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# Adapted from: https://github.com/huggingface/diffusers/blob/main/src/diffusers/models/embeddings.py
import math
import numpy as np
import torch
from einops import rearrange
from torch import nn
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 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] Tensor of positional embeddings.
"""
assert len(timesteps.shape) == 1, "Timesteps should be a 1d-array"
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[None, :]
# 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
def get_3d_sincos_pos_embed(embed_dim, grid, w, h, f):
"""
grid_size: int of the grid height and width return: pos_embed: [grid_size*grid_size, embed_dim] or
[1+grid_size*grid_size, embed_dim] (w/ or w/o cls_token)
"""
grid = rearrange(grid, "c (f h w) -> c f h w", h=h, w=w)
grid = rearrange(grid, "c f h w -> c h w f", h=h, w=w)
grid = grid.reshape([3, 1, w, h, f])
pos_embed = get_3d_sincos_pos_embed_from_grid(embed_dim, grid)
pos_embed = pos_embed.transpose(1, 0, 2, 3)
return rearrange(pos_embed, "h w f c -> (f h w) c")
def get_3d_sincos_pos_embed_from_grid(embed_dim, grid):
if embed_dim % 3 != 0:
raise ValueError("embed_dim must be divisible by 3")
# use half of dimensions to encode grid_h
emb_f = get_1d_sincos_pos_embed_from_grid(embed_dim // 3, grid[0]) # (H*W*T, D/3)
emb_h = get_1d_sincos_pos_embed_from_grid(embed_dim // 3, grid[1]) # (H*W*T, D/3)
emb_w = get_1d_sincos_pos_embed_from_grid(embed_dim // 3, grid[2]) # (H*W*T, D/3)
emb = np.concatenate([emb_h, emb_w, emb_f], axis=-1) # (H*W*T, D)
return emb
def get_1d_sincos_pos_embed_from_grid(embed_dim, pos):
"""
embed_dim: output dimension for each position pos: a list of positions to be encoded: size (M,) out: (M, D)
"""
if embed_dim % 2 != 0:
raise ValueError("embed_dim must be divisible by 2")
omega = np.arange(embed_dim // 2, dtype=np.float64)
omega /= embed_dim / 2.0
omega = 1.0 / 10000**omega # (D/2,)
pos_shape = pos.shape
pos = pos.reshape(-1)
out = np.einsum("m,d->md", pos, omega) # (M, D/2), outer product
out = out.reshape([*pos_shape, -1])[0]
emb_sin = np.sin(out) # (M, D/2)
emb_cos = np.cos(out) # (M, D/2)
emb = np.concatenate([emb_sin, emb_cos], axis=-1) # (M, D)
return emb
class SinusoidalPositionalEmbedding(nn.Module):
"""Apply positional information to a sequence of embeddings.
Takes in a sequence of embeddings with shape (batch_size, seq_length, embed_dim) and adds positional embeddings to
them
Args:
embed_dim: (int): Dimension of the positional embedding.
max_seq_length: Maximum sequence length to apply positional embeddings
"""
def __init__(self, embed_dim: int, max_seq_length: int = 32):
super().__init__()
position = torch.arange(max_seq_length).unsqueeze(1)
div_term = torch.exp(torch.arange(0, embed_dim, 2) * (-math.log(10000.0) / embed_dim))
pe = torch.zeros(1, max_seq_length, embed_dim)
pe[0, :, 0::2] = torch.sin(position * div_term)
pe[0, :, 1::2] = torch.cos(position * div_term)
self.register_buffer("pe", pe)
def forward(self, x):
_, seq_length, _ = x.shape
x = x + self.pe[:, :seq_length]
return x
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