import math
from typing import Dict
import numpy as np
import torch
from torch import nn
import torch.nn.functional as F
from torch_scatter import scatter_add, scatter_mean
import utils
class EnVariationalDiffusion(nn.Module):
"""
The E(n) Diffusion Module.
"""
def __init__(
self,
dynamics: nn.Module, atom_nf: int, residue_nf: int,
n_dims: int, size_histogram: Dict,
timesteps: int = 1000, parametrization='eps',
noise_schedule='learned', noise_precision=1e-4,
loss_type='vlb', norm_values=(1., 1.), norm_biases=(None, 0.),
virtual_node_idx=None):
super().__init__()
assert loss_type in {'vlb', 'l2'}
self.loss_type = loss_type
if noise_schedule == 'learned':
assert loss_type == 'vlb', 'A noise schedule can only be learned' \
' with a vlb objective.'
# Only supported parametrization.
assert parametrization == 'eps'
if noise_schedule == 'learned':
self.gamma = GammaNetwork()
else:
self.gamma = PredefinedNoiseSchedule(noise_schedule,
timesteps=timesteps,
precision=noise_precision)
# The network that will predict the denoising.
self.dynamics = dynamics
self.atom_nf = atom_nf
self.residue_nf = residue_nf
self.n_dims = n_dims
self.num_classes = self.atom_nf
self.T = timesteps
self.parametrization = parametrization
self.norm_values = norm_values
self.norm_biases = norm_biases
self.register_buffer('buffer', torch.zeros(1))
# distribution of nodes
self.size_distribution = DistributionNodes(size_histogram)
# indicate if virtual nodes are present
self.vnode_idx = virtual_node_idx
if noise_schedule != 'learned':
self.check_issues_norm_values()
def check_issues_norm_values(self, num_stdevs=8):
zeros = torch.zeros((1, 1))
gamma_0 = self.gamma(zeros)
sigma_0 = self.sigma(gamma_0, target_tensor=zeros).item()
# Checked if 1 / norm_value is still larger than 10 * standard
# deviation.
norm_value = self.norm_values[1]
if sigma_0 * num_stdevs > 1. / norm_value:
raise ValueError(
f'Value for normalization value {norm_value} probably too '
f'large with sigma_0 {sigma_0:.5f} and '
f'1 / norm_value = {1. / norm_value}')
def sigma_and_alpha_t_given_s(self, gamma_t: torch.Tensor,
gamma_s: torch.Tensor,
target_tensor: torch.Tensor):
"""
Computes sigma t given s, using gamma_t and gamma_s. Used during sampling.
These are defined as:
alpha t given s = alpha t / alpha s,
sigma t given s = sqrt(1 - (alpha t given s) ^2 ).
"""
sigma2_t_given_s = self.inflate_batch_array(
-torch.expm1(F.softplus(gamma_s) - F.softplus(gamma_t)), target_tensor
)
# alpha_t_given_s = alpha_t / alpha_s
log_alpha2_t = F.logsigmoid(-gamma_t)
log_alpha2_s = F.logsigmoid(-gamma_s)
log_alpha2_t_given_s = log_alpha2_t - log_alpha2_s
alpha_t_given_s = torch.exp(0.5 * log_alpha2_t_given_s)
alpha_t_given_s = self.inflate_batch_array(
alpha_t_given_s, target_tensor)
sigma_t_given_s = torch.sqrt(sigma2_t_given_s)
return sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s
def kl_prior_with_pocket(self, xh_lig, xh_pocket, mask_lig, mask_pocket,
num_nodes):
"""Computes the KL between q(z1 | x) and the prior p(z1) = Normal(0, 1).
This is essentially a lot of work for something that is in practice
negligible in the loss. However, you compute it so that you see it when
you've made a mistake in your noise schedule.
"""
batch_size = len(num_nodes)
# Compute the last alpha value, alpha_T.
ones = torch.ones((batch_size, 1), device=xh_lig.device)
gamma_T = self.gamma(ones)
alpha_T = self.alpha(gamma_T, xh_lig)
# Compute means.
mu_T_lig = alpha_T[mask_lig] * xh_lig
mu_T_lig_x, mu_T_lig_h = mu_T_lig[:, :self.n_dims], \
mu_T_lig[:, self.n_dims:]
# Compute standard deviations (only batch axis for x-part, inflated for h-part).
sigma_T_x = self.sigma(gamma_T, mu_T_lig_x).squeeze()
sigma_T_h = self.sigma(gamma_T, mu_T_lig_h).squeeze()
# Compute means.
mu_T_pocket = alpha_T[mask_pocket] * xh_pocket
mu_T_pocket_x, mu_T_pocket_h = mu_T_pocket[:, :self.n_dims], \
mu_T_pocket[:, self.n_dims:]
# Compute KL for h-part.
zeros_lig = torch.zeros_like(mu_T_lig_h)
zeros_pocket = torch.zeros_like(mu_T_pocket_h)
ones = torch.ones_like(sigma_T_h)
mu_norm2 = self.sum_except_batch((mu_T_lig_h - zeros_lig) ** 2, mask_lig) + \
self.sum_except_batch((mu_T_pocket_h - zeros_pocket) ** 2, mask_pocket)
kl_distance_h = self.gaussian_KL(mu_norm2, sigma_T_h, ones, d=1)
# Compute KL for x-part.
zeros_lig = torch.zeros_like(mu_T_lig_x)
zeros_pocket = torch.zeros_like(mu_T_pocket_x)
ones = torch.ones_like(sigma_T_x)
mu_norm2 = self.sum_except_batch((mu_T_lig_x - zeros_lig) ** 2, mask_lig) + \
self.sum_except_batch((mu_T_pocket_x - zeros_pocket) ** 2, mask_pocket)
subspace_d = self.subspace_dimensionality(num_nodes)
kl_distance_x = self.gaussian_KL(mu_norm2, sigma_T_x, ones, subspace_d)
return kl_distance_x + kl_distance_h
def compute_x_pred(self, net_out, zt, gamma_t, batch_mask):
"""Commputes x_pred, i.e. the most likely prediction of x."""
