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import math
import torch
import numpy as np
from torch import nn, einsum
from einops import rearrange, repeat
from diffusers.models.embeddings import TimestepEmbedding
from rotary_embedding_torch.rotary_embedding_torch import rotate_half
from timm.models.vision_transformer import PatchEmbed
class Timesteps(nn.Module):
def __init__(
self,
num_channels: int,
flip_sin_to_cos: bool = True,
downscale_freq_shift: float = 0,
):
super().__init__()
self.num_channels = num_channels
self.flip_sin_to_cos = flip_sin_to_cos
self.downscale_freq_shift = downscale_freq_shift
def forward(self, timesteps):
t_emb = get_timestep_embedding(
timesteps,
self.num_channels,
flip_sin_to_cos=self.flip_sin_to_cos,
downscale_freq_shift=self.downscale_freq_shift,
)
return t_emb
class StochasticUnknownTimesteps(Timesteps):
def __init__(
self,
num_channels: int,
p: float = 1.0,
):
super().__init__(num_channels)
self.unknown_token = (
nn.Parameter(torch.randn(1, num_channels)) if p > 0.0 else None
)
self.p = p
def forward(self, timesteps: torch.Tensor, mask: Optional[torch.Tensor] = None):
t_emb = super().forward(timesteps)
# if p == 0.0 - return original embeddings both during training and inference
if self.p == 0.0:
return t_emb
# training or mask is None - randomly replace embeddings with unknown token with probability p
# (mask can only be None for logging training visualization when using latents)
# or if p == 1.0 - always replace embeddings with unknown token even during inference)
if self.training or self.p == 1.0 or mask is None:
mask = torch.rand(t_emb.shape[:-1], device=t_emb.device) < self.p
mask = mask[..., None].expand_as(t_emb)
return torch.where(mask, self.unknown_token, t_emb)
# # inference with p < 1.0 - replace embeddings with unknown token only for masked timesteps
# if mask is None:
# assert False, "mask should be provided when 0.0 < p < 1.0"
mask = mask[..., None].expand_as(t_emb)
return torch.where(mask, self.unknown_token, t_emb)
class StochasticTimeEmbedding(nn.Module):
def __init__(
self,
dim: int,
time_embed_dim: int,
use_fourier: bool = False,
p: float = 0.0,
):
super().__init__()
self.use_fourier = use_fourier
if self.use_fourier:
assert p == 0.0, "Fourier embeddings do not support stochastic timesteps"
self.timesteps = (
FourierEmbedding(dim, bandwidth=1)
if use_fourier
else StochasticUnknownTimesteps(dim, p)
)
self.embedding = TimestepEmbedding(dim, time_embed_dim)
def forward(self, timesteps: torch.Tensor, mask: Optional[torch.Tensor] = None):
return self.embedding(
self.timesteps(timesteps)
if self.use_fourier
else self.timesteps(timesteps, mask)
)
class FourierEmbedding(torch.nn.Module):
"""
Adapted from EDM2 - https://github.com/NVlabs/edm2/blob/38d5a70fe338edc8b3aac4da8a0cefbc4a057fb8/training/networks_edm2.py#L73
"""
def __init__(self, num_channels, bandwidth=1):
super().__init__()
self.register_buffer("freqs", 2 * np.pi * torch.randn(num_channels) * bandwidth)
self.register_buffer("phases", 2 * np.pi * torch.rand(num_channels))
def forward(self, x):
y = x.to(torch.float32)
y = y[..., None] * self.freqs.to(torch.float32)
y = y + self.phases.to(torch.float32)
y = y.cos() * np.sqrt(2)
return y.to(x.dtype)
def get_timestep_embedding(
timesteps: torch.Tensor,
embedding_dim: int,
flip_sin_to_cos: bool = False,
downscale_freq_shift: float = 1,
scale: float = 1,
max_period: int = 10000,
):
"""
This matches the implementation in Denoising Diffusion Probabilistic Models: Create sinusoidal timestep embeddings.
:param timesteps: a 1-D or 2-D Tensor of N indices, one per batch element.
These may be fractional.
