - 1}}{\alpha_ {t}}} \widehat {\boldsymbol {x} _ {t}} + \sqrt {\alpha_ {t - 1}} \left(\sqrt {\frac {1}{\alpha_ {t - 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \tag {3}
+$$
+
+Diffusion inversion [12, 44, 71] targets to recover the exact backward diffusion process (i.e.  $\widehat{\pmb{x}_t},\epsilon_\theta (\widehat{\pmb{x}_t},t),t = 1,\dots,T)$  from a known final prediction  $\widehat{\pmb{x_0}}$  . One of the common technique for such inversion is DDIM inversion [12, 71], which reverses Eq. (3) under a local linear approximation:
+
+$$
+\widetilde {\boldsymbol {x} _ {t + 1}} = \sqrt {\frac {\alpha_ {t + 1}}{\alpha_ {t}}} \widetilde {\boldsymbol {x} _ {t}} + \sqrt {\alpha_ {t + 1}} \left(\sqrt {\frac {1}{\alpha_ {t + 1}} - 1} - \sqrt {\frac {1}{\alpha_ {t}} - 1}\right) \cdot \epsilon_ {\theta} (\widetilde {\boldsymbol {x} _ {t}}, t), \tag {4}
+$$
+
+where  $\widetilde{\boldsymbol{x}_t}$  represent the estimated  $\widehat{\boldsymbol{x}}_t$  at time  $t$ . However, DDIM inversion is only a rough estimation. For text-to-image diffusion, a more advanced technique, Null-Text Inversion [44], optimizes additional null-text embeddings  $\{\varnothing_t\}_{t=1}^T$  for each step  $t$ , simulating the backward process with  $\epsilon_{\theta}(\boldsymbol{x}_t,t,\xi,\varnothing_t)$ , where  $\xi$  is the input text embedding. The predicted null-text  $\varnothing_t$  is the null input of the classifier-free guidance [23] with a guidance scale  $w$ :
+
+$$
+\epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \xi , \varnothing_ {t}\right) = w \cdot \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \xi\right) + (1 - w) \cdot \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \varnothing_ {t}\right). \tag {5}
+$$
+
+Low-rank adaptation (LoRA) [25] is initially proposed to efficiently adapt large pretrained models to downstream tasks. The key assumption of LoRA is that the weight changes required during adaptation maintain a low rank. Given a pretrained model weight  $W_0 \in \mathbb{R}^{d \times k}$ , its updated weight  $\Delta W$  is expressed as a low rank decomposition:
+
+$$
+W _ {0} + \Delta W = W _ {0} + B A, \tag {6}
+$$
+
+where  $B \in \mathbb{R}^{d \times r}$ ,  $A \in \mathbb{R}^{r \times k}$  and  $r \ll \min(d, k)$ . During adaptation,  $W_0$  is frozen, while  $B$  and  $A$  are trainable.
+
+# 3.2. Smooth Diffusion
+
+As previously mentioned, modern diffusion models (DM) do not guarantee latent space smoothness, creating not only research gaps between GANs and diffusions but also unexpected challenges in downstream tasks. To address these issues, we propose Smooth Diffusion, a novel class of high-performing diffusion models with enhanced smoothness over its latent space. The underlining of Smooth Diffusion is the newly proposed training scheme in which we carried out a Step-wise Variation Regularization to enhance model smoothness.
+
+To better explain our aims, we adopt the same terminologies from the standard inference-time diffusion process (Fig. 2a), involving a  $T$  steps procedure that transforms the random noise  $\epsilon$  (i.e.,  $\pmb{x}_T$ ) to the prediction  $\widehat{\pmb{x}_0}$ . The overall objective of Smooth Diffusion can then be written in Eq. 7: in which we expect that a fixed-size change  $\Delta \epsilon$  on  $\epsilon$  (i.e.,  $\Delta \pmb{x}_T$  on  $\pmb{x}_T$ ) will finally lead to a non-zero, fixed-size change  $\Delta \widehat{\pmb{x}_0}$  on  $\widehat{\pmb{x}_0}$ , up to a constant ratio  $C$ :
+
+$$
+\epsilon_ {\theta} \left(\widehat {\boldsymbol {x} _ {t}}, t\right). \quad \| \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} \Leftrightarrow C \| \Delta \boldsymbol {x} _ {T} \| _ {2} = C \| \Delta \boldsymbol {\epsilon} \| _ {2}, \forall \boldsymbol {\epsilon}, \tag {7}
+$$
+
+Notice that by definition,  $\pmb{x}_T$  is the initial input of the backward diffusion loop in Eq. 3. Since  $\pmb{x}_T$  is close to  $\epsilon \sim N(\mathbf{0},\mathbf{1})$ , for simplicity, we make them equivalent in all the following equations.
+
+Nevertheless, one may notice that our inference-time objective in Eq. 7 cannot be directly transformed into a train-
+
+![](images/dbb434c32f3441287b89912a156f2fe21d026268eb991c3a1f5e99f730510003.jpg)  
+(a) Inference-time Diffusion:
+
+![](images/cb32d12ab776eed89c972d5c62bdcd8662fcc44433dcfb5de8bc64ffbb9b07af.jpg)  
+(b) Training-time Diffusion:  
+Denoising prediction at a single step  $t$
+
+![](images/eb89a8343410e614f5db8e7109f04876fcf987f2919e0e6370dbec8346e03c9c.jpg)  
+Denoising prediction through  $T$  steps  
+(c) Inference-time Smooth Diffusion:  
+Variation constraint through  $T$  steps
+
+![](images/abbdeec74ef59c411237cf34463eb3e831cd71f2230127b59f9e9af621458a9d.jpg)  
+(d) Training-time Smooth Diffusion:  
+Variation constraint at a single step  $t$  
+Figure 2. Illustration of Smooth Diffusion. Smooth Diffusion (c) enforces the ratio between the variation of the input latent  $(\|\Delta \epsilon\|_2$  or  $\|\Delta x_T\|_2)$  and the variation of the output prediction  $(\|\Delta \widehat{x_0}\|_2)$  is a constant  $C$ . Training-time Diffusion (b) optimizes a "t-step snapshot" of the denoising prediction process in Inference-time Diffusion (a). Similarly, we propose Training-time Smooth Diffusion (d) to optimize a "t-step snapshot" of the variation constraint in Inference-time Smooth Diffusion (c). DM: Diffusion model.
+
+ing loss function. This is because, in one training iteration (i.e., back-propagation), diffusion models optimize only a "t-step snapshot" of the diffusion process (Fig. 2b), where  $t$  is uniformly sampled from 1 to  $T$ . Hence, the proposed "global" objective (Eq. 7) for the entire  $T$ -step process is not accessible in training. Therefore, we need to reformulate our global objective into a step-wise objective shown in Eq. 8, which can later be integrated into the diffusion training process as a loss function:
+
+$$
+\| \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} \Leftrightarrow C \| \Delta \boldsymbol {x} _ {t} \| _ {2} = C \sqrt {1 - \bar {\alpha} _ {t}} \| \Delta \boldsymbol {\epsilon} \| _ {2}, \forall \boldsymbol {\epsilon}, \tag {8}
+$$
+
+where  $C$  is a non-zero constant. This step-wise objective indicates that at each training step, variations  $\Delta \epsilon$  on  $\epsilon$  should imply variations  $\Delta x_{t}$  on  $\pmb{x}_{t}$  with a ratio proportional to  $\sqrt{1 - \overline{\alpha_t}}$ . The rationale of Eq. 8 is intuitive: If  $\pmb{x}_t$  and  $\widehat{\pmb{x_0}}$  show smooth changes at any  $t$ , then the relation between the latent noise  $\epsilon$  (i.e.  $\pmb{x}_T$ ) and  $\widehat{\pmb{x_0}}$  is just the accumulation of smooth variations and thus can be smooth as well.
+
+# 3.3. Step-wise Variation Regularization
+
+While the motivation and formulation of the Smooth Diffusion objective are presented, how to realize such an objective remains unexplained. Therefore, in this section, we introduce Step-wise Variation Regularization to effectively integrate the step-wise objective into diffusion training.
+
+We draw inspiration from the regularization techniques [32, 51] adopted in GAN training. The core idea of Step-wise Variation Regularization is to bound the Jacobian matrix  $\mathbf{J}_{\epsilon} = \partial \widehat{\pmb{x}_0} / \partial \pmb{\epsilon}$  of the diffusion system by minimizing the following regularization loss at any  $\pmb{x}_0, \pmb{\epsilon}$ , and step  $t$ :
+
+$$
+\mathcal {L} _ {\text {r e g}} = \mathbb {E} _ {\Delta \widehat {\boldsymbol {x} _ {0}}, \epsilon} \left(\sqrt {1 - \overline {{\alpha_ {t}}}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} - a\right) ^ {2}, \tag {9}
+$$
+
+where  $\Delta \widehat{\mathbf{x}_0}$  is the normally sampled pixel intensities normalized to unit length,  $\epsilon$  is a normally sampled noise in Eq. 2, and  $a$  is the exponential moving average of  $\sqrt{1 - \overline{\alpha_t}}\| \mathbf{J}_{\epsilon}^{\mathrm{T}}\Delta \widehat{\mathbf{x}_0}\| _2$  computed online during training. In practice, we compute Eq. 9 via standard backpropagation with the following identity:
+
+$$
+\sqrt {1 - \bar {\alpha} _ {t}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} = \| \nabla_ {\epsilon} (\sqrt {1 - \bar {\alpha} _ {t}} \widehat {\boldsymbol {x} _ {0}} \cdot \Delta \widehat {\boldsymbol {x} _ {0}}) \| _ {2}. \tag {10}
+$$
+
+The identity holds since  $\Delta \widehat{\pmb{x}_0}$  is independently sampled, and uncorrelated with  $\epsilon$ .
+
+Next, we prove that the proposed objective in Eq. 9 exactly matches our optimization goal in Eq. 8. One preliminary result, proven in [32], is that in high dimensions, Eq. 9 is minimized when  $\mathbf{J}_{\epsilon}$  is orthogonal at any  $\epsilon$  up to a global scaling factor  $\mathcal{K}$  (i.e.  $\mathbf{J}_{\epsilon} \cdot \mathbf{J}_{\epsilon}^{\mathrm{T}} = \mathcal{K} \cdot \mathbf{I}$ ). By applying the orthogonality of  $\mathbf{J}_{\epsilon}$ , we have the following:
+
+$$
+\mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \mathbf {J} _ {\epsilon} ^ {- 1} \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \frac {\partial \boldsymbol {\epsilon}}{\partial \widehat {\boldsymbol {x} _ {0}}} \cdot \Delta \widehat {\boldsymbol {x} _ {0}} = \mathcal {K} \Delta \boldsymbol {\epsilon}. \tag {11}
+$$
+
+When  $\mathcal{L}_{\mathrm{reg}}$  in Eq. 9 reaches its optimal, we then have:
+
+$$
+a = \sqrt {1 - \bar {\alpha} _ {t}} \| \mathbf {J} _ {\epsilon} ^ {\mathrm {T}} \Delta \widehat {\boldsymbol {x} _ {0}} \| _ {2} = \sqrt {1 - \bar {\alpha} _ {t}} \mathcal {K} \| \Delta \boldsymbol {\epsilon} \| _ {2}. \tag {12}
+$$
+
+Notice that  $a = a\| \Delta \widehat{\pmb{x}_0}\| _2$  , since  $\| \Delta \widehat{\pmb{x}_0}\| _2 = 1$  is the aforementioned random unit length vector. Hence, we can finally reformulate the expression:
+
+$$
+\begin{array}{l} \left\| \Delta \widehat {\boldsymbol {x} _ {0}} \right\| _ {2} = \frac {\mathcal {K}}{a} \sqrt {1 - \overline {{\alpha_ {t}}}} \| \Delta \boldsymbol {\epsilon} \| _ {2} \tag {13} \\ = \mathcal {C} \sqrt {1 - \bar {\alpha} _ {t}} \| \Delta \epsilon \| _ {2}, \\ \end{array}
+$$
+
+which exactly matches our proposed objective in Eq. 8.
+
+To summarize, during training, the Smooth Diffusion objective encompasses a combination of  $\mathcal{L}_{\mathrm{base}}$  and  $\mathcal{L}_{\mathrm{reg}}$ :
+
+$$
+\mathcal {L} = \mathcal {L} _ {\text {b a s e}} + \lambda \mathcal {L} _ {\text {r e g}}, \tag {14}
+$$
+
+![](images/ae97956fef2e9c401807af508e6c4a441f9a97fb1e0044d0ca44e4ed01668be8.jpg)  
+Figure 3. Image interpolation comparison results. For Smooth Diffusion and Stable Diffusion [62], real images (Image A and B) are inverted into latents using NTI [44]. We perform spherical linear interpolations between latents (also known as Stable Diffusion Walk [29]) and concatenate the resulting images as a transition sequence. VAE Inter. performs interpolations within the VAE space of Stable Diffusion. ANID [78] first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion.
+
+where  $\mathcal{L}_{\mathrm{base}}$  denotes the basic training objective of a diffusion model and  $\lambda$  represents a ratio parameter controlling the intensity of Step-wise Variation Regularization.
+
+# 4. Experiments
+
+# 4.1. Experimental Setup
+
+Baselines and settings. We select the Stable Diffusion [62] as the primary baseline for all tasks. Additionally, for image interpolation, we adopt a VAE-space interpolation and ANID [78] as competitors. For image inversion, we integrate Smooth Diffusion and Stable Diffusion with DDIM inversion [71] and Null-text inversion [44]. For text-based image editing, SDEdit [42], Prompt-to-Prompt (P2P) [21], Plug-and-Play (PnP) [75], Diffusion Disentanglement (Disentangle) [82], Pix2Pix-Zero [55] and Cycle Diffusion [81] are chosen as SOTA approaches. For drag-based image editing, we compare Smooth Diffusion with Stable Diffusion within the framework of DragDiffusion [69].
+
+Implementation details. Smooth Diffusion is trained atop pretrained Stable Diffusion-V1.5 [62], using LoRA [25] finetuning technique. The UNet of Smooth Diffusion is set as trainable with a LoRA rank of 8, while the VAE and text encoder are frozen. We leverage the LAION Aesthetics  $6.5+$  as the training dataset, which contains 625K image-text pairs with predicted aesthetics scores of 6.5 or higher from LAION-5B [67]. Smooth diffusion is typically trained for 30K iterations with a batch size of 96, 3 samples per GPU, a total of 4 A100 GPUs, and a gradient accumulation of 8. The AdamW [35] optimizer is adopted with a constant learning rate of  $1 \times 10^{-4}$  and a weight decay of  $1 \times 10^{-4}$ .
+
+The ratio parameter  $\lambda$  in Eq. 14 is set to 1. During inference, the total number of diffusion steps is set to 50 and the classifier-free guidance [23] scale is set to 7.5.
+
+Evaluation metrics. To evaluate the general text-to-image generation performance, we report the popular FID [22] and CLIP Score [58] on the MS-COCO validation set [38]. To assess the latent space smoothness, we propose an interpolation standard deviation (ISTD) as an evaluation metric. In specific, we randomly draw 500 text prompts from the MS-COCO validation set. For each prompt, we sample a pair of Gaussian noises and uniformly interpolate them from one to the other 9 times with mix ratios from 0.1 to 0.9. Fed into diffusion models together with a prompt, we could obtain a total of 11 generated images, 2 from the source Gaussian noises and 9 from the interpolated noises. We calculate the standard deviation of L2 distances between every two adjacent images in the pixel space. Finally, we average the standard deviations over 500 prompts as ISTD. Ideally, a zero value of ISTD indicates that consistent and uniform visual fluctuations in the pixel space for identical fixed-size changes in the latent space, resulting in a smooth latent space. For image inversion, mean square error (MSE), LPIPS [93], SSIM [79] and PSNR [27] are adopted to evaluate the image reconstruction capability.
+
+# 4.2. Latent Space Interpolation
+
+Qualitative comparison. The most straightforward way to demonstrate the smoothness of the latent space is through the observation of interpolation results between latent noises. In Fig. 3, we present interpolation compa
+
+isons between Smooth Diffusion and Stable Diffusion using real images. To generate these comparisons, we utilize the NTI [44] to invert a pair of real images into latent noises  $\boldsymbol{x}_T$ , sharing the same  $\{\varnothing_t\}_{t=1}^T$ . We then perform uniform spherical linear interpolations between latent noises (also known as Stable Diffusion Walk [29]), resulting in 9 intermediate noises with mix ratios from 0.1 to 0.9. Subsequently, we concatenate the 11 images produced from these noises to create an image transition sequence in the figures.
+
+Notably, as highlighted by the red boxes, Stable Diffusion exhibits significant visual fluctuations during the transition. In particular, the interpolated images may introduce new attributes that are unrelated to the source images, e.g., the undesired grasslands in the second row of Fig. 3. In contrast, our approach, Smooth Diffusion, not only avoids introducing obvious irrelevant attributes in the interpolated images but also ensures that the visual effects change smoothly throughout the transition. Additional interpolation results can be seen in supplementary materials.
+
+In addition to Stable Diffusion, Fig. 3 also includes two other baseline methods for comparison: 1) VAE Interpolation (VAE Inter.), which performs interpolations within the VAE space of Stable Diffusion. However, the results closely resemble pixel-space interpolations, with significant degradation of visual details, particularly in the highlighted red box area. 2) ANID [78], which first adds noise to real images and subsequently denoises the interpolated noisy images using Stable Diffusion. In Fig. 3, ANID with a 50-step scheduler exhibits highly blurred interpolation results. When ANID operates with a default 200-step scheduler, the blurring can be alleviated, but the quality of the interpolated images remains far from satisfactory.
+
+<table><tr><td>Method</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>Stable Diffusion</td><td>38.63</td><td>12.70</td><td>31.46</td></tr><tr><td>Smooth Diffusion</td><td>16.54</td><td>12.10</td><td>31.54</td></tr></table>
+
+Quantitative comparison. The goal of Smooth Diffusion is to enhance the latent space smoothness without image generation performance degradation compared to Stable Diffusion. In pursuit of this goal, we employ the ISTD introduced in Sec. 4.1 to evaluate the latent space smoothness. Additionally, we utilize FID [22] and CLIP Score [58] to assess generators' overall performance. The results presented in Tab. 1 demonstrate that Smooth Diffusion significantly outperforms Stable Diffusion in terms of ISTD, indicating a substantial improvement in the latent space smoothness. Furthermore, Smooth Diffusion exhibits superior performance in both FID and CLIP Score, suggesting that the
+
+"A man using his laptop computer while a cat sits on his lap"
+
+![](images/f5539feab45d8d5b4e8001fbed5189398141e688cec7f9e65a71b6d475cd7a2b.jpg)  
+"A large tower that has a big clock at top
+
+![](images/2b1f88ee370d4360c76f1e4dda4efdd708aa893003f2298ab26feecaf588a3cb.jpg)  
+"A room with a couch, table set with dinnerware and a television"
+
+![](images/f1c57bc4847e375c6325958b4c4898f8036a149dcefe514e90e4d9c5a51f855d.jpg)  
+Source  
+Smooth Diff. +NTI (Ours)  
+able Diff.  
++NTI  
+Smooth Diff  
++DDIM (Ours)  
+able Diff  
++DDIM  
+Figure 4. Image reconstruction comparison results. We integrate Smooth Diffusion and Stable Diffusion [62] with NTI [44] (column 2 & 3) and DDIM inversion [71] (column 4 & 5).
+
+Table 1. Quantitative evaluations of image interpolation and text-to-image generation. We evaluate Smooth Diffusion and Stable Diffusion [62] with ISTD, FID [22] and CLIP Score [58]. The better results are in bold.  
+
+<table><tr><td>Method</td><td>MSE (↓)</td><td>LPIPS (↓)</td><td>SSIM (↑)</td><td>PSNR (↑)</td></tr><tr><td>Stable Diff. + DDIM</td><td>0.1756</td><td>0.5385</td><td>0.2662</td><td>13.97</td></tr><tr><td>Smooth Diff. + DDIM</td><td>0.1086</td><td>0.4326</td><td>0.3418</td><td>16.17</td></tr><tr><td>Stable Diff. + NTI</td><td>0.0156</td><td>0.1656</td><td>0.6068</td><td>25.63</td></tr><tr><td>Smooth Diff. + NTI</td><td>0.0153</td><td>0.1635</td><td>0.6102</td><td>25.74</td></tr><tr><td>VAE Reconstruction</td><td>0.0148</td><td>0.1590</td><td>0.6136</td><td>25.98</td></tr></table>
+
+Table 2. Quantitative evaluations of image reconstruction. We integrate Stable Diffusion and Smooth Diffusion [62] with DDIM inversion [71] (row 2 & 3) and NTI [44] (row 4 & 5). MSE, LPIPS [93], SSIM [79] and PSNR [27] are evaluated. VAE Reconstruction results are provided as the optimal values.
+
+enhancement of latent space smoothness and the overall image generation quality are not mutually exclusive but complement each other when the regularization term is applied with a suitable strength ratio.
+
+# 4.3. Image Inversion and Reconstruction
+
+Previous research [32] in the realm of GANs discovered that a smoother latent space has a positive impact on the accuracy of image inversion and reconstruction. We empirically validate this finding within the context of diffusion models. In specific, two representative inversion techniques, DDIM inversion [71] and Null-text inversion (NTI) [44] are adopted and integrated with Smooth Diffusion and Stable Diffusion separately. We both qualitatively and quantitatively compare the image inversion and reconstruction performance of these integrated models using 500 randomly sampled images from the MS-COCO validation set [38].
+
+As illustrated in the two rightmost columns of Fig. 4, when employing a straightforward DDIM inversion, Smooth Diffusion outperforms Stable Diffusion by a considerable margin in terms of reconstruction quality. This improvement is evident in various aspects, such as an accurate generation of character identities, a faithful recreation of the city view behind the tower, and a correct reproduc
+
+![](images/ee7827b792b76aebb68e1b4bcc082d4866ca9169f22c3f9d29a004ee262cb628.jpg)  
+Local Edit (Replace Item)
+
+![](images/612347a0c4f9d704b4e06fd85d11f4f9dafeddf20e06d16be55d69c182eca9ed.jpg)
+
+![](images/ec5a3d46abc975d3d63f92cbca55efd6e2c13e0813b931b44f11d97a6bfb4a33.jpg)  
+"A banana on the table"  $\rightarrow$  "A banana and an apple on the table"
+
+![](images/68e345f4d89c403a49553365ec38af08e4931cdb4bcc3534787e7656bbeae946.jpg)
+
+![](images/5c47747b20560cc66b304444fa8dd03db99749aee61f04fc795ced15ba31a5d1.jpg)
+
+![](images/4f90cdb1c212d06eff27314789349bce0c906e1b3686e7ff6c0120ff2aa1fc43.jpg)
+
+![](images/cbc9023170989899a322e1f84623e558439ce5ba10878d58984e6a15b090d99e.jpg)
+
+![](images/672db70021d9d25bc33e5b31804ce0d12050656b1487e095d0f2d41937a46566.jpg)
+
+![](images/70d3bb033ae2fff962b47a60c921df6c9422e3ec5e57b49dd918b5948424fb86.jpg)
+
+![](images/9d18898001464a72cbd414292cd23f9d154cf0fa0fe20eddb22c0a10718dc7fb.jpg)  
+Local Edit (Add Item)
+
+![](images/20b35f1d5c67817b007983bb8fe5cd273d91f99cf414f450a29b167601eae654.jpg)
+
+![](images/0a4358efe99e94b251c5aa2e6d594823b09f015256d5278868a32c510b117cb1.jpg)
+
+![](images/a5287125e4cc412e782b22a990b6663bf9abbe22cb272cfb77d3c05488e00bda.jpg)
+
+![](images/baad5f50cfc57ba3ed4b110359eaf946f4ff9982eaaa83b00903bddce3814291.jpg)
+
+![](images/351dfb9ecca76a7e5562f0191ee25583aac6facae37e640dc8c77624fb9d64f8.jpg)
+
+![](images/b9846993c93e15d1132a84855317490e088059368757ac4aab59cdc8f26d0cbe.jpg)
+
+![](images/abf8bd5f457bee13f39171ef1744fe8b06da3f64795962a4587d9b83d4e1a7e3.jpg)
+
+![](images/944e58bc83b2afae72b0453b571b40c6a0d6063a883edb47e00b324a7d2026f9.jpg)  
+Global Edit (Transfer Style)  
+Source  
+Figure 5. Text-based image editing comparison results. We compare Smooth Diffusion and Stable Diffusion [62] (column 2 & 3), considering both local and global edits through the straightforward pipeline described in Sec. 4.4. Additionally, we present results from SOTA approaches, including SDEdit [42], P2P [21], PnP [75], Disentangle [82], Pix2Pix-Zero [55], and Cycle Diffusion [81], as references.
+
+![](images/248e1d56594e55d016660a3773fe0af4d9a4d960522426e41e1d36e907c21c51.jpg)  
+Smooth Diff.
+
+![](images/6cbc0586d92939d164632d92b370a05673ebe898fa5f4a48e3b411539729f1bd.jpg)  
+Stable Diff.
+
+![](images/5bcfe2d4fa39a518d7b4c3895b8df511019b936493f990b9eb840539de4e3f30.jpg)  
+SDEdit
+
+![](images/5857ecb9ed067d76cb4f302193b84cf7cd7f7b70f5898e88c014defd997006ab.jpg)  
+P2P
+
+![](images/387db9a95a751af37d265786cee3e6694163edfa2f435d758988c598cbe9bf64.jpg)  
+PnP
+
+![](images/114420e81f7e92fc91caa8f3fbc0c1d904043243ff42f026b457604ead82f656.jpg)  
+Disentangle
+
+![](images/222c2426f6793dd5ebe32cb66fcef44f26a3c2a153d754e3c011f5ee263e9b33.jpg)  
+Pix2Pix-Zero
+
+![](images/7d345b38d77f69a0f2eb74c8d793a31b4e5c35fab636f790727b5b7cec086f6b.jpg)  
+Cycle Diff.
+
+tion of room layouts. This phenomenon underscores the fact that the latent space of Smooth Diffusion is more tolerant of the errors introduced by the local linear approximation in DDIM inversion. Consequently, the reconstruction results produced by Smooth Diffusion manage to retain the contents of the source images to a greater extent. On the other hand, when the optimization-based NTI technique is employed, the disparity between Smooth Diffusion and Stable Diffusion is not as pronounced. Nonetheless, there are still instances where Stable Diffusion exhibits subpar results, such as the ruined man's face in Fig. 4.
+
+To quantify the image reconstruction performance, MSE, LPIPS [93], SSIM [79] and PSNR [27] are reported in Tab. 2. Notably, the reconstruction error encompasses two components: 1) the error from different inversion methods and U-Net parameters and 2) the error from the shared pretrained VAE [36]. Hence, we included the VAE reconstruction errors as optimal values for our method. The results exhibit a consistent outperformance of Smooth Diffusion over Stable Diffusion across all metrics, whether using DDIM inversion or NTI. Moreover, "Smooth Diffusion + NTI" performs results close to VAE reconstruction, indicating its superiority attributed to a smoother latent space.
+
+# 4.4. Image Editing
+
+The superiority of Smooth Diffusion in image inversion and reconstruction has motivated us to explore its potential for enhancing image editing tasks. In this section, we delve into two typical image editing scenarios: text-based image editing and drag-based image editing.
+
+Text-based image editing. There have been numerous methods [21, 42, 55, 75, 81, 82] proposed in the literature, each with its own unique designs aimed at achieving the SOTA performance. In contrast, we adopt a simpler pipeline akin to the image inversion and reconstruction pro
+
+cess discussed in Sec. 4.3. The key distinction lies in our approach to modify the text prompt during the later time steps of the reconstruction process. In specific, the original  $\epsilon_{\theta}(\boldsymbol{x}_t,t,\mathcal{C},\varnothing_t)$  in Eq. (5) during NTI reconstruction (diffusion sampling) process is replaced with:
+
+$$
+\epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C}, \varnothing_ {t}\right) = \left\{ \begin{array}{l} \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C} _ {\text {s r c}}, \varnothing_ {t}\right), t > T \times r, \\ \epsilon_ {\theta} \left(\boldsymbol {x} _ {t}, t, \mathcal {C} _ {\text {t r g}}, \varnothing_ {t}\right), t \leq T \times r, \end{array} \right. \tag {15}
+$$
+
+where  $\mathcal{C}_{\mathrm{src}}$  represents the source text prompt for inversion, while  $\mathcal{C}_{\mathrm{trg}}$  corresponds to the target text prompt for editing. The parameter  $r$  serves as a threshold, determining when to switch from  $\mathcal{C}_{\mathrm{src}}$  to  $\mathcal{C}_{\mathrm{trg}}$ . In practice,  $r$  is typically chosen within  $\{0.6, 0.7, 0.8, 0.9\}$ , with the exact value depending on the specific input images and target visual effects.