if self.parametrization == 'x':
x_pred = net_out
elif self.parametrization == 'eps':
sigma_t = self.sigma(gamma_t, target_tensor=net_out)
alpha_t = self.alpha(gamma_t, target_tensor=net_out)
eps_t = net_out
x_pred = 1. / alpha_t[batch_mask] * (zt - sigma_t[batch_mask] * eps_t)
else:
raise ValueError(self.parametrization)
return x_pred
def log_constants_p_x_given_z0(self, n_nodes, device):
"""Computes p(x|z0)."""
batch_size = len(n_nodes)
degrees_of_freedom_x = self.subspace_dimensionality(n_nodes)
zeros = torch.zeros((batch_size, 1), device=device)
gamma_0 = self.gamma(zeros)
# Recall that sigma_x = sqrt(sigma_0^2 / alpha_0^2) = SNR(-0.5 gamma_0).
log_sigma_x = 0.5 * gamma_0.view(batch_size)
return degrees_of_freedom_x * (- log_sigma_x - 0.5 * np.log(2 * np.pi))
def log_pxh_given_z0_without_constants(
self, ligand, z_0_lig, eps_lig, net_out_lig,
pocket, z_0_pocket, eps_pocket, net_out_pocket,
gamma_0, epsilon=1e-10):
# Discrete properties are predicted directly from z_t.
z_h_lig = z_0_lig[:, self.n_dims:]
z_h_pocket = z_0_pocket[:, self.n_dims:]
# Take only part over x.
eps_lig_x = eps_lig[:, :self.n_dims]
net_lig_x = net_out_lig[:, :self.n_dims]
eps_pocket_x = eps_pocket[:, :self.n_dims]
net_pocket_x = net_out_pocket[:, :self.n_dims]
# Compute sigma_0 and rescale to the integer scale of the data.
sigma_0 = self.sigma(gamma_0, target_tensor=z_0_lig)
sigma_0_cat = sigma_0 * self.norm_values[1]
# Computes the error for the distribution
# N(x | 1 / alpha_0 z_0 + sigma_0/alpha_0 eps_0, sigma_0 / alpha_0),
# the weighting in the epsilon parametrization is exactly '1'.
log_p_x_given_z0_without_constants_ligand = -0.5 * (
self.sum_except_batch((eps_lig_x - net_lig_x) ** 2, ligand['mask'])
)
log_p_x_given_z0_without_constants_pocket = -0.5 * (
self.sum_except_batch((eps_pocket_x - net_pocket_x) ** 2,
pocket['mask'])
)
# Compute delta indicator masks.
# un-normalize
ligand_onehot = ligand['one_hot'] * self.norm_values[1] + self.norm_biases[1]
pocket_onehot = pocket['one_hot'] * self.norm_values[1] + self.norm_biases[1]
estimated_ligand_onehot = z_h_lig * self.norm_values[1] + self.norm_biases[1]
estimated_pocket_onehot = z_h_pocket * self.norm_values[1] + self.norm_biases[1]
# Centered h_cat around 1, since onehot encoded.
centered_ligand_onehot = estimated_ligand_onehot - 1
centered_pocket_onehot = estimated_pocket_onehot - 1
# Compute integrals from 0.5 to 1.5 of the normal distribution
# N(mean=z_h_cat, stdev=sigma_0_cat)
log_ph_cat_proportional_ligand = torch.log(
self.cdf_standard_gaussian((centered_ligand_onehot + 0.5) / sigma_0_cat[ligand['mask']])
- self.cdf_standard_gaussian((centered_ligand_onehot - 0.5) / sigma_0_cat[ligand['mask']])
+ epsilon
)
log_ph_cat_proportional_pocket = torch.log(
self.cdf_standard_gaussian((centered_pocket_onehot + 0.5) / sigma_0_cat[pocket['mask']])
- self.cdf_standard_gaussian((centered_pocket_onehot - 0.5) / sigma_0_cat[pocket['mask']])
+ epsilon
)
# Normalize the distribution over the categories.
log_Z = torch.logsumexp(log_ph_cat_proportional_ligand, dim=1,
keepdim=True)
log_probabilities_ligand = log_ph_cat_proportional_ligand - log_Z
log_Z = torch.logsumexp(log_ph_cat_proportional_pocket, dim=1,
keepdim=True)
log_probabilities_pocket = log_ph_cat_proportional_pocket - log_Z
# Select the log_prob of the current category using the onehot
# representation.
log_ph_given_z0_ligand = self.sum_except_batch(
log_probabilities_ligand * ligand_onehot, ligand['mask'])
log_ph_given_z0_pocket = self.sum_except_batch(
log_probabilities_pocket * pocket_onehot, pocket['mask'])
# Combine log probabilities of ligand and pocket for h.
log_ph_given_z0 = log_ph_given_z0_ligand + log_ph_given_z0_pocket
return log_p_x_given_z0_without_constants_ligand, \
log_p_x_given_z0_without_constants_pocket, log_ph_given_z0
def sample_p_xh_given_z0(self, z0_lig, z0_pocket, lig_mask, pocket_mask,
batch_size, fix_noise=False):
"""Samples x ~ p(x|z0)."""
