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"""
---
title: Latent Diffusion Models
summary: >
Annotated PyTorch implementation/tutorial of latent diffusion models from paper
High-Resolution Image Synthesis with Latent Diffusion Models
---
# Latent Diffusion Models
Latent diffusion models use an auto-encoder to map between image space and
latent space. The diffusion model works on the diffusion space, which makes it
a lot easier to train.
It is based on paper
[High-Resolution Image Synthesis with Latent Diffusion Models](https://papers.labml.ai/paper/2112.10752).
They use a pre-trained auto-encoder and train the diffusion U-Net on the latent
space of the pre-trained auto-encoder.
For a simpler diffusion implementation refer to our [DDPM implementation](../ddpm/index.html).
We use same notations for $\alpha_t$, $\beta_t$ schedules, etc.
"""
from typing import List, Tuple, Optional, Union
import torch
import torch.nn as nn
import torch.nn.functional as F
from .architecture.unet import UNetModel
import random
def gather(consts: torch.Tensor, t: torch.Tensor):
"""Gather consts for $t$ and reshape to feature map shape"""
c = consts.gather(-1, t)
return c.reshape(-1, 1, 1, 1)
class LatentDiffusion(nn.Module):
"""
## Latent diffusion model
This contains following components:
* [AutoEncoder](model/autoencoder.html)
* [U-Net](model/unet.html) with [attention](model/unet_attention.html)
"""
eps_model: UNetModel
#first_stage_model: Optional[Autoencoder] = None
def __init__(
self,
unet_model: UNetModel,
latent_scaling_factor: float,
n_steps: int,
linear_start: float,
linear_end: float,
debug_mode: Optional[bool] = False
):
"""
:param unet_model: is the [U-Net](model/unet.html) that predicts noise
$\epsilon_\text{cond}(x_t, c)$, in latent space
:param autoencoder: is the [AutoEncoder](model/autoencoder.html)
:param latent_scaling_factor: is the scaling factor for the latent space. The encodings of
the autoencoder are scaled by this before feeding into the U-Net.
:param n_steps: is the number of diffusion steps $T$.
:param linear_start: is the start of the $\beta$ schedule.
:param linear_end: is the end of the $\beta$ schedule.
"""
super().__init__()
# Wrap the [U-Net](model/unet.html) to keep the same model structure as
# [CompVis/stable-diffusion](https://github.com/CompVis/stable-diffusion).
self.eps_model = unet_model
self.latent_scaling_factor = latent_scaling_factor
# Number of steps $T$
self.n_steps = n_steps
# $\beta$ schedule
beta = torch.linspace(
linear_start**0.5, linear_end**0.5, n_steps, dtype=torch.float64
) ** 2
# $\alpha_t = 1 - \beta_t$
alpha = 1. - beta
# $\bar\alpha_t = \prod_{s=1}^t \alpha_s$
alpha_bar = torch.cumprod(alpha, dim=0)
self.alpha = nn.Parameter(alpha.to(torch.float32), requires_grad=False)
self.beta = nn.Parameter(beta.to(torch.float32), requires_grad=False)
self.alpha_bar = nn.Parameter(alpha_bar.to(torch.float32), requires_grad=False)
self.alpha_bar_prev = torch.cat([alpha_bar.new_tensor([1.]), alpha_bar[:-1]])
self.sigma_ddim = torch.sqrt((1-self.alpha_bar_prev)/(1-self.alpha_bar)*(1-self.alpha_bar/self.alpha_bar_prev))
self.sigma2 = self.beta
self.debug_mode = debug_mode
@property
def device(self):
"""
### Get model device
"""
return next(iter(self.eps_model.parameters())).device
def forward(self, x: torch.Tensor, t: torch.Tensor):
"""
### Predict noise
Predict noise given the latent representation $x_t$, time step $t$, and the
conditioning context $c$.