+
+Through this straightforward pipeline, we conducted a comparative analysis of the editing performance between Smooth Diffusion and Stable Diffusion, as presented in the three left-most columns of Fig. 5. We also included editing results obtained from SOTA methods as references. Our evaluation encompasses both local and global editing tasks. The local editing tasks involve replacing items (e.g., changing "cream" to "strawberries") and adding items (e.g., "apple"). On the other hand, the global editing tasks pertain to global style transfer, such as transforming an image into a "cartoon style". It is evident that while Stable Diffusion excels in achieving precise image reconstruction with NTI, as discussed in Sec. 4.3, even minor modifications to the text prompt can significantly impact the content of the generated images. For instance, it can affect elements like the style of the cake, the shape of the banana, and the haircut of the girl. In contrast, Smooth Diffusion not only accurately generates edited images in accordance with the target text prompts but also effectively preserves the unedited contents. Furthermore, when compared to SOTA methods, even with this straightforward pipeline, Smooth Diffusion consistently delivers competitive results across all cases.
+
+![](images/7841f881951452a64d3834f27f00765f86b6308cf1d148483b0328cbbd5aeaea.jpg)  
+Figure 6. Drag-based image editing comparison results. We implement Smooth Diffusion and Stable Diffusion [62] within the framework of DragDiffusion [69], respectively.
+
+Drag-based image editing. As an emerging research avenue in the community, drag-based image editing [45, 53, 69] has garnered considerable attention recently. DragDiffusion [69] first introduces a framework for drag-based image editing employing Stable Diffusion. In the task 3 of Fig. 1 and Fig. 6, we showcase that by integrating Smooth Diffusion into the DragDiffusion framework, some previously unsuccessful editing operations with Stable Diffusion can be enabled. As illustrated, Smooth Diffusion achieves operations such as making the tree grow taller without damaging existing branches (Fig. 1), rotating the cat head, creating a new mountain top without destroying the original one, and letting new flowers grow in the vase (Fig. 6). These operations, however, fail with Stable Diffusion, indicating the non-smoothness of its latent space.
+
+# 4.5. Ablation Studies
+
+Regularization ratio. In Tab. 3, we examine the impact of different strength ratios  $\lambda$  in Eq. (14). This ratio adjusts the intensity of the step-wise variation regularization. Specifically, when a weaker regularization is applied (e.g.,  $\lambda = 0.1$ ), we observe a slight improvement in the CLIP Score. However, there is a significant increase in ISTD, indicating a notable degradation in latent space smoothness. In contrast, employing a stronger regularization (e.g.,  $\lambda = 10$ ) leads to a smoother latent space, as demonstrated by the decrease in ISTD. However, in this case, we observe an unexpected increase in FID, indicating a notable decline in the quality of generated images. Therefore, selecting an appropriate trade-off value for  $\lambda$  becomes crucial based on the specific experimental settings. In our default setting, we find that  $\lambda = 1$  serves as a suitable value.
+
+LoRA rank. In Tab. 4, we examine the impact of different ranks of the LoRA component utilized in our Smooth diffusion. We discover that LoRA ranks within the range
+
+<table><tr><td>Ratio</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>0.1</td><td>24.23</td><td>12.15</td><td>31.56</td></tr><tr><td>1 (default)</td><td>16.54</td><td>12.11</td><td>31.49</td></tr><tr><td>10</td><td>11.51</td><td>17.44</td><td>31.41</td></tr></table>
+
+of [4,16] are all suitable values for our default setting. We select a default rank of 8 because of its lowest ISTD among the first three rows in Tab. 4. Furthermore, we train a fully finetuned model, referred to as "full," which showcases a further decrease in ISTD. However, this comes at the expense of significantly degrading the quality of the generated images, as indicated by an increased FID and decreased CLIP Score. This decline in performance underscores the vulnerability of fully fine-tuned models to collapse within our default setting, emphasizing the need for additional meticulous design considerations.
+
+Table 3. Ablation results of different regularization ratios. The best results are in bold, and the second-best results are underlined.  
+
+<table><tr><td>Rank</td><td>ISTD (↓)</td><td>FID (↓)</td><td>CLIP Score (↑)</td></tr><tr><td>4</td><td>16.76</td><td>12.36</td><td>31.49</td></tr><tr><td>8 (default)</td><td>16.54</td><td>12.11</td><td>31.54</td></tr><tr><td>16</td><td>16.65</td><td>11.49</td><td>31.61</td></tr><tr><td>full</td><td>11.52</td><td>27.27</td><td>28.86</td></tr></table>
+
+Table 4. Ablation results of different LoRA ranks. The best results are in bold, and the second-best results are underlined.
+
+# 5. Conclusion
+
+In this article, we explored Smooth Diffusion, an innovative diffusion model that enhances latent space smoothness for generation. Smooth Diffusion adopts the novel Stepwise Variation Regularization, which successfully maintains variation between arbitrary input latent and generated images at a more bounded range. Smooth Diffusion was trained on top of the prevailing text-to-image model, from which we carried out extensive research, including but not limited to interpolation, inversion, and editing, all of which had shown competitive performance. Through qualitative and quantitative measurements, we demonstrated that Smooth Diffusion managed to make a smoother latent space without compromising the output quality. We believe that Smooth Diffusion will become a valuable solution for other challenging tasks, such as video generation, in the future.
+
+# Acknowledgements
+
+This work is supported in part by the ML Center at Georgia Tech, NSF CAREER Award #2239840, and the National AI Institute for Exceptional Education (Award #2229873) by National Science Foundation and the Institute of Education Sciences, U.S. Department of Education. Huang is in part supported by the National Key R&D Program (#2021ZD0140407) and NSFC (62321005 & 42327901).
+
+# References
+
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+        "text": "SnAG: Scalable and Accurate Video Grounding",
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+        "text": "Fangzhou Mu*, Sicheng Mo*, Yin Li  \nUniversity of Wisconsin-Madison",
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+        "text": "Abstract",
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+        "text": "Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is  $43\\%$  more accurate and  $1.5 \\times$  faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release.",
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+        "text": "1. Introduction",
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+        "type": "text",
+        "text": "Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing.",
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+        "text": "Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos.",
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+        "img_path": "images/b9a807416c0ebc2e4ad55975342dc123777b8a8af446635bc0de09fcd6219e94.jpg",
+        "image_caption": [
+            "Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding."
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+        "text": "On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation.",
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+        "text": "In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy.",
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+    {
+        "type": "text",
+        "text": "Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains  $13.75\\%$  R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1),  $43\\%$  more accurate and  $1.5\\times$  faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves  $46.26\\%$  R@1, tIoU=0.7 on Charades-STA [43], outperforming the",
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+        "type": "header",
+        "text": "CVF",
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+        "page_idx": 0
+    },
+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "* indicates equal contribution",
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+    {
+        "type": "page_number",
+        "text": "18930",
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+    {
+        "type": "text",
+        "text": "previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design.",
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+    {
+        "type": "text",
+        "text": "Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference.",
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+        "text": "2. Related Work",
+        "text_level": 1,
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+            266,
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion).",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Two-stage methods first generate temporal segments as proposals, then score their \"actionness\" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos.",
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+    {
+        "type": "text",
+        "text": "Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings",
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+    {
+        "type": "text",
+        "text": "are concatenated at input, and attention-based feature fusion is carried out throughout the model.",
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+    {
+        "type": "text",
+        "text": "Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks.",
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+        "type": "text",
+        "text": "Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos.",
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+    {
+        "type": "text",
+        "text": "3. Scaling Up Video Grounding",
+        "text_level": 1,
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+        "type": "text",
+        "text": "Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video  $\\mathbf{V}$  as a time-indexed sequence  $[\\mathbf{v}_t]_{t=1}^T = [\\mathbf{v}_1, \\mathbf{v}_2, \\dots, \\mathbf{v}_T]$ , where  $\\mathbf{v}_t$  represents a short video clip centered at time  $t$ .<sup>1</sup>  $\\mathbf{V}$  is paired with  $N$  sentence queries  $\\{\\mathrm{Q}_j\\}_{j=1}^N$ , each describing a moment  $\\mathbf{y}_j = (s_j, e_j)$  in the video.",
+        "bbox": [
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+        "type": "text",
+        "text": "Long-form video grounding is characterized by a great number of time steps  $T$  (e.g., tens of thousands) and text queries  $N$  (hundreds) for an input video  $\\mathbf{V}$ . With a large  $T$ , it is no longer feasible to feed the full video  $\\mathbf{V}$  into a model, and thus more viable to consider a sliding window setting. Specifically, a video  $\\mathbf{V}$  is further partitioned into a set of  $M$  snippets  $\\{\\mathbf{V}_{i=1}^{M}\\}$ , each  $\\mathbf{V}_{i} = [\\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}}$  taken from a local time window of size  $T_{w}$  that may overlap with others. We consider the learning of a function  $\\mathcal{F}$ , realized in a deep",
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+    {
+        "type": "page_footnote",
+        "text": "1Like prior works, we consider video features and text embeddings extracted using pre-trained models (e.g., C3D [48] and BERT [10]). Yet the formulation can be easily extended to raw video frames and text tokens.",
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+    },
+    {
+        "type": "page_number",
+        "text": "18931",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "image",
+        "img_path": "images/4803639b0a1f16039b839ad918d58e34425082f99caff1fafa9a2122313a6aae.jpg",
+        "image_caption": [
+            "Figure 2. (a) Cross-modal fusion is key to a video grounding model  $\\mathcal{F}$ . Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query  $\\rightarrow$  video) whereas SnAG resorts to video-centric sampling (video  $\\rightarrow$  many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/24f620b34609b9f3f19062804931b668980e1121d4689609c7c691dd26f796f2.jpg",
+        "image_caption": [],
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+    {
+        "type": "image",
+        "img_path": "images/2ae59873afb84ef2c5185ee19976e539c33b58e59f038c76a8a3cd9d0b114779.jpg",
+        "image_caption": [],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "network, to predict the start time  $s_j$  and end time  $e_j$  of the moment  $\\mathbf{y}_j$  given a snippet  $\\mathbf{V}_i$  and a query  $\\mathrm{Q}_j$ .",
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "3.1. Background: Cross-Modal Fusion",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We review cross-modal fusion - a key design choice of  $\\mathcal{F}$  and define the notation used for the rest of the paper.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Early fusion. A straightforward design is to fuse information from a video snippet  $\\mathbf{V}_i$  and a text query  $\\mathrm{Q}_j$  at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} _ {E} \\left(\\mathbf {V} _ {i}, \\mathrm {Q} _ {j}\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {1}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mapsto$  defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment  $\\mathbf{y}_j$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Late fusion. Another possible design is to first embed the video snippet  $\\mathbf{V}_i$  and text query  $\\mathrm{Q}_j$ , then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} _ {L} \\left(g \\left(\\mathbf {V} _ {i}\\right), h \\left(\\mathrm {Q} _ {j}\\right)\\right) \\mapsto \\mathbf {y} _ {j}, \\tag {2}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "where  $g(\\cdot)$  is the video encoder and  $h(\\cdot)$  the text encoder. With slight abuse of the symbols,  $\\mathcal{F}_L$  here denotes the rest part of the grounding model, including feature fusion. The key is to keep  $\\mathcal{F}_L$  lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration  $(M)$  and number of text queries  $(N)$ .",
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+    {
+        "type": "text",
+        "text": "3.2. Scalable Inference",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by  $\\mathcal{C}(\\cdot)$ . For example,  $\\mathcal{C}(g)$  is the cost of the video encoder  $g(\\cdot)$ , and  $\\mathcal{C}(h)$  the cost of the text encoder  $h(\\cdot)$ .",
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+    },
+    {
+        "type": "text",
+        "text": "Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight  $\\mathcal{F}_L$  is used for late fusion, thus  $\\mathcal{C}(\\mathcal{F}_L) \\ll \\mathcal{C}(g) + \\mathcal{C}(h)$ ; and (b) the video encoder  $g(\\cdot)$  has a much higher cost than the text encoder, thus  $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ .",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that  $\\mathcal{C}(g)$  scales w.r.t. the length of input video snippet (i.e., the local window size  $T_w$ ), whereas  $\\mathcal{C}(h)$  remains constant due to limited sequence length of text queries. For example, a realization of  $g(\\cdot)$  using a vanilla Transformer has a complexity of  $\\mathcal{O}(T_w^2)$ . Thus, using a larger local window size naturally leads to  $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with  $M$  snippets and  $N$  queries has a cost of  $MN\\mathcal{C}(\\mathcal{F}_E)$ , whereas late fusion has a cost of  $MN\\mathcal{C}(\\mathcal{F}_L) + MC(g) + NC(h)$ . This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b)).",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "Let us assume that the cost of both models can be controlled by setting  $\\mathcal{C}(\\mathcal{F}_E) = \\mathcal{C}(\\mathcal{F}_L) + \\mathcal{C}(g) + \\mathcal{C}(h)$ , i.e., eval",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "18932",
+        "bbox": [
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+        ],
+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With  $\\mathcal{C}(\\mathcal{F}_L) = \\alpha (\\mathcal{C}(g) + \\mathcal{C}(h))$  for some small  $\\alpha$ , the ratio between the cost of early and late fusion in inference is",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {R} _ {\\text {i n f}} = \\frac {\\mathcal {C} (\\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\\mathcal {C} (\\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\\\ = \\frac {M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M N \\mathcal {C} (g) + M N \\mathcal {C} (h)}{M N \\mathcal {C} \\left(\\mathcal {F} _ {L}\\right) + M \\mathcal {C} (g) + N \\mathcal {C} (h)} (4) \\\\ = \\frac {M N (1 + \\alpha)}{M N \\alpha + M \\mathbf {R} _ {g / (g + h)} + N (1 - \\mathbf {R} _ {g / (g + h)})} (5) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{N} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}N,&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&N \\rightarrow \\infty\\end{array}, \\right. (6) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbf{R}_{g / (g + h)} = \\mathcal{C}(g) / (\\mathcal{C}(g) + \\mathcal{C}(h))$ , and the approximation in Eq. 6 is a result of  $\\mathbf{R}_{g / (g + h)} \\approx 1$  with  $\\mathcal{C}(g) \\gg \\mathcal{C}(h)$ . Eq. 6 reveals that early fusion is  $N$  times the cost of late fusion as snippet length grows ( $\\alpha \\to 0$ ), and is particularly inefficient for videos with many queries ( $N \\to \\infty$ ).",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "3.3. Scalable Training",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments  $\\{\\mathbf{V}^{(k)},\\mathbf{Q}^{(k)},\\mathbf{y}^{(k)}\\}$ , training a model  $\\mathcal{F}$  amounts to minimizing a loss function  $\\mathcal{L}$  over mini-batches  $B$  sampled from the dataset:",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\Sigma_ {(k, i, j) \\in B} \\mathcal {L} \\left(\\mathcal {F} \\left(\\mathbf {V} _ {i} ^ {(k)}, \\mathrm {Q} _ {j} ^ {(k)}\\right), \\mathbf {y} _ {j} ^ {(k)}\\right). \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries. $^{2}$  This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathrm {Q} _ {j} ^ {(k)}, \\mathbf {y} _ {j} ^ {(k)}\\right) \\right\\} _ {j \\times k}\\right), \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $U(\\cdot)$  denotes a discrete uniform distribution and  $\\{(\\mathbf{V}_i^{(k')},\\mathbf{Q}_j^{(k')},\\mathbf{y}_{j'}^{(k')})_{+}\\}$  is the union of all valid triplets: a moment  $\\mathbf{y}_{j'}^{(k')}$  of a text query  $\\mathbf{Q}_{j'}^{(k')}$  in a video snippet  $\\mathbf{V}_i^{(k')}$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "This sampling process is repeated  $|B|$  times to construct a mini-batch, with  $|B|$  the batch size. With a large",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "dataset, the resulting mini-batch will contain  $|B|$  snippet-query pairs, each likely from a different video.",
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+    {
+        "type": "text",
+        "text": "Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet  $\\mathbf{V}_i^{(k)}$  as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling:",
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+    {
+        "type": "equation",
+        "text": "\n$$\nk ^ {\\prime} \\sim P (k) = \\frac {M _ {+} ^ {(k)}}{\\Sigma_ {k} M _ {+} ^ {(k)}} \\quad i ^ {\\prime} \\sim P (i; k ^ {\\prime}) = \\frac {N _ {i} ^ {\\left(k ^ {\\prime}\\right)}}{\\Sigma_ {k} N _ {i} ^ {\\left(k ^ {\\prime}\\right)}} \\tag {9}\n$$\n",
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\left\\{\\mathrm {Q} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j ^ {\\prime}} ^ {(k ^ {\\prime})} \\right\\} ^ {B _ {q}} \\sim U \\left(\\left\\{\\left(\\mathbf {V} _ {i ^ {\\prime}} ^ {(k ^ {\\prime})}, \\mathrm {Q} _ {j} ^ {(k ^ {\\prime})}, \\mathbf {y} _ {j} ^ {(k ^ {\\prime})}\\right) _ {+} \\right\\}\\right),\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            279,
+            851,
+            303
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $M_{+}^{(k)}$  denotes the number of valid snippets in a video  $\\mathbf{V}^{(k)}$ , and  $N_{i}^{(k^{\\prime})}$  the number of queries in a snippet  $\\mathbf{V}_{i}^{(k^{\\prime})}$ . Importantly, a total of  $B_{q}$  queries are drawn for the selected video snippet  $\\mathbf{V}_{i^{\\prime}}^{(k^{\\prime})}$ .",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "This sampling process is repeated  $|B| / B_q$  times for a mini-batch, leading to  $|B| / B_q$  video snippets, each likely from a different video yet with multiple  $(B_q)$  text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets.",
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets  $(\\alpha \\rightarrow 0)$  and large  $B_{q}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} \\mathbf {R} _ {\\text {t r a i n}} = \\frac {\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {v i d e o - c e n t r i c t r a i n i n g})}{\\mathcal {C} (\\text {l a t e f u s i o n} + \\text {q u e y - c e n t r i c t r a i n i n g})} (10) \\\\ \\approx \\frac {1 + \\alpha}{\\frac {1}{B _ {q}} + \\alpha} \\rightarrow \\left\\{\\begin{array}{l l}B _ {q},&\\alpha \\rightarrow 0\\\\1 + \\frac {1}{\\alpha},&B _ {q} \\rightarrow \\infty\\end{array}. \\right. (11) \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "3.4. Scalable Video Grounding: An Instantiation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Video encoder  $g$ . We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation  $[\\mathbf{Z}^{(l)}]_{l=1}^{L} = [\\mathbf{Z}^{(1)}, \\mathbf{Z}^{(2)}, \\dots, \\mathbf{Z}^{(L)}]$  using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "page_footnote",
+        "text": "2A video snippet without any query is often discarded during training.",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "18933",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Text encoder  $h$ . Our text encoder is a vanilla Transformer. It takes a query Q with  $K$  tokens  $[\\mathbf{q}_1, \\dots, \\mathbf{q}_K]$  and outputs their embeddings  $\\mathbf{E} = [\\mathbf{e}_1, \\dots, \\mathbf{e}_K]$ . This computation is light compared to video encoding as  $K \\ll T_w$  for long videos.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Cross-modal late fusion  $\\mathcal{F}_L$ . Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates  $[\\mathbf{Z}^{(l)}]_{l=1}^L$  with an affine transformation given by  $\\mathbf{E}$ :",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} (\\mathbf {W}, \\mathbf {B}) ^ {(l)} = \\operatorname {M C A} (\\operatorname {L N} (\\mathbf {Z} ^ {(l)}), \\operatorname {L N} (\\mathbf {E})), \\\\ \\tilde {\\mathbf {Z}} ^ {(l)} = \\mathbf {W} ^ {(l)} \\odot \\mathbf {Z} ^ {(l)} + \\mathbf {B} ^ {(l)}, \\tag {12} \\\\ \\mathbf {X} ^ {(l)} = \\tilde {\\mathbf {c}} \\odot \\operatorname {M L P} (\\operatorname {L N} (\\bar {\\mathbf {Z}} ^ {(l)})) + \\bar {\\mathbf {Z}} ^ {(l)}, \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights  $\\mathbf{W}^{(l)}$  and biases  $\\mathbf{B}^{(l)}$ .  $\\tilde{\\mathbf{c}}$  are learnable per-channel scales, and  $\\mathbf{X}^{(l)}$  the modulated video representations prior to moment decoding.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score  $p_t^{(l)}$  for all  $\\mathbf{x}_t^{(l)}$  within  $[\\mathbf{X}^{(l)}]_{l=1}^L$ , and a regression head predicts the normalized distances from  $t$  to the moment boundaries  $(d_t^s, d_t^e)$  if  $\\mathbf{x}_t^{(l)}$  is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment  $\\hat{\\mathbf{y}} = (\\hat{s}, \\hat{e})$  is given by",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n(t, l) = \\underset {t, l} {\\arg \\max } p _ {t} ^ {(l)}, \\tag {13}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            200,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\hat {s} = 2 ^ {l - 1} \\cdot (t - d _ {t} ^ {s}), \\quad \\hat {e} = 2 ^ {l - 1} \\cdot (t + d _ {t} ^ {e}).\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions.",
+        "bbox": [
+            76,
+            542,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26]  $\\mathcal{L}_{cls}$  for moment classification and a Distance-IoU loss [69]  $\\mathcal{L}_{reg}$  defined on positive time steps for distance regression. Formally,",
+        "bbox": [
+            76,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} = \\frac {1}{C} \\left(\\mathcal {L} _ {c l s} + \\lambda_ {r e g} \\mathbb {1} _ {t} ^ {(l)} \\mathcal {L} _ {r e g}\\right), \\tag {14}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+            672,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\mathbb{1}_t^{(l)}$  is an indicator function that evaluates to one on positive time steps,  $C = \\sum_{t,l}\\mathbb{1}_t^{(l)}$  is the total number of positive samples within the snippet, and  $\\lambda_{reg}$  balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "4. Experiments",
+        "text_level": 1,
+        "bbox": [
+            76,
+            800,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/88f4a85d6f7b967b7228f9f976dd1b4879b479a7ffcf06079a78ac26f9738e87.jpg",
+        "image_caption": [
+            "Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades)."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            560,
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/650f6dc82d2c841ac5f51499f1a53ecc671a5bcc24fd5f229c19556b7175f3d2.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\"></td><td rowspan=\"2\">Model</td><td colspan=\"3\">R@1</td><td colspan=\"3\">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>Avg</td><td>0.3</td><td>0.5</td><td>Avg</td></tr><tr><td rowspan=\"6\">SF + BERT</td><td>2D-TAN [67]</td><td>5.04</td><td>2.02</td><td>3.53</td><td>12.89</td><td>5.88</td><td>9.39</td></tr><tr><td>VSLNet [64]</td><td>5.45</td><td>3.12</td><td>4.29</td><td>10.74</td><td>6.63</td><td>8.69</td></tr><tr><td>CONE [17]</td><td>10.40</td><td>5.03</td><td>7.72</td><td>22.74</td><td>11.87</td><td>17.31</td></tr><tr><td>SOONet [36]</td><td>8.00</td><td>3.76</td><td>5.88</td><td>22.40</td><td>11.09</td><td>16.75</td></tr><tr><td>SnAG (video-centric)</td><td>9.83</td><td>6.83</td><td>8.33</td><td>27.93</td><td>19.27</td><td>23.60</td></tr><tr><td>SnAG (query-centric)</td><td>10.43</td><td>7.15</td><td>8.79</td><td>27.59</td><td>19.33</td><td>23.46</td></tr><tr><td rowspan=\"4\">EgoVLP</td><td>VSLNet [64]</td><td>10.84</td><td>6.81</td><td>8.83</td><td>18.84</td><td>13.45</td><td>16.15</td></tr><tr><td>CONE [17]</td><td>14.15</td><td>8.18</td><td>11.17</td><td>30.33</td><td>18.02</td><td>24.18</td></tr><tr><td>SnAG (video-centric)</td><td>15.72</td><td>10.78</td><td>13.25</td><td>38.39</td><td>27.44</td><td>32.92</td></tr><tr><td>SnAG (query-centric)</td><td>15.87</td><td>11.26</td><td>13.57</td><td>38.26</td><td>27.16</td><td>32.71</td></tr></table>",
+        "bbox": [
+            503,
+            357,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined.",
+        "bbox": [
+            500,
+            512,
+            888,
+            539
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3).",
+        "bbox": [
+            498,
+            566,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are  $\\sim 30$  seconds long with  $\\sim 2.4$  queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of  $\\sim 3.65$  queries. Several works [35, 57] advise against using these datasets as benchmarks for the",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_footnote",
+        "text": "3All experiments are conducted using the Ego4D  $\\nu I$  dataset.",
+        "bbox": [
+            514,
+            886,
+            834,
+            898
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "18934",
+        "bbox": [
+            480,
+            944,
+            517,
+            955
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "table",
+        "img_path": "images/9fb014012dd588b5a1f1f657cd85e4227cdf987e63c2364b29be03978fca3c89.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"3\">R@1</td><td colspan=\"3\">R@5</td><td colspan=\"3\">R@10</td><td colspan=\"3\">R@50</td></tr><tr><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td></tr><tr><td>CLIP [39]</td><td>6.57</td><td>3.13</td><td>1.39</td><td>15.05</td><td>9.85</td><td>5.44</td><td>20.26</td><td>14.13</td><td>8.38</td><td>37.92</td><td>28.71</td><td>18.80</td></tr><tr><td>VLG-Net [46]</td><td>3.64</td><td>2.76</td><td>1.65</td><td>11.66</td><td>9.31</td><td>5.99</td><td>17.39</td><td>14.56</td><td>9.77</td><td>39.78</td><td>34.27</td><td>24.93</td></tr><tr><td>Moment-DETR [21]</td><td>0.31</td><td>0.24</td><td>0.16</td><td>1.52</td><td>1.14</td><td>0.28</td><td>2.79</td><td>2.06</td><td>1.20</td><td>11.08</td><td>7.97</td><td>4.71</td></tr><tr><td>CONE [17]</td><td>8.90</td><td>6.87</td><td>4.10</td><td>20.51</td><td>16.11</td><td>9.59</td><td>27.20</td><td>21.53</td><td>12.82</td><td>43.36</td><td>34.73</td><td>20.56</td></tr><tr><td>SOONet [36]</td><td>11.26</td><td>9.00</td><td>5.32</td><td>23.21</td><td>19.64</td><td>13.14</td><td>30.36</td><td>26.00</td><td>17.84</td><td>50.32</td><td>44.78</td><td>32.59</td></tr><tr><td>SnAG (video-centric)</td><td>10.28</td><td>8.46</td><td>5.55</td><td>24.42</td><td>20.60</td><td>13.75</td><td>32.23</td><td>27.50</td><td>19.00</td><td>52.28</td><td>46.68</td><td>35.24</td></tr><tr><td>SnAG (query-centric)</td><td>10.18</td><td>8.37</td><td>5.44</td><td>24.30</td><td>20.35</td><td>13.51</td><td>32.05</td><td>27.25</td><td>18.75</td><td>52.05</td><td>46.53</td><td>34.83</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined.",