t_zeros = torch.zeros(size=(batch_size, 1), device=z0_lig.device)
gamma_0 = self.gamma(t_zeros)
# Computes sqrt(sigma_0^2 / alpha_0^2)
sigma_x = self.SNR(-0.5 * gamma_0)
net_out_lig, net_out_pocket = self.dynamics(
z0_lig, z0_pocket, t_zeros, lig_mask, pocket_mask)
# Compute mu for p(zs | zt).
mu_x_lig = self.compute_x_pred(net_out_lig, z0_lig, gamma_0, lig_mask)
mu_x_pocket = self.compute_x_pred(net_out_pocket, z0_pocket, gamma_0,
pocket_mask)
xh_lig, xh_pocket = self.sample_normal(mu_x_lig, mu_x_pocket, sigma_x,
lig_mask, pocket_mask, fix_noise)
x_lig, h_lig = self.unnormalize(
xh_lig[:, :self.n_dims], z0_lig[:, self.n_dims:])
x_pocket, h_pocket = self.unnormalize(
xh_pocket[:, :self.n_dims], z0_pocket[:, self.n_dims:])
h_lig = F.one_hot(torch.argmax(h_lig, dim=1), self.atom_nf)
h_pocket = F.one_hot(torch.argmax(h_pocket, dim=1), self.residue_nf)
return x_lig, h_lig, x_pocket, h_pocket
def sample_normal(self, mu_lig, mu_pocket, sigma, lig_mask, pocket_mask,
fix_noise=False):
"""Samples from a Normal distribution."""
if fix_noise:
# bs = 1 if fix_noise else mu.size(0)
raise NotImplementedError("fix_noise option isn't implemented yet")
eps_lig, eps_pocket = self.sample_combined_position_feature_noise(
lig_mask, pocket_mask)
return mu_lig + sigma[lig_mask] * eps_lig, \
mu_pocket + sigma[pocket_mask] * eps_pocket
def noised_representation(self, xh_lig, xh_pocket, lig_mask, pocket_mask,
gamma_t):
# Compute alpha_t and sigma_t from gamma.
alpha_t = self.alpha(gamma_t, xh_lig)
sigma_t = self.sigma(gamma_t, xh_lig)
# Sample zt ~ Normal(alpha_t x, sigma_t)
eps_lig, eps_pocket = self.sample_combined_position_feature_noise(
lig_mask, pocket_mask)
# Sample z_t given x, h for timestep t, from q(z_t | x, h)
z_t_lig = alpha_t[lig_mask] * xh_lig + sigma_t[lig_mask] * eps_lig
z_t_pocket = alpha_t[pocket_mask] * xh_pocket + \
sigma_t[pocket_mask] * eps_pocket
return z_t_lig, z_t_pocket, eps_lig, eps_pocket
def log_pN(self, N_lig, N_pocket):
"""
Prior on the sample size for computing
log p(x,h,N) = log p(x,h|N) + log p(N), where log p(x,h|N) is the
model's output
Args:
N: array of sample sizes
Returns:
log p(N)
"""
log_pN = self.size_distribution.log_prob(N_lig, N_pocket)
return log_pN
def delta_log_px(self, num_nodes):
return -self.subspace_dimensionality(num_nodes) * \
np.log(self.norm_values[0])
def forward(self, ligand, pocket, return_info=False):
"""
Computes the loss and NLL terms
"""
# Normalize data, take into account volume change in x.
ligand, pocket = self.normalize(ligand, pocket)
# Likelihood change due to normalization
delta_log_px = self.delta_log_px(ligand['size'] + pocket['size'])
# Sample a timestep t for each example in batch
# At evaluation time, loss_0 will be computed separately to decrease
# variance in the estimator (costs two forward passes)
lowest_t = 0 if self.training else 1
t_int = torch.randint(
lowest_t, self.T + 1, size=(ligand['size'].size(0), 1),
device=ligand['x'].device).float()
s_int = t_int - 1 # previous timestep
# Masks: important to compute log p(x | z0).
t_is_zero = (t_int == 0).float()
t_is_not_zero = 1 - t_is_zero
# Normalize t to [0, 1]. Note that the negative
# step of s will never be used, since then p(x | z0) is computed.
s = s_int / self.T
t = t_int / self.T
# Compute gamma_s and gamma_t via the network.
gamma_s = self.inflate_batch_array(self.gamma(s), ligand['x'])
gamma_t = self.inflate_batch_array(self.gamma(t), ligand['x'])
# Concatenate x, and h[categorical].
xh_lig = torch.cat([ligand['x'], ligand['one_hot']], dim=1)
xh_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)
# Find noised representation
z_t_lig, z_t_pocket, eps_t_lig, eps_t_pocket = \
self.noised_representation(xh_lig, xh_pocket, ligand['mask'],
pocket['mask'], gamma_t)
# Neural net prediction.
net_out_lig, net_out_pocket = self.dynamics(
z_t_lig, z_t_pocket, t, ligand['mask'], pocket['mask'])
# For LJ loss term
xh_lig_hat = self.xh_given_zt_and_epsilon(z_t_lig, net_out_lig, gamma_t,
ligand['mask'])
# Compute the L2 error.
error_t_lig = self.sum_except_batch((eps_t_lig - net_out_lig) ** 2,
ligand['mask'])
error_t_pocket = self.sum_except_batch(
(eps_t_pocket - net_out_pocket) ** 2, pocket['mask'])
# Compute weighting with SNR: (1 - SNR(s-t)) for epsilon parametrization
SNR_weight = (1 - self.SNR(gamma_s - gamma_t)).squeeze(1)
assert error_t_lig.size() == SNR_weight.size()
# The _constants_ depending on sigma_0 from the
# cross entropy term E_q(z0 | x) [log p(x | z0)].
neg_log_constants = -self.log_constants_p_x_given_z0(
n_nodes=ligand['size'] + pocket['size'], device=error_t_lig.device)
