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import torch
import torch.distributions as td
import torch.nn as nn
from torchtyping import TensorType
from sim_priors_pk.models.diffusion.noise import GaussianProcess, Normal, OrnsteinUhlenbeck
class DiscreteDiffusion(nn.Module):
"""
Discrete diffusion (https://arxiv.org/abs/2006.11239)
Args:
dim: Dimension of data
num_steps: Number of diffusion steps
beta_fn: Scheduler for noise levels
noise_fn: Type of noise
parallel_elbo: Whether to compute ELBO in parallel or not
"""
def __init__(
self,
dim: int,
num_steps: int,
beta_fn: Callable,
noise_fn: Callable,
parallel_elbo: bool = False,
is_time_series: bool = False,
predict_gaussian_noise: bool = True,
**kwargs,
):
super().__init__()
self.dim = dim
self.num_steps = num_steps
self.parallel_elbo = parallel_elbo
self.is_time_series = is_time_series
self.predict_gaussian_noise = predict_gaussian_noise
betas = beta_fn(torch.linspace(0, 1, num_steps))
alphas = torch.cumprod(1 - betas, dim=0)
self.register_buffer("betas", betas) # Register betas as a buffer
self.register_buffer("alphas", alphas) # Register alphas as a buffer
self.noise = noise_fn
def forward(
self,
x: TensorType[..., "dim"], # noqa: F821
i: TensorType[..., 1],
**kwargs,
) -> Tuple[TensorType[..., "dim"], TensorType[..., "dim"]]: # noqa: F821
noise_gaussian = torch.randn_like(x)
if self.is_time_series:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
noise = L @ noise_gaussian
else:
noise = noise_gaussian
alpha = self.alphas[i.long()].to(x)
y = torch.sqrt(alpha) * x + torch.sqrt(1 - alpha) * noise
if self.predict_gaussian_noise:
return y, noise_gaussian
else:
return y, noise
def get_loss(
self,
model: Callable,
x: TensorType[..., "dim"],
**kwargs,
) -> TensorType[..., "dim"]:
i = torch.randint(0, self.num_steps, size=(x.shape[0],))
i = i.view(-1, *(1,) * len(x.shape[1:])).expand_as(x[..., :1]).to(x)
x_noisy, noise = self.forward(x, i, **kwargs)
pred_noise = model(x_noisy, i=i, **kwargs)
loss = (pred_noise - noise) ** 2
return loss
@torch.no_grad()
def sample(
self,
model: Callable,
num_samples: Union[int, Tuple],
device: str = "cpu",
**kwargs,
) -> TensorType["*num_samples", "dim"]:
if isinstance(num_samples, int):
num_samples = (num_samples,)
x = self.noise(*num_samples, **kwargs).to(device)
if self.is_time_series and self.predict_gaussian_noise:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
else:
L = None
for diff_step in reversed(range(0, self.num_steps)):
alpha = self.alphas[diff_step]
beta = self.betas[diff_step]
# An alternative can be:
# alpha_prev = self.alphas[diff_step - 1]
# sigma = beta * (1 - alpha_prev) / (1 - alpha)
sigma = beta
if diff_step == 0:
z = 0
else:
z = self.noise(*num_samples, **kwargs).to(device)
i = torch.Tensor([diff_step]).expand_as(x[..., :1]).to(device)
pred_noise = model(x, i=i, **kwargs)
if L is not None:
pred_noise = L @ pred_noise
x = (x - beta * pred_noise / (1 - alpha).sqrt()) / (1 - beta).sqrt() + sigma.sqrt() * z
return x
@torch.no_grad()
def log_prob(
self,
model: Callable,
x: TensorType[..., "dim"],
num_samples: int = 1,
**kwargs,
) -> TensorType[..., 1]:
if self.is_time_series and self.predict_gaussian_noise:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
else:
L = None
func = self._elbo_parallel if self.parallel_elbo else self._elbo_sequential
return func(model, x, num_samples=num_samples, L=L, **kwargs)
def _elbo_parallel(
self,
model: Callable,
x: TensorType[..., "dim"],
L: TensorType[..., "seq_len", "seq_len"],
num_samples: int = 1,
**kwargs,
) -> TensorType[..., 1]:
"""
Computes ELBO over all diffusion steps in parallel,
then averages over `num_samples` runs.
If diffusion `num_steps` large (and `num_samples` small)
it will be heavy on the GPU memory.
Args:
model: Denoising diffusion model
x: Clean input data
num_samples: How many times to compute ELBO, final
result is averaged over all ELBO samples
**kwargs: Can be time, latent etc. depending on a model
"""
elbo = 0
i = expand_to_x(torch.arange(self.num_steps), x).expand(-1, *x[..., :1].shape).contiguous()
alphas = expand_to_x(self.alphas, x)
betas = expand_to_x(self.betas, x)
xt, kwargs = expand_x_and_kwargs(x, kwargs, self.num_steps)
for _ in range(num_samples):
# Get diffused outputs
xt, _ = self.forward(x, i, **kwargs) # [num_steps, ..., dim]
# Output predicted noise
epsilon = model(xt, i=i, **kwargs)
if L is not None:
epsilon = L @ epsilon
# p(x_{t-1} | p_t)
p_mu = get_p_mu(xt, betas, alphas, epsilon)
px = td.Independent(td.Normal(p_mu[1:], betas[1:].sqrt()), 1)
# p(x_0 | x_1)
log_prob_x0_x1 = td.Independent(td.Normal(p_mu[0], betas[0].sqrt()), 1).log_prob(x)
assert log_prob_x0_x1.shape == x.shape[:-1]
# q(x_{t-1} | x_0, x_t), t > 1
qx = get_qx(x.unsqueeze(0), xt[1:], alphas[1:], alphas[:-1], betas[1:])
# KL[q(x_{t-1} | p_t) || p(x_{t-1} | p_t)]
kl_q_p = td.kl_divergence(qx, px).sum(0)
assert kl_q_p.shape == x.shape[:-1]
# ELBO
elbo_contribution = (log_prob_x0_x1 - kl_q_p) / num_samples
elbo += elbo_contribution
elbo = reduce_elbo(elbo, x)
return elbo
def _elbo_sequential(
self,
model: Callable,
x: TensorType[..., "dim"],
L: TensorType[..., "seq_len", "seq_len"],
num_samples: int = 1,
**kwargs,
) -> TensorType[..., 1]:
"""
Computes ELBO as a sum of diffusion steps - sequentially.