+        "bbox": [
+            150,
+            233,
+            815,
+            247
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/4f7ff842d2c213510aaad27a0c0318e2f50342257769de09c20c3dd7e2749bba.jpg",
+        "image_caption": [
+            "Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            81,
+            261,
+            467,
+            424
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness.",
+        "bbox": [
+            75,
+            482,
+            468,
+            512
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement.",
+        "bbox": [
+            75,
+            516,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Evaluation metric. We report  $\\mathrm{Recall}@\\mathbf{k}$  at various temporal intersection-over-union threshold  $\\theta$  ( $\\mathbf{R}@\\mathbf{k}$ , tIoU= $\\theta$ ) for all datasets. It measures the percentage of sentence queries with at least one of the top- $k$  moment predictions whose temporal overlap with the ground-truth moment exceeds  $\\theta$ .",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "4.1. Long Videos, Many Queries",
+        "text_level": 1,
+        "bbox": [
+            76,
+            756,
+            328,
+            772
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for",
+        "bbox": [
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+            779,
+            468,
+            900
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "sentence embeddings. We train on the train split and report  $\\mathrm{R}@\\{1,5\\}$ , tIoU=\\{0.5, 0.7\\} on the test split. We report results using both video-centric and query-centric training on all datasets.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of  $8.79\\% / 23.60\\%$  with SlowFast/BERT features, and  $13.57\\% / 32.92\\%$  with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization.",
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+    },
+    {
+        "type": "text",
+        "text": "Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with  $T_{w} = 16384$  (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding.",
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+    {
+        "type": "text",
+        "text": "Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of  $44.86\\%$  /  $70.66\\%$  at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin  $(+7.5\\% \\mathrm{R} @ 1, +12.1\\% \\mathrm{R} @ 5)$ . This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In",
+        "bbox": [
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+    },
+    {
+        "type": "page_footnote",
+        "text": "4CONE [17] leverages external CLIP [39] features in several steps.",
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+        "page_idx": 5
+    },
+    {
+        "type": "page_footnote",
+        "text": "5MAD videos are not publicly available due to copyright issues.",
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+    },
+    {
+        "type": "page_number",
+        "text": "18935",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/d45490b02b2602cd98d4a768e4f2caedcd7932de3e15250099104b16917fe4d8.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"2\">Model</td><td colspan=\"2\">R@1</td><td colspan=\"2\">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>0.3</td><td>0.5</td></tr><tr><td colspan=\"5\">(a) Fusion stage (early vs. late fusion)</td></tr><tr><td>No fusion</td><td>10.85</td><td>7.85</td><td>46.46</td><td>31.19</td></tr><tr><td>SnAG-E</td><td>53.34</td><td>44.01</td><td>79.56</td><td>69.41</td></tr><tr><td>SnAG-EL</td><td>54.84</td><td>44.54</td><td>81.13</td><td>70.11</td></tr><tr><td>SnAG-M</td><td>51.41</td><td>40.79</td><td>77.56</td><td>65.71</td></tr><tr><td>SnAG (ours)</td><td>55.14</td><td>44.94</td><td>81.10</td><td>70.66</td></tr><tr><td colspan=\"5\">(b) Fusion operation (global vs. token-wise)</td></tr><tr><td>Cat</td><td>49.39</td><td>39.24</td><td>77.31</td><td>65.36</td></tr><tr><td>Add</td><td>51.91</td><td>41.81</td><td>77.98</td><td>66.51</td></tr><tr><td>Scale</td><td>55.01</td><td>43.96</td><td>80.63</td><td>70.11</td></tr><tr><td>Add + Scale</td><td>53.36</td><td>43.09</td><td>80.43</td><td>69.58</td></tr><tr><td>XAttn</td><td>54.84</td><td>45.06</td><td>79.96</td><td>70.08</td></tr><tr><td>XAttn-affine (ours)</td><td>55.14</td><td>44.94</td><td>81.10</td><td>70.66</td></tr></table>",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale).",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions (\"take from\", \"place on\", and \"turn on\"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action (\"take from\") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword \"before\" to identify the correct moment before the action (\"pick up\"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action.",
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Short Videos, Few Queries",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains  $33.52\\%$  R@1 and  $64.11\\%$  R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains  $46.26\\%$  R@1 and  $71.94\\%$  R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark.",
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+    },
+    {
+        "type": "text",
+        "text": "Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of  $30.56\\% / 63.41\\%$  at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler.",
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+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablation Studies",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion.",
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+    {
+        "type": "text",
+        "text": "Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results.",
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+    {
+        "type": "text",
+        "text": "Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance.",
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+    {
+        "type": "text",
+        "text": "4.4. Efficiency Analysis",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Finally, we conduct an efficiency analysis of our method.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies  $\\sim 50\\%$  of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries.",
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+    {
+        "type": "text",
+        "text": "Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "$B_{q}$  in video-centric training. We further study how  $B_{q}$ , the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size  $|B| = 32$  for a mini-batch  $B$ , vary  $B_{q}$  between 1 and  $|B|$ , and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e.,  $B_{q} = 1$ ). Fig. 5(d) reveals that test accuracy is unaffected even with a large  $B_{q} = 32$  (i.e., a single video per mini-batch), while training time and GPU memory usage",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "18936",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/7b2e2f2420a0476bbd4d20cac505faa8c66f64acebdf9cb49634a9a2f6a4bc92.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td rowspan=\"3\">Method</td><td colspan=\"4\">TACoS (C3D)</td><td colspan=\"4\">Charades-STA (I3D)</td><td colspan=\"4\">Charades-STA (C3D)</td><td colspan=\"4\">ActivityNet-Captions (C3D)</td></tr><tr><td colspan=\"2\">R@1</td><td colspan=\"2\">R@5</td><td colspan=\"2\">R@1</td><td colspan=\"2\">R@5</td><td colspan=\"2\">R@1</td><td colspan=\"2\">R@5</td><td colspan=\"2\">R@1</td><td colspan=\"2\">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>0.3</td><td>0.5</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td></tr><tr><td>CTRL ICCV 17 [13]</td><td>18.32</td><td>13.30</td><td>36.69</td><td>25.42</td><td>-</td><td>-</td><td>-</td><td>-</td><td>23.63</td><td>8.89</td><td>58.92</td><td>29.52</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>QSPN AAAI 19 [56]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>35.60</td><td>15.80</td><td>79.40</td><td>45.40</td><td>27.70</td><td>13.60</td><td>59.20</td><td>38.30</td></tr><tr><td>SCDM NeurIPS 19 [58]</td><td>27.64</td><td>23.27</td><td>40.06</td><td>33.49</td><td>54.92</td><td>34.26</td><td>76.50</td><td>60.02</td><td>-</td><td>-</td><td>-</td><td>-</td><td>36.90</td><td>20.28</td><td>66.84</td><td>42.92</td></tr><tr><td>2D-TAN AAAI 20 [67]</td><td>45.61</td><td>35.77</td><td>69.11</td><td>57.31</td><td>56.64</td><td>36.21</td><td>89.14</td><td>61.13</td><td>41.10</td><td>23.25</td><td>81.53</td><td>48.55</td><td>46.16</td><td>29.21</td><td>78.80</td><td>60.85</td></tr><tr><td>CBP AAAI 20 [51]</td><td>27.31</td><td>24.79</td><td>43.64</td><td>37.40</td><td>-</td><td>-</td><td>-</td><td>-</td><td>36.80</td><td>18.87</td><td>70.94</td><td>50.19</td><td>35.76</td><td>17.80</td><td>65.89</td><td>46.20</td></tr><tr><td>DRN CVPR 20 [60]</td><td>-</td><td>23.17</td><td>-</td><td>33.36</td><td>53.09</td><td>31.75</td><td>89.06</td><td>60.05</td><td>45.40</td><td>26.40</td><td>88.01</td><td>55.38</td><td>45.45</td><td>24.36</td><td>77.97</td><td>50.30</td></tr><tr><td>BPNet AAAI 21 [55]</td><td>25.96</td><td>20.96</td><td>-</td><td>-</td><td>50.75</td><td>31.64</td><td>-</td><td>-</td><td>38.25</td><td>20.51</td><td>-</td><td>-</td><td>42.07</td><td>24.69</td><td>-</td><td>-</td></tr><tr><td>CPNet AAAI 21 [24]</td><td>42.61</td><td>28.29</td><td>-</td><td>-</td><td>60.27</td><td>38.74</td><td>-</td><td>-</td><td>40.32</td><td>22.47</td><td>-</td><td>-</td><td>40.56</td><td>21.63</td><td>-</td><td>-</td></tr><tr><td>SMIN CVPR 21 [50]</td><td>48.01</td><td>35.24</td><td>65.18</td><td>53.36</td><td>64.06</td><td>40.75</td><td>89.49</td><td>68.09</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.46</td><td>30.34</td><td>81.16</td><td>62.11</td></tr><tr><td>CBLN CVPR 21 [29]</td><td>38.98</td><td>27.65</td><td>73.12</td><td>46.24</td><td>61.13</td><td>38.22</td><td>90.33</td><td>61.69</td><td>47.94</td><td>28.22</td><td>88.20</td><td>57.47</td><td>48.12</td><td>27.60</td><td>79.32</td><td>63.41</td></tr><tr><td>CPN CVPR 21 [68]</td><td>47.69</td><td>36.33</td><td>-</td><td>-</td><td>51.07</td><td>31.54</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>45.10</td><td>28.10</td><td>-</td><td>-</td></tr><tr><td>DeNet CVPR 21 [70]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>59.70</td><td>38.52</td><td>91.24</td><td>66.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>43.79</td><td>-</td><td>74.13</td><td>-</td></tr><tr><td>MATN CVPR 21 [66]</td><td>48.79</td><td>37.57</td><td>67.63</td><td>57.91</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.02</td><td>31.78</td><td>78.02</td><td>63.18</td></tr><tr><td>VLG-Net ICCVW 21 [46]</td><td>45.46</td><td>34.19</td><td>70.38</td><td>56.56</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>46.32</td><td>29.82</td><td>77.15</td><td>63.33</td></tr><tr><td>APGN EMNLP 21 [28]</td><td>40.47</td><td>27.86</td><td>59.98</td><td>47.12</td><td>62.58</td><td>38.86</td><td>91.24</td><td>62.11</td><td>48.20</td><td>29.37</td><td>89.05</td><td>58.49</td><td>48.92</td><td>28.64</td><td>78.87</td><td>63.19</td></tr><tr><td>IA-Net EMNLP 21 [30]</td><td>37.91</td><td>26.27</td><td>57.62</td><td>46.39</td><td>61.29</td><td>37.91</td><td>89.78</td><td>62.04</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.57</td><td>27.95</td><td>78.99</td><td>63.12</td></tr><tr><td>RaNet EMNLP 21 [14]</td><td>43.34</td><td>33.54</td><td>67.33</td><td>55.09</td><td>60.40</td><td>39.65</td><td>89.57</td><td>64.54</td><td>-</td><td>-</td><td>-</td><td>-</td><td>45.59</td><td>28.67</td><td>75.93</td><td>62.97</td></tr><tr><td>MGSL-Net AAAI 22 [30]</td><td>42.54</td><td>32.27</td><td>63.39</td><td>50.13</td><td>63.98</td><td>41.03</td><td>93.21</td><td>63.85</td><td>-</td><td>-</td><td>-</td><td>-</td><td>51.87</td><td>31.42</td><td>82.60</td><td>66.71</td></tr><tr><td>MMN AAAI 22 [52]</td><td>39.24</td><td>26.17</td><td>62.03</td><td>47.39</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.59</td><td>29.26</td><td>79.50</td><td>64.76</td></tr><tr><td>SSRN EMNLP 22 [71]</td><td>45.10</td><td>34.33</td><td>65.26</td><td>51.85</td><td>65.59</td><td>42.65</td><td>94.76</td><td>65.48</td><td>50.39</td><td>31.42</td><td>90.68</td><td>59.94</td><td>54.49</td><td>33.15</td><td>84.72</td><td>68.48</td></tr><tr><td>G2L ICCV 23 [22]</td><td>42.74</td><td>30.95</td><td>65.83</td><td>49.86</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr><tr><td>SnAG (video-centric)</td><td>56.44</td><td>44.86</td><td>81.15</td><td>70.66</td><td>64.62</td><td>46.26</td><td>92.55</td><td>71.94</td><td>51.72</td><td>33.52</td><td>92.55</td><td>64.11</td><td>48.55</td><td>30.56</td><td>81.71</td><td>63.41</td></tr><tr><td>SnAG (query-centric)</td><td>55.01</td><td>44.51</td><td>80.68</td><td>70.13</td><td>65.13</td><td>45.91</td><td>92.80</td><td>71.75</td><td>51.10</td><td>31.77</td><td>90.22</td><td>62.15</td><td>47.55</td><td>29.65</td><td>81.55</td><td>62.21</td></tr></table>",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined.",
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+    {
+        "type": "image",
+        "img_path": "images/034aec85e20ee7f163d3d00cae17d23a683054193ab09b09a375bc8f2fad07e0.jpg",
+        "image_caption": [
+            "Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to  $50\\%$  training time,  $40\\%$  GPU memory and  $80\\%$  test time, and delivers up to  $40\\%$  faster convergence relative to query-centric training / inference. (d) Effect of  $B_{q}$  on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as  $B_{q}$  grows, while the test accuracy is unaffected."
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+    {
+        "type": "text",
+        "text": "drop by a significant  $55\\%$  and  $42\\%$ , approaching the upper bound by our analysis.",
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+    {
+        "type": "text",
+        "text": "Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time.",
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+    {
+        "type": "text",
+        "text": "Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is  $33\\%$  faster than CONE [17] ( $\\sim 18$  mins) and  $63\\%$  faster than SOONet [36] ( $\\sim 32$  mins).<sup>6</sup>",
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+    {
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+        "text": "5. Conclusion",
+        "text_level": 1,
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+        "type": "text",
+        "text": "In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding.",
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+        "text": "Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221.",
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+        "text": "$^{6}$ SOONet reports an inference time of 8.2 mins on a single A100 GPU.",
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+    {
+        "type": "text",
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2024/SnAG_ Scalable and Accurate Video Grounding/4d098779-b5a1-4518-ac90-5b419d9005ac_origin.pdf

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+# SnAG: Scalable and Accurate Video Grounding
+
+Fangzhou Mu*, Sicheng Mo*, Yin Li  
+University of Wisconsin-Madison
+
+# Abstract
+
+Temporal grounding of text descriptions in videos is a central problem in vision-language learning and video understanding. Existing methods often prioritize accuracy over scalability — they have been optimized for grounding only a few text queries within short videos, and fail to scale up to long videos with hundreds of queries. In this paper, we study the effect of cross-modal fusion on the scalability of video grounding models. Our analysis establishes late fusion as a more cost-effective fusion scheme for long-form videos with many text queries. Moreover, it leads us to a novel, video-centric sampling scheme for efficient training. Based on these findings, we present SnAG, a simple baseline for scalable and accurate video grounding. Without bells and whistles, SnAG is  $43\%$  more accurate and  $1.5 \times$  faster than CONE, a state of the art for long-form video grounding on the challenging MAD dataset, while achieving highly competitive results on short videos. Our code is available at https://github.com/fmu2/snag_release.
+
+# 1. Introduction
+
+Localizing moments within an untrimmed video based on text descriptions, also known as temporal video grounding, involves joint reasoning about visual, textual and temporal information, and thus remains a challenging problem in video understanding. Video grounding is gaining traction amid the rapid advances in vision-language learning, with a range of applications such as intelligent personal assistants, human-robot interaction, and interactive video editing.
+
+Despite recent progress, one largely overlooked aspect of video grounding is the scalability of models with respect to video duration and the number of text descriptions (i.e., queries). Previous methods (e.g., [46, 67]) are primarily designed for grounding only a few queries within short video snippets. However, the growing availability of long videos (e.g., on streaming platforms) and demand to query their rich contents introduce a paradigm shift, necessitating efficient grounding of large volumes of queries in long videos.
+
+![](images/b9a807416c0ebc2e4ad55975342dc123777b8a8af446635bc0de09fcd6219e94.jpg)  
+Figure 1. SnAG achieves the best accuracy and throughput simultaneously on the MAD dataset [45] for long-form video grounding.
+
+On latest long-form video grounding benchmarks [16, 45], these methods struggle to scale up due to their high computational cost, and suffer major performance degradation.
+
+In this paper, we take a principled approach to studying the problem of scalable video grounding, focusing on the design of cross-modal fusion—a key model component that combines visual and textual information. Specifically, we present an analysis that connects the computational cost of video grounding models to their fusion schemes. Our analysis and empirical results challenge the widely adopted early fusion, showing that late fusion scales better in inference by amortizing the cost of long video processing among text queries. Importantly, this insight further motivates the design of a novel, video-centric sampling scheme for scalable training, without compromising grounding accuracy.
+
+Following these findings, we present SnAG, a scalable and accurate model for long-form video grounding. SnAG features a minimalist, late-fusion design for scalable inference, while supporting video-centric sampling for scalable training. Notwithstanding its simplicity, SnAG achieves superior results across all benchmarks designed for long-form video grounding. Without bells and whistles, SnAG attains  $13.75\%$  R@5, tIoU=0.5 on MAD [45] with an inference speed of 45.3 queries per second on a P100 GPU (Fig. 1),  $43\%$  more accurate and  $1.5\times$  faster than the concurrent method of CONE [17]. In the meantime, SnAG is highly competitive on short-video benchmarks. It achieves  $46.26\%$  R@1, tIoU=0.7 on Charades-STA [43], outperforming the
+
+previous state of the art (SSRN [71]) by 3.61 absolute percentage points while being simpler in model design.
+
+Contributions. (1) We present one of the first studies to understand the effect of fusion schemes on the computational cost of video grounding. (2) Our analysis offers new insights and leads to a new training scheme for scalable video grounding. (3) Based on our findings, we further deliver a simple model that attains superior results across major benchmarks for long-form video grounding while achieving significant efficiency gains in both training and inference.
+
+# 2. Related Work
+
+Video grounding. Previous works on video grounding can be categorized based on whether proposals are generated as moment candidates (two-stage vs. single-stage), and how text queries inform action localization (cross-modal fusion).
+
+Two-stage methods first generate temporal segments as proposals, then score their "actionness" and optionally refine their boundaries. Early works [1, 13] densely sample proposals using sliding windows and score them independently. One line of work [8, 28, 54-56] subsequently conditions proposal generation on sentence queries and/or video context to avoid dense sampling. By contrast, another line of work [14, 46, 50, 66, 67] takes the opposite path of enumerating all segments, yet organizes them in a 2D adjacency map to reason about their relations.
+
+Single-stage methods localize moments in a single shot without using proposals, and thus are often more efficient than two-stage methods. Some models decode moment boundaries from global features [23, 24, 33, 59, 70] or learnable queries [21, 25, 53]. Others densely predict onset and offset probabilities [15, 29, 34, 41, 63-65, 68], or classify and refine pre-set anchors [6, 30, 51, 58, 62] at every moment. Most relevant to our work are models that represent moment candidates as points [7, 11, 27, 31, 60]. Analogous to point-based object detectors [47], they classify every point in time and regress moment boundaries relative to the points. Despite their simplicity and efficiency, the performance of single-stage models lags behind two-stage models on standard benchmarks made up of short videos.
+
+Cross-modal fusion combines video and text information for video grounding. Early models [1, 13] fuse video and text representations right before final prediction. This simple, late-fusion approach is abandoned by subsequent models, which turn to early fusion (e.g., [56, 60, 62, 67]) with sophisticated model design (e.g., LSTM [6, 15, 29, 51, 56, 65], GCN [7, 27, 46], memory bank [8, 27]), feature hierarchies [14, 33, 50], losses [23, 34, 56, 66], and inference procedures [68, 70]. Early fusion is believed to strengthen cross-modal reasoning, albeit at a price of model complexity. Recent Transformer-based models [3, 21, 53, 66] inherit this early-fusion design; video features and text embeddings
+
+are concatenated at input, and attention-based feature fusion is carried out throughout the model.
+
+Our method demonstrates a single-stage Transformer model with a simple late fusion mechanism based on crossattention. Late fusion allows us to amortize the cost of video processing across many sentence queries, resulting in scalable training and inference on long-form videos. Without bells and whistles, our model outperforms all prior methods on long-video benchmarks, and attains competitive performance on standard, short-video benchmarks.
+
+Long-form video grounding. Recent efforts [16, 45] put forth new challenges for sentence grounding in long videos. Previous methods tailored for short videos [46, 64, 67] fall short on these benchmarks. They have no access to long-range video context, require dense sliding window inference, and yield unsatisfactory results. Concurrent works [17, 36] present multi-stage approaches with sophisticated pre-processing, ranking and training procedures for efficient long-form video grounding. However, their efficiency stems from the restrictive assumption that moments are covered by short windows. By contrast, SnAG offers a simple, single-stage solution with superior accuracy, without making assumptions about moment duration.
+
+Localizing moments in videos. Closely related to video grounding, temporal action localization (e.g., [32, 42, 44]) aims to identify moments of actions from within a closed set of action categories. Solutions to the two tasks often evolve in tandem and share remarkably similar model design. SnAG is inspired by our prior work [61], yet extends its design for the more challenging task of video grounding, with the goal of scaling up video grounding for long videos.
+
+# 3. Scaling Up Video Grounding
+
+Our goal is to scale up video grounding for long-form videos with many queries. Denote an input video  $\mathbf{V}$  as a time-indexed sequence  $[\mathbf{v}_t]_{t=1}^T = [\mathbf{v}_1, \mathbf{v}_2, \dots, \mathbf{v}_T]$ , where  $\mathbf{v}_t$  represents a short video clip centered at time  $t$ .<sup>1</sup>  $\mathbf{V}$  is paired with  $N$  sentence queries  $\{\mathrm{Q}_j\}_{j=1}^N$ , each describing a moment  $\mathbf{y}_j = (s_j, e_j)$  in the video.
+
+Long-form video grounding is characterized by a great number of time steps  $T$  (e.g., tens of thousands) and text queries  $N$  (hundreds) for an input video  $\mathbf{V}$ . With a large  $T$ , it is no longer feasible to feed the full video  $\mathbf{V}$  into a model, and thus more viable to consider a sliding window setting. Specifically, a video  $\mathbf{V}$  is further partitioned into a set of  $M$  snippets  $\{\mathbf{V}_{i=1}^{M}\}$ , each  $\mathbf{V}_{i} = [\mathbf{v}_{t}]_{t=t_{i}}^{t_{i} + T_{w}}$  taken from a local time window of size  $T_{w}$  that may overlap with others. We consider the learning of a function  $\mathcal{F}$ , realized in a deep
+
+![](images/4803639b0a1f16039b839ad918d58e34425082f99caff1fafa9a2122313a6aae.jpg)  
+Figure 2. (a) Cross-modal fusion is key to a video grounding model  $\mathcal{F}$ . Models using early fusion jointly encode video and sentence query. SnAG revisits late fusion for scalable video grounding by decoupling expensive video encoding and inexpensive query encoding. (b) Video-centric model evaluation. With late fusion, the output of video encoder can be cached and re-used by queries of the same video in both training and inference. (c) Mini-batch sampling in training. Previous methods adopt query-centric sampling (query  $\rightarrow$  video) whereas SnAG resorts to video-centric sampling (video  $\rightarrow$  many queries) for efficient training. (d) Model overview. SnAG is a simple instantiation of late fusion and video-centric training for video grounding. It separately encodes a video and its queries using Transformers, applies simple cross-attention for cross-modal fusion, and decodes moments represented as points using lightweight convolutional heads.
+
+![](images/24f620b34609b9f3f19062804931b668980e1121d4689609c7c691dd26f796f2.jpg)
+
+![](images/2ae59873afb84ef2c5185ee19976e539c33b58e59f038c76a8a3cd9d0b114779.jpg)
+
+network, to predict the start time  $s_j$  and end time  $e_j$  of the moment  $\mathbf{y}_j$  given a snippet  $\mathbf{V}_i$  and a query  $\mathrm{Q}_j$ .
+
+# 3.1. Background: Cross-Modal Fusion
+
+We review cross-modal fusion - a key design choice of  $\mathcal{F}$  and define the notation used for the rest of the paper.
+
+Early fusion. A straightforward design is to fuse information from a video snippet  $\mathbf{V}_i$  and a text query  $\mathrm{Q}_j$  at input (Fig. 2(a)). This early fusion strategy is widely adopted in prior works [21, 53, 60, 62, 66, 67], and can be written as
+
+$$
+\mathcal {F} _ {E} \left(\mathbf {V} _ {i}, \mathrm {Q} _ {j}\right) \mapsto \mathbf {y} _ {j}, \tag {1}
+$$
+
+where  $\mapsto$  defines any necessary post-processing of the model outputs (e.g., re-scaling, non-maximum suppression) in order to decode the moment  $\mathbf{y}_j$ .
+
+Late fusion. Another possible design is to first embed the video snippet  $\mathbf{V}_i$  and text query  $\mathrm{Q}_j$ , then fuse their features for grounding (Fig. 2(a)). This late fusion strategy follows
+
+$$
+\mathcal {F} _ {L} \left(g \left(\mathbf {V} _ {i}\right), h \left(\mathrm {Q} _ {j}\right)\right) \mapsto \mathbf {y} _ {j}, \tag {2}
+$$
+
+where  $g(\cdot)$  is the video encoder and  $h(\cdot)$  the text encoder. With slight abuse of the symbols,  $\mathcal{F}_L$  here denotes the rest part of the grounding model, including feature fusion. The key is to keep  $\mathcal{F}_L$  lightweight, i.e., its cost should be a minor portion in comparison to the rest of the model.
+
+Design choice. The conventional wisdom favors the design of early fusion for video grounding. Early fusion is believed to offer better interactions between visual and textual features, resulting in strong empirical results. In what follows, we analyze the computational cost of early and late fusion
+
+during inference and training, and show that proper design of late fusion allows significantly improved scalability in video duration  $(M)$  and number of text queries  $(N)$ .
+
+# 3.2. Scalable Inference
+
+We start by analyzing the computational cost of early vs. late fusion in inference. Denote the computational cost of a function by  $\mathcal{C}(\cdot)$ . For example,  $\mathcal{C}(g)$  is the cost of the video encoder  $g(\cdot)$ , and  $\mathcal{C}(h)$  the cost of the text encoder  $h(\cdot)$ .
+
+Computational cost. We make two key observations regarding the computational cost of a video grounding model: (a) a lightweight  $\mathcal{F}_L$  is used for late fusion, thus  $\mathcal{C}(\mathcal{F}_L) \ll \mathcal{C}(g) + \mathcal{C}(h)$ ; and (b) the video encoder  $g(\cdot)$  has a much higher cost than the text encoder, thus  $\mathcal{C}(g) \gg \mathcal{C}(h)$ .
+
+The first observation stems from the design of late fusion. To justify the second observation, it is important to notice that  $\mathcal{C}(g)$  scales w.r.t. the length of input video snippet (i.e., the local window size  $T_w$ ), whereas  $\mathcal{C}(h)$  remains constant due to limited sequence length of text queries. For example, a realization of  $g(\cdot)$  using a vanilla Transformer has a complexity of  $\mathcal{O}(T_w^2)$ . Thus, using a larger local window size naturally leads to  $\mathcal{C}(g) \gg \mathcal{C}(h)$ .
+
+Cost analysis: early vs. late fusion. Evaluating an early-fusion model on a video with  $M$  snippets and  $N$  queries has a cost of  $MN\mathcal{C}(\mathcal{F}_E)$ , whereas late fusion has a cost of  $MN\mathcal{C}(\mathcal{F}_L) + MC(g) + NC(h)$ . This is because an early-fusion model has to compare each snippet to every query, yet late fusion allows re-using video features for all queries of the video (i.e., video-centric evaluation, see Fig. 2(b)).