# The KL between q(zT | x) and p(zT) = Normal(0, 1).
# Should be close to zero.
kl_prior = self.kl_prior_with_pocket(
xh_lig, xh_pocket, ligand['mask'], pocket['mask'],
ligand['size'] + pocket['size'])
if self.training:
# Computes the L_0 term (even if gamma_t is not actually gamma_0)
# and this will later be selected via masking.
log_p_x_given_z0_without_constants_ligand, \
log_p_x_given_z0_without_constants_pocket, log_ph_given_z0 = \
self.log_pxh_given_z0_without_constants(
ligand, z_t_lig, eps_t_lig, net_out_lig,
pocket, z_t_pocket, eps_t_pocket, net_out_pocket, gamma_t)
loss_0_x_ligand = -log_p_x_given_z0_without_constants_ligand * \
t_is_zero.squeeze()
loss_0_x_pocket = -log_p_x_given_z0_without_constants_pocket * \
t_is_zero.squeeze()
loss_0_h = -log_ph_given_z0 * t_is_zero.squeeze()
# apply t_is_zero mask
error_t_lig = error_t_lig * t_is_not_zero.squeeze()
error_t_pocket = error_t_pocket * t_is_not_zero.squeeze()
else:
# Compute noise values for t = 0.
t_zeros = torch.zeros_like(s)
gamma_0 = self.inflate_batch_array(self.gamma(t_zeros), ligand['x'])
# Sample z_0 given x, h for timestep t, from q(z_t | x, h)
z_0_lig, z_0_pocket, eps_0_lig, eps_0_pocket = \
self.noised_representation(xh_lig, xh_pocket, ligand['mask'],
pocket['mask'], gamma_0)
net_out_0_lig, net_out_0_pocket = self.dynamics(
z_0_lig, z_0_pocket, t_zeros, ligand['mask'], pocket['mask'])
log_p_x_given_z0_without_constants_ligand, \
log_p_x_given_z0_without_constants_pocket, log_ph_given_z0 = \
self.log_pxh_given_z0_without_constants(
ligand, z_0_lig, eps_0_lig, net_out_0_lig,
pocket, z_0_pocket, eps_0_pocket, net_out_0_pocket, gamma_0)
loss_0_x_ligand = -log_p_x_given_z0_without_constants_ligand
loss_0_x_pocket = -log_p_x_given_z0_without_constants_pocket
loss_0_h = -log_ph_given_z0
# sample size prior
log_pN = self.log_pN(ligand['size'], pocket['size'])
info = {
'eps_hat_lig_x': scatter_mean(
net_out_lig[:, :self.n_dims].abs().mean(1), ligand['mask'],
dim=0).mean(),
'eps_hat_lig_h': scatter_mean(
net_out_lig[:, self.n_dims:].abs().mean(1), ligand['mask'],
dim=0).mean(),
'eps_hat_pocket_x': scatter_mean(
net_out_pocket[:, :self.n_dims].abs().mean(1), pocket['mask'],
dim=0).mean(),
'eps_hat_pocket_h': scatter_mean(
net_out_pocket[:, self.n_dims:].abs().mean(1), pocket['mask'],
dim=0).mean(),
}
loss_terms = (delta_log_px, error_t_lig, error_t_pocket, SNR_weight,
loss_0_x_ligand, loss_0_x_pocket, loss_0_h,
neg_log_constants, kl_prior, log_pN,
t_int.squeeze(), xh_lig_hat)
return (*loss_terms, info) if return_info else loss_terms
def xh_given_zt_and_epsilon(self, z_t, epsilon, gamma_t, batch_mask):
""" Equation (7) in the EDM paper """
alpha_t = self.alpha(gamma_t, z_t)
sigma_t = self.sigma(gamma_t, z_t)
xh = z_t / alpha_t[batch_mask] - epsilon * sigma_t[batch_mask] / \
alpha_t[batch_mask]
return xh
def sample_p_zt_given_zs(self, zs_lig, zs_pocket, ligand_mask, pocket_mask,
gamma_t, gamma_s, fix_noise=False):
sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s = \
self.sigma_and_alpha_t_given_s(gamma_t, gamma_s, zs_lig)
mu_lig = alpha_t_given_s[ligand_mask] * zs_lig
mu_pocket = alpha_t_given_s[pocket_mask] * zs_pocket
zt_lig, zt_pocket = self.sample_normal(
mu_lig, mu_pocket, sigma_t_given_s, ligand_mask, pocket_mask,
fix_noise)
# Remove center of mass
zt_x = self.remove_mean_batch(
torch.cat((zt_lig[:, :self.n_dims], zt_pocket[:, :self.n_dims]),
dim=0),
torch.cat((ligand_mask, pocket_mask))
)
zt_lig = torch.cat((zt_x[:len(ligand_mask)],
zt_lig[:, self.n_dims:]), dim=1)
zt_pocket = torch.cat((zt_x[len(ligand_mask):],
zt_pocket[:, self.n_dims:]), dim=1)
return zt_lig, zt_pocket
def sample_p_zs_given_zt(self, s, t, zt_lig, zt_pocket, ligand_mask,
pocket_mask, fix_noise=False):
"""Samples from zs ~ p(zs | zt). Only used during sampling."""