Args:
model: Denoising diffusion model
x: Clean input data
num_samples: How many times to compute ELBO, final
result is averaged over all ELBO samples
**kwargs: Can be time, latent etc. depending on a model
"""
elbo = 0
x, kwargs = expand_x_and_kwargs(x, kwargs, num_samples)
for i in range(self.num_steps):
# Prepare variables
beta = self.betas[i].to(x)
alpha = self.alphas[i].to(x)
step = torch.Tensor([i]).expand_as(x[..., :1]).to(x)
# Diffuse and predict noise
xt, _ = self.forward(x, i=step, **kwargs)
epsilon = model(xt, i=step, **kwargs)
if L is not None:
epsilon = L @ epsilon
assert xt.shape == x.shape == epsilon.shape
# p(x_{t-1} | p_t)
p_mu = get_p_mu(xt, beta, alpha, epsilon)
px = td.Independent(td.Normal(p_mu, beta.sqrt()), 1)
if i == 0:
elbo = elbo + px.log_prob(x).mean(0)
else:
prev_alpha = self.alphas[i - 1]
# q(x_{t-1} | x_0, x_t), t > 1
qx = get_qx(x, xt, alpha, prev_alpha, beta)
# KL[q(x_{t-1} | p_t) || p(x_{t-1} | p_t)]
kl = td.kl_divergence(qx, px).mean(0)
elbo = elbo - kl
elbo = reduce_elbo(elbo, x)
return elbo
class GaussianDiffusion(DiscreteDiffusion):
"""Discrete diffusion with Gaussian noise"""
def __init__(self, dim: int, num_steps: int, beta_fn: Callable, **kwargs):
super().__init__(dim, num_steps, beta_fn, noise_fn=Normal(dim), **kwargs)
class OUDiffusion(DiscreteDiffusion):
"""Discrete diffusion with noise coming from an OU process"""
def __init__(
self,
dim: int,
num_steps: int,
beta_fn: Callable,
predict_gaussian_noise: bool,
theta: float = 0.5,
**kwargs,
):
super().__init__(
dim=dim,
num_steps=num_steps,
beta_fn=beta_fn,
noise_fn=OrnsteinUhlenbeck(dim, theta=theta),
is_time_series=True,
predict_gaussian_noise=predict_gaussian_noise,
**kwargs,
)
class GPDiffusion(DiscreteDiffusion):
"""Discrete diffusion with noise coming from a Gaussian process"""
def __init__(
self,
dim: int,
num_steps: int,
beta_fn: Callable,
predict_gaussian_noise: bool,
sigma: float = 0.1,
**kwargs,
):
super().__init__(
dim=dim,
num_steps=num_steps,
beta_fn=beta_fn,
noise_fn=GaussianProcess(dim, sigma=sigma),
is_time_series=True,
predict_gaussian_noise=predict_gaussian_noise,
**kwargs,
)
def expand_to_x(inputs, x):
return inputs.view(-1, *(1,) * len(x.shape)).to(x)
def expand_x_and_kwargs(x, kwargs, N):
# Expand dimensions
x = x.unsqueeze(0).repeat_interleave(N, dim=0)
# A hacky solution to repeat dimensions in all kwargs (latent, t, etc.)
for key, value in kwargs.items():
if torch.is_tensor(value):
kwargs[key] = value.unsqueeze(0).repeat_interleave(N, dim=0)
return x, kwargs
def reduce_elbo(
elbo: TensorType["batch", Any],
x: TensorType[Any],
) -> TensorType["batch", 1]:
# Reduce ELBO over all but batch dimension: (B, ...) -> (B,)
elbo = elbo.view(elbo.shape[0], -1).sum(1)
if len(x.shape) > 2:
elbo = elbo / x.shape[-2]
return elbo.unsqueeze(1)
def get_p_mu(xt, beta, alpha, epsilon):
mu = 1 / (1 - beta).sqrt() * (xt - beta / (1 - alpha).sqrt() * epsilon)
return mu
def get_qx(x, xt, alpha, prev_alpha, beta):
q_mu_1 = torch.sqrt(prev_alpha) * beta / (1 - alpha) * x
q_mu_2 = torch.sqrt(1 - beta) * (1 - prev_alpha) / (1 - alpha) * xt
q_mu = q_mu_1 + q_mu_2
q_sigma = beta * (1 - prev_alpha) / (1 - alpha)
qx = td.Independent(td.Normal(q_mu, q_sigma.expand_as(q_mu).sqrt()), 1)
return qx
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