:param embedding_dim: the dimension of the output. :param max_period: controls the minimum frequency of the
embeddings. :return: an [N x dim] or [N x M x dim] Tensor of positional embeddings.
"""
if len(timesteps.shape) not in [1, 2]:
raise ValueError("Timesteps should be a 1D or 2D tensor")
half_dim = embedding_dim // 2
exponent = -math.log(max_period) * torch.arange(
start=0, end=half_dim, dtype=torch.float32, device=timesteps.device
)
exponent = exponent / (half_dim - downscale_freq_shift)
emb = torch.exp(exponent)
emb = timesteps[..., None].float() * emb
# scale embeddings
emb = scale * emb
# concat sine and cosine embeddings
emb = torch.cat([torch.sin(emb), torch.cos(emb)], dim=-1)
# flip sine and cosine embeddings
if flip_sin_to_cos:
emb = torch.cat([emb[..., half_dim:], emb[..., :half_dim]], dim=-1)
# zero pad
if embedding_dim % 2 == 1:
emb = torch.nn.functional.pad(emb, (0, 1, 0, 0))
return emb
class RotaryEmbeddingND(nn.Module):
"""
Minimal Axial RoPE generalized to N dimensions.
"""
def __init__(
self,
dims: Tuple[int, ...],
sizes: Tuple[int, ...],
theta: float = 10000.0,
flatten: bool = True,
):
"""
Args:
dims: the number of dimensions for each axis.
sizes: the maximum length for each axis.
"""
super().__init__()
self.n_dims = len(dims)
self.dims = dims
self.theta = theta
self.flatten = flatten
Colon = slice(None)
all_freqs = []
for i, (dim, seq_len) in enumerate(zip(dims, sizes)):
freqs = self.get_freqs(dim, seq_len)
all_axis = [None] * len(dims)
all_axis[i] = Colon
new_axis_slice = (Ellipsis, *all_axis, Colon)
all_freqs.append(freqs[new_axis_slice].expand(*sizes, dim))
all_freqs = torch.cat(all_freqs, dim=-1)
if flatten: # flatten all but the last dimension
all_freqs = rearrange(all_freqs, "... d -> (...) d")
self.register_buffer("freqs", all_freqs, persistent=False)
def get_freqs(self, dim: int, seq_len: int) -> torch.Tensor:
freqs = 1.0 / (
self.theta ** (torch.arange(0, dim, 2)[: (dim // 2)].float() / dim)
)
pos = torch.arange(seq_len, dtype=freqs.dtype)
freqs = einsum("..., f -> ... f", pos, freqs)
freqs = repeat(freqs, "... n -> ... (n r)", r=2)
return freqs
def forward(self, x: torch.Tensor) -> torch.Tensor:
"""
Args:
x: a [... x N x ... x D] if flatten=False, [... x (N x ...) x D] if flatten=True tensor of queries or keys.
Returns:
a tensor of rotated queries or keys. (same shape as x)
"""
# slice the freqs to match the input shape
seq_shape = x.shape[-2:-1] if self.flatten else x.shape[-self.n_dims - 1 : -1]
slice_tuple = tuple(slice(0, seq_len) for seq_len in seq_shape)
freqs = self.freqs[slice_tuple]
return x * freqs.cos() + rotate_half(x) * freqs.sin()
class RotaryEmbedding1D(RotaryEmbeddingND):
"""
RoPE1D for Time Series Transformer.
Handles tensors of shape [B x T x C] or [B x (T x C)].
"""
def __init__(
self,
dim: int,
seq_len: int,
theta: float = 10000.0,
flatten: bool = True,
):
super().__init__((dim,), (seq_len,), theta, flatten)
class RotaryEmbedding2D(RotaryEmbeddingND):
"""
RoPE2D for Image Transformer.
Handles tensors of shape [B x H x W x C] or [B x (H x W) x C].
"""
def __init__(
self,
dim: int,
sizes: Tuple[int, int],
theta: float = 10000.0,
flatten: bool = True,
):
assert dim % 2 == 0, "RotaryEmbedding2D requires even dim"
super().__init__((dim // 2,) * 2, sizes, theta, flatten)
class RotaryEmbedding3D(RotaryEmbeddingND):
"""
RoPE3D for Video Transformer.