gamma_s = self.gamma(s)
gamma_t = self.gamma(t)
sigma2_t_given_s, sigma_t_given_s, alpha_t_given_s = \
self.sigma_and_alpha_t_given_s(gamma_t, gamma_s, zt_lig)
sigma_s = self.sigma(gamma_s, target_tensor=zt_lig)
sigma_t = self.sigma(gamma_t, target_tensor=zt_lig)
# Neural net prediction.
eps_t_lig, eps_t_pocket = self.dynamics(
zt_lig, zt_pocket, t, ligand_mask, pocket_mask)
# Compute mu for p(zs | zt).
combined_mask = torch.cat((ligand_mask, pocket_mask))
self.assert_mean_zero_with_mask(
torch.cat((zt_lig[:, :self.n_dims],
zt_pocket[:, :self.n_dims]), dim=0),
combined_mask)
self.assert_mean_zero_with_mask(
torch.cat((eps_t_lig[:, :self.n_dims],
eps_t_pocket[:, :self.n_dims]), dim=0),
combined_mask)
# Note: mu_{t->s} = 1 / alpha_{t|s} z_t - sigma_{t|s}^2 / sigma_t / alpha_{t|s} epsilon
# follows from the definition of mu_{t->s} and Equ. (7) in the EDM paper
mu_lig = zt_lig / alpha_t_given_s[ligand_mask] - \
(sigma2_t_given_s / alpha_t_given_s / sigma_t)[ligand_mask] * \
eps_t_lig
mu_pocket = zt_pocket / alpha_t_given_s[pocket_mask] - \
(sigma2_t_given_s / alpha_t_given_s / sigma_t)[pocket_mask] * \
eps_t_pocket
# Compute sigma for p(zs | zt).
sigma = sigma_t_given_s * sigma_s / sigma_t
# Sample zs given the paramters derived from zt.
zs_lig, zs_pocket = self.sample_normal(mu_lig, mu_pocket, sigma,
ligand_mask, pocket_mask,
fix_noise)
# Project down to avoid numerical runaway of the center of gravity.
zs_x = self.remove_mean_batch(
torch.cat((zs_lig[:, :self.n_dims],
zs_pocket[:, :self.n_dims]), dim=0),
torch.cat((ligand_mask, pocket_mask))
)
zs_lig = torch.cat((zs_x[:len(ligand_mask)],
zs_lig[:, self.n_dims:]), dim=1)
zs_pocket = torch.cat((zs_x[len(ligand_mask):],
zs_pocket[:, self.n_dims:]), dim=1)
return zs_lig, zs_pocket
def sample_combined_position_feature_noise(self, lig_indices,
pocket_indices):
"""
Samples mean-centered normal noise for z_x, and standard normal noise
for z_h.
"""
z_x = self.sample_center_gravity_zero_gaussian_batch(
size=(len(lig_indices) + len(pocket_indices), self.n_dims),
lig_indices=lig_indices,
pocket_indices=pocket_indices
)
z_h_lig = self.sample_gaussian(
size=(len(lig_indices), self.atom_nf),
device=lig_indices.device)
z_lig = torch.cat([z_x[:len(lig_indices)], z_h_lig], dim=1)
z_h_pocket = self.sample_gaussian(
size=(len(pocket_indices), self.residue_nf),
device=pocket_indices.device)
z_pocket = torch.cat([z_x[len(lig_indices):], z_h_pocket], dim=1)
return z_lig, z_pocket
@torch.no_grad()
def sample(self, n_samples, num_nodes_lig, num_nodes_pocket,
return_frames=1, timesteps=None, device='cpu'):
"""
Draw samples from the generative model. Optionally, return intermediate
states for visualization purposes.
"""
timesteps = self.T if timesteps is None else timesteps
assert 0 < return_frames <= timesteps
assert timesteps % return_frames == 0
lig_mask = utils.num_nodes_to_batch_mask(n_samples, num_nodes_lig,
device)
pocket_mask = utils.num_nodes_to_batch_mask(n_samples, num_nodes_pocket,
device)
combined_mask = torch.cat((lig_mask, pocket_mask))
z_lig, z_pocket = self.sample_combined_position_feature_noise(
lig_mask, pocket_mask)
self.assert_mean_zero_with_mask(
torch.cat((z_lig[:, :self.n_dims], z_pocket[:, :self.n_dims]), dim=0),
combined_mask
)
out_lig = torch.zeros((return_frames,) + z_lig.size(),
device=z_lig.device)
out_pocket = torch.zeros((return_frames,) + z_pocket.size(),
device=z_pocket.device)
# Iteratively sample p(z_s | z_t) for t = 1, ..., T, with s = t - 1.
for s in reversed(range(0, timesteps)):
s_array = torch.full((n_samples, 1), fill_value=s,
device=z_lig.device)
t_array = s_array + 1
s_array = s_array / timesteps
t_array = t_array / timesteps
z_lig, z_pocket = self.sample_p_zs_given_zt(
s_array, t_array, z_lig, z_pocket, lig_mask, pocket_mask)
# save frame
if (s * return_frames) % timesteps == 0:
idx = (s * return_frames) // timesteps
out_lig[idx], out_pocket[idx] = \
self.unnormalize_z(z_lig, z_pocket)
# Finally sample p(x, h | z_0).
x_lig, h_lig, x_pocket, h_pocket = self.sample_p_xh_given_z0(
z_lig, z_pocket, lig_mask, pocket_mask, n_samples)
self.assert_mean_zero_with_mask(
torch.cat((x_lig, x_pocket), dim=0), combined_mask
)
# Correct CoM drift for examples without intermediate states
if return_frames == 1:
x = torch.cat((x_lig, x_pocket))
max_cog = scatter_add(x, combined_mask, dim=0).abs().max().item()
if max_cog > 5e-2:
print(f'Warning CoG drift with error {max_cog:.3f}. Projecting '
f'the positions down.')