+
+Let us assume that the cost of both models can be controlled by setting  $\mathcal{C}(\mathcal{F}_E) = \mathcal{C}(\mathcal{F}_L) + \mathcal{C}(g) + \mathcal{C}(h)$ , i.e., eval
+
+uating either model on a pair of video snippet and sentence query has the same cost (post-processing excluded). With  $\mathcal{C}(\mathcal{F}_L) = \alpha (\mathcal{C}(g) + \mathcal{C}(h))$  for some small  $\alpha$ , the ratio between the cost of early and late fusion in inference is
+
+$$
+\begin{array}{l} \mathbf {R} _ {\text {i n f}} = \frac {\mathcal {C} (\text {i n f e r e n c e w i t h e a r l y f u s i o n})}{\mathcal {C} (\text {i n f e r e n c e w i t h l a t e f u s i o n})} (3) \\ = \frac {M N \mathcal {C} \left(\mathcal {F} _ {L}\right) + M N \mathcal {C} (g) + M N \mathcal {C} (h)}{M N \mathcal {C} \left(\mathcal {F} _ {L}\right) + M \mathcal {C} (g) + N \mathcal {C} (h)} (4) \\ = \frac {M N (1 + \alpha)}{M N \alpha + M \mathbf {R} _ {g / (g + h)} + N (1 - \mathbf {R} _ {g / (g + h)})} (5) \\ \approx \frac {1 + \alpha}{\frac {1}{N} + \alpha} \rightarrow \left\{\begin{array}{l l}N,&\alpha \rightarrow 0\\1 + \frac {1}{\alpha},&N \rightarrow \infty\end{array}, \right. (6) \\ \end{array}
+$$
+
+where  $\mathbf{R}_{g / (g + h)} = \mathcal{C}(g) / (\mathcal{C}(g) + \mathcal{C}(h))$ , and the approximation in Eq. 6 is a result of  $\mathbf{R}_{g / (g + h)} \approx 1$  with  $\mathcal{C}(g) \gg \mathcal{C}(h)$ . Eq. 6 reveals that early fusion is  $N$  times the cost of late fusion as snippet length grows ( $\alpha \to 0$ ), and is particularly inefficient for videos with many queries ( $N \to \infty$ ).
+
+# 3.3. Scalable Training
+
+We now show that late fusion further unlocks a novel training scheme that scales well for long-form video grounding.
+
+Training and mini-batch sampling. Given a set of paired videos, text queries, and their moments  $\{\mathbf{V}^{(k)},\mathbf{Q}^{(k)},\mathbf{y}^{(k)}\}$ , training a model  $\mathcal{F}$  amounts to minimizing a loss function  $\mathcal{L}$  over mini-batches  $B$  sampled from the dataset:
+
+$$
+\Sigma_ {(k, i, j) \in B} \mathcal {L} \left(\mathcal {F} \left(\mathbf {V} _ {i} ^ {(k)}, \mathrm {Q} _ {j} ^ {(k)}\right), \mathbf {y} _ {j} ^ {(k)}\right). \tag {7}
+$$
+
+A key design largely overlooked in video grounding is the mini-batch sampling scheme during training. With multiple queries associated with a video snippet, a combination of late fusion and proper sampling scheme allows us to reuse video representations in training as is done in inference.
+
+Query-centric sampling. Virtually all prior works sample mini-batches uniformly at random from all pairs of valid video snippets and text queries. $^{2}$  This can be interpreted as ancestral sampling: first draw a text query (and its moment), then select a video snippet covering the moment:
+
+$$
+\mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})} \sim U \left(\left\{\left(\mathrm {Q} _ {j} ^ {(k)}, \mathbf {y} _ {j} ^ {(k)}\right) \right\} _ {j \times k}\right), \tag {8}
+$$
+
+$$
+\mathbf {V} _ {i ^ {\prime}} ^ {(k ^ {\prime})} \sim U \left(\left\{\left(\mathbf {V} _ {i} ^ {(k ^ {\prime})}, \mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})}\right) _ {+} \right\}\right),
+$$
+
+where  $U(\cdot)$  denotes a discrete uniform distribution and  $\{(\mathbf{V}_i^{(k')},\mathbf{Q}_j^{(k')},\mathbf{y}_{j'}^{(k')})_{+}\}$  is the union of all valid triplets: a moment  $\mathbf{y}_{j'}^{(k')}$  of a text query  $\mathbf{Q}_{j'}^{(k')}$  in a video snippet  $\mathbf{V}_i^{(k')}$ .
+
+This sampling process is repeated  $|B|$  times to construct a mini-batch, with  $|B|$  the batch size. With a large
+
+dataset, the resulting mini-batch will contain  $|B|$  snippet-query pairs, each likely from a different video.
+
+Video-centric sampling. To speed up the training of late fusion models, we propose video-centric sampling that considers every video snippet  $\mathbf{V}_i^{(k)}$  as a sample. Specifically, we first draw a video based on its importance score, then sample a snippet within the video, and finally select multiple text queries associated with the snippet. This is defined as the following ancestral sampling:
+
+$$
+k ^ {\prime} \sim P (k) = \frac {M _ {+} ^ {(k)}}{\Sigma_ {k} M _ {+} ^ {(k)}} \quad i ^ {\prime} \sim P (i; k ^ {\prime}) = \frac {N _ {i} ^ {\left(k ^ {\prime}\right)}}{\Sigma_ {k} N _ {i} ^ {\left(k ^ {\prime}\right)}} \tag {9}
+$$
+
+$$
+\left\{\mathrm {Q} _ {j ^ {\prime}} ^ {(k ^ {\prime})}, \mathbf {y} _ {j ^ {\prime}} ^ {(k ^ {\prime})} \right\} ^ {B _ {q}} \sim U \left(\left\{\left(\mathbf {V} _ {i ^ {\prime}} ^ {(k ^ {\prime})}, \mathrm {Q} _ {j} ^ {(k ^ {\prime})}, \mathbf {y} _ {j} ^ {(k ^ {\prime})}\right) _ {+} \right\}\right),
+$$
+
+where  $M_{+}^{(k)}$  denotes the number of valid snippets in a video  $\mathbf{V}^{(k)}$ , and  $N_{i}^{(k^{\prime})}$  the number of queries in a snippet  $\mathbf{V}_{i}^{(k^{\prime})}$ . Importantly, a total of  $B_{q}$  queries are drawn for the selected video snippet  $\mathbf{V}_{i^{\prime}}^{(k^{\prime})}$ .
+
+This sampling process is repeated  $|B| / B_q$  times for a mini-batch, leading to  $|B| / B_q$  video snippets, each likely from a different video yet with multiple  $(B_q)$  text queries. This mini-batch thus allows us to re-use the video representations for the sampled snippets.
+
+Cost analysis: query-centric vs. video-centric sampling. Fig. 2(c) illustrates the key difference between query-centric and video-centric sampling. Similar to our analysis in Section 3.2, it is easy to show that late fusion combined with video-centric training enables substantial speedup for long snippets  $(\alpha \rightarrow 0)$  and large  $B_{q}$ :
+
+$$
+\begin{array}{l} \mathbf {R} _ {\text {t r a i n}} = \frac {\mathcal {C} (\text {l a t e f u s i o n} + \text {v i d e o - c e n t r i c t r a i n i n g})}{\mathcal {C} (\text {l a t e f u s i o n} + \text {q u e y - c e n t r i c t r a i n i n g})} (10) \\ \approx \frac {1 + \alpha}{\frac {1}{B _ {q}} + \alpha} \rightarrow \left\{\begin{array}{l l}B _ {q},&\alpha \rightarrow 0\\1 + \frac {1}{\alpha},&B _ {q} \rightarrow \infty\end{array}. \right. (11) \\ \end{array}
+$$
+
+# 3.4. Scalable Video Grounding: An Instantiation
+
+We now present an instantiation with late fusion and video-centric training for scalable video grounding. Our instantiation, dubbed SnAG, is shown in Fig. 2(d). SnAG is a single-stage Transformer model where every time step represents a moment candidate. It combines (a) a multi-scale Transformer-based video encoder; (b) a Transformer-based text encoder; (c) cross-attentions for late fusion; and (d) convolutional heads for moment decoding.
+
+Video encoder  $g$ . We use the ActionFormer backbone [61] as our video encoder, given its superior performance on the closely related task of temporal action localization. It transforms input video features into a multi-scale representation  $[\mathbf{Z}^{(l)}]_{l=1}^{L} = [\mathbf{Z}^{(1)}, \mathbf{Z}^{(2)}, \dots, \mathbf{Z}^{(L)}]$  using Transformer layers with local self-attentions [9]. We refer readers to the original paper [61] for more details on model architecture.
+
+Text encoder  $h$ . Our text encoder is a vanilla Transformer. It takes a query Q with  $K$  tokens  $[\mathbf{q}_1, \dots, \mathbf{q}_K]$  and outputs their embeddings  $\mathbf{E} = [\mathbf{e}_1, \dots, \mathbf{e}_K]$ . This computation is light compared to video encoding as  $K \ll T_w$  for long videos.
+
+Cross-modal late fusion  $\mathcal{F}_L$ . Our model uses a simple variant of cross-attention for fusion. Specifically, it modulates  $[\mathbf{Z}^{(l)}]_{l=1}^L$  with an affine transformation given by  $\mathbf{E}$ :
+
+$$
+\begin{array}{l} (\mathbf {W}, \mathbf {B}) ^ {(l)} = \operatorname {M C A} (\operatorname {L N} (\mathbf {Z} ^ {(l)}), \operatorname {L N} (\mathbf {E})), \\ \tilde {\mathbf {Z}} ^ {(l)} = \mathbf {W} ^ {(l)} \odot \mathbf {Z} ^ {(l)} + \mathbf {B} ^ {(l)}, \tag {12} \\ \mathbf {X} ^ {(l)} = \tilde {\mathbf {c}} \odot \operatorname {M L P} (\operatorname {L N} (\bar {\mathbf {Z}} ^ {(l)})) + \bar {\mathbf {Z}} ^ {(l)}, \\ \end{array}
+$$
+
+where LN is Layer Normalization [2], MLP is Multi-Layer Perceptron, and MCA is Multi-head Cross-Attention [49], whose output is split into affine weights  $\mathbf{W}^{(l)}$  and biases  $\mathbf{B}^{(l)}$ .  $\tilde{\mathbf{c}}$  are learnable per-channel scales, and  $\mathbf{X}^{(l)}$  the modulated video representations prior to moment decoding.
+
+Moment decoding. After fusion, our model decodes each time step into a moment candidate, similar to previous video grounding models [7, 27, 31, 60]. Briefly, a classification head predicts a score  $p_t^{(l)}$  for all  $\mathbf{x}_t^{(l)}$  within  $[\mathbf{X}^{(l)}]_{l=1}^L$ , and a regression head predicts the normalized distances from  $t$  to the moment boundaries  $(d_t^s, d_t^e)$  if  $\mathbf{x}_t^{(l)}$  is classified positive. Both heads are lightweight, each comprising three 1D convolutions. The decoded moment  $\hat{\mathbf{y}} = (\hat{s}, \hat{e})$  is given by
+
+$$
+(t, l) = \underset {t, l} {\arg \max } p _ {t} ^ {(l)}, \tag {13}
+$$
+
+$$
+\hat {s} = 2 ^ {l - 1} \cdot (t - d _ {t} ^ {s}), \quad \hat {e} = 2 ^ {l - 1} \cdot (t + d _ {t} ^ {e}).
+$$
+
+At inference time, we further apply Soft-NMS [4] to merge overlapping moment predictions.
+
+Training and loss function. We use video-centric training as described in Section 3.3. The loss function for a pair of video snippet and text query is the sum of two terms: a Focal loss [26]  $\mathcal{L}_{cls}$  for moment classification and a Distance-IoU loss [69]  $\mathcal{L}_{reg}$  defined on positive time steps for distance regression. Formally,
+
+$$
+\mathcal {L} = \frac {1}{C} \left(\mathcal {L} _ {c l s} + \lambda_ {r e g} \mathbb {1} _ {t} ^ {(l)} \mathcal {L} _ {r e g}\right), \tag {14}
+$$
+
+where  $\mathbb{1}_t^{(l)}$  is an indicator function that evaluates to one on positive time steps,  $C = \sum_{t,l}\mathbb{1}_t^{(l)}$  is the total number of positive samples within the snippet, and  $\lambda_{reg}$  balances the two loss terms. Center sampling [61] is used for selecting positive time steps around the center of a target moment.
+
+# 4. Experiments
+
+Our main experiments include extensive comparisons of SnAG to strong baselines on five challenging benchmarks for video grounding. We further provide ablations on cross-modal fusion and analyze the efficiency of SnAG in both training and inference. More results are in the supplement.
+
+![](images/88f4a85d6f7b967b7228f9f976dd1b4879b479a7ffcf06079a78ac26f9738e87.jpg)  
+Figure 3. Visualization of dataset statistics. Circle radius is in proportion to average number of queries per video. Long-video benchmarks (Ego4D-NLQ, MAD and TACoS) consist of longer videos with more queries and exhibit low moment coverage compared to short-video benchmarks (ANet-Captions and Charades).
+
+<table><tr><td rowspan="2"></td><td rowspan="2">Model</td><td colspan="3">R@1</td><td colspan="3">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>Avg</td><td>0.3</td><td>0.5</td><td>Avg</td></tr><tr><td rowspan="6">SF + BERT</td><td>2D-TAN [67]</td><td>5.04</td><td>2.02</td><td>3.53</td><td>12.89</td><td>5.88</td><td>9.39</td></tr><tr><td>VSLNet [64]</td><td>5.45</td><td>3.12</td><td>4.29</td><td>10.74</td><td>6.63</td><td>8.69</td></tr><tr><td>CONE [17]</td><td>10.40</td><td>5.03</td><td>7.72</td><td>22.74</td><td>11.87</td><td>17.31</td></tr><tr><td>SOONet [36]</td><td>8.00</td><td>3.76</td><td>5.88</td><td>22.40</td><td>11.09</td><td>16.75</td></tr><tr><td>SnAG (video-centric)</td><td>9.83</td><td>6.83</td><td>8.33</td><td>27.93</td><td>19.27</td><td>23.60</td></tr><tr><td>SnAG (query-centric)</td><td>10.43</td><td>7.15</td><td>8.79</td><td>27.59</td><td>19.33</td><td>23.46</td></tr><tr><td rowspan="4">EgoVLP</td><td>VSLNet [64]</td><td>10.84</td><td>6.81</td><td>8.83</td><td>18.84</td><td>13.45</td><td>16.15</td></tr><tr><td>CONE [17]</td><td>14.15</td><td>8.18</td><td>11.17</td><td>30.33</td><td>18.02</td><td>24.18</td></tr><tr><td>SnAG (video-centric)</td><td>15.72</td><td>10.78</td><td>13.25</td><td>38.39</td><td>27.44</td><td>32.92</td></tr><tr><td>SnAG (query-centric)</td><td>15.87</td><td>11.26</td><td>13.57</td><td>38.26</td><td>27.16</td><td>32.71</td></tr></table>
+
+Table 1. Results on Ego4D-NLQ. SnAG outperforms all baselines. Best results are in bold and second best underlined.
+
+Datasets. We categorize five benchmark datasets into two groups based on their video and query statistics (Fig. 3).
+
+Long videos, many queries. Ego4D-NLQ [16] is a large collection of egocentric videos on daily human activities. The videos are 3.5 to 20 minutes long with an average of 11.6 queries. MAD [45] contains 1.2K hours of movies with 384K queries transcribed from audio description. The videos are 47 to 202 minutes long. TACoS [40] is a conventional benchmark with 10.1 hours of cooking videos, with an average of 143.5 queries per video. These datasets expose the scalability challenges that motivate our work and thus are the main focus of our experiments.
+
+Short videos, few queries. Charades-STA [43] is an action recognition dataset later annotated for video grounding [13]. The videos are  $\sim 30$  seconds long with  $\sim 2.4$  queries per video. ActivityNet-Captions [20] was collected for dense video captioning and later repurposed for video grounding. The videos are two minutes long on average with a small set of  $\sim 3.65$  queries. Several works [35, 57] advise against using these datasets as benchmarks for the
+
+<table><tr><td rowspan="2">Model</td><td colspan="3">R@1</td><td colspan="3">R@5</td><td colspan="3">R@10</td><td colspan="3">R@50</td></tr><tr><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td><td>0.1</td><td>0.3</td><td>0.5</td></tr><tr><td>CLIP [39]</td><td>6.57</td><td>3.13</td><td>1.39</td><td>15.05</td><td>9.85</td><td>5.44</td><td>20.26</td><td>14.13</td><td>8.38</td><td>37.92</td><td>28.71</td><td>18.80</td></tr><tr><td>VLG-Net [46]</td><td>3.64</td><td>2.76</td><td>1.65</td><td>11.66</td><td>9.31</td><td>5.99</td><td>17.39</td><td>14.56</td><td>9.77</td><td>39.78</td><td>34.27</td><td>24.93</td></tr><tr><td>Moment-DETR [21]</td><td>0.31</td><td>0.24</td><td>0.16</td><td>1.52</td><td>1.14</td><td>0.28</td><td>2.79</td><td>2.06</td><td>1.20</td><td>11.08</td><td>7.97</td><td>4.71</td></tr><tr><td>CONE [17]</td><td>8.90</td><td>6.87</td><td>4.10</td><td>20.51</td><td>16.11</td><td>9.59</td><td>27.20</td><td>21.53</td><td>12.82</td><td>43.36</td><td>34.73</td><td>20.56</td></tr><tr><td>SOONet [36]</td><td>11.26</td><td>9.00</td><td>5.32</td><td>23.21</td><td>19.64</td><td>13.14</td><td>30.36</td><td>26.00</td><td>17.84</td><td>50.32</td><td>44.78</td><td>32.59</td></tr><tr><td>SnAG (video-centric)</td><td>10.28</td><td>8.46</td><td>5.55</td><td>24.42</td><td>20.60</td><td>13.75</td><td>32.23</td><td>27.50</td><td>19.00</td><td>52.28</td><td>46.68</td><td>35.24</td></tr><tr><td>SnAG (query-centric)</td><td>10.18</td><td>8.37</td><td>5.44</td><td>24.30</td><td>20.35</td><td>13.51</td><td>32.05</td><td>27.25</td><td>18.75</td><td>52.05</td><td>46.53</td><td>34.83</td></tr></table>
+
+Table 2. Results on MAD. SnAG outperforms all baselines. Best results are in bold and second best underlined.
+
+![](images/4f7ff842d2c213510aaad27a0c0318e2f50342257769de09c20c3dd7e2749bba.jpg)  
+Figure 4. Visualization of moment predictions. SnAG can (a) comprehend complex text queries with multiple objects and actions; (b) reason about temporal ordering of events.
+
+temporal biases in their moment annotations. Nevertheless, we report results on these datasets for completeness.
+
+Baselines. On TACoS, Charades and ANet-Captions, we compare to strong baselines including two-stage [28, 55, 56] and single-stage [30, 50, 70] models with various fusion operations (LSTM [29, 51], GCN [27, 46], co-attention [24, 68], etc.). On Ego4D and MAD, we compare to their official baselines (2D-TAN [67] and VSLNet [64] for Ego4D, CLIP [39] and VLG-Net [46] for MAD) as well as the concurrent method of CONE [17] and SOONet [36] that similarly address scalable video grounding. We discuss additional baselines in the supplement.
+
+Evaluation metric. We report  $\mathrm{Recall}@\mathbf{k}$  at various temporal intersection-over-union threshold  $\theta$  ( $\mathbf{R}@\mathbf{k}$ , tIoU= $\theta$ ) for all datasets. It measures the percentage of sentence queries with at least one of the top- $k$  moment predictions whose temporal overlap with the ground-truth moment exceeds  $\theta$ .
+
+# 4.1. Long Videos, Many Queries
+
+Experiment setup. For Ego4D, We consider (1) SlowFast [12] video features with BERT [10] text features, and (2) EgoVLP [38] video and text features. We train on the train split and report R@{1, 5}, tIoU={0.3, 0.5} on the val split. For MAD, we use CLIP [39] features for both videos and text. We train on the train split and report R@{1, 5, 10, 50}, tIoU={0.1, 0.3, 0.5} on the test split. For TACoS, we use C3D video features [48] and GloVe [37] for
+
+sentence embeddings. We train on the train split and report  $\mathrm{R}@\{1,5\}$ , tIoU=\{0.5, 0.7\} on the test split. We report results using both video-centric and query-centric training on all datasets.
+
+Results on Ego4D-NLQ (Table 1). SnAG sets the new state of the art, achieving mean R@1 / R@5 scores of  $8.79\% / 23.60\%$  with SlowFast/BERT features, and  $13.57\% / 32.92\%$  with EgoVLP features, doubling or even tripling the results of the official baselines [64, 67]. Compared to the strong baselines of CONE [17] and SOONet [36], SnAG improves mean R@1 and R@5 respectively by more than 1.05 and 6.29 absolute percentage points without taking advantage of external features. Further, SnAG demonstrates a larger performance gain on the more stringent tIoU threshold of 0.5, indicating more precise moment localization.
+
+Results on MAD (Table 2). SnAG sets new records on the challenging MAD dataset. It improves over CLIP [39] and VLG-Net [46] on mean R@1 / R@5 at tIoU=0.5 by 3.90 / 7.76 absolute percentage points. In the meantime, it outperforms CONE [17] and SOONet [36], with larger gain for more stringent tIoU thresholds. Further, SnAG achieves stronger results as input snippet length increases, reaching the best accuracy with  $T_{w} = 16384$  (Supplement Fig. A). This scaling behavior highlights the strength of our scalable model design for long-form video grounding.
+
+Results on TACoS (Table 4 (left)). SnAG achieves an R@1 / R@5 of  $44.86\%$  /  $70.66\%$  at tIoU=0.5, outperforming the strongest baseline of MATN [66] by a significant margin  $(+7.5\% \mathrm{R} @ 1, +12.1\% \mathrm{R} @ 5)$ . This confirms that our simple single-stage design with late fusion is a strong alternative to multi-stage models with sophisticated fusion mechanisms. Importantly, our scalable design enables learning from full-resolution video features, whereas the baselines often aggressively reduce feature resolution to contain their training and inference cost on long-form videos. We hypothesize that full-resolution video features capture detailed event dynamics and are key to the strong performance of SnAG.
+
+Result visualization. We visualize predictions of SnAG and the baselines on TACoS and Ego4D-NLQ videos. In
+
+<table><tr><td rowspan="2">Model</td><td colspan="2">R@1</td><td colspan="2">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>0.3</td><td>0.5</td></tr><tr><td colspan="5">(a) Fusion stage (early vs. late fusion)</td></tr><tr><td>No fusion</td><td>10.85</td><td>7.85</td><td>46.46</td><td>31.19</td></tr><tr><td>SnAG-E</td><td>53.34</td><td>44.01</td><td>79.56</td><td>69.41</td></tr><tr><td>SnAG-EL</td><td>54.84</td><td>44.54</td><td>81.13</td><td>70.11</td></tr><tr><td>SnAG-M</td><td>51.41</td><td>40.79</td><td>77.56</td><td>65.71</td></tr><tr><td>SnAG (ours)</td><td>55.14</td><td>44.94</td><td>81.10</td><td>70.66</td></tr><tr><td colspan="5">(b) Fusion operation (global vs. token-wise)</td></tr><tr><td>Cat</td><td>49.39</td><td>39.24</td><td>77.31</td><td>65.36</td></tr><tr><td>Add</td><td>51.91</td><td>41.81</td><td>77.98</td><td>66.51</td></tr><tr><td>Scale</td><td>55.01</td><td>43.96</td><td>80.63</td><td>70.11</td></tr><tr><td>Add + Scale</td><td>53.36</td><td>43.09</td><td>80.43</td><td>69.58</td></tr><tr><td>XAttn</td><td>54.84</td><td>45.06</td><td>79.96</td><td>70.08</td></tr><tr><td>XAttn-affine (ours)</td><td>55.14</td><td>44.94</td><td>81.10</td><td>70.66</td></tr></table>
+
+Table 3. Ablations results on TACoS. (a) Late fusion yields comparable results to early fusion (E, EL, M); (b) Fusion with tokenwise sentence embeddings (XAttn) produces better results than fusion with global sentence embeddings (Cat, Add, Scale).
+
+Fig. 4(a), a long query describes the complex interplay between two objects (pan and stove) and three actions ("take from", "place on", and "turn on"). VLG-Net [46] recognized both objects yet none of the actions, while 2D-TAN [67] identified one action ("take from") but at the same time missed one object (pan). By contrast, SnAG followed the query semantics and produced accurate localization. The other query in Fig. 4(b) tests the understanding of temporal context. SnAG leveraged the keyword "before" to identify the correct moment before the action ("pick up"), whereas VSLNet [64] only attended to the object (can), thus mistakenly predicting a moment after the action.
+
+# 4.2. Short Videos, Few Queries
+
+Experiment setup. We extract video features using both C3D [48] (pretrained on Sports-1M [18]) and I3D [5] (pretrained on Kinetics [19]) for Charades-STA, and use the official C3D features for ActivityNet-Captions. We use GloVe word embeddings [37] to represent sentence queries for both datasets. We train on their respective train splits, report R@{1, 5}, tIoU={0.5, 0.7} on the test split of Charades-STA, and R@{1, 5}, tIoU={0.3, 0.5} on the val_2 split of ActivityNet-Captions. Following standard practice, we resize all video features to a uniform length of 256.
+
+Results on Charades-STA (Table 4 (middle)). SnAG outperforms all previous methods by a wide margin. It obtains  $33.52\%$  R@1 and  $64.11\%$  R@5 at tIoU=0.7 with C3D features, 2.10 and 4.52 absolute percentage points higher than the latest SSRN [71] baseline. It further attains  $46.26\%$  R@1 and  $71.94\%$  R@5 at tIoU=0.7 with I3D features, setting new state of the art on this competitive benchmark.
+
+Results on ActivityNet-Captions (Table 4 (right)). SnAG achieves competitive results, reaching an R@1 / R@5 score of  $30.56\% / 63.41\%$  at tIoU=0.7. It is only outperformed by a few latest models [22, 27, 71] while being much simpler.
+
+# 4.3. Ablation Studies
+
+We conduct extensive ablations on TACoS to study key design choices for cross-modal fusion.
+
+Early vs. late fusion. Does late fusion enable better scalability at the expense of accuracy? We study three variants of SnAG with common early-fusion designs: (1) SnAG-E with fusion before the pyramid; (2) SnAG-EL with fusion before and after the pyramid; (3) SnAG-M with repeated fusion within the pyramid. Table 3 confirms that early and late fusion yield comparable results.
+
+Choice of fusion operation. We study fusion operations used by strong baselines, including point-wise addition, multiplication, and concatenation of video representations with global sentence embeddings, as well as vanilla cross-attention with token-level sentence embeddings. According to Table 3, token-level embeddings produce better results, and our cross-attention variant further boosts performance.
+
+# 4.4. Efficiency Analysis
+
+Finally, we conduct an efficiency analysis of our method.
+
+Breakdown of model capacity. A key design choice of SnAG is to carefully balance the model capacity among its video encoder, text encoder, and moment decoder including the fusion module and the localization heads. For a detailed breakdown of model capacity, we measure their respective parameter size and MACs in percentage. Fig. 5(a) indicates that SnAG's video encoder absorbs a significant portion of parameters and compute, such that per-query evaluation (i.e., text encoding, fusion, and decoding) occupies  $\sim 50\%$  of the total computation. This design is naturally in favor of video-centric training and inference, where the costly video encoding is shared among many queries.
+
+Video-centric vs. query-centric training. Fig. 5(b) presents the training time and GPU memory usage of video-centric training relative to conventional query-centric training. The results show that the amount of saving correlates with snippet length and number of queries. Video-centric training is thus preferred for long videos with many queries.
