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from typing import Callable, Optional, Tuple, Union
import numpy as np
import torch
import torch.distributions as td
import torch.nn as nn
from torchdiffeq import odeint
from torchsde import sdeint
from torchtyping import TensorType
from sim_priors_pk.models.diffusion.noise import GaussianProcess, Normal, OrnsteinUhlenbeck
class ContinuousDiffusion(nn.Module):
"""
Continuous diffusion using SDEs (https://arxiv.org/abs/2011.13456)
Args:
dim: Dimension of data
beta_fn: Scheduler for noise levels
t1: Final diffusion time
noise_fn: Type of noise
predict_gaussian_noise: Whether to approximate score with unit normal
loss_weighting: Function returning loss weights given diffusion time
"""
def __init__(
self,
dim: int,
beta_fn: Callable,
t1: float = 1.0,
noise_fn: Callable = None,
loss_weighting: Callable = None,
is_time_series: bool = False,
predict_gaussian_noise: bool = True,
**kwargs,
):
super().__init__()
self.dim = dim
self.t1 = t1
self.predict_gaussian_noise = predict_gaussian_noise
self.is_time_series = is_time_series
self.beta_fn = beta_fn
self.noise = noise_fn
self.loss_weighting = partial(loss_weighting or (lambda beta, i: 1), beta_fn)
def forward(
self,
x: TensorType[..., "dim"],
i: TensorType[..., 1],
_return_all: Optional[bool] = False, # For internal use only
**kwargs,
) -> Tuple[TensorType[..., "dim"], TensorType[..., "dim"]]:
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
beta_int = self.beta_fn.integral(i)
mean = x * torch.exp(-beta_int / 2)
std = (1 - torch.exp(-beta_int)).clamp(1e-5).sqrt()
y = mean + std * noise
if _return_all:
return y, noise, mean, std, cov if self.is_time_series else None
if self.predict_gaussian_noise:
return y, noise_gaussian
else:
return y, noise
def get_loss(
self,
model: Callable,
x: TensorType[..., "dim"],
**kwargs,
) -> TensorType[..., 1]:
i = torch.rand(x.shape[0], *(1,) * len(x.shape[1:])).expand_as(x[..., :1]).to(x)
i = i * self.t1
x_noisy, noise = self.forward(x, i, **kwargs)
pred_noise = model(x_noisy, i=i, **kwargs)
loss = self.loss_weighting(i) * (pred_noise - noise) ** 2
return loss
def _get_score(self, model, x, i, L=None, **kwargs):
"""
Returns score: ∇_xs log p(xs)
"""
if isinstance(i, float):
i = torch.Tensor([i]).to(x)
if i.shape[:-1] != x.shape[:-1]:
i = i.view(*(1,) * len(x.shape)).expand_as(x[..., :1])
beta_int = self.beta_fn.integral(i)
std = (1 - torch.exp(-beta_int)).clamp(1e-5).sqrt()
noise = model(x, i=i, **kwargs)
if L is not None:
# We have to compute the score using -Sigma.inv() @ noise / std
# assuming noise~N(0, Sigma).
# If `predict_gaussian_noise=False`, compute (LL^T).inv()
# Else, we can simplify (LL^T).inv() @ L @ noise
# to (L^T).inv() @ noise, where noise~N(0, I).
# So we anyways have to do (L^T).inv(), and sometimes L.inv()
if not self.predict_gaussian_noise:
noise = torch.linalg.solve_triangular(L, noise, upper=False)
noise = torch.linalg.solve_triangular(L.transpose(-1, -2), noise, upper=True)
score = -noise / std
return score
@torch.no_grad()
def log_prob(
self,
model: Callable,
x: Union[TensorType[..., "dim"], TensorType[..., "seq_len", "dim"]],
num_samples: int = 1,
**kwargs,
) -> TensorType[..., 1]:
model.train() # Allows backprop through RNN
self._e = torch.randn(num_samples, *x.shape).to(x)
if self.is_time_series:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
else:
L = None
def drift(i, state):
y, _ = state
with torch.set_grad_enabled(True):
y = y.requires_grad_(True)
score = self._get_score(model, y, i=i, L=L, **kwargs)
if self.is_time_series:
# Have to include `cov` since g(t) = "scalar" * L @ dW
score = cov @ score
dy = -0.5 * self.beta_fn(i) * (y + score)
divergence = divergence_approx(dy, y, self._e, num_samples=num_samples)
return dy, -divergence
interval = torch.Tensor([0, self.t1]).to(x)
# states = odeint(drift, (x, torch.zeros_like(x).to(x)), interval, rtol=1e-6, atol=1e-5)
states = odeint(
drift,
(x, torch.zeros_like(x).to(x)),
interval,
method="rk4",
options={"step_size": 0.01},
)
y, div = states[0][-1], states[1][-1]
if self.is_time_series:
p0 = td.Independent(
torch.distributions.MultivariateNormal(