x = self.remove_mean_batch(x, combined_mask)
x_lig, x_pocket = x[:len(x_lig)], x[len(x_lig):]
# Overwrite last frame with the resulting x and h.
out_lig[0] = torch.cat([x_lig, h_lig], dim=1)
out_pocket[0] = torch.cat([x_pocket, h_pocket], dim=1)
# remove frame dimension if only the final molecule is returned
return out_lig.squeeze(0), out_pocket.squeeze(0), lig_mask, pocket_mask
def get_repaint_schedule(self, resamplings, jump_length, timesteps):
""" Each integer in the schedule list describes how many denoising steps
need to be applied before jumping back """
repaint_schedule = []
curr_t = 0
while curr_t < timesteps:
if curr_t + jump_length < timesteps:
if len(repaint_schedule) > 0:
repaint_schedule[-1] += jump_length
repaint_schedule.extend([jump_length] * (resamplings - 1))
else:
repaint_schedule.extend([jump_length] * resamplings)
curr_t += jump_length
else:
residual = (timesteps - curr_t)
if len(repaint_schedule) > 0:
repaint_schedule[-1] += residual
else:
repaint_schedule.append(residual)
curr_t += residual
return list(reversed(repaint_schedule))
@torch.no_grad()
def inpaint(self, ligand, pocket, lig_fixed, pocket_fixed, resamplings=1,
jump_length=1, return_frames=1, timesteps=None):
"""
Draw samples from the generative model while fixing parts of the input.
Optionally, return intermediate states for visualization purposes.
See:
Lugmayr, Andreas, et al.
"Repaint: Inpainting using denoising diffusion probabilistic models."
Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern
Recognition. 2022.
"""
timesteps = self.T if timesteps is None else timesteps
assert 0 < return_frames <= timesteps
assert timesteps % return_frames == 0
assert jump_length == 1 or return_frames == 1, \
"Chain visualization is only implemented for jump_length=1"
if len(lig_fixed.size()) == 1:
lig_fixed = lig_fixed.unsqueeze(1)
if len(pocket_fixed.size()) == 1:
pocket_fixed = pocket_fixed.unsqueeze(1)
ligand, pocket = self.normalize(ligand, pocket)
n_samples = len(ligand['size'])
combined_mask = torch.cat((ligand['mask'], pocket['mask']))
xh0_lig = torch.cat([ligand['x'], ligand['one_hot']], dim=1)
xh0_pocket = torch.cat([pocket['x'], pocket['one_hot']], dim=1)
# Center initial system, subtract COM of known parts
mean_known = scatter_mean(
torch.cat((ligand['x'][lig_fixed.bool().view(-1)],
pocket['x'][pocket_fixed.bool().view(-1)])),
torch.cat((ligand['mask'][lig_fixed.bool().view(-1)],
pocket['mask'][pocket_fixed.bool().view(-1)])),
dim=0
)
xh0_lig[:, :self.n_dims] = \
xh0_lig[:, :self.n_dims] - mean_known[ligand['mask']]
xh0_pocket[:, :self.n_dims] = \
xh0_pocket[:, :self.n_dims] - mean_known[pocket['mask']]
# Noised representation at step t=T
z_lig, z_pocket = self.sample_combined_position_feature_noise(
ligand['mask'], pocket['mask'])
# Output tensors
out_lig = torch.zeros((return_frames,) + z_lig.size(),
device=z_lig.device)
out_pocket = torch.zeros((return_frames,) + z_pocket.size(),
device=z_pocket.device)
# Iteratively sample according to a pre-defined schedule
schedule = self.get_repaint_schedule(resamplings, jump_length, timesteps)
s = timesteps - 1
for i, n_denoise_steps in enumerate(schedule):
for j in range(n_denoise_steps):
# Denoise one time step: t -> s
s_array = torch.full((n_samples, 1), fill_value=s,
device=z_lig.device)
t_array = s_array + 1
s_array = s_array / timesteps
t_array = t_array / timesteps
# sample known nodes from the input
gamma_s = self.inflate_batch_array(self.gamma(s_array),
ligand['x'])
z_lig_known, z_pocket_known, _, _ = self.noised_representation(
xh0_lig, xh0_pocket, ligand['mask'], pocket['mask'], gamma_s)
# sample inpainted part
z_lig_unknown, z_pocket_unknown = self.sample_p_zs_given_zt(
s_array, t_array, z_lig, z_pocket, ligand['mask'],
pocket['mask'])
# move center of mass of the noised part to the center of mass
# of the corresponding denoised part before combining them
# -> the resulting system should be COM-free
com_noised = scatter_mean(