+
+$B_{q}$  in video-centric training. We further study how  $B_{q}$ , the number of text query samples per video, trades off accuracy for efficiency in video-centric training. On MAD, we fix the batch size  $|B| = 32$  for a mini-batch  $B$ , vary  $B_{q}$  between 1 and  $|B|$ , and report training time, GPU memory usage and test accuracy relative to query-centric training (i.e.,  $B_{q} = 1$ ). Fig. 5(d) reveals that test accuracy is unaffected even with a large  $B_{q} = 32$  (i.e., a single video per mini-batch), while training time and GPU memory usage
+
+<table><tr><td rowspan="3">Method</td><td colspan="4">TACoS (C3D)</td><td colspan="4">Charades-STA (I3D)</td><td colspan="4">Charades-STA (C3D)</td><td colspan="4">ActivityNet-Captions (C3D)</td></tr><tr><td colspan="2">R@1</td><td colspan="2">R@5</td><td colspan="2">R@1</td><td colspan="2">R@5</td><td colspan="2">R@1</td><td colspan="2">R@5</td><td colspan="2">R@1</td><td colspan="2">R@5</td></tr><tr><td>0.3</td><td>0.5</td><td>0.3</td><td>0.5</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td><td>0.5</td><td>0.7</td></tr><tr><td>CTRL ICCV 17 [13]</td><td>18.32</td><td>13.30</td><td>36.69</td><td>25.42</td><td>-</td><td>-</td><td>-</td><td>-</td><td>23.63</td><td>8.89</td><td>58.92</td><td>29.52</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>QSPN AAAI 19 [56]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>35.60</td><td>15.80</td><td>79.40</td><td>45.40</td><td>27.70</td><td>13.60</td><td>59.20</td><td>38.30</td></tr><tr><td>SCDM NeurIPS 19 [58]</td><td>27.64</td><td>23.27</td><td>40.06</td><td>33.49</td><td>54.92</td><td>34.26</td><td>76.50</td><td>60.02</td><td>-</td><td>-</td><td>-</td><td>-</td><td>36.90</td><td>20.28</td><td>66.84</td><td>42.92</td></tr><tr><td>2D-TAN AAAI 20 [67]</td><td>45.61</td><td>35.77</td><td>69.11</td><td>57.31</td><td>56.64</td><td>36.21</td><td>89.14</td><td>61.13</td><td>41.10</td><td>23.25</td><td>81.53</td><td>48.55</td><td>46.16</td><td>29.21</td><td>78.80</td><td>60.85</td></tr><tr><td>CBP AAAI 20 [51]</td><td>27.31</td><td>24.79</td><td>43.64</td><td>37.40</td><td>-</td><td>-</td><td>-</td><td>-</td><td>36.80</td><td>18.87</td><td>70.94</td><td>50.19</td><td>35.76</td><td>17.80</td><td>65.89</td><td>46.20</td></tr><tr><td>DRN CVPR 20 [60]</td><td>-</td><td>23.17</td><td>-</td><td>33.36</td><td>53.09</td><td>31.75</td><td>89.06</td><td>60.05</td><td>45.40</td><td>26.40</td><td>88.01</td><td>55.38</td><td>45.45</td><td>24.36</td><td>77.97</td><td>50.30</td></tr><tr><td>BPNet AAAI 21 [55]</td><td>25.96</td><td>20.96</td><td>-</td><td>-</td><td>50.75</td><td>31.64</td><td>-</td><td>-</td><td>38.25</td><td>20.51</td><td>-</td><td>-</td><td>42.07</td><td>24.69</td><td>-</td><td>-</td></tr><tr><td>CPNet AAAI 21 [24]</td><td>42.61</td><td>28.29</td><td>-</td><td>-</td><td>60.27</td><td>38.74</td><td>-</td><td>-</td><td>40.32</td><td>22.47</td><td>-</td><td>-</td><td>40.56</td><td>21.63</td><td>-</td><td>-</td></tr><tr><td>SMIN CVPR 21 [50]</td><td>48.01</td><td>35.24</td><td>65.18</td><td>53.36</td><td>64.06</td><td>40.75</td><td>89.49</td><td>68.09</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.46</td><td>30.34</td><td>81.16</td><td>62.11</td></tr><tr><td>CBLN CVPR 21 [29]</td><td>38.98</td><td>27.65</td><td>73.12</td><td>46.24</td><td>61.13</td><td>38.22</td><td>90.33</td><td>61.69</td><td>47.94</td><td>28.22</td><td>88.20</td><td>57.47</td><td>48.12</td><td>27.60</td><td>79.32</td><td>63.41</td></tr><tr><td>CPN CVPR 21 [68]</td><td>47.69</td><td>36.33</td><td>-</td><td>-</td><td>51.07</td><td>31.54</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>45.10</td><td>28.10</td><td>-</td><td>-</td></tr><tr><td>DeNet CVPR 21 [70]</td><td>-</td><td>-</td><td>-</td><td>-</td><td>59.70</td><td>38.52</td><td>91.24</td><td>66.83</td><td>-</td><td>-</td><td>-</td><td>-</td><td>43.79</td><td>-</td><td>74.13</td><td>-</td></tr><tr><td>MATN CVPR 21 [66]</td><td>48.79</td><td>37.57</td><td>67.63</td><td>57.91</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.02</td><td>31.78</td><td>78.02</td><td>63.18</td></tr><tr><td>VLG-Net ICCVW 21 [46]</td><td>45.46</td><td>34.19</td><td>70.38</td><td>56.56</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>46.32</td><td>29.82</td><td>77.15</td><td>63.33</td></tr><tr><td>APGN EMNLP 21 [28]</td><td>40.47</td><td>27.86</td><td>59.98</td><td>47.12</td><td>62.58</td><td>38.86</td><td>91.24</td><td>62.11</td><td>48.20</td><td>29.37</td><td>89.05</td><td>58.49</td><td>48.92</td><td>28.64</td><td>78.87</td><td>63.19</td></tr><tr><td>IA-Net EMNLP 21 [30]</td><td>37.91</td><td>26.27</td><td>57.62</td><td>46.39</td><td>61.29</td><td>37.91</td><td>89.78</td><td>62.04</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.57</td><td>27.95</td><td>78.99</td><td>63.12</td></tr><tr><td>RaNet EMNLP 21 [14]</td><td>43.34</td><td>33.54</td><td>67.33</td><td>55.09</td><td>60.40</td><td>39.65</td><td>89.57</td><td>64.54</td><td>-</td><td>-</td><td>-</td><td>-</td><td>45.59</td><td>28.67</td><td>75.93</td><td>62.97</td></tr><tr><td>MGSL-Net AAAI 22 [30]</td><td>42.54</td><td>32.27</td><td>63.39</td><td>50.13</td><td>63.98</td><td>41.03</td><td>93.21</td><td>63.85</td><td>-</td><td>-</td><td>-</td><td>-</td><td>51.87</td><td>31.42</td><td>82.60</td><td>66.71</td></tr><tr><td>MMN AAAI 22 [52]</td><td>39.24</td><td>26.17</td><td>62.03</td><td>47.39</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>48.59</td><td>29.26</td><td>79.50</td><td>64.76</td></tr><tr><td>SSRN EMNLP 22 [71]</td><td>45.10</td><td>34.33</td><td>65.26</td><td>51.85</td><td>65.59</td><td>42.65</td><td>94.76</td><td>65.48</td><td>50.39</td><td>31.42</td><td>90.68</td><td>59.94</td><td>54.49</td><td>33.15</td><td>84.72</td><td>68.48</td></tr><tr><td>G2L ICCV 23 [22]</td><td>42.74</td><td>30.95</td><td>65.83</td><td>49.86</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td><td>51.68</td><td>33.35</td><td>81.32</td><td>67.60</td></tr><tr><td>SnAG (video-centric)</td><td>56.44</td><td>44.86</td><td>81.15</td><td>70.66</td><td>64.62</td><td>46.26</td><td>92.55</td><td>71.94</td><td>51.72</td><td>33.52</td><td>92.55</td><td>64.11</td><td>48.55</td><td>30.56</td><td>81.71</td><td>63.41</td></tr><tr><td>SnAG (query-centric)</td><td>55.01</td><td>44.51</td><td>80.68</td><td>70.13</td><td>65.13</td><td>45.91</td><td>92.80</td><td>71.75</td><td>51.10</td><td>31.77</td><td>90.22</td><td>62.15</td><td>47.55</td><td>29.65</td><td>81.55</td><td>62.21</td></tr></table>
+
+Table 4. Results on TACoS, Charades-STA and ActivityNet-Captions. SnAG outperforms all baselines on TACoS and Charade-STA by a large margin, while being highly competitive on ActivityNet-Captions. Best results are in bold and second best underlined.
+
+![](images/034aec85e20ee7f163d3d00cae17d23a683054193ab09b09a375bc8f2fad07e0.jpg)  
+Figure 5. (a) Model capacity. T, E, M denotes TACoS, Ego4D and MAD, respectively (also in (b)). Shaded bar: % of parameters, Colored bar: % of MACs. SnAG places more parameters and compute in video encoder for less expensive per-query evaluation (fusion + decoding). (b, c) Video-centric vs. query-centric inference (b) and training (c). SnAG saves up to  $50\%$  training time,  $40\%$  GPU memory and  $80\%$  test time, and delivers up to  $40\%$  faster convergence relative to query-centric training / inference. (d) Effect of  $B_{q}$  on training efficiency and test accuracy on MAD. Training on MAD is faster and takes less GPU memory as  $B_{q}$  grows, while the test accuracy is unaffected.
+
+![](images/afa7c78d392044d86a41785a82fcc08744cbb838a9d761b7c29ffd1e790003c8.jpg)
+
+![](images/38a25ea3e1e8cc1a63805f1c3481bb9e9b47d1bc2d05ecb0fa054fca392e1f6d.jpg)
+
+![](images/405277267d74f9782f2007159bcbaabc91e6951ae176f18e1597779abe9490c2.jpg)
+
+drop by a significant  $55\%$  and  $42\%$ , approaching the upper bound by our analysis.
+
+Video-centric vs. query-centric inference. We now ask to what extent the re-use of video representations enabled by SnAG's late fusion design accelerates inference. Fig. 5(b) presents the percentage of time spent by our video-centric inference scheme relative to query-centric inference, where the full model is evaluated on each and every video-query pair. Consistent with earlier findings on video-centric training, longer videos with more queries result in more saving in inference time. On the challenging MAD dataset, this alone brings a major reduction (65%) in test time.
+
+Inference speed. With window filtering [17], inference of SnAG on the val split of MAD takes 12 minutes on a single P100 GPU. This is  $33\%$  faster than CONE [17] ( $\sim 18$  mins) and  $63\%$  faster than SOONet [36] ( $\sim 32$  mins).<sup>6</sup>
+
+# 5. Conclusion
+
+In this paper, we presented a simple and accurate model towards scaling up video grounding. We provided extensive analysis on the complexity of video grounding models from the perspective of cross-modal fusion, and argued that late fusion is key to scalability in video duration and query size. Our model, SnAG, is a simple instantiation of late fusion with minimalist design. It achieves superior accuracy and efficiency on a spectrum of challenging benchmarks and compares favorably to strong baselines including those dedicated to efficient inference on long videos. We hope our analysis and model design can shed light on video grounding and more broadly scalable video understanding.
+
+Acknowledgement: This work was partially supported by NIH grant R01OH012313, by grants from McPherson Eye Research Institute and VCGRE at UW Madison, and by the Army Research Lab under contract number W911NF-2020221.
+
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+        "type": "text",
+        "text": "Snap Video: Scaled Spatiotemporal Transformers for Text-to-Video Synthesis",
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+        "text": "Willi Menapace $^{1,2,*}$  Aliaksandr Siarohin $^{1}$  Ivan Skorokhodov $^{1}$  Ekaterina Deyneka $^{1}$  Tsai-Shien Chen $^{1,3,*}$  Anil Kag $^{1}$  Yuwei Fang $^{1}$  Aleksei Stoliar $^{1}$  Elisa Ricci $^{2,4}$  Jian Ren $^{1}$  Sergey Tulyakov $^{1}$",
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+        "type": "text",
+        "text": "Snap Inc. $^{1}$  University of Trento $^{2}$  UC Merced $^{3}$  Fondazione Bruno Kessler $^{4}$  snap-research.github.io/snapvideo",
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+        "img_path": "images/5220570b82c70914207643a95a7455af305220f6b4b5eaa5be18467d5534f856.jpg",
+        "image_caption": [
+            "Figure 1. Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). See the Website for additional samples."
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+        "type": "text",
+        "text": "Abstract",
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+        "type": "text",
+        "text": "Contemporary models for generating images show remarkable quality and versatility. Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is  $\\sim 4.5$  faster at inference). This allows us to efficiently train a text-to-video model with billions of",
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+    {
+        "type": "text",
+        "text": "parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods.",
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+    {
+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations.",
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+        "type": "text",
+        "text": "Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame",
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+    {
+        "type": "header",
+        "text": "CVF",
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+        "text": "* Work performed while interning at Snap Inc.",
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+    {
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+    {
+        "type": "text",
+        "text": "works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48].",
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+    {
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+        "text": "We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions.",
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+        "text": "Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant  $3.31 \\times$  reduction in training time and  $4.49 \\times$  reduction in inference time while achieving higher generation quality.",
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+    {
+        "type": "text",
+        "text": "We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants",
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+        "text": "of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in  $81\\%$  of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17]).",
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+        "text": "2. Related Work",
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+    {
+        "type": "text",
+        "text": "Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged.",
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+    {
+        "type": "text",
+        "text": "The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows.",
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+        "text": "Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities.",
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+        "type": "page_number",
+        "text": "7039",
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+        "text": "High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation.",
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+        "type": "text",
+        "text": "A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions.",
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+        "type": "text",
+        "text": "In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details.",
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+        "text": "Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos.",
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+        "type": "text",
+        "text": "3. Method",
+        "text_level": 1,
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+        "text": "We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2",
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+        "text": "highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures.",
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+        "type": "text",
+        "text": "3.1. Introduction to EDM",
+        "text_level": 1,
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+        "text": "Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process  $p(\\pmb{x}_{\\sigma}|\\pmb{x}) \\sim \\mathcal{N}(\\pmb{x}, \\pmb{\\sigma}^2\\mathbf{I})$ , where  $\\pmb{\\sigma} \\in [\\pmb{\\sigma}_{\\mathrm{min}}, \\pmb{\\sigma}_{\\mathrm{max}}]$  represents the diffusion timestep coinciding with the standard deviation of the applied noise, and  $x_{\\sigma}$  represents the data at the current noise level. A denoiser function  $\\mathcal{D}_{\\theta}$  is learned to model the reverse process using the denoising objective:",
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+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {D} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ \\lambda (\\boldsymbol {\\sigma}) \\| \\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - \\boldsymbol {x} \\| _ {2} ^ {2} \\right], \\tag {1}\n$$\n",
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+        "type": "text",
+        "text": "where  $\\lambda$  is the loss weighting function,  $\\pmb{x} \\sim p_{\\mathrm{data}}$  is a data sample,  $\\epsilon$  is gaussian noise, and  $\\sigma \\sim p_{\\mathrm{train}}$  is sampled from a training distribution.  $\\mathcal{D}_{\\theta}(\\pmb{x}_{\\sigma})$  is defined as:",
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+        "type": "equation",
+        "text": "\n$$\n\\mathcal {D} _ {\\theta} \\left(\\boldsymbol {x} _ {\\sigma}\\right) = c _ {\\text {o u t}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}\\right) + c _ {\\text {s k i p}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\sigma}, \\tag {2}\n$$\n",
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+    {
+        "type": "text",
+        "text": "where  $\\mathcal{F}_{\\theta}$  is a neural network, and  $c_{\\mathrm{out}}$ ,  $c_{\\mathrm{skip}}$  and  $c_{\\mathrm{in}}$  represent scaling functions. In particular, the denoising objective  $\\mathcal{L}(\\mathcal{F}_{\\theta})$  can equivalently be expressed in terms of  $\\mathcal{F}_{\\theta}$  as:",
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+        "type": "equation",
+        "text": "\n$$\n\\mathcal {L} \\left(\\mathcal {F} _ {\\theta}\\right) = \\mathbb {E} _ {\\boldsymbol {\\sigma}, \\boldsymbol {x}, \\boldsymbol {\\epsilon}} \\left[ w (\\boldsymbol {\\sigma}) \\left\\| \\mathcal {F} _ {\\theta} \\left(c _ {\\text {i n}} (\\boldsymbol {\\sigma}) \\boldsymbol {x} _ {\\boldsymbol {\\sigma}}\\right) - c _ {\\text {n r m}} (\\boldsymbol {\\sigma}) \\mathcal {F} _ {\\mathrm {t g t}} \\right\\| _ {2} ^ {2} \\right], \\tag {3}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "where  $\\mathcal{F}_{\\mathrm{tgt}}$  represents the training target,  $c_{\\mathrm{nm}}$  is a normalization factor, and  $w$  is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1.",
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+        "type": "text",
+        "text": "A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample  $\\pmb{x}$  starting from gaussian noise  $\\pmb{x}_{\\sigma_{\\mathrm{max}}} \\sim \\mathcal{N}(\\mathbf{0}, \\sigma_{\\mathrm{max}}^2 \\mathbf{I})$ .",
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+    {
+        "type": "text",
+        "text": "3.2. EDM for High-Resolution Video Generation",
+        "text_level": 1,
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+        "type": "text",
+        "text": "EDM is originally proposed as an image generation framework and its parameters are optimized for  $64 \\times 64\\mathrm{px}$  image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video  $\\boldsymbol{x}_{\\sigma} \\in \\mathbb{R}^{T \\times s \\cdot H \\times s \\cdot W} \\sim \\mathcal{N}(\\boldsymbol{x}, \\sigma^2\\mathbf{I})$  where  $T$  is the number of frames and  $s$  is an upsampling factor. We build the corresponding clean and noisy frames at original resolution  $\\tilde{\\boldsymbol{x}}$ ,  $\\tilde{\\boldsymbol{x}}_{\\sigma} \\in \\mathbb{R}^{1 \\times H \\times W}$  by averaging values in each  $T \\times s \\times s$  block of pixels. As a consequence of averaging, the noise",
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "7040",
+        "bbox": [
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+    {
+        "type": "table",
+        "img_path": "images/4ce66b533645f0c594a5fe77744b7466c20736e3fb07cab81944bbfed7d6cff7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td></td><td>EDM [25]</td><td>Our</td></tr><tr><td colspan=\"4\">Training and Losses</td></tr><tr><td>Forw. process</td><td>xσ</td><td>x/σin + σε</td><td>x/σin + σε</td></tr><tr><td>Training target</td><td>Ftgt</td><td>σx - σ2data ε + σ2data(σin-1)/σin x</td><td>- σx + σ2data ε</td></tr><tr><td>Eff. loss weigh.</td><td>w(σ)</td><td>1</td><td>(σ2 + σ2data)2/(σ2 + σ2data)2</td></tr><tr><td>Loss weigh.</td><td>λ(σ)</td><td>1/σ2data + 1/σ2</td><td>1/σ2data + 1/σ2</td></tr><tr><td colspan=\"4\">Network Parametrization</td></tr><tr><td>Input scaling</td><td>cin(σ)</td><td>1/√σ2data + σ2</td><td>1/√σ2data/σ2 + σ2</td></tr><tr><td>Output scaling</td><td>cout(σ)</td><td>σσ2data/√σ2+ σ2data</td><td>- σinσσdata√σ2+ σ2data/σ2+ σ2</td></tr><tr><td>Skip scaling</td><td>cskip(σ)</td><td>σ2data/σ2+ σ2data</td><td>σinσ2data/σinσ2+ σ2data</td></tr><tr><td>Target scaling</td><td>cnrm(σ)</td><td>1/σdata√σ2+ σ2data</td><td>1/σdata√σ2+ σ2data</td></tr></table>",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor  $\\sigma_{\\mathrm{in}}$ . Our framework is equivalent to EDM for  $\\sigma_{\\mathrm{in}} = 1$  but avoids the unstable term  $\\frac{\\sigma_{\\mathrm{data}}^2(\\sigma_{\\mathrm{in}} - 1)}{\\sigma_{\\mathrm{in}}\\sigma} x$  induced by  $\\sigma_{\\mathrm{in}} \\neq 1$  in  $\\mathcal{F}_{\\mathrm{tgt}}$ . This form highlights that the train target and loss weight match the  $v$ -prediction [45] framework for  $\\sigma_{\\mathrm{data}} = 1$ . All other framework parameters are unaltered with respect to EDM.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "variance is reduced by a factor  $Ts^2$ , i.e.  $\\tilde{x}_{\\sigma} \\sim \\mathcal{N}(\\tilde{x}, \\frac{\\sigma^2}{Ts^2}\\mathbf{I})$ , thus  $\\tilde{x}_{\\sigma}$  has an increased signal-to-noise-ratio with respect to  $x_{\\sigma}$  (see Fig. 2):  $SNR_{\\tilde{x}_{\\sigma}} = Ts^2 SNR_{x_{\\sigma}}$ . If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering  $x$  and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to  $T$  or  $s$  should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor  $\\sigma_{\\mathrm{in}} = s\\sqrt{T}$  as illustrated in Fig. 2. Consequently, we redefine the forward process as  $p(\\boldsymbol{x}_{\\sigma}|\\boldsymbol{x}) \\sim \\mathcal{N}(\\boldsymbol{x} / \\sigma_{\\mathrm{in}}, \\sigma^2\\mathbf{I})$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target  $\\mathcal{F}_{\\mathrm{tgt}}$  in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures  $\\mathcal{F}_{\\mathrm{tgt}}$  remains unchanged, the effective loss weight  $w(\\sigma)$  is such that it keeps the loss weight  $\\lambda (\\sigma)$  unchanged,  $c_{\\mathrm{in}}(\\sigma)$  and  $c_{\\mathrm{nm}}(\\sigma)$  normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for  $\\sigma_{\\mathrm{in}} = 1$  (see Appx. F).",
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+    },
+    {
+        "type": "image",
+        "img_path": "images/9e11ee40e7d83893d84b6e8237365779c1162475aca6016c22edde858235273a.jpg",
+        "image_caption": [
+            "Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise  $\\sigma$  is applied to an image. Middle: the same noise  $\\sigma$  is applied to a 16-frames-long video  $x$  without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by  $\\sigma_{\\mathrm{in}}$  before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as  $\\tilde{x} + \\sigma \\epsilon$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Finally, we modify the sampler according to the newly defined forward process that requires the signal component in  $x_{\\sigma}$  to be scaled by  $\\sigma_{\\mathrm{in}}$ . This is achieved by dividing the  $\\mathcal{D}_{\\theta}(x_{\\sigma})$  by  $\\sigma_{\\mathrm{in}}$  and multiplying the final denoised sample  $x_0$  by  $\\sigma_{\\mathrm{in}}$  to restore the signal magnitude.",
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+    },
+    {
+        "type": "text",
+        "text": "3.3. Image-Video Modality Matching",
+        "text_level": 1,
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of  $T$  frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as  $T$  frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities.",
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+    {
+        "type": "text",
+        "text": "3.4. Scalable Video Generator",
+        "text_level": 1,
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+        "type": "text",
+        "text": "U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the  $T$  video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and",
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+    {
+        "type": "page_number",
+        "text": "7041",
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+    {
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+        "img_path": "images/2ea42f1c5e2f6813aedea4975141396e0f032cd2ae571fb1300c7fa3f2c7d101.jpg",
+        "image_caption": [
+            "(a) Computational Paradigms for Videos"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            83,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/561d720c549782cb403330e2642f70b63d952d23b5ee5139c84d5d4ac716c591.jpg",
+        "image_caption": [
+            "(b) Snap Video FIT Architecture",
+            "Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video  $\\pmb{x}_{\\sigma}$ , the model estimates the denoised video  $\\hat{\\pmb{x}}_{\\sigma}$  by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level  $\\sigma$ , frame-rate  $\\nu$  and resolution  $r$  is provided through an additional read operation."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention \"read\" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise \"read\" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise \"write\" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro",
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+    {
+        "type": "text",
+        "text": "jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps.",
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+    {
+        "type": "text",
+        "text": "While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size  $T_{p} \\times H_{p} \\times W_{p}$  spanning both the spatial and temporal dimensions. We find values of  $T_{p} > 1$  to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all  $T$  video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention \"read\" or \"write\" operation.",
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+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "7042",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current  $\\sigma$ , to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input.",
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+    },
+    {
+        "type": "text",
+        "text": "To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing  $36 \\times 64\\mathrm{px}$  videos and a second-stage upsampling model producing  $288 \\times 512\\mathrm{px}$  videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search.",
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+    },
+    {
+        "type": "text",
+        "text": "We present detailed model hyperparameters in Appx. B.",
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+    },
+    {
+        "type": "text",
+        "text": "3.5. Training",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We train Snap Video using the LAMB [68] optimizer with a learning rate of  $5e^{-3}$ , a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose  $\\sigma_{\\mathrm{in}} = s\\sqrt{T}$ . Considering videos with  $T = 16$  frames and the original 64px resolution for which EDM was designed, we set  $\\sigma_{\\mathrm{in}} = 4$  for the first-stage and  $\\sigma_{\\mathrm{in}} = 32$  for the second-stage model.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We present training details and parameters in Appx. C.",
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "3.6. Inference",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality.",
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+    },
+    {
+        "type": "text",
+        "text": "4. Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "text",
+        "text": "In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website.",
+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "table",
+        "img_path": "images/f3c4b31bcee68ccdc657a825489525d685f20d9d9faa3cf631a55f9c832117bc.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td><td>Train Thr. ↓</td><td>Inf. Thr. ↓</td></tr><tr><td>U-Net 85M [10]</td><td>8.21</td><td>45.94</td><td>0.2319</td><td>133.2</td><td>49.6</td></tr><tr><td>U-Net 284M [10]</td><td>4.90</td><td>23.76</td><td>0.2391</td><td>230.3</td><td>105.1</td></tr><tr><td>Snap Video FIT 500M</td><td>3.07</td><td>27.79</td><td>0.2459</td><td>69.5</td><td>23.4</td></tr><tr><td>Snap Video FIT 3.9B</td><td>2.51</td><td>12.31</td><td>0.2579</td><td>526.0</td><td>130.4</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "table",
+        "img_path": "images/00876750a38d64d436c139b9d91f6936b6ad643a041013b0cec07ab09e642664.jpg",
+        "table_caption": [
+            "Table 2. Performance of different architectures and model sizes on our internal dataset in  $64 \\times 36\\mathrm{px}$  resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>σdata</td><td>σin</td><td>Imgs. as Videos</td><td>FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td></tr><tr><td>(i)</td><td>0.5</td><td>1.0</td><td>✓</td><td>6.58</td><td>39.95</td><td>0.2370</td></tr><tr><td>(ii)</td><td>0.5</td><td>4.0</td><td>✓</td><td>4.03</td><td>31.00</td><td>0.2449</td></tr><tr><td>(iv)</td><td>1.0</td><td>2.0</td><td>✓</td><td>4.45</td><td>34.89</td><td>0.2428</td></tr><tr><td>(iii)</td><td>1.0</td><td>1/4.0</td><td>X</td><td>3.50</td><td>24.88</td><td>0.2469</td></tr><tr><td>Ours</td><td>1.0</td><td>4.0</td><td>✓</td><td>3.07</td><td>27.79</td><td>0.2459</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Table 3. Ablation of different diffusion process configurations varying  $\\sigma_{\\mathrm{data}}$ , input scaling  $\\sigma_{\\mathrm{in}}$ , and treatment of images as infinite-framerate videos, evaluated on our internal dataset in  $64 \\times 36$ px resolution.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.1. Datasets",
+        "text_level": 1,
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We make use of the following datasets for evaluation which are never observed during training:",
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "UCF-101 [55] is a video dataset containing 13.320  $320 \\times 240$ px Youtube videos from 101 action categories.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "MSR-VTT [65] is a dataset containing  $10.000320 \\times 240\\mathrm{px}$  web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "4.2. Evaluation Protocol",
+        "text_level": 1,
+        "bbox": [
+            500,
+            755,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in  $64 \\times 36\\mathrm{px}$  resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on  $50\\mathrm{k}$  generated videos.",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero-",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "7043",
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in  $512 \\times 288\\mathrm{px}$  resolution at 24fps for all settings. We evaluate both at the native  $512 \\times 288\\mathrm{px}$  resolution with 16:9 aspect ratio and in the  $288 \\times 288\\mathrm{px}$  square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters:",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46].",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63].",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion.",
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.3. Ablations",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Our 500M parameters FIT trains  $3.31 \\times$  faster than the baseline 284M parameters U-Net, performs inference  $4.49 \\times$  faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a  $1.24 \\times$  increase in inference time with respect to the 284M U-Net.",
+        "bbox": [
+            75,
+            628,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM  $\\sigma_{\\mathrm{data}}$ , (iii) our framework with a reduced value of  $\\sigma_{\\mathrm{in}}$ , (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting  $\\sigma_{\\mathrm{data}} = 1$ , an effect that we attribute to the creation of a training target and loss weighting matching the widely used  $v$ -prediction formulation of",
+        "bbox": [
+            75,
+            734,
+            468,
+            901
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/0bbcf0ef03f6ba5b256263e96334419081db5d9d109e17325f9950d1bb736b85.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>FVD ↓</td><td>FID ↓</td><td>IS ↑</td></tr><tr><td>CogVideo [23] (Chinese)</td><td>751.3</td><td>-</td><td>23.55</td></tr><tr><td>CogVideo [23] (English)</td><td>701.6</td><td>-</td><td>25.27</td></tr><tr><td>MagicVideo [72]</td><td>655</td><td>-</td><td>-</td></tr><tr><td>LVDM [17]</td><td>641.8</td><td>-</td><td>-</td></tr><tr><td>Video LDM [4]</td><td>550.6</td><td>-</td><td>33.45</td></tr><tr><td>VideoFactory [62]</td><td>410.0</td><td>-</td><td>-</td></tr><tr><td>Make-A-Video [48]</td><td>367.2</td><td>-</td><td>33.00</td></tr><tr><td>PYoCo [13]</td><td>355.2</td><td>-</td><td>47.46</td></tr><tr><td>Snap Video (288 × 288 px)</td><td>260.1</td><td>39.0</td><td>38.89</td></tr><tr><td>Snap Video (512 × 288 px)</td><td>200.2</td><td>28.1</td><td>38.89</td></tr></table>",
+        "bbox": [
+            532,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "table",
+        "img_path": "images/c38176274d080f1c4a77ac21fbc4cff6e1dcc85b5daf60613a0f37329beea830.jpg",
+        "table_caption": [
+            "Table 4. Zero-shot evaluation results on UCF101 [55]."