torch.zeros_like(y).transpose(-1, -2),
cov.unsqueeze(-3).repeat_interleave(self.dim, dim=-3),
),
1,
)
log_prob = p0.log_prob(y.transpose(-1, -2)) - div.sum([-1, -2])
log_prob = log_prob / x.shape[-2]
else:
p0 = td.Independent(td.Normal(torch.zeros_like(y), torch.ones_like(y)), 1)
log_prob = p0.log_prob(y) - div.sum(-1)
return log_prob.unsqueeze(-1)
@torch.no_grad()
def sample(
self,
model: Callable,
num_samples: int,
device: str = None,
use_ode: bool = True,
**kwargs,
) -> TensorType["num_samples", "dim"]:
if isinstance(num_samples, int):
num_samples = (num_samples,)
sampler = self.ode_sample if use_ode else self.sde_sample
return sampler(model, num_samples, device, **kwargs)
@torch.no_grad()
def ode_sample(
self,
model: Callable,
num_samples: int,
device: str = None,
**kwargs,
) -> TensorType["num_samples", "dim"]:
if self.is_time_series:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
else:
L = None
def drift(i, y):
score = self._get_score(model, y, i=i, L=L, **kwargs)
if self.is_time_series:
# Have to include `cov` since g(t) = "scalar" * L @ dW
score = cov @ score
return -0.5 * self.beta_fn(i) * (y + score)
x = self.noise(*num_samples, **kwargs).to(device)
t = torch.Tensor([self.t1, 0]).to(device)
y = odeint(drift, x, t, method="rk4", options={"step_size": 0.01})[1]
# y = odeint(drift, x, t, rtol=1e-6, atol=1e-5)[1]
return y
@torch.no_grad()
def sde_sample(
self,
model: Callable,
num_samples: int,
device: str = None,
**kwargs,
) -> TensorType["num_samples", "dim"]:
if self.is_time_series:
cov = self.noise.covariance(**kwargs)
L = torch.linalg.cholesky(cov)
else:
L = None
is_time_series = self.is_time_series
x = self.noise(*num_samples, **kwargs).to(device)
shape = x.shape
x = x.transpose(-2, -1).flatten(0, -2)
class SDE(nn.Module):
noise_type = "general" if is_time_series else "diagonal"
sde_type = "ito"
def __init__(self, beta_fn, _get_score):
super().__init__()
self.beta_fn = beta_fn
self._get_score = _get_score
def f(self, i, inp):
i = -i
inp = inp.view(*shape) # Reshape back to original
score = self._get_score(model, inp, i=i, L=L, **kwargs)
if is_time_series:
score = cov @ score
dx = self.beta_fn(i) * (0.5 * inp + score)
if is_time_series:
return dx.transpose(-1, -2).flatten(0, -2)
return dx.view(-1, shape[-1])
def g(self, i, inp):
i = -i
beta = -self.beta_fn(i).sqrt()
if is_time_series:
return (beta * L).repeat_interleave(shape[-1], dim=0)
return beta.view(1, 1).repeat(np.prod(shape[:-1]), shape[-1]).to(device)
sde = SDE(self.beta_fn, self._get_score)
interval = torch.Tensor([-self.t1, 0]).to(device) # Time from -t1 to 0
step_size = self.t1 / 100
if not is_time_series:
x = x.view(-1, shape[-1])
else:
x = x.view(-1, shape[-2])
y = sdeint(sde, x, interval, dt=step_size)[-1]
y = y.view(*shape)
return y
class ContinuousGaussianDiffusion(ContinuousDiffusion):
"""Continuous diffusion using Gaussian noise"""
def __init__(self, dim: int, beta_fn: Callable, predict_gaussian_noise=None, **kwargs):
super().__init__(dim, beta_fn, noise_fn=Normal(dim), predict_gaussian_noise=True, **kwargs)
class ContinuousOUDiffusion(ContinuousDiffusion):
"""Continuous diffusion using noise coming from an OU process"""
def __init__(
self,
dim: int,
beta_fn: Callable,
predict_gaussian_noise: bool = False,
theta: float = 0.5,
**kwargs,
):
super().__init__(
dim=dim,
beta_fn=beta_fn,
noise_fn=OrnsteinUhlenbeck(dim, theta=theta),
predict_gaussian_noise=predict_gaussian_noise,
is_time_series=True,
**kwargs,
)
class ContinuousGPDiffusion(ContinuousDiffusion):
"""Continuous diffusion using noise coming from a Gaussian process"""
def __init__(
self,
dim: int,
beta_fn: Callable,
predict_gaussian_noise: bool = False,
sigma: float = 0.1,
**kwargs,
):
super().__init__(
dim=dim,
beta_fn=beta_fn,
noise_fn=GaussianProcess(dim, sigma=sigma),
predict_gaussian_noise=predict_gaussian_noise,
is_time_series=True,
**kwargs,
)
def divergence_approx(output, input, e, num_samples=1):
out = 0
for i in range(num_samples):
out += torch.autograd.grad(output, input, e[i], create_graph=True)[0].detach() * e[i]
return out / num_samples
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