torch.cat((z_lig_known[:, :self.n_dims][lig_fixed.bool().view(-1)],
z_pocket_known[:, :self.n_dims][pocket_fixed.bool().view(-1)])),
torch.cat((ligand['mask'][lig_fixed.bool().view(-1)],
pocket['mask'][pocket_fixed.bool().view(-1)])),
dim=0
)
com_denoised = scatter_mean(
torch.cat((z_lig_unknown[:, :self.n_dims][lig_fixed.bool().view(-1)],
z_pocket_unknown[:, :self.n_dims][pocket_fixed.bool().view(-1)])),
torch.cat((ligand['mask'][lig_fixed.bool().view(-1)],
pocket['mask'][pocket_fixed.bool().view(-1)])),
dim=0
)
z_lig_known[:, :self.n_dims] = \
z_lig_known[:, :self.n_dims] + (com_denoised - com_noised)[ligand['mask']]
z_pocket_known[:, :self.n_dims] = \
z_pocket_known[:, :self.n_dims] + (com_denoised - com_noised)[pocket['mask']]
# combine
z_lig = z_lig_known * lig_fixed + \
z_lig_unknown * (1 - lig_fixed)
z_pocket = z_pocket_known * pocket_fixed + \
z_pocket_unknown * (1 - pocket_fixed)
self.assert_mean_zero_with_mask(
torch.cat((z_lig[:, :self.n_dims],
z_pocket[:, :self.n_dims]), dim=0), combined_mask
)
# save frame at the end of a resample cycle
if n_denoise_steps > jump_length or i == len(schedule) - 1:
if (s * return_frames) % timesteps == 0:
idx = (s * return_frames) // timesteps
out_lig[idx], out_pocket[idx] = \
self.unnormalize_z(z_lig, z_pocket)
# Noise combined representation
if j == n_denoise_steps - 1 and i < len(schedule) - 1:
# Go back jump_length steps
t = s + jump_length
t_array = torch.full((n_samples, 1), fill_value=t,
device=z_lig.device)
t_array = t_array / timesteps
gamma_s = self.inflate_batch_array(self.gamma(s_array),
ligand['x'])
gamma_t = self.inflate_batch_array(self.gamma(t_array),
ligand['x'])
z_lig, z_pocket = self.sample_p_zt_given_zs(
z_lig, z_pocket, ligand['mask'], pocket['mask'],
gamma_t, gamma_s)
s = t
s -= 1
# Finally sample p(x, h | z_0).
x_lig, h_lig, x_pocket, h_pocket = self.sample_p_xh_given_z0(
z_lig, z_pocket, ligand['mask'], pocket['mask'], n_samples)
self.assert_mean_zero_with_mask(
torch.cat((x_lig, x_pocket), dim=0), combined_mask
)
# Correct CoM drift for examples without intermediate states
if return_frames == 1:
x = torch.cat((x_lig, x_pocket))
max_cog = scatter_add(x, combined_mask, dim=0).abs().max().item()
if max_cog > 5e-2:
print(f'Warning CoG drift with error {max_cog:.3f}. Projecting '
f'the positions down.')
x = self.remove_mean_batch(x, combined_mask)
x_lig, x_pocket = x[:len(x_lig)], x[len(x_lig):]
# Overwrite last frame with the resulting x and h.
out_lig[0] = torch.cat([x_lig, h_lig], dim=1)
out_pocket[0] = torch.cat([x_pocket, h_pocket], dim=1)
# remove frame dimension if only the final molecule is returned
return out_lig.squeeze(0), out_pocket.squeeze(0), ligand['mask'], \
pocket['mask']
@staticmethod
def gaussian_KL(q_mu_minus_p_mu_squared, q_sigma, p_sigma, d):
"""Computes the KL distance between two normal distributions.
Args:
q_mu_minus_p_mu_squared: Squared difference between mean of
distribution q and distribution p: ||mu_q - mu_p||^2
q_sigma: Standard deviation of distribution q.
p_sigma: Standard deviation of distribution p.
d: dimension
Returns:
The KL distance
"""
return d * torch.log(p_sigma / q_sigma) + \
0.5 * (d * q_sigma ** 2 + q_mu_minus_p_mu_squared) / \
(p_sigma ** 2) - 0.5 * d
@staticmethod
def inflate_batch_array(array, target):
"""
Inflates the batch array (array) with only a single axis
(i.e. shape = (batch_size,), or possibly more empty axes
(i.e. shape (batch_size, 1, ..., 1)) to match the target shape.
"""
target_shape = (array.size(0),) + (1,) * (len(target.size()) - 1)
return array.view(target_shape)
def sigma(self, gamma, target_tensor):
"""Computes sigma given gamma."""
return self.inflate_batch_array(torch.sqrt(torch.sigmoid(gamma)),
target_tensor)
def alpha(self, gamma, target_tensor):
"""Computes alpha given gamma."""
return self.inflate_batch_array(torch.sqrt(torch.sigmoid(-gamma)),
target_tensor)
@staticmethod
def SNR(gamma):
"""Computes signal to noise ratio (alpha^2/sigma^2) given gamma."""