+        ],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>CLIP-FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td></tr><tr><td>NUWA [64] (Chinese)</td><td>47.68</td><td>-</td><td>0.2439</td></tr><tr><td>CogVideo [23] (Chinese)</td><td>24.78</td><td>-</td><td>0.2614</td></tr><tr><td>CogVideo [23] (English)</td><td>23.59</td><td>-</td><td>0.2631</td></tr><tr><td>MagicVideo [72]</td><td>-</td><td>998</td><td>-</td></tr><tr><td>LVDM [17]</td><td>-</td><td>-</td><td>0.2381</td></tr><tr><td>Latent-Shift [2]</td><td>15.23</td><td>-</td><td>0.2773</td></tr><tr><td>Video LDM [4]</td><td>-</td><td>-</td><td>0.2929</td></tr><tr><td>VideoFactory [62]</td><td>-</td><td>-</td><td>0.3005</td></tr><tr><td>Make-A-Video [48]</td><td>13.17</td><td>-</td><td>0.3049</td></tr><tr><td>PYoCo [13]</td><td>9.73</td><td>-</td><td>-</td></tr><tr><td>Snap Video (288 × 288 px)</td><td>8.48</td><td>110.4</td><td>0.2793</td></tr><tr><td>Snap Video (512 × 288 px)</td><td>9.35</td><td>104.0</td><td>0.2793</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Table 5. Zero-shot evaluation results on MSR-VTT [65].",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "Salimans et al. [45] (see Tab. 1). Using  $\\sigma_{\\mathrm{in}} < s\\sqrt{T}$  (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "4.4. Quantitative Evaluation",
+        "text_level": 1,
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM.",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1]",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "page_number",
+        "text": "7044",
+        "bbox": [
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/2fa82ded38c5ae7b26fc3839ffcf7eca9c46cddc346d8f0d30486611bcb9a4c6.jpg",
+        "image_caption": [
+            "Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            76,
+            88,
+            480,
+            343
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "image",
+        "img_path": "images/382a92480806ce18863c9abc916323b1b4c2e639fad98e114ce94840ca3bda3c.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
+            483,
+            88,
+            890,
+            343
+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "table",
+        "img_path": "images/b92148db4ca1d8a1c2aa8c33531fdc2a30a80e985d078a2bf48f7a3bcb9f4906.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>Photorealism</td><td>Video-Text Align.</td><td>Mot. Quant.</td><td>Mot. Qual.</td></tr><tr><td>Gen-2 [11]</td><td>44.3</td><td>81.0</td><td>96.0</td><td>78.7</td></tr><tr><td>PikaLab [1]</td><td>61.5</td><td>80.3</td><td>89.2</td><td>70.5</td></tr><tr><td>Floor33 [17]</td><td>76.3</td><td>80.9</td><td>88.0</td><td>79.1</td></tr></table>",
+        "bbox": [
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+        ],
+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Table 6. User study on photorealism, video-text alignment, motion quantity and quality against publicly-accessible video generators on 65 dynamic scene prompts. % of votes in favor of our method.",
+        "bbox": [
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+        "text": "and Floor33 [17]. We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics.",
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+        "text": "4.5. Qualitative Evaluation",
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+        "text": "In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state-",
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+    {
+        "type": "text",
+        "text": "of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2.",
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+        "text": "5. Conclusions",
+        "text_level": 1,
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+        "text": "In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion.",
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+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
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2024/Snap Video_ Scaled Spatiotemporal Transformers for Text-to-Video Synthesis/adef51ac-64f5-47cc-b577-559e45a201d6_origin.pdf

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2024/Snap Video_ Scaled Spatiotemporal Transformers for Text-to-Video Synthesis/full.md

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+# Snap Video: Scaled Spatiotemporal Transformers for Text-to-Video Synthesis
+
+Willi Menapace $^{1,2,*}$  Aliaksandr Siarohin $^{1}$  Ivan Skorokhodov $^{1}$  Ekaterina Deyneka $^{1}$  Tsai-Shien Chen $^{1,3,*}$  Anil Kag $^{1}$  Yuwei Fang $^{1}$  Aleksei Stoliar $^{1}$  Elisa Ricci $^{2,4}$  Jian Ren $^{1}$  Sergey Tulyakov $^{1}$
+
+Snap Inc. $^{1}$  University of Trento $^{2}$  UC Merced $^{3}$  Fondazione Bruno Kessler $^{4}$  snap-research.github.io/snapvideo
+
+![](images/5220570b82c70914207643a95a7455af305220f6b4b5eaa5be18467d5534f856.jpg)  
+Figure 1. Samples produced by the proposed text-to-video generation method for a selection of prompts. Thanks to joint spatiotemporal video modeling, our generator can synthesize temporally coherent videos with large motion (left) while retaining the semantic control capabilities typical of large-scale text-to-video generators (right). See the Website for additional samples.
+
+![](images/506832b796cc84ccf0482793d3c8b2c44e40f92da38ae97d7274f447287a5401.jpg)
+
+# Abstract
+
+Contemporary models for generating images show remarkable quality and versatility. Swayed by these advantages, the research community repurposes them to generate videos. Since video content is highly redundant, we argue that naively bringing advances of image models to the video generation domain reduces motion fidelity, visual quality and impairs scalability. In this work, we build Snap Video, a video-first model that systematically addresses these challenges. To do that, we first extend the EDM framework to take into account spatially and temporally redundant pixels and naturally support video generation. Second, we show that a U-Net—a workhorse behind image generation—scales poorly when generating videos, requiring significant computational overhead. Hence, we propose a new transformer-based architecture that trains 3.31 times faster than U-Nets (and is  $\sim 4.5$  faster at inference). This allows us to efficiently train a text-to-video model with billions of
+
+parameters for the first time, reach state-of-the-art results on a number of benchmarks, and generate videos with substantially higher quality, temporal consistency, and motion complexity. The user studies showed that our model was favored by a large margin over the most recent methods.
+
+# 1. Introduction
+
+Creating and sharing visual content is one of the key ways for people to express themselves in the digital world. Accessible to only professionals in the past, the capability to create [30, 40, 43, 69] and edit [6, 37, 42] images with stunning quality and realism was unlocked to everyone by the advent of large text-to-image models and their variations.
+
+Fueled by this progress, large-scale text-to-video models [4, 13, 21, 48, 62] are rapidly advancing too. Current large-scale diffusion-based video generation frame
+
+works are strongly rooted into their image counterparts [4, 13]. The availability of consolidated image generation architectures such as U-Nets [41] with publicly-available image-pretrained models [40] made them a logical foundation onto which to build large-scale video generators with the main architectural modifications focusing on the insertion of ad-hoc layers to capture temporal dependencies [4, 13, 21, 48, 62]. Similarly, training is performed under image-based diffusion frameworks with the model being applied both to videos and to a separate set of images to improve the diversity of the results [13, 21, 22, 48].
+
+We argue that such an approach is suboptimal under multiple aspects which we systematically address in this work. First, image and video modalities present intrinsic differences given by the similarity of content in successive video frames [7, 13]. By analogy, image and video compression algorithms are based on vastly different approaches [33]. To address this issue, we rewrite the EDM [25] framework with a focus on high-resolution videos. Differently from past work where videos were treated as a sequence of images, we perform joint video-image training by treating images as high frame-rate videos to avoid modality mismatches introduced by the absence of the temporal dimension within purely image-based training. Second, the widely adopted U-Net [41] architecture is required to fully processes each video frame. This increases computational overhead compared to purely text-to-image models, posing a very practical limit on model scalability. The latter is a critical factor in obtaining high-quality of results [13, 21]. Extending U-Net-based architectures to naturally support spatial and temporal dimensions requires volumetric attention operations, which have prohibitive computational demands. Inability to do so affects the outputs, resulting in dynamic images or motion artifacts being generated instead of videos with coherent and diverse actions.
+
+Following our compression analogy, we propose to leverage repetition between frames and introduce a scalable transformer architecture that treats spatial and temporal dimensions as a single, compressed, 1D latent vector. This highly compressed representation allows us to perform spatio-temporal computation jointly and enables modelling of complex motions. Our architecture is inspired by FIT [8], which we scale to billions of parameters for the first time. Compared to U-Nets, our model features a significant  $3.31 \times$  reduction in training time and  $4.49 \times$  reduction in inference time while achieving higher generation quality.
+
+We evaluate Snap Video on the widely-adopted UCF101 [55] and MSR-VTT [65] datasets. Our generator shows state-of-the-art performance across the range of benchmarks with particular regard to the quality of the generated motion. Most interestingly, we performed a number of user studies against the most recent open- and close-source methods and found that according to the participants
+
+of the study our model features photorealism comparable to Gen-2 [11], while being significantly better than Pika [1] and Floor33 [17]. Most excitedly, the preference of user-study participants favoured Snap Video by a large margin when text alignment and motion quality were assessed. Compared to Gen-2 [11] on prompt-video alignment our model was preferred in  $81\%$  of cases (80% against Pika [1], 81% against Floor33 [17]), generated most dynamic videos with most amount of motion (96% against Gen2 [11], 89% against Pika [1], 88% against Floor33 [17]) and had the best motion quality (79% against Gen-2 [11], 71% against Pika [1], 79% against Floor33 [17]).
+
+# 2. Related Work
+
+Video Generation Video generation is a challenging and long-studied task. Due to its complexity, a large number of works focus on modeling narrow domains [5, 9, 12, 28, 35, 44, 47, 49, 56, 58, 59, 66, 70, 71] and adopt adversarial training [5, 9, 28, 44, 47, 49, 58, 59, 71] or autoregressive generation techniques [12, 35, 56, 66, 70]. To address the narrow domain limitation, the task of text-to-video generation was proposed [34] and both autoregressive models [23, 34, 61, 63, 64] and GANs [29] emerged.
+
+The recent success of diffusion models in the context of text-to-image generation [3, 40, 43] fostered tremendous progress in the task [2, 4, 13, 16, 17, 21, 22, 32, 48, 62, 67, 72]. ImagenVideo [21] and Make-A-Video [48] propose a deep cascade of temporal and spatial upsamplers to generate videos and jointly train their models on image and video datasets. PYoCo [13] introduces a correlated noise model to capture similarities between video frames. Video LDM [4] adopts a latent diffusion paradigm where a pretrained latent image generator and latent decoder are finetuned to generate temporally coherent videos.AnimateDiff [16] freezes a pre-trained latent image generator and trains only a newly inserted motion modeling module. These works employ U-Nets with separable spatial and temporal computation which poses a limitation on motion modeling capabilities. VideoFactory [62] improves upon this paradigm by proposing a Swapped Spatiotemporal CrossAttention that improves interactions between the spatial and temporal modalities along 3D windows.
+
+Differently from this corpus of works which adapts the U-Net [41] architecture to the video generation task, we show that employing transformer-based FIT [8] architectures results in significant training time savings, scalability improvements, and performance increase thanks to their learnable compressed video representation. In particular, we show that the global joint spatiotemporal modeling strategy enabled by our compressed video representation results in significant improvements in temporal consistency and motion modeling capabilities.
+
+High-Resolution Generation Different approaches have been proposed to enable the generation of high-resolution outputs. Cascaded diffusion models [3, 13, 21, 43, 48] adopt a set of independent diffusion models designed to successively upsample the results of the previous step. Latent diffusion models [2, 4, 17, 40, 72] make use of a pretrained autoencoder to encode the input into a low-dimensional set of latent vectors and learn a diffusion model on this latent representation.
+
+A different family of methods generates high-resolution outputs end-to-end without employing cascades of models or latent diffusion. Simple Diffusion [24] and Chen [7] directly generate high-resolution images by adapting the noise schedule of the diffusion process. f-DM [14] and RDM [57] design a diffusion process that seamlessly transitions between different resolutions. MDM [15] proposes a strategy where a single model is trained to simultaneously denoise inputs at progressively higher resolutions.
+
+In this work, we adopt a two-stage cascaded model out of two considerations: (i) it avoids temporal inconsistencies in the forms of flickering of high-frequency details that may be introduced by latent autoencoders [4], (ii) it increases model capacity with respect to an end-to-end model by creating two specialized models, one for the low resolution focusing on motion modeling and scene structure, and one for the high-resolution, focusing on high-frequency details.
+
+Diffusion Frameworks Diffusion generative models are a set of techniques modeling generation as a pair of processes: a forward process progressively destructing a sample with noise, and a reverse process modeling generation as the progressive denoising of a sample. Different formulations of diffusion models have been proposed in the literature. Denoising Diffusion Probabilistic Models (DDPMs) [20, 50] formulate the forward and backward process as Markov chains. Score-based Generative Models (SGMs) [51, 52] model the score of the probability density function of a series of data distributions perturbed with increasing levels of noise, i.e. the direction of largest increase in the data log probability density function. An avenue of works [53, 54] generalizes DDPMs and SGMs to infinite noise levels through Stochastic Differential Equations (SDEs). In this work, we adopt the SGM framework of EDM [25] which we reformulate for the generation of high-resolution videos.
+
+# 3. Method
+
+We propose the generation of high-resolution videos by rewriting the EDM [25] diffusion framework for high-dimensional inputs and proposing an efficient transformer architecture based on FITs [8] which we scale to billions of parameters and tens of thousands input patches. Sec. 3.1 provides an introduction to the EDM framework, Sec 3.2
+
+highlights the challenges of applying diffusion frameworks to high dimensional inputs and proposes a revisited EDM-based diffusion framework. Sec. 3.3 proposes a method to reduce the gap between image and video modalities for joint training. Finally, Sec. 3.4 describes our scalable video generation architecture, while Sec. 3.5 and Sec. 3.6 respectively describe the training and inference procedures.
+
+# 3.1. Introduction to EDM
+
+Diffusion models have achieved remarkable success in image and video generation. Among the proposed frameworks, Karras et al. [25] provide a unified view of common diffusion frameworks and formulate EDM. EDM defines a variance-exploding forward diffusion process  $p(\pmb{x}_{\sigma}|\pmb{x}) \sim \mathcal{N}(\pmb{x}, \pmb{\sigma}^2\mathbf{I})$ , where  $\pmb{\sigma} \in [\pmb{\sigma}_{\mathrm{min}}, \pmb{\sigma}_{\mathrm{max}}]$  represents the diffusion timestep coinciding with the standard deviation of the applied noise, and  $x_{\sigma}$  represents the data at the current noise level. A denoiser function  $\mathcal{D}_{\theta}$  is learned to model the reverse process using the denoising objective:
+
+$$
+\mathcal {L} \left(\mathcal {D} _ {\theta}\right) = \mathbb {E} _ {\boldsymbol {\sigma}, \boldsymbol {x}, \boldsymbol {\epsilon}} \left[ \lambda (\boldsymbol {\sigma}) \| \mathcal {D} _ {\theta} \left(\boldsymbol {x} _ {\boldsymbol {\sigma}}\right) - \boldsymbol {x} \| _ {2} ^ {2} \right], \tag {1}
+$$
+
+where  $\lambda$  is the loss weighting function,  $\pmb{x} \sim p_{\mathrm{data}}$  is a data sample,  $\epsilon$  is gaussian noise, and  $\sigma \sim p_{\mathrm{train}}$  is sampled from a training distribution.  $\mathcal{D}_{\theta}(\pmb{x}_{\sigma})$  is defined as:
+
+$$
+\mathcal {D} _ {\theta} \left(\boldsymbol {x} _ {\sigma}\right) = c _ {\text {o u t}} (\boldsymbol {\sigma}) \mathcal {F} _ {\theta} \left(c _ {\text {i n}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\sigma}\right) + c _ {\text {s k i p}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\sigma}, \tag {2}
+$$
+
+where  $\mathcal{F}_{\theta}$  is a neural network, and  $c_{\mathrm{out}}$ ,  $c_{\mathrm{skip}}$  and  $c_{\mathrm{in}}$  represent scaling functions. In particular, the denoising objective  $\mathcal{L}(\mathcal{F}_{\theta})$  can equivalently be expressed in terms of  $\mathcal{F}_{\theta}$  as:
+
+$$
+\mathcal {L} \left(\mathcal {F} _ {\theta}\right) = \mathbb {E} _ {\boldsymbol {\sigma}, \boldsymbol {x}, \boldsymbol {\epsilon}} \left[ w (\boldsymbol {\sigma}) \left\| \mathcal {F} _ {\theta} \left(c _ {\text {i n}} (\boldsymbol {\sigma}) \boldsymbol {x} _ {\boldsymbol {\sigma}}\right) - c _ {\text {n r m}} (\boldsymbol {\sigma}) \mathcal {F} _ {\mathrm {t g t}} \right\| _ {2} ^ {2} \right], \tag {3}
+$$
+
+where  $\mathcal{F}_{\mathrm{tgt}}$  represents the training target,  $c_{\mathrm{nm}}$  is a normalization factor, and  $w$  is a weighting function. These forms, derived in Appx. E, are presented in Tab. 1.
+
+A second order Runge-Kutta sampler is proposed to reverse the diffusion process and produce sample  $\pmb{x}$  starting from gaussian noise  $\pmb{x}_{\sigma_{\mathrm{max}}} \sim \mathcal{N}(\mathbf{0}, \sigma_{\mathrm{max}}^2 \mathbf{I})$ .
+
+# 3.2. EDM for High-Resolution Video Generation
+
+EDM is originally proposed as an image generation framework and its parameters are optimized for  $64 \times 64\mathrm{px}$  image generation. Alterations in spatial resolution or the introduction of videos with shared content between frames allow the denoising network to trivially recover a noisy frame in the original resolution with higher signal-to-noise-ratio (SNR), which the original framework was designed to see at lower noise levels. To see why, consider a noisy video  $\boldsymbol{x}_{\sigma} \in \mathbb{R}^{T \times s \cdot H \times s \cdot W} \sim \mathcal{N}(\boldsymbol{x}, \sigma^2\mathbf{I})$  where  $T$  is the number of frames and  $s$  is an upsampling factor. We build the corresponding clean and noisy frames at original resolution  $\tilde{\boldsymbol{x}}$ ,  $\tilde{\boldsymbol{x}}_{\sigma} \in \mathbb{R}^{1 \times H \times W}$  by averaging values in each  $T \times s \times s$  block of pixels. As a consequence of averaging, the noise
+
+<table><tr><td></td><td></td><td>EDM [25]</td><td>Our</td></tr><tr><td colspan="4">Training and Losses</td></tr><tr><td>Forw. process</td><td>xσ</td><td>x/σin + σε</td><td>x/σin + σε</td></tr><tr><td>Training target</td><td>Ftgt</td><td>σx - σ2data ε + σ2data(σin-1)/σin x</td><td>- σx + σ2data ε</td></tr><tr><td>Eff. loss weigh.</td><td>w(σ)</td><td>1</td><td>(σ2 + σ2data)2/(σ2 + σ2data)2</td></tr><tr><td>Loss weigh.</td><td>λ(σ)</td><td>1/σ2data + 1/σ2</td><td>1/σ2data + 1/σ2</td></tr><tr><td colspan="4">Network Parametrization</td></tr><tr><td>Input scaling</td><td>cin(σ)</td><td>1/√σ2data + σ2</td><td>1/√σ2data/σ2 + σ2</td></tr><tr><td>Output scaling</td><td>cout(σ)</td><td>σσ2data/√σ2+ σ2data</td><td>- σinσσdata√σ2+ σ2data/σ2+ σ2</td></tr><tr><td>Skip scaling</td><td>cskip(σ)</td><td>σ2data/σ2+ σ2data</td><td>σinσ2data/σinσ2+ σ2data</td></tr><tr><td>Target scaling</td><td>cnrm(σ)</td><td>1/σdata√σ2+ σ2data</td><td>1/σdata√σ2+ σ2data</td></tr></table>
+
+Table 1. Definitions of functions in Eq. (1), Eq. (2) and Eq. (3) for the EDM and our proposed diffusion framework as derived in Appx. E and Appx. F, where we highlight the terms induced by the input scaling factor  $\sigma_{\mathrm{in}}$ . Our framework is equivalent to EDM for  $\sigma_{\mathrm{in}} = 1$  but avoids the unstable term  $\frac{\sigma_{\mathrm{data}}^2(\sigma_{\mathrm{in}} - 1)}{\sigma_{\mathrm{in}}\sigma} x$  induced by  $\sigma_{\mathrm{in}} \neq 1$  in  $\mathcal{F}_{\mathrm{tgt}}$ . This form highlights that the train target and loss weight match the  $v$ -prediction [45] framework for  $\sigma_{\mathrm{data}} = 1$ . All other framework parameters are unaltered with respect to EDM.
+
+variance is reduced by a factor  $Ts^2$ , i.e.  $\tilde{x}_{\sigma} \sim \mathcal{N}(\tilde{x}, \frac{\sigma^2}{Ts^2}\mathbf{I})$ , thus  $\tilde{x}_{\sigma}$  has an increased signal-to-noise-ratio with respect to  $x_{\sigma}$  (see Fig. 2):  $SNR_{\tilde{x}_{\sigma}} = Ts^2 SNR_{x_{\sigma}}$ . If pixels in each block share similar content, a typical situation in high-resolution videos, then the information in the averaged frame is useful for recovering  $x$  and can be exploited at training time by the denoiser function. This creates a train-inference mismatch during the initial sampling steps as the average frame does not yet contain a well-formed signal, yet the denoiser is reliant on its presence. Thus, for best performance, any alteration to  $T$  or  $s$  should instead maintain the same signal-to-noise ratio at the original resolution for which the diffusion framework was designed.
+
+To restore the optimal SNR at the original resolution, the magnitude of the input signal can be reduced [7] by a corresponding factor  $\sigma_{\mathrm{in}} = s\sqrt{T}$  as illustrated in Fig. 2. Consequently, we redefine the forward process as  $p(\boldsymbol{x}_{\sigma}|\boldsymbol{x}) \sim \mathcal{N}(\boldsymbol{x} / \sigma_{\mathrm{in}}, \sigma^2\mathbf{I})$ .
+
+We rewrite the EDM framework to introduce the input scaling factor in Appx. F and highlight the changes in Tab. 1. We notice that a naive introduction of the scaling factor would alter the training target  $\mathcal{F}_{\mathrm{tgt}}$  in a way that makes the objective explode for small noise values (see Appx. E). We thus leverage the training objective expressed in the form of Eq. (3) to rewrite the EDM process in a way that ensures  $\mathcal{F}_{\mathrm{tgt}}$  remains unchanged, the effective loss weight  $w(\sigma)$  is such that it keeps the loss weight  $\lambda (\sigma)$  unchanged,  $c_{\mathrm{in}}(\sigma)$  and  $c_{\mathrm{nm}}(\sigma)$  normalize the input and training target to have unit variance, and the framework is equivalent to the original EDM formulation for  $\sigma_{\mathrm{in}} = 1$  (see Appx. F).
+
+![](images/9e11ee40e7d83893d84b6e8237365779c1162475aca6016c22edde858235273a.jpg)  
+Figure 2. Analysis of Signal-to-Noise Ratio (SNR). Top: noise  $\sigma$  is applied to an image. Middle: the same noise  $\sigma$  is applied to a 16-frames-long video  $x$  without scaling. A clean image can be easily restored by simply taking average, indicating an increased SNR. Bottom: to maintain the original SNR, we scale down the 16 frames by  $\sigma_{\mathrm{in}}$  before noise application. Averaging is not able to restore the images, indicating the SNR is maintained as  $\tilde{x} + \sigma \epsilon$ .
+
+Finally, we modify the sampler according to the newly defined forward process that requires the signal component in  $x_{\sigma}$  to be scaled by  $\sigma_{\mathrm{in}}$ . This is achieved by dividing the  $\mathcal{D}_{\theta}(x_{\sigma})$  by  $\sigma_{\mathrm{in}}$  and multiplying the final denoised sample  $x_0$  by  $\sigma_{\mathrm{in}}$  to restore the signal magnitude.
+
+# 3.3. Image-Video Modality Matching
+
+Due to the limited amount of captioned video data with respect to images, joint image-video training is widely adopted [13, 21, 22, 48] with the same diffusion process typically applied to both modalities. However, as shown in Sec. 3.2, the presence of  $T$  frames in videos calls for a different process with respect to an image with the same resolution. A possibility would be to adopt different input scaling factors for the two modalities. We argue that this solution is undesirable in that it increases the complexity of the framework and image training would not foster the denoising model to learn temporal reasoning, a fundamental capability of a video generator. To sidestep these issues while using a unified diffusion process, we match the image and video modalities by treating images as  $T$  frames videos with infinite frame-rate and introduce a variable frame-rate training procedure blending the gap between the image and video modalities.
+
+# 3.4. Scalable Video Generator
+
+U-Nets [41] have shown success in video generation where they are typically augmented with temporal attention or convolutions for modeling the temporal dimension [4, 13, 21, 22, 48]. However, such an approach requires a full U-Net forward pass for each of the  $T$  video frames, rapidly becoming prohibitively expensive (see Fig. 3a). These factors pose a practical limit on model scalability—a primary factor in achieving high generation quality [13, 17, 21, 48]—and
+
+![](images/2ea42f1c5e2f6813aedea4975141396e0f032cd2ae571fb1300c7fa3f2c7d101.jpg)  
+(a) Computational Paradigms for Videos
+
+![](images/561d720c549782cb403330e2642f70b63d952d23b5ee5139c84d5d4ac716c591.jpg)  
+(b) Snap Video FIT Architecture  
+Figure 3. (a-left) U-Net-based text-to-image architectures are adapted to do video generation by inserting temporal layers applied sequentially with spatial layers, creating separable spatiotemporal blocks. Spatial computation is repeated for each frame independently, limiting scalability. (a-right) Our scalable transformer-based model jointly performs spatial and temporal computation on a learnable compressed video representation for improved motion modeling and scalability. (b) The proposed Snap Video FIT architecture. Given a noisy input video  $\pmb{x}_{\sigma}$ , the model estimates the denoised video  $\hat{\pmb{x}}_{\sigma}$  by recurrent application of FIT blocks. Each block reads information from the patch tokens into a small set of latent tokens on which computation is performed. The results are written to the patch tokens. Conditioning information in the form of text embeddings, noise level  $\sigma$ , frame-rate  $\nu$  and resolution  $r$  is provided through an additional read operation.
+
+similarly limit possibilities for joint spatio-temporal modeling [62]. We argue that treating spatial and temporal modeling in a separable way [4, 13, 21, 48] causes motion artifacts, temporal inconsistencies or generation of dynamic images rather than videos with vivid motion. Video frames, however, contain spatially and temporally redundant content that is amenable to compression [33]. We argue that learning and operating on a compressed video representation and jointly modeling the spatial and temporal dimensions are necessary steps to achieve the scalability and motion-modeling capabilities required for high-quality video generation.
