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# Copyright (c) 2025 FoundationVision
# SPDX-License-Identifier: MIT
"""
Finite Scalar Quantization: VQ-VAE Made Simple - https://arxiv.org/abs/2309.15505
Code adapted from Jax version in Appendix A.1
"""
from typing import List, Optional
import torch
import torch.nn as nn
from torch.nn import Module
from torch import Tensor, int32
from torch.cuda.amp import autocast
from einops import rearrange, pack, unpack
# helper functions
def exists(v):
return v is not None
def default(*args):
for arg in args:
if exists(arg):
return arg
return None
def pack_one(t, pattern):
return pack([t], pattern)
def unpack_one(t, ps, pattern):
return unpack(t, ps, pattern)[0]
# tensor helpers
def round_ste(z: Tensor) -> Tensor:
"""Round with straight through gradients."""
zhat = z.round()
return z + (zhat - z).detach()
# main class
class FSQ(Module):
def __init__(
self,
num_lvl: int,
# levels: List[int],
dim: Optional[int] = None,
num_codebooks = 1,
keep_num_codebooks_dim: Optional[bool] = None,
scale: Optional[float] = None
):
super().__init__()
levels = [num_lvl] * dim
_levels = torch.tensor(levels, dtype=int32)
self.register_buffer("_levels", _levels, persistent = False)
# _basis = torch.cumprod(torch.tensor([1] + levels[:-1]), dim=0, dtype=int32)
# self.register_buffer("_basis", _basis, persistent = False)
self.scale = scale
codebook_dim = len(levels)
self.codebook_dim = codebook_dim
effective_codebook_dim = codebook_dim * num_codebooks
self.num_codebooks = num_codebooks
self.effective_codebook_dim = effective_codebook_dim
keep_num_codebooks_dim = default(keep_num_codebooks_dim, num_codebooks > 1)
assert not (num_codebooks > 1 and not keep_num_codebooks_dim)
self.keep_num_codebooks_dim = keep_num_codebooks_dim
self.dim = default(dim, len(_levels) * num_codebooks)
has_projections = self.dim != effective_codebook_dim
self.project_in = nn.Linear(self.dim, effective_codebook_dim) if has_projections else nn.Identity()
self.project_out = nn.Linear(effective_codebook_dim, self.dim) if has_projections else nn.Identity()
self.has_projections = has_projections
# self.codebook_size = self._levels.prod().item()
# implicit_codebook = self.indices_to_codes(torch.arange(self.codebook_size), project_out = False)
# self.register_buffer("implicit_codebook", implicit_codebook, persistent = False)
def bound(self, z: Tensor, eps: float = 1e-3) -> Tensor:
"""Bound `z`, an array of shape (..., d)."""
half_l = (self._levels - 1) * (1 - eps) / 2
offset = torch.where(self._levels % 2 == 0, 0.5, 0.0)
shift = (offset / half_l).tan()
return (z + shift).tanh() * half_l - offset
def quantize(self, z: Tensor) -> Tensor:
"""Quantizes z, returns quantized zhat, same shape as z."""
quantized = round_ste(self.bound(z)) # -2, -1, 0, 1, 2 for L=5
half_width = self._levels // 2 # Renormalize to [-1, 1]. half_width = 2 for L=5
return quantized / half_width
def _scale_and_shift(self, zhat_normalized: Tensor) -> Tensor:
half_width = self._levels // 2
return (zhat_normalized * half_width) + half_width
def _scale_and_shift_inverse(self, zhat: Tensor) -> Tensor:
half_width = self._levels // 2
return (zhat - half_width) / half_width
def codes_to_indices(self, zhat: Tensor) -> Tensor:
"""Converts a `code` to an index in the codebook."""
assert zhat.shape[-1] == self.codebook_dim
zhat = self._scale_and_shift(zhat) # {-1, -1/2, 0, 1/2, 1} -> {-2, -1, 0, 1, 2} -> {0, 1, 2, 3, 4}
# return (zhat * self._basis).sum(dim=-1).to(int32)
return zhat.to(int32)
def indices_to_codes(
self,
indices: Tensor,
project_out = True,
**kwargs,
) -> Tensor:
"""Inverse of `codes_to_indices`."""
# is_img_or_video = indices.ndim >= (3 + int(self.keep_num_codebooks_dim))
# if is_img_or_video:
# indices = rearrange(indices, 'b d ... -> b ... d')
# indices = rearrange(indices, '... -> ... 1')
# codes_non_centered = (indices // self._basis) % self._levels
codes = self._scale_and_shift_inverse(indices) # {0, 1, 2, 3, 4} -> {-1, -1/2, 0, 1/2, 1}
# if self.keep_num_codebooks_dim:
# codes = rearrange(codes, '... c d -> ... (c d)')
if project_out:
codes = self.project_out(codes)
# if is_img_or_video:
codes = rearrange(codes, 'b ... d -> b d ...')
return codes
@autocast(enabled = False)
def forward(self, z: Tensor) -> Tensor:
"""
einstein notation
b - batch
n - sequence (or flattened spatial dimensions)
d - feature dimension
c - number of codebook dim
"""
is_img_or_video = z.ndim >= 4
# standardize image or video into (batch, seq, dimension)
if is_img_or_video:
z = rearrange(z, 'b d ... -> b ... d') # (b, c, t, h, w) -> (b, t, h, w, c)
# z, ps = pack_one(z, 'b * d') # (b, thw, c), (t, h, w)
assert z.shape[-1] == self.dim, f'expected dimension of {self.dim} but found dimension of {z.shape[-1]}'
z = self.project_in(z)
# z = rearrange(z, 'b n (c d) -> b n c d', c = self.num_codebooks) # (b, thw, 1, c)
codes = self.quantize(z)
indices = self.codes_to_indices(codes)
# codes = rearrange(codes, 'b n c d -> b n (c d)')
out = self.project_out(codes)
# reconstitute image or video dimensions
if is_img_or_video:
# out = unpack_one(out, ps, 'b * d')
out = rearrange(out, 'b ... d -> b d ...')
# indices = rearrange(indices, 'b ... d -> b d ...')
# # indices = unpack_one(indices, ps, 'b * c')
# if not self.keep_num_codebooks_dim:
# # indices = rearrange(indices, '... 1 -> ...')
# pass
return out, None, indices, None
if __name__ == "__main__":
num_lvl = 5
dim = 16
T, H, W = 21, 32, 32
quantizer = FSQ(num_lvl, dim)
z = torch.randn(2, dim, T, H, W)
out, indices = quantizer(z) |