Handles tensors of shape [B x T x H x W x C] or [B x (T x H x W) x C].
"""
def __init__(
self,
dim: int,
sizes: Tuple[int, int, int],
theta: float = 10000.0,
flatten: bool = True,
):
assert dim % 2 == 0, "RotaryEmbedding3D requires even dim"
dim //= 2
# if dim is not divisible by 3,
# split into 3 dimensions such that height and width have the same number of frequencies
match dim % 3:
case 0:
dims = (dim // 3,) * 3
case 1:
dims = (dim // 3 + 1, dim // 3, dim // 3)
case 2:
dims = (dim // 3, dim // 3 + 1, dim // 3 + 1)
super().__init__(tuple(d * 2 for d in dims), sizes, theta, flatten)
class RandomEmbeddingDropout(nn.Module):
"""
Randomly nullify the input embeddings with a given probability.
"""
def __init__(self, p: float = 0.0):
super().__init__()
self.p = p
def forward(self, emb: torch.Tensor, mask: Optional[torch.Tensor] = None):
"""
Randomly nullify the input embeddings with a probability p during training. For inference, the embeddings are nullified only if mask is provided.
Args:
emb: input embeddings of shape (B, ...)
mask: mask tensor of shape (B, ). Only allowed during inference. If provided, embeddings for masked batches will be zeroed.
"""
if mask is not None:
assert not self.training, "embedding mask is only allowed during inference"
assert mask.ndim == 1, "embedding mask should be of shape (B,)"
if self.training and self.p > 0:
mask = torch.rand(emb.shape[:1], device=emb.device) < self.p
if mask is not None:
mask = rearrange(mask, "... -> ..." + " 1" * (emb.ndim - 1))
emb = torch.where(mask, torch.zeros_like(emb), emb)
return emb
class RandomDropoutCondEmbedding(TimestepEmbedding):
"""
A layer for processing conditions into embeddings, randomly dropping embeddings of each frame during training.
NOTE: If dropout_prob is 0, it will fall back to `TimestepEmbedding`. We use this trick to ensure the backward compatibility with our previous checkpoints.
"""
def __init__(
self,
cond_dim: int,
cond_emb_dim: int,
dropout_prob: float = 0.0,
):
self.dropout_prob = dropout_prob
if dropout_prob == 0:
super().__init__(cond_dim, cond_emb_dim)
else:
nn.Module.__init__(self)
self.dropout = RandomEmbeddingDropout(p=dropout_prob)
self.embedding = TimestepEmbedding(cond_dim, cond_emb_dim)
def forward(self, cond: torch.Tensor, mask: Optional[torch.Tensor] = None):
if self.dropout_prob == 0:
return super().forward(cond)
return self.dropout(self.embedding(cond), mask)
class RandomDropoutPatchEmbed(nn.Module):
def __init__(
self,
dropout_prob: float = 0.1,
img_size: Optional[int] = 224,
patch_size: int = 16,
in_chans: int = 3,
embed_dim: int = 768,
bias: bool = True,
flatten: bool = True,
**patch_embed_kwargs,
):
super().__init__()
self.dropout = RandomEmbeddingDropout(p=dropout_prob)
self.patch_embedder = PatchEmbed(
img_size=img_size,
patch_size=patch_size,
in_chans=in_chans,
embed_dim=embed_dim,
bias=bias,
flatten=flatten,
**patch_embed_kwargs,
)
self.ndim = 3 if flatten else 4
def forward(
self, x: torch.Tensor, mask: Optional[torch.Tensor] = None
) -> torch.Tensor:
"""
Args:
x: tensor to be patchified of shape (*B, C, H, W)
Returns:
patchified tensor of shape (*B, num_patches, embed_dim)
"""
orig_shape = x.shape
x = rearrange(x, "... c h w -> (...) c h w")
x = self.patch_embedder(x)
x = x.reshape(*orig_shape[:-3], *x.shape[-self.ndim + 1 :])
return self.dropout(x, mask)
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