+
+FITs [8] are efficient transformer-based architectures that have recently been proposed for high-resolution image synthesis and video generation. Their main idea, summarized in Fig. 3 is that of learning a compressed representation of their input through a set of learnable latent tokens and of focusing computation on this learnable latent space, allowing input dimensionality to grow with little performance penalty. First, FITs perform patchification of the input and produce a sequence of patch tokens which are later divided into groups. A set of latent tokens is then instantiated and a sequence of computational blocks is applied. Each block first performs a cross attention "read" operation between latent tokens and conditioning signals such as the diffusion timestep, then an additional groupwise "read" cross attention operation between latent and patch tokens of corresponding groups to compress patch information, applies a series of self attention operations to the latent tokens, and performs a groupwise "write" cross attention operation that decompresses information in the latent tokens to update the patch tokens. Finally, the patch tokens are pro
+
+jected back to the pixel space to form the output. Self conditioning is applied on the set of latent tokens to preserve the compressed video representation computed in previous sampling steps.
+
+While promising, these architectures have not yet been scaled to the billion-parameters size of state-of-the-art U-Net-based video generators, nor they have been applied to high-resolution video generation. In the following, we highlight the architectural considerations necessary to achieve these goals. Temporal modeling is a fundamental aspect of a high-quality video generator. FITs produce patch tokens by considering three dimensional patches of size  $T_{p} \times H_{p} \times W_{p}$  spanning both the spatial and temporal dimensions. We find values of  $T_{p} > 1$  to limit temporal modeling performance, so we consider patches spanning the spatial dimension only. In addition, similarly to patches, FITs group patch tokens into groups spanning both the temporal and spatial dimensions, and perform cross attention operations group by group. We observe that the temporal size of each group should be configured so that each group covers all  $T$  video frames for best temporal modeling. Furthermore, videos contain more information with respect to images due to the presence of the temporal dimension, thus we increase the number of latent tokens representing the size of the compressed space in which joint spatiotemporal computation is performed. Finally, FITs make use of local layers which perform self attention operations on patch tokens corresponding to the same group. We find this operation to be computationally expensive for large amounts of patch tokens (147.456 for our largest resolution) and replace it with a feed forward module after each cross attention "read" or "write" operation.
+
+Our model makes use of conditioning information represented by a sequence of conditioning tokens to control the generation process. In addition to the token representing the current  $\sigma$ , to enable text conditioning, we introduce a T5-11B [39] text encoder extracting text embeddings from the input text. To support variable video framereates and large differences in resolution and aspect ratios in the training data, we concatenate additional tokens representing the framerate and original resolution of the current input.
+
+To generate high-resolution outputs, we implement a model cascade consisting of a first-stage model producing  $36 \times 64\mathrm{px}$  videos and a second-stage upsampling model producing  $288 \times 512\mathrm{px}$  videos. To improve upsampling quality, we corrupt the second-stage low-resolution inputs with a variable level of noise during training [21, 43] and during inference apply a level of noise to the first-stage outputs obtained by hyperparameter search.
+
+We present detailed model hyperparameters in Appx. B.
+
+# 3.5. Training
+
+We train Snap Video using the LAMB [68] optimizer with a learning rate of  $5e^{-3}$ , a cosine learning schedule and a total batch size of 2048 videos and 2048 images, achievable thanks to our scalable video generator architecture. We train the first-stage model over 550k steps and finetune the second-stage model on high-resolution videos starting from the first-stage model weights for 370k iterations. Following the observations in Sec 3.2, we pose  $\sigma_{\mathrm{in}} = s\sqrt{T}$ . Considering videos with  $T = 16$  frames and the original 64px resolution for which EDM was designed, we set  $\sigma_{\mathrm{in}} = 4$  for the first-stage and  $\sigma_{\mathrm{in}} = 32$  for the second-stage model.
+
+We present training details and parameters in Appx. C.
+
+# 3.6. Inference
+
+We produce video samples from gaussian noise and user-provided conditioning information using the deterministic sampler of [25] and our two-stage cascade. We use 256 sampling steps for the first-stage and 40 for the second-stage model, and employ classifier free guidance [19] to improve text-video alignment (see Appx. D.1) unless otherwise specified. We find dynamic thresholding [43] and oscillating guidance [21] to consistently improve quality.
+
+# 4. Evaluation
+
+In this section, we perform evaluation of Snap Video against baselines and validate our design choices. Sec. 4.1 introduces the employed datasets, Sec. 4.3 shows ablations of our diffusion framework and architectural choices, Sec. 4.4 quantitatively compares our method to state-of-the-art large-scale video generators and Sec. 4.5 performs qualitative evaluation. We complement evaluation by showcasing samples in the Appendix and Website.
+
+<table><tr><td></td><td>FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td><td>Train Thr. ↓</td><td>Inf. Thr. ↓</td></tr><tr><td>U-Net 85M [10]</td><td>8.21</td><td>45.94</td><td>0.2319</td><td>133.2</td><td>49.6</td></tr><tr><td>U-Net 284M [10]</td><td>4.90</td><td>23.76</td><td>0.2391</td><td>230.3</td><td>105.1</td></tr><tr><td>Snap Video FIT 500M</td><td>3.07</td><td>27.79</td><td>0.2459</td><td>69.5</td><td>23.4</td></tr><tr><td>Snap Video FIT 3.9B</td><td>2.51</td><td>12.31</td><td>0.2579</td><td>526.0</td><td>130.4</td></tr></table>
+
+Table 2. Performance of different architectures and model sizes on our internal dataset in  $64 \times 36\mathrm{px}$  resolution. We observe strong performance gains with scaling and note that FITs present better performance with improved speed with respect to U-Nets. Train and inference throughputs in ms/video/GPU.  
+
+<table><tr><td></td><td>σdata</td><td>σin</td><td>Imgs. as Videos</td><td>FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td></tr><tr><td>(i)</td><td>0.5</td><td>1.0</td><td>✓</td><td>6.58</td><td>39.95</td><td>0.2370</td></tr><tr><td>(ii)</td><td>0.5</td><td>4.0</td><td>✓</td><td>4.03</td><td>31.00</td><td>0.2449</td></tr><tr><td>(iv)</td><td>1.0</td><td>2.0</td><td>✓</td><td>4.45</td><td>34.89</td><td>0.2428</td></tr><tr><td>(iii)</td><td>1.0</td><td>1/4.0</td><td>X</td><td>3.50</td><td>24.88</td><td>0.2469</td></tr><tr><td>Ours</td><td>1.0</td><td>4.0</td><td>✓</td><td>3.07</td><td>27.79</td><td>0.2459</td></tr></table>
+
+Table 3. Ablation of different diffusion process configurations varying  $\sigma_{\mathrm{data}}$ , input scaling  $\sigma_{\mathrm{in}}$ , and treatment of images as infinite-framerate videos, evaluated on our internal dataset in  $64 \times 36$ px resolution.
+
+# 4.1. Datasets
+
+We train our models on an internal dataset consisting of 1.265M images and 238k hours of videos, each with a corresponding text caption. Due to the difficulty in acquiring high-quality captions for videos, we develop a video captioning model that we use to produce synthetic video captions for the portion of videos in the dataset missing such annotation.
+
+We make use of the following datasets for evaluation which are never observed during training:
+
+UCF-101 [55] is a video dataset containing 13.320  $320 \times 240$ px Youtube videos from 101 action categories.
+
+MSR-VTT [65] is a dataset containing  $10.000320 \times 240\mathrm{px}$  web-crawled videos, each manually annotated with 20 text captions. The test set contains 2.990 videos and 59.800 corresponding captions.
+
+# 4.2. Evaluation Protocol
+
+To validate the choices operated on the diffusion framework and on model architecture, present method ablations performed in  $64 \times 36\mathrm{px}$  resolution using the first-stage model only, and compute FID [18], FVD [60] and CLIPSIM [63] metrics against the test set of our internal dataset on  $50\mathrm{k}$  generated videos.
+
+To evaluate our method against baselines, we follow the protocols highlighted in [4, 13, 32, 48, 62, 72] for zero-
+
+shot evaluation on the UCF-101 [55] and MSR-VTT [65] datasets. We generate 16 frames videos in  $512 \times 288\mathrm{px}$  resolution at 24fps for all settings. We evaluate both at the native  $512 \times 288\mathrm{px}$  resolution with 16:9 aspect ratio and in the  $288 \times 288\mathrm{px}$  square aspect ratio typically employed on these benchmarks. We note that the evaluation protocols of [4, 13, 32, 48, 62, 72] present different choices regarding the number of generated samples, distribution of class labels, choice of text prompts. We make use of the following evaluation parameters:
+
+Zero-shot UCF-101 [55] We generate 10,000 videos [4, 62] sampling classes with the same distribution as the original dataset. We produce a text prompt for each class label [13] and compute FVD [60] and Inception Score [46].
+
+Zero-shot MSR-VTT [65] We generate a video sample for each of the 59.800 test prompts [13, 48] and compute CLIP-FID [27] and CLIPSIM [63].
+
+To provide a more complete performance assessment and compare against state-of-the-art closed-source methods not reporting results for these benchmarks, we perform a user study evaluating photorealism, video-text-alignment and, most importantly, the quantity and quality of the generated motion, important characteristics of a video generator that may signal the generation of dynamic images, i.e. videos with dim motion, or motion artifacts rather than videos with vivid and high-quality motion.
+
+# 4.3. Ablations
+
+To evaluate the proposed FIT architecture, we consider the U-Net of [10], which we adapt to the video generation setting by interleaving temporal attention operations. We consider two U-Net variants of different capacities and a smaller variant of our FIT to evaluate the scalability of both architectures. We detail the architectures in Appx. B and show results in Tab. 2.
+
+Our 500M parameters FIT trains  $3.31 \times$  faster than the baseline 284M parameters U-Net, performs inference  $4.49 \times$  faster and surpasses it in terms of FID and CLIPSIM. In addition, both FITs and U-Nets show strong performance gains with scaling. Our largest FIT scales to 3.9B parameters with only a  $1.24 \times$  increase in inference time with respect to the 284M U-Net.
+
+To evaluate the choices operated on our diffusion framework, we ablate different configurations of the diffusion process using our 500M FIT architecture. We produce the following variations: (i) the original EDM framework, (ii) our scaled diffusion framework with EDM  $\sigma_{\mathrm{data}}$ , (iii) our framework with a reduced value of  $\sigma_{\mathrm{in}}$ , (iv) our framework with images not treated as infinite-frame-rate videos. Our framework improves over EDM under all metrics (i) and shows benefits in setting  $\sigma_{\mathrm{data}} = 1$ , an effect that we attribute to the creation of a training target and loss weighting matching the widely used  $v$ -prediction formulation of
+
+<table><tr><td></td><td>FVD ↓</td><td>FID ↓</td><td>IS ↑</td></tr><tr><td>CogVideo [23] (Chinese)</td><td>751.3</td><td>-</td><td>23.55</td></tr><tr><td>CogVideo [23] (English)</td><td>701.6</td><td>-</td><td>25.27</td></tr><tr><td>MagicVideo [72]</td><td>655</td><td>-</td><td>-</td></tr><tr><td>LVDM [17]</td><td>641.8</td><td>-</td><td>-</td></tr><tr><td>Video LDM [4]</td><td>550.6</td><td>-</td><td>33.45</td></tr><tr><td>VideoFactory [62]</td><td>410.0</td><td>-</td><td>-</td></tr><tr><td>Make-A-Video [48]</td><td>367.2</td><td>-</td><td>33.00</td></tr><tr><td>PYoCo [13]</td><td>355.2</td><td>-</td><td>47.46</td></tr><tr><td>Snap Video (288 × 288 px)</td><td>260.1</td><td>39.0</td><td>38.89</td></tr><tr><td>Snap Video (512 × 288 px)</td><td>200.2</td><td>28.1</td><td>38.89</td></tr></table>
+
+Table 4. Zero-shot evaluation results on UCF101 [55].  
+
+<table><tr><td></td><td>CLIP-FID ↓</td><td>FVD ↓</td><td>CLIPSIM ↑</td></tr><tr><td>NUWA [64] (Chinese)</td><td>47.68</td><td>-</td><td>0.2439</td></tr><tr><td>CogVideo [23] (Chinese)</td><td>24.78</td><td>-</td><td>0.2614</td></tr><tr><td>CogVideo [23] (English)</td><td>23.59</td><td>-</td><td>0.2631</td></tr><tr><td>MagicVideo [72]</td><td>-</td><td>998</td><td>-</td></tr><tr><td>LVDM [17]</td><td>-</td><td>-</td><td>0.2381</td></tr><tr><td>Latent-Shift [2]</td><td>15.23</td><td>-</td><td>0.2773</td></tr><tr><td>Video LDM [4]</td><td>-</td><td>-</td><td>0.2929</td></tr><tr><td>VideoFactory [62]</td><td>-</td><td>-</td><td>0.3005</td></tr><tr><td>Make-A-Video [48]</td><td>13.17</td><td>-</td><td>0.3049</td></tr><tr><td>PYoCo [13]</td><td>9.73</td><td>-</td><td>-</td></tr><tr><td>Snap Video (288 × 288 px)</td><td>8.48</td><td>110.4</td><td>0.2793</td></tr><tr><td>Snap Video (512 × 288 px)</td><td>9.35</td><td>104.0</td><td>0.2793</td></tr></table>
+
+Table 5. Zero-shot evaluation results on MSR-VTT [65].
+
+Salimans et al. [45] (see Tab. 1). Using  $\sigma_{\mathrm{in}} < s\sqrt{T}$  (see Sec. 3.2) impairs performance (iii). Finally, treating images as infinite-frame-rate videos consistently improves FID.
+
+# 4.4. Quantitative Evaluation
+
+We perform comparison of Snap Video against baselines on the UCF101 [55], and MSR-VTT [65] datasets respectively in Tab. 4 and Tab. 5. FID and FVD video quality metrics show improvements over the baselines which we attribute to the employed diffusion framework and joint spatiotemporal modeling performed by our architecture. On UCF101, our method produces the second-best IS of 38.89, demonstrating good video-text alignment. While our method surpasses Make-A-Video [48] on UCF101, we note that it produces a lower CLIPSIM score on MSR-VTT. We attribute this behavior to the use of T5 [39] text embeddings in place of the commonly used CLIP [38] embeddings which were observed [43] to produce higher text-image alignment despite similar CLIPSIM.
+
+To provide a comprehensive evaluation we run a user study to evaluate photorealism, video-text alignment, quantity of motion and quality of motion, important aspects of a video generator. Three publicly-accessible state-of-the-art video generators are considered: Gen-2 [11], PikaLabs [1]
+
+![](images/2fa82ded38c5ae7b26fc3839ffcf7eca9c46cddc346d8f0d30486611bcb9a4c6.jpg)  
+Figure 4. Qualitative results comparing Snap Video to state-of-the-art video generators on publicly available samples. While baseline methods present motion artifacts (top-left, top-right, bottom-right) or produce dynamic images (bottom-left), our method produces more temporally coherent motion. Best viewed in the Website.
+
+![](images/382a92480806ce18863c9abc916323b1b4c2e639fad98e114ce94840ca3bda3c.jpg)
+
+<table><tr><td></td><td>Photorealism</td><td>Video-Text Align.</td><td>Mot. Quant.</td><td>Mot. Qual.</td></tr><tr><td>Gen-2 [11]</td><td>44.3</td><td>81.0</td><td>96.0</td><td>78.7</td></tr><tr><td>PikaLab [1]</td><td>61.5</td><td>80.3</td><td>89.2</td><td>70.5</td></tr><tr><td>Floor33 [17]</td><td>76.3</td><td>80.9</td><td>88.0</td><td>79.1</td></tr></table>
+
+Table 6. User study on photorealism, video-text alignment, motion quantity and quality against publicly-accessible video generators on 65 dynamic scene prompts. % of votes in favor of our method.
+
+and Floor33 [17]. We filter a set of 65 prompts from [31] describing scenes with vivid motions, and generate a video for each method with default options. We ask the participants to express preference between paired samples from Snap Video and each baseline, gathering votes from 5 users for each sample. Results are shown in Tab. 6 and video samples provided along with the employed prompt list in Appx. D.2 and in the Website. Our method produces results with photorealism comparable to Gen-2, while surpassing PikaLab and Floor33, and outperforms all baselines with respect to video-text alignment. Most importantly, we note that baselines often produce dynamic images, i.e. videos with dim motion, or videos with motion artifacts, a finding we attribute to the challenges in modeling large motion. In contrast, our method, thanks to the joint spatiotemporal modeling approach, produces vivid and high-quality motion as shown by the motion metrics.
+
+# 4.5. Qualitative Evaluation
+
+In this section, we perform qualitative evaluation of our framework. In Fig. 4, Appx. D.3 and the Website, we present qualitative results comparing our method to state-
+
+of-the-art generators [4, 13, 21, 48] on samples publicly released by the authors. While such prompts might have been selected to highlight strengths of the baselines, our method produces more photorealistic samples aligned to the text descriptions. Most importantly, our samples present vivid and high-quality motion avoiding flickering artifacts that are present in the baselines due to temporal inconsistencies. We accompany qualitative evaluation with a user study performed on the same set of samples in Appx. D.2.
+
+# 5. Conclusions
+
+In this work, we highlight the shortcomings of diffusion processes and architectures commonly used in text-to-video generation, and systematically address them by treating videos as first-class citizens. First, we propose a modification to the EDM [25] diffusion framework for the generation of high-resolution videos and treat images as high frame-rate videos to avoid image-video modality mismatches. Second, we replace U-Nets [41] with efficient transformer-based FITs [8] which we scale to billions of parameters. Thanks to their learnable compressed representation of videos, they significantly improve training times, scalability and performance with particular regards to temporal consistency and motion modeling capabilities due to the joint spatiotemporal modeling on the compressed representation. When evaluated on UCF101 [55] and MSR-VTT [65] and in user studies, Snap Video attains state-of-the-art performance with particular regard to the quality of the modeled motion.
+
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+        "image_caption": [
+            "Figure 1. We propose a novel snapshot Lidar imaging system that is inspired by off-axis holography techniques.  $(1^{\\mathrm{st}}$  col.) Off-axis holography uses oblique illumination to separate the hologram and its twin in Fourier space.  $(2^{\\mathrm{nd}}$  col.) We leverage the rolling-shutter effect of amplitude modulated continuous wave time-of-flight (AMCW-ToF) cameras to emulate the off-axis principle, thereby separating the time-of-flight hologram and its twin in Fourier space.  $(3^{\\mathrm{rd}}$  col.) The conventional operation of AMCW-ToF Lidars requires four measurements, whereas our technique is  $4\\mathrm{x}$  faster, improving both the data bandwidth and temporal resolution.  $(4^{\\mathrm{th}}$  col.) Reconstructed phase (that encodes depth) from measurements—The reconstructions are quite similar even with  $4\\mathrm{x}$  fewer measurements."
+        ],
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+        "type": "text",
+        "text": "Abstract",
+        "text_level": 1,
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+        "text": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras are finding applications as flash Li-dars in autonomous navigation, robotics, and AR/VR applications. A conventional CW-ToF camera requires illuminating the scene with a temporally varying light source and demodulating a set of quadrature measurements to recover the scene's depth and intensity. Capturing the four measurements in sequence renders the system slow, invariably causing inaccuracies in depth estimates due to motion in the scene or the camera. To mitigate this problem, we propose a snapshot Lidar that captures amplitude and phase simultaneously as a single time-of-flight hologram. Uniquely, our approach requires minimal changes to existing CW-ToF imaging hardware. To demonstrate the efficacy of the proposed system, we design and build a lab prototype, and evaluate it under varying scene geometries, illumina",
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+        "type": "text",
+        "text": "tion conditions, and compare the reconstructed depth measurements against conventional techniques. We rigorously evaluate the robustness of our system on diverse real-world scenes to show that our technique results in a significant reduction in data bandwidth with minimal loss in reconstruction accuracy. As high-resolution CW-ToF cameras are becoming ubiquitous, increasing their temporal resolution by four times enables robust real-time capture of geometries of dynamic scenes.",
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+        "type": "text",
+        "text": "1. Introduction",
+        "text_level": 1,
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+        "text": "Amplitude modulated continuous-wave time-of-flight (AMCW-ToF) cameras, also known as correlation-based time-of-flight or indirect time-of-flight cameras, are used as flash Lidars to compute scene depth, and are used in autonomous navigation, robotics [6, 13], and augmented reality [8]. AMCW-ToF cameras operate by projecting a",
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+    {
+        "type": "header",
+        "text": "CVF",
+        "bbox": [
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+    {
+        "type": "header",
+        "text": "This CVPR paper is the Open Access version, provided by the Computer Vision Foundation. Except for this watermark, it is identical to the accepted version; the final published version of the proceedings is available on IEEE Xplore.",
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+    {
+        "type": "page_number",
+        "text": "25203",
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+    {
+        "type": "table",
+        "img_path": "images/36d7375630fd731530dac31a473d82fc97cd2e08fa355ff169bb9b8ae57904b7.jpg",
+        "table_caption": [],
+        "table_footnote": [],
+        "table_body": "<table><tr><td></td><td>illumination</td><td>reference</td><td>physics</td></tr><tr><td>holography</td><td>coherent beam</td><td>planar beam</td><td>optical interference</td></tr><tr><td>off-axis</td><td>coherent beam</td><td>tilted beam</td><td>optical interference</td></tr><tr><td>CW-ToF</td><td>AMCW</td><td>electronic shutter</td><td>electronic multiplication</td></tr><tr><td>proposed</td><td>AMCW</td><td>rolling shutter</td><td>electronic multiplication</td></tr></table>",
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+        "page_idx": 1
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+    {
+        "type": "text",
+        "text": "Table 1. Principles of holography, off-axis holography, CW-ToF, and proposed snapshot CW-ToF. We draw parallels between off-axis holographic setup, and our proposed Fourier embedded ToF, that allow us to show that using a rolling-shutter sensor and varying the reference phase during CW-ToF acquisition results in a snapshot capture of the \"ToF hologram\" that contains both the amplitude and depth (encoded in phase) of the scene.",
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+    {
+        "type": "text",
+        "text": "temporally varying (often a sinusoidal) light source, and then correlating it on the sensor side with an appropriate (also often a sinusoid) decoding function. Depth is encoded in the phase of the measurements, and hence up to four measurements (quadrature) are required to robustly estimate the depth and intensity of the scene. These quadrature measurements are captured by temporal multiplexing, which invariably leads to lower frame rates and suffers from motion artifacts.",
+        "bbox": [
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+        "type": "text",
+        "text": "Inspired by snapshot off-axis holography techniques, we propose a snapshot CW-ToF imaging technique that measures amplitude and depth using a single capture. The key observation is that by defining the time-of-flight hologram as the complex sinusoid whose amplitude and phase are proportional to the intensity and depth of the scene, we can draw parallels between holography and CW-ToF imaging techniques. This novel formulation of the ToF hologram enables us to translate off-axis techniques to CW-ToF imaging. In particular, by using rolling-shutter CW-ToF sensors [1] and spatially varying the reference phase of the coded exposure, we can emulate the off-axis holography effect and recover the complex-valued ToF hologram. In Tab. 1, we highlight the similarities and differences between holography, off-axis holography, CW-ToF, and the proposed imaging techniques.",
+        "bbox": [
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+        "page_idx": 1
+    },
+    {
+        "type": "text",
+        "text": "To achieve snapshot depth imaging, we leverage the image formation model of CW-ToF cameras, and demonstrate our modification to enable the capture of a ToF hologram with unipolar (all-positive decoding function) and bipolar (positive and negative decoding function) codes. We then show analytical and computational techniques to recover amplitude and depth from a rolling-shutter image and the need for optical prefiltering to prevent aliasing and noise folding.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "We design and build a hardware setup built in the lab",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "with a Melexis 75027 device with region-of-interest support and a galvanometer to emulate the rolling-shutter effect. Using this device, in Sec. 6, we demonstrate that the proposed technique reduces data bandwidth and improves frame rate on various scenes containing diffuse, specular, and refractive objects. The proposed technique is robust to dead and saturated pixels, thereby enabling depth imaging with slightly faulty sensors, and extremely bright settings. We carefully evaluate design parameters including prefiltering window size, and spatial phase variation rate, and provide an experimentally optimal set of values that are agnostic to scene conditions. We empirically show that the proposed Fourier-based reconstruction technique is superior to the standard N-bucket technique for reconstruction.",
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+    {
+        "type": "text",
+        "text": "2. Related Work",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "Continuous wave time-of-flight cameras. CW-ToF cameras measure depth at each spatial pixel with a temporally modulated light source. The intensity of the scene is encoded in the amplitude, and depth in the phase, of the measurements. Typically four or more images, with different phases, are required to recover both amplitude and depth. These four measurements are obtained either with a spatially multiplexed sensor (similar to a Bayer pattern), or with sequential measurements [12]. Spatial multiplexing results in severe aliasing artifacts, and is inherently expensive and cumbersome to manufacture. In contrast, sequential measurements invariably result in motion artifacts when capturing dynamic scenes.",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Advances in CWToF sensing With the increasing number of practical applications for CWToF, work has been done to enhance its capabilities and mitigate its limitations. CS-ToF [20] is a compressive ToF imaging architecture aimed at overcoming sensor resolution limitations. As compressive sensing relies on the assumption of a linear measurement process for high resolution image estimation, CS-ToF uses a phasor representation inspired by Gupta [9] and O'Toole [25] of the ToF output to create a linear model between the scene and ToF measurements. In a process similar to single pixel imaging, laser light is reflected off of an object onto a high resolution digital micro-mirror device (DMD), and then relayed onto a lower resolution ToF sensor. By changing the DMD codes across multiple exposures, CS-ToF performs spatiotemporal multiplexing of the scene's amplitude and phase; however, sacrificing temporal resolution for spatial resolution. CWToF has also been combined with other modalities such as spectrum [27], light transport [24, 31], and light fields [15] that have significantly expanded the applications of CWToF cameras. Nevertheless, it is worth noting that there are few, if any, approaches that capture CWToF data in a snapshot manner, that is crucial for dynamic scenes.",
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+        "type": "page_number",
+        "text": "25204",
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+        "type": "text",
+        "text": "Superheterodyned interferometry. A related technology that enables snapshot ToF sensing is superheterodyned interferometric time-of-flight (SH-ToF) [21, 22], where two closely spaced illumination wavelengths combine to produce a much larger (heterodyned) synthetic wavelength. This approach however still requires capturing two separate images (one with each wavelength) to produce the final superheterodyned measurement. Recent work by Ballester et al. [3] demonstrated that SH-ToF can be combined with the off-axis holography to obtain a snapshot ToF imaging system. We next briefly discuss off-axis holography to understand its relevance to ToF sensing.",
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+        "page_idx": 2
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+    {
+        "type": "text",
+        "text": "Off-axis holography Off-axis holography [7, 19] is a widely known imaging technique for reconstructing the amplitude  $(E_{s}(x,y))$  and phase  $(\\phi_s(x,y))$  of a hologram with a single measurement. The experimental setup schematic is shown in the first column of Fig. 1. The measurement by the camera is given by",
+        "bbox": [
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+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} I = \\left| E _ {s} (x, y) e ^ {- \\phi_ {s} (x, y)} + E _ {r} e ^ {- k \\sin (\\theta) x} \\right| ^ {2} \\\\ = \\left| E _ {s} (x, y) \\right| ^ {2} + \\left| E _ {r} \\right| ^ {2} + E _ {r} ^ {*} E _ {s} (x, y) e ^ {k \\sin (\\theta) x - \\phi_ {s} (x, y)} \\\\ + E _ {r} E _ {s} ^ {*} (x, y) e ^ {- k \\sin (\\theta) x + \\phi_ {s} (x, y)} \\tag {1} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "Off-axis holography embeds the hologram  $(E_{s}(x,y)e^{-\\phi_{s}(x,y)})$  and its twin  $(E_{s}^{*}(x,y)e^{\\phi_{s}(x,y)})$  separately in the Fourier domain allowing us to recover the hologram computationally. Ballester et al. [2] showed that off-axis techniques can be used in synthetic wavelength interferometry. Specifically, the system consisted of a colocated, dual wavelength illumination source, and two, spatially separated reference beams. The separated location implied that the phasor information was encoded in different parts of the Fourier spectrum, enabling a simple frequency domain post-processing algorithm to estimate depth information with a single image. Our technique is inspired by off-axis holography. Two key observations that enable our technique are (i) expressing the time-of-flight image formation model with complex sinusoids allows us to draw parallels between holography and AMCW-ToF (ii) the rolling-shutter effect allows us to emulate off-axis technique.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Applications of CW-ToF cameras. Beyond depth imaging, CW-ToF cameras enable a plethora of important applications in imaging. For example, Callenberg et al. [4] showed that a CW-ToF camera can enable difference imaging, that is often useful for implementing convolutional operations within sensors. Achar et al. [1] showed that ToF sensors can be used to tease out sub-surface features through epipolar gating. Similarly, Naik et al. [24] and Kadambi et al. [16] showed that a light transport matrix-based formulation of ToF measurements enabled measur",
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+        "page_idx": 2
+    },
+    {
+        "type": "image",
+        "img_path": "images/858b901540602697be8862ab2f107e769bd32009fed8a8a8ecd6cb7b20ba7b2c.jpg",
+        "image_caption": [
+            "Figure 2. CW-ToF imaging systems. CW-ToF cameras use high-frequency illumination sources and exposure codes to indirectly measure the object's depth. The measurement is the product of the delayed illumination signal and programmatically phase-shifted exposure code. The delay encodes object depth and is recoverable by taking multiple measurements with varying phase-shift  $(\\theta)$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "ing multipath interferences, that are key to measuring geometric properties of complex objects like metal and glass. Our proposed work enables a similar slew of applications beyond depth imaging, including sub-surface imaging and multipath interference reduction (via epipolar gating).",
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+    {
+        "type": "text",
+        "text": "3. Technical Background",
+        "text_level": 1,
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+    {
+        "type": "text",
+        "text": "As shown in Fig. 2, an amplitude-modulated continuous-wave time-of-flight camera (AMCW-ToF) has an illumination source whose amplitude  $(e(t))$  varies over time at several tens of MHz. While these amplitude variations are typically sinusoidal, other modulations have been successfully demonstrated in the past [9-11] for various applications. The light received  $(r(t))$  at the sensor is attenuated and delayed based on the light transport of the scene  $(r(t) = Ae(t - \\tau))$ , where  $\\tau$  is the total time-of-travel of the light beam. Assuming a collocated light source and sensor and no multi-bounce paths,  $\\tau = 2d\\omega /c$ , where  $d$  is the distance to the object,  $\\omega$  is the modulation frequency, and  $c$  is the speed of light. The sensor temporal exposure (s(t)) is also modulated, typically as a square wave (unipolar or bipolar) with the same frequency as the illumination. Recent sensors mostly use bipolar coding with a two-bucket architecture [30], and the exposure duration is approximated with a sinusoidal modulation. The measurement by the sensor is given by",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} m _ {\\theta} = \\frac {1}{T} \\int_ {t = 0} ^ {T} A r (t) s (t) d t \\\\ = \\frac {A}{T} \\int_ {t = 0} ^ {T} \\sin (\\omega t + \\phi) \\sin (\\omega t + \\theta) d t = \\frac {A}{2} \\cos (\\theta - \\phi). \\tag {2} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
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+    {
+        "type": "text",
+        "text": "Most hardware implementations of CWToF Lidar mea",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "page_number",
+        "text": "25205",
+        "bbox": [
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+        "page_idx": 2
+    },
+    {
+        "type": "text",
+        "text": "sure four images  $m_0, m_{\\pi/2}, m_\\pi$ , and  $m_{3\\pi/2}$  and compute amplitude and phase as",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA = 2 \\sqrt {(m _ {0} - m _ {\\pi}) ^ {2} + (m _ {\\pi / 2} - m _ {3 \\pi / 2}) ^ {2}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\phi = \\arctan \\frac {m _ {\\pi / 2} - m _ {3 \\pi / 2}}{m _ {0} - m _ {\\pi}}. \\tag {3}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "The quadrature technique is also extended to the N-tap technique [28] by taking  $\\mathbf{N}$  measurements corresponding to  $\\theta = \\{0, 2\\pi / N, 4\\pi / N, c \\dots, 2\\pi (N - 1) / N\\}$  and computing amplitude and phase as:",
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nA = \\sqrt {\\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2} + \\left(\\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N}\\right) ^ {2}}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\phi = \\arctan \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} / \\sum_ {n = 0} ^ {N - 1} m _ {\\frac {2 \\pi n}{N}} \\cos \\frac {2 \\pi n}{N} \\tag {4}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Unlike these techniques, we reconstruct amplitude and phase using a single image, which we discuss next.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "4. Proposed Technique: Snapshot CWTof",
+        "text_level": 1,
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+    },
+    {
+        "type": "text",
+        "text": "The key idea for measuring amplitude and depth using a single image is to spatially vary the phase  $\\theta$  linearly along rows or columns during the exposure. We can achieve this spatial variation with simple hardware modifications by either (1) changing the existing hardware design with different exposure phase offsets per row/column, (2) using a rolling-shutter camera and changing the phase offset of either the illumination or sensor during each row capture, or (3) using a fast line sensor (or hardware region-of-interest supporting camera) and scanning the scene line by line with a Galvanic mirror while changing the phase offset of each line. We used the last alternative in this paper, as the Melexis 75027 supports hardware ROI [23].",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "To understand how linearly varying  $\\theta$  embeds both amplitude and phase in the captured image, we follow the notation from O'Toole et al. [26], Li et al. [21], and Gupta et al. [9] and represent the amplitude and phase images with complex sinusoidal notation as  $I(x,y) = A(x,y)e^{-j2d\\omega /c}$  and the Fourier Transform of this sinusoid as  $\\mathcal{I}(\\omega_x,\\omega_y)$ . For brevity, we define  $\\phi = 2d\\omega /c$  as the phase shift of the illumination signal. Varying  $\\theta$  linearly during the measurement results in",
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\begin{array}{l} m _ {\\theta = k x} (x, y) = \\frac {A (x , y)}{2} \\cos (k x - \\phi (x, y)) \\\\ = \\frac {A (x , y)}{4} \\left(e ^ {j (k x - \\phi (x, y))} + e ^ {- j (k x - \\phi (x, y))}\\right) \\tag {5} \\\\ \\end{array}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Taking the Fourier transform on both sides, we get",
+        "bbox": [
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+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\mathcal {F} _ {m _ {k x}} \\left(\\omega_ {x}, \\omega_ {y}\\right) = \\frac {1}{4} \\left(\\mathcal {I} \\left(\\omega_ {x} - k, \\omega_ {y}\\right) + \\mathcal {I} ^ {*} \\left(k - \\omega_ {x}, - \\omega_ {y}\\right)\\right), \\tag {6}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "which is similar to the off-axis holography Eq. (1). Therefore, we will refer to the complex sinusoidal notation  $(I(x,y))$  as the ToF hologram and its complex conjugate  $(I^{*}(x,y))$  as the ToF twin.",
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+    {
+        "type": "text",
+        "text": "As depicted in Fig. 3, to recover the ToF hologram from the image captured by varying  $\\theta$  linearly, we take the Fourier transform of the measured image, filter the ToF twin, right shift the ToF hologram, and compute the inverse Fourier transform. The amplitude and phase of the inverse Fourier transform result are the amplitude and phase of the scene.",
+        "bbox": [
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+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Extension to unipolar codes. Most recent ToF sensors use a two-bucket architecture to suppress background illumination; hence, the codes are bipolar. However, our technique is also amenable to unipolar-coded time-of-flight cameras and imperfect two-bucket architecture cameras. In this case, the measurement model becomes",
+        "bbox": [
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\nm _ {\\theta} = \\frac {A}{2} \\cos (\\theta - \\phi) + a. \\tag {7}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            607,
+            369,
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+            398
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "where  $a$  is proportional to the ambient background light intensity. In this case, the Fourier transform has a DC component that can be filtered out along with the ToF twin.",
+        "bbox": [
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+            402,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Aliasing, noise folding, and prefiltering. From Fig. 3 (b), we notice that the ToF hologram and twin overlap in the Fourier domain. This overlap results in aliasing, where the high-frequency content of the ToF twin may appear as low-frequency content of the ToF hologram, and noise folding, where the twin's noise folds into the ToF hologram's noise.",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "To mitigate aliasing and noise folding, we optically filter the high-resolution ToF hologram before the linear phase shifting and measurement. In the hardware implementation, we achieve this by simply defocusing the imaging lens in front of the sensor. This simple blurring operation reduces aliasing and noise folding artifacts (Fig. 3 (d, e)).",
+        "bbox": [
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+            571,
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+            662
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "text",
+        "text": "Therefore, while the proposed snapshot Lidar technique can capture amplitude and phase with a single image, it does so by sacrificing spatial resolution for temporal resolution. As spatial resolutions of imaging sensors keep increasing (compare PMD vs DME660 vs. Melexis) due to better fabrication techniques, trading spatial resolution for improving temporal resolution is arguably more useful.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Phase noise. As with any optical measurements, the recovered phase will have noise due to shot noise in the measurements. This shot noise is present even for the standard N-bucket technique [17, 18]. The standard deviation of the phase noise for the snapshot technique is",
+        "bbox": [
+            496,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\sigma_ {\\phi} ^ {2} \\approx \\frac {\\partial \\phi}{\\partial m _ {k x}} m _ {k x} \\tag {8}\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            635,
+            866,
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+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "page_number",
+        "text": "25206",
+        "bbox": [
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+            944,
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+            955
+        ],
+        "page_idx": 3
+    },
+    {
+        "type": "image",
+        "img_path": "images/82f479d141147271f6a5fef43b6752e959fa1bbd78127fcf9202efa2fe8bfd05.jpg",
+        "image_caption": [
+            "(a) snapshot image"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            89,
+            250,
+            263
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/bb781112949977db1a30be2964b570d37f9ae631392b586de5bcf3fcdf676fc3.jpg",
+        "image_caption": [
+            "(b) Fourier transform"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            251,
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/0116208e53f9efb098138a9b858810ddb3c5756a52da370617890f66057846ed.jpg",
+        "image_caption": [
+            "(c) filtered and shifted",
+            "Figure 3. Snapshot CWToF decoding, and effect of prefiltering. (a) captured snapshot CW-ToF image. (b) Fourier transform of snapshot image. (c) We filter out the twin and frequency shift the hologram in the Fourier domain to recover the ToF hologram. (d) We reconstruct the phase by computing the phase of the inverse Fourier transform of (c). (top row vs. bottom row) We prefilter the ToF hologram using a defocused imaging lens, which can decrease the overlap between the hologram and its twin. The prefiltering decreases aliasing and noise folding, resulting in a 3dB SNR gain ( $2 \\times$  smaller phase error). (e) zoomed-in offsets. (left) Without prefiltering, the high-frequency phase noise of the twin shows up as the low-frequency phase noise. (right) aliasing decreases with prefiltering."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            403,
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+            263
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/9eb1412beb1e5884ffd91c73034ea91a2485e48bd85359707b0260488fa7b931.jpg",
+        "image_caption": [
+            "(d) recovered phase"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            555,
+            90,
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+        "page_idx": 4
+    },
+    {
+        "type": "image",
+        "img_path": "images/06156c8f4d30381cc2babfc53d103a89f08a5d6db9024d4ac46cb8597556ef80.jpg",
+        "image_caption": [
+            "(e) zoomed in offsets"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            705,
+            88,
+            885,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "where  $\\phi$  is explicitly expressed as",
+        "bbox": [
+            76,
+            390,
+            303,
+            406
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "equation",
+        "text": "\n$$\n\\phi (x, y) = \\arctan \\left(\\frac {m _ {k x} (x , y) \\sin (k x) * \\operatorname {s i n c} (k x)}{m _ {k x} (x , y) \\cos (k x) * \\operatorname {s i n c} (k x)}\\right).\n$$\n",
+        "text_format": "latex",
+        "bbox": [
+            91,
+            412,
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+            448
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Here,  $\\circledast$  is spatial convolution. We show the derivation in the supplementary material. An analytical comparison of the noise variance between the N-bucket and snapshot techniques is not feasible. Instead, in Sec. 6, we show empirical comparison and show that the snapshot phase measurement does not result in additional phase noise.",
+        "bbox": [
+            75,
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+            470,
+            546
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "5. Experimental setup",
+        "text_level": 1,
+        "bbox": [
+            76,
+            558,
+            266,
+            575
+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "To implement our method, we use the EVK75027-110-940-2 evaluation kit (EVK) by Melexis which uses diffused  $940\\mathrm{nm}$  VCSEL diodes for illumination and a Melexis 75027 CWToF sensor. While the sensor is a global shutter, we can create the rolling shutter effect by taking advantage of the sensor's hardware programmable ROI to reduce the per-frame capture/readout to a single row.",
+        "bbox": [
+            75,
+            583,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "For our experiments, we mount the EVK75027 to a linear 3D stage and carefully align the view to a set of 2-axis galvanic mirrors (GVS012) from Thorlabs. Then, we reduce the ROI of the camera to a single line, and steer the view of the galvos with a DAQ. Additionally, we separated the illumination board from the rest of the EVK and mounted it on top of the galvanic mirrors for approximate collocation of light source and apparent camera location. The MLX75027 module contained a firmware lock on the frame rate at 100 fps, severely limiting our capture speed when the ROI is reduced to only a single line. However, our setup demonstrates a proof-of-concept, and future versions of Melexis cameras without a firmware lock will enable a real-time operation.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "One way to emulate snapshot measurements from our setup is to capture multiple images with varying phases and appropriately select the rows/columns in the image. In practice, we found it to be significantly simpler and convenient to conduct most of our experiments. In Fig. 4, we show the hardware prototype with fast-scanning galvonic mirrors. Additionally in Fig. 5, we compare results from an emulated versus hardware implemented snapshot capture and notice that the techniques result in the same amplitude and phase estimates. For more details about the hardware prototype and emulation method, we refer the reader to the supplemental material.",
+        "bbox": [
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+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "6. Experiments",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "In this section, we use the hardware setup and emulation technique described in Sec. 5 to evaluate the proposed snapshot technique systematically. We show that (1) prefiltering improves signal-to-noise ratio (SNR) and prefiltering with cylindrical lenses is better than regular lenses; (2) the optimal phase variation rate is  $(k = \\frac{\\pi}{2}\\mathrm{line}^{-1})$ ; (3) the Fourier technique is superior to the N-bucket technique for snapshot images; (4) the snapshot technique does not add any additional noise and (5) is robust to saturated and dead pixels; (6) rotating the phase variation (by rotating the camera itself) decreases aliasing. In the supplementary, we show extended results and a comparison with the dual phase mode of the epc660 camera. We share our code on GitHub.",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "text",
+        "text": "Optimal prefiltering kernel. As mentioned in Sec. 4, prefiltering reduces aliasing and noise folding artifacts. As aliasing and noise folding occur in the direction of the rolling shutter, blurring the ToF hologram only in the rolling shutter direction is better than isotropic blurring as shown in Fig. 6. We can implement hardware anisotropic blurring by",
+        "bbox": [
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+        ],
+        "page_idx": 4
+    },
+    {
+        "type": "page_number",
+        "text": "25207",
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+        "page_idx": 4
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+        "img_path": "images/177cc8cf5178c9d80f3da230e8ba5f6a36d86ed42c212337a748dc69c859c7d6.jpg",
+        "image_caption": [],
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+        ],
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+    {
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+        "img_path": "images/548834f57c7c163227eabea55c2d0433f86eb4e93fe6ea77bbad2e737fef1e3b.jpg",
+        "image_caption": [
+            "camera components"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            96,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/4781d74b6cf3ced22fb6781c5ae156e0e529d0f48649239e66fe28fae44228e1.jpg",
+        "image_caption": [
+            "galvo/synchronization components"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            256,
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+        ],
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+    {
+        "type": "image",
+        "img_path": "images/965c574f4f684df40ca0ce49fd399496c1fb82bbec46a58cf0e81d159bca0eb0.jpg",
+        "image_caption": [
+            "a. hardware setup"
+        ],
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/5ebd0578bf192c7f07b226dfb7482e868403baf62e87d563b8bb52b068800a89.jpg",
+        "image_caption": [
+            "b. emulation method"
+        ],
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+        "bbox": [
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+        ],
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+    },
+    {
+        "type": "image",
+        "img_path": "images/bc1a395ae3ab4ce0a6e9b1fe922696bd070b616be4805467decec7f880c82f46.jpg",
+        "image_caption": [
+            "Figure 4. Lab prototype, and rolling shutter encoding scheme. (a) Rolling shutter hardware prototype with the camera components outlined in yellow and galvonic mirrors/synchronization hardware outlined in blue. (b) Compositing quadrature images to create an emulated rolling shutter snapshot."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "using a defocused cylindrical lens. Note that the optimal kernel for prefiltering is a 1D sinc function in the spatial domain (corresponding to eliminating all the overlapping frequencies). However, that is not physically possible. Designing the optimal optically-realizable kernel is beyond the scope of this paper.",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Assuming a 1D-Gaussian prefiltering kernel, we computed the effect of blur kernel size (measured in standard deviation  $\\sigma$ ) on the phase reconstruction accuracy. As shown in Fig. 7 (a), for all values of  $k$ , the SNR initially improves when  $\\sigma$  is increased and then decreases showing that an optimal blur kernel size exists. This phenomenon occurs as prefiltering initially reduces the overlap between the ToF hologram and the twin but later reduces the frequency con",
+        "bbox": [
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+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/89fb19e5ccee86a86e4eeb78d269f1859c05757e13efa86547e49f38ece1c33d.jpg",
+        "image_caption": [],
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+    {
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+        "img_path": "images/ffefeba3148c77b7c91ea04d0df1f5f4d55ef5fd450d36d43ccc05e6ad93d1a8.jpg",
+        "image_caption": [
+            "Figure 5. Advantages of emulated snapshot capture. Amplitude and depth reconstructed by snapshot data captured with emulations (this paper) vs. single line ROI (ideal optical setup) and galvanic mirrors. The emulated measurements and the reconstructed phase are similar to the full prototype. We hence demonstrated all experiments with an emulated setup, as it enables a faithful evaluation of a true snapshot system.",
+            "Figure 6. Robustness to noise due to prefiltering. Prefiltering reduces aliasing and noise folding artifacts to improve the reconstruction quality. Compared to the 2D-blur kernel, the 1D-blur kernel in the direction of rolling shutter direction results in a significantly higher-quality reconstruction. Since the ToF hologram and twin overlap occur only in the rolling shutter direction, a 1D blur kernel preserves the spatial frequencies in the direction orthogonal to rolling shutter."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            477,
+            887,
+            670
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "tent in the captured ToF hologram.",
+        "bbox": [
+            500,
+            820,
+            728,
+            835
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "text",
+        "text": "Optimal phase variation rate  $k$ . In Fig. 7 (b), we plot optimal  $\\sigma$  value as a function of  $R = 2\\pi / k$ , which represents the average number of rows required before the  $\\theta$",
+        "bbox": [
+            496,
+            854,
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+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "page_number",
+        "text": "25208",
+        "bbox": [
+            478,
+            944,
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+            955
+        ],
+        "page_idx": 5
+    },
+    {
+        "type": "image",
+        "img_path": "images/24c1aa4ee3c15c6cc8289286a30a8e365a0c59ce7612da9cda2d7f4c08b2c4c5.jpg",
+        "image_caption": [
+            "(a)"
+        ],
+        "image_footnote": [],
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+            237
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/78cf7a686275308789645f8694480559643bafe0490e3d32daf380819851548b.jpg",
+        "image_caption": [
+            "(b)"
+        ],
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d55e5df3a4e1e5e0b2172ab01c90a51e81106aa340e36f8b53615c292b00c8b.jpg",
+        "image_caption": [
+            "Figure 7. Optimal prefilter size and phase variation rate. (a) We show the effect of the standard deviation of the blur kernel (blur kernel size) on the phase reconstruction accuracy for various phase variation rates  $(k)$ . The optimal prefilter size depends on the phase variation rate. (b) The best phase reconstruction rate that results in best reconstruction quality is around  $R = 4$ , and this is consistently observed for various scenes.  $R = 4$  results in the least overlap between the ToF holography and its twin."
+        ],
+        "image_footnote": [],
+        "bbox": [
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+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/28c9620ca409e7e3a451d10660bbab5decd8a4479ef1dd06567804f095f35b97.jpg",
+        "image_caption": [
+            "Phase"
+        ],
+        "image_footnote": [],
+        "bbox": [
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+            513
+        ],
+        "page_idx": 6
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+        "image_caption": [],
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+    },
+    {
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+        "img_path": "images/c310f7b4257fd98e4898ab2f063aa804ebc5ad1240ceb8d437d8c7ddc9f4f50a.jpg",
+        "image_caption": [],
+        "image_footnote": [],
+        "bbox": [
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+            606
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/6d74681d7cd7ee3edc1cab6348769271829f2d887fa47e7dcf87fd6781e94999.jpg",
+        "image_caption": [
+            "10² 104 106 -2 0 2"
+        ],
+        "image_footnote": [],
+        "bbox": [
+            80,
+            609,
+            295,
+            702
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/4d2f7a93faa60db4e1d640fdb5e36d56edb25245174a22814aaf600616d7e11a.jpg",
+        "image_caption": [
+            "Figure 8. Visualization of the effect of changing the phase variation rate. In practice, we take the Discrete Fourier Transform which is circular. The smaller the overlap between the hologram and twin, the better we can reconstruct the phase."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            300,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "value resets. From the graph, we can notice that the best SNR occurs at around  $R = 3.5$ . While the optimal value depends on the noise and frequency content of the scene, we observed that it is always around  $R = 4.0$ , and the SNR difference between the optimal and  $R = 4.0$  is not signifi",
+        "bbox": [
+            75,
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+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "image",
+        "img_path": "images/72e36c2de69899ed3af6bcee2d812a192d341b95611786c70902778b9760d4d4.jpg",
+        "image_caption": [
+            "Figure 9. For the snapshot image, instead of the proposed Fourier technique, we can also use the standard N-bucket technique by using neighboring rows as a proxy for the remaining phases. However, the N-bucket technique performs significantly worse compared to the Fourier technique at all the phase variation rates and cannot handle non-integer values of  $R$ ."
+        ],
+        "image_footnote": [],
+        "bbox": [
+            500,
+            90,
+            883,
+            229
+        ],
+        "page_idx": 6
+    },
+    {
+        "type": "text",
+        "text": "cant. At  $R = 4$ , the overlap between the ToF hologram and the twin is minimal, and  $\\sigma = 1$  corresponds to suppressing half of the higher frequency content; hence, the optimal SNR is always around  $R = 4$ . When  $R = 0$ , the twin and hologram are inseparable and the phase cannot be correctly recovered as shown in Fig. 8. In the rest of the paper, we use the phase variation rate of  $k = \\pi /2$  and  $\\sigma = 1$ .",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Comparison with N-bucket technique Instead of the Fourier reconstruction method detailed in Sec. 4, we can also use the standard N-bucket technique presented in Sec. 3 by grouping R-rows with phase variations  $\\theta = \\{0,2\\pi /R,4\\pi /R,\\dots ,(R - 1) / R\\}$ . Note that the N-bucket technique does not decrease the number of effective rows, as we can always group  $R / 2$  rows around the current row to get all the phase variations, in a sliding window manner. However, unlike the Fourier reconstruction method, the N-bucket technique works only for integer values of  $R$ .",
+        "bbox": [
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+    {
+        "type": "text",
+        "text": "In Fig. 9, we compare the N-bucket technique with the Fourier technique and observe that the Fourier technique uniformly works better than the standard N-bucket technique for snapshot phase reconstruction.",
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+    {
+        "type": "text",
+        "text": "Comparison with conventional operation We compare the proposed snapshot technique with the conventional four-bucket method for the same exposure duration. We capture the snapshot image with an exposure duration of  $T$  where  $T = 100\\mu s$  while the four quadrature measurements are captured with  $T / 4$ . In Fig. 10, we compare phase reconstruction results for both techniques. For a fair comparison, we have prefiltered the phasors for both the conventional and snapshot techniques. Our method has an SNR of 29.86 dB for phase reconstruction, slightly higher than 28.56 dB for the conventional method but our technique performs uniformly better than the conventional technique for all  $\\sigma$",
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+    {
+        "type": "page_number",
+        "text": "25209",
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+    {
+        "type": "image",
+        "img_path": "images/d334c6d5286d85f8a94c67785a80e6425b2e7e60155c75a56e199f5e1738ba3c.jpg",
+        "image_caption": [
+            "Figure 10. Comparisons against quadrature reconstruction. For the same total exposure duration and optimal kernel size, our method performs similarly or marginally better, compared to the conventional quadrature measurement technique. Importantly, however, our technique requires  $4 \\times$  less bandwidth."
+        ],
+        "image_footnote": [],
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+    {
+        "type": "text",
+        "text": "values. While the proposed technique performs slightly better in this case, the required bandwidth is  $4 \\times$  smaller than the conventional method as our technique requires only one image.",
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+    {
+        "type": "text",
+        "text": "Optimal phase variation direction Rotating the Fourier shift direction, implementable by rotating the camera along its optical axis, can also reduce the aliasing artifacts depending on the edges in the scene. We acquire the optimal result when the majority of the high-frequency edges are parallel to the direction of the phase shift (which is the same as being perpendicular to the phase variation direction). In Fig. 11, we demonstrate the result of reconstructing a scene made up of rectilinear block objects. To ensure the scene stays the same when rotated, we apply a circular mask when comparing the result with the ground truth and compute the SNR. As the graph shows, rotating the input at  $75^{\\circ}$  yields the best result, since only a few rectilinear edges align with the vertical axis, the same orientation for the phase shift.",
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+    {
+        "type": "text",
+        "text": "7. Conclusions",
+        "text_level": 1,
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "Inspired by off-axis holography, we proposed a snapshot Lidar using CW-ToF cameras, which captures amplitude and depth using a single image. We showed how defining a time-of-flight hologram and using rolling-shutter cameras allows us to translate off-axis principles to CW-ToF cameras. Extensive experiments with our lab prototype demon",
+        "bbox": [
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+    },
+    {
+        "type": "image",
+        "img_path": "images/3875e5faa66e806a6e41bcefe263ca9f63978f31614bd6a3d8a51a50726e144f.jpg",
+        "image_caption": [
+            "Figure 11. Improving reconstruction by rotating the camera. Rotating the rolling shutter or phase variation direction improves the reconstruction quality. When the phase variation direction is perpendicular to the dominant edge direction, then we attain the highest SNR. We change the phase variation direction by simply rotating the camera."
+        ],
+        "image_footnote": [],
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+    },
+    {
+        "type": "text",
+        "text": "strated that our snapshot imaging approach performs as well as conventional quadrature measurement-based approaches, while requiring  $4 \\times$  fewer measurements.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "As mentioned in the related work, continuous-wave time-of-flight cameras saw a proliferation of applications in the last decade. Translating the snapshot techniques proposed in this paper for non-sinusoidal codes [10], Doppler time-of-flight imaging [13, 14], frequency-based light transport probing [25], and time-gating [28], while non-trivial, can significantly improve all the applications.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "Our approach relies on spatial modulation to compute the ToF hologram, which required pre-filtering to avoid aliasing. As part of future work, we will explore machine learning-based techniques to relax the aliasing requirements. Data-free techniques such as deep image priors [29], and generative approaches such as diffusion models [5] will enable us to solve the inverse problem more robustly, and without explicit anti-aliasing constraints.",
+        "bbox": [
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+    },
+    {
+        "type": "text",
+        "text": "We have translated snapshot off-axis imaging techniques to CWToF imaging. However, a wide variety of imaging ideas including high dynamic range imaging, light-field imaging, polarization imaging, and spectral imaging today are implemented with assorted pixels, which are expensive, prone to aliasing, or require custom demosaicking algorithms. Extending off-axis principles to create assorted frequency-embedding is an interesting future direction.",
+        "bbox": [
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "8. Acknowledgements",
+        "text_level": 1,
+        "bbox": [
+            500,
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+        "page_idx": 7
+    },
+    {
+        "type": "text",
+        "text": "The authors thank Jeremy Klotz for his help with the hardware prototype. The research is partially supported by a Burke Research Initiation Award.",
+        "bbox": [
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+    },
+    {
+        "type": "page_number",
+        "text": "25210",
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+    },
+    {
+        "type": "text",
+        "text": "References",
+        "text_level": 1,
+        "bbox": [
+            78,
+            89,
+            173,
+            104
+        ],
+        "page_idx": 8
+    },
+    {
+        "type": "list",
+        "sub_type": "ref_text",
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