return torch.exp(-gamma)
def normalize(self, ligand=None, pocket=None):
if ligand is not None:
ligand['x'] = ligand['x'] / self.norm_values[0]
# Casting to float in case h still has long or int type.
ligand['one_hot'] = \
(ligand['one_hot'].float() - self.norm_biases[1]) / \
self.norm_values[1]
if pocket is not None:
pocket['x'] = pocket['x'] / self.norm_values[0]
pocket['one_hot'] = \
(pocket['one_hot'].float() - self.norm_biases[1]) / \
self.norm_values[1]
return ligand, pocket
def unnormalize(self, x, h_cat):
x = x * self.norm_values[0]
h_cat = h_cat * self.norm_values[1] + self.norm_biases[1]
return x, h_cat
def unnormalize_z(self, z_lig, z_pocket):
# Parse from z
x_lig, h_lig = z_lig[:, :self.n_dims], z_lig[:, self.n_dims:]
x_pocket, h_pocket = z_pocket[:, :self.n_dims], z_pocket[:, self.n_dims:]
# Unnormalize
x_lig, h_lig = self.unnormalize(x_lig, h_lig)
x_pocket, h_pocket = self.unnormalize(x_pocket, h_pocket)
return torch.cat([x_lig, h_lig], dim=1), \
torch.cat([x_pocket, h_pocket], dim=1)
def subspace_dimensionality(self, input_size):
"""Compute the dimensionality on translation-invariant linear subspace
where distributions on x are defined."""
return (input_size - 1) * self.n_dims
@staticmethod
def remove_mean_batch(x, indices):
mean = scatter_mean(x, indices, dim=0)
x = x - mean[indices]
return x
@staticmethod
def assert_mean_zero_with_mask(x, node_mask, eps=1e-10):
largest_value = x.abs().max().item()
error = scatter_add(x, node_mask, dim=0).abs().max().item()
rel_error = error / (largest_value + eps)
assert rel_error < 1e-2, f'Mean is not zero, relative_error {rel_error}'
@staticmethod
def sample_center_gravity_zero_gaussian_batch(size, lig_indices,
pocket_indices):
assert len(size) == 2
x = torch.randn(size, device=lig_indices.device)
# This projection only works because Gaussian is rotation invariant
# around zero and samples are independent!
x_projected = EnVariationalDiffusion.remove_mean_batch(
x, torch.cat((lig_indices, pocket_indices)))
return x_projected
@staticmethod
def sum_except_batch(x, indices):
return scatter_add(x.sum(-1), indices, dim=0)
@staticmethod
def cdf_standard_gaussian(x):
return 0.5 * (1. + torch.erf(x / math.sqrt(2)))
@staticmethod
def sample_gaussian(size, device):
x = torch.randn(size, device=device)
return x
class DistributionNodes:
def __init__(self, histogram):
histogram = torch.tensor(histogram).float()
histogram = histogram + 1e-3 # for numerical stability
prob = histogram / histogram.sum()
self.idx_to_n_nodes = torch.tensor(
[[(i, j) for j in range(prob.shape[1])] for i in range(prob.shape[0])]
).view(-1, 2)
self.n_nodes_to_idx = {tuple(x.tolist()): i
for i, x in enumerate(self.idx_to_n_nodes)}
self.prob = prob
self.m = torch.distributions.Categorical(self.prob.view(-1),
validate_args=True)
self.n1_given_n2 = \
[torch.distributions.Categorical(prob[:, j], validate_args=True)
for j in range(prob.shape[1])]
self.n2_given_n1 = \
[torch.distributions.Categorical(prob[i, :], validate_args=True)
for i in range(prob.shape[0])]
# entropy = -torch.sum(self.prob.view(-1) * torch.log(self.prob.view(-1) + 1e-30))
entropy = self.m.entropy()
print("Entropy of n_nodes: H[N]", entropy.item())
def sample(self, n_samples=1):
idx = self.m.sample((n_samples,))
num_nodes_lig, num_nodes_pocket = self.idx_to_n_nodes[idx].T
return num_nodes_lig, num_nodes_pocket
def sample_conditional(self, n1=None, n2=None):
assert (n1 is None) ^ (n2 is None), \
"Exactly one input argument must be None"
m = self.n1_given_n2 if n2 is not None else self.n2_given_n1
c = n2 if n2 is not None else n1
return torch.tensor([m[i].sample() for i in c], device=c.device)
def log_prob(self, batch_n_nodes_1, batch_n_nodes_2):
assert len(batch_n_nodes_1.size()) == 1
assert len(batch_n_nodes_2.size()) == 1
idx = torch.tensor(
[self.n_nodes_to_idx[(n1, n2)]
for n1, n2 in zip(batch_n_nodes_1.tolist(), batch_n_nodes_2.tolist())]
)
# log_probs = torch.log(self.prob.view(-1)[idx] + 1e-30)
log_probs = self.m.log_prob(idx)
return log_probs.to(batch_n_nodes_1.device)
def log_prob_n1_given_n2(self, n1, n2):
assert len(n1.size()) == 1
assert len(n2.size()) == 1
log_probs = torch.stack([self.n1_given_n2[c].log_prob(i.cpu())
for i, c in zip(n1, n2)])
return log_probs.to(n1.device)
def log_prob_n2_given_n1(self, n2, n1):
assert len(n2.size()) == 1
assert len(n1.size()) == 1
log_probs = torch.stack([self.n2_given_n1[c].log_prob(i.cpu())
for i, c in zip(n2, n1)])
return log_probs.to(n2.device)
class PositiveLinear(torch.nn.Module):
"""Linear layer with weights forced to be positive."""
def __init__(self, in_features: int, out_features: int, bias: bool = True,
weight_init_offset: int = -2):
super(PositiveLinear, self).__init__()
self.in_features = in_features
self.out_features = out_features
self.weight = torch.nn.Parameter(
torch.empty((out_features, in_features)))
if bias:
self.bias = torch.nn.Parameter(torch.empty(out_features))
else:
self.register_parameter('bias', None