$$\epsilon_\text{cond}(x_t, c)$$
"""
return self.eps_model(x, t)
def q_xt_x0(self, x0: torch.Tensor,
t: torch.Tensor) -> Tuple[torch.Tensor, torch.Tensor]:
"""
#### Get $q(x_t|x_0)$ distribution
"""
# [gather](utils.html) $\alpha_t$ and compute $\sqrt{\bar\alpha_t} x_0$
mean = gather(self.alpha_bar, t)**0.5 * x0
# $(1-\bar\alpha_t) \mathbf{I}$
var = 1 - gather(self.alpha_bar, t)
#
return mean, var
def q_sample(
self, x0: torch.Tensor, t: torch.Tensor, eps: Optional[torch.Tensor] = None
):
"""
#### Sample from $q(x_t|x_0)$
"""
# $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$
if eps is None:
eps = torch.randn_like(x0)
# get $q(x_t|x_0)$
mean, var = self.q_xt_x0(x0, t)
# Sample from $q(x_t|x_0)$
return mean + (var**0.5) * eps
def p_sample(self, xt: torch.Tensor, t: torch.Tensor):
"""
#### Sample from $\textcolor{lightgreen}{p_\theta}(x_{t-1}|x_t)$
"""
# $\textcolor{lightgreen}{\epsilon_\theta}(x_t, t)$
eps_theta = self.eps_model(xt, t)
# [gather](utils.html) $\bar\alpha_t$
alpha_bar = gather(self.alpha_bar, t)
# [gather](utils.html) $\bar\alpha_t-1$
alpha_bar_prev = gather(self.alpha_bar_prev, t)
# [gather](utils.html) $\sigma_t$
sigma_ddim = gather(self.sigma_ddim, t)
# DDIM sampling
# $\frac{x_t-\sqrt{1-\bar\alpha_t}\epsilon}{\sqrt{\bar\alpha_t}}$
predicted_x0 = (xt - (1-alpha_bar)**0.5 * eps_theta) / (alpha_bar)**.5
# $\sqrt{1-\alpha_{t-1}-\sigma_t^2}$
direction_to_xt = (1 - alpha_bar_prev - sigma_ddim**2)**0.5 * eps_theta
# $\epsilon \sim \mathcal{N}(\mathbf{0}, \mathbf{I})$
eps = torch.randn(xt.shape, device=xt.device)
# Sample
x_tm_1 = alpha_bar_prev**0.5 * predicted_x0 + direction_to_xt + sigma_ddim * eps
return x_tm_1
def loss(
self,
x0: torch.Tensor,
#autoreg_cond: Union[torch.Tensor, None], #This means it can be either a tensor or none
#external_cond: Union[torch.Tensor, None],
noise: Optional[torch.Tensor] = None,
):
"""
#### Simplified Loss
"""
# Get batch size
batch_size = x0.shape[0]
# Get random $t$ for each sample in the batch
t = torch.randint(
0, self.n_steps, (batch_size, ), device=x0.device, dtype=torch.long
)
#autoreg_cond = -torch.ones(x0.size(0), 1, self.eps_model.d_cond, device=x0.device, dtype=x0.dtype)
#cond = autoreg_cond
if x0.size(1) == self.eps_model.out_channels: # generating form
if self.debug_mode:
print('In the mode of root level:', x0.size())
if noise is None:
x0 = x0.to(torch.float32)
noise = torch.randn_like(x0)
xt = self.q_sample(x0, t, eps=noise)
eps_theta = self.eps_model(xt, t)
loss = F.mse_loss(noise, eps_theta)
else:
if self.debug_mode:
print('In the mode of non-root level:', x0.size())
if noise is None:
noise = torch.randn_like(x0[:, 0: 2])
front_t = self.q_sample(x0[:, 0: 2], t, eps=noise)
background_cond = x0[:, 2:]
xt = torch.cat([front_t, background_cond], 1)
eps_theta = self.eps_model(xt, t)
loss = F.mse_loss(noise, eps_theta)
if self.debug_mode:
print('loss:', loss)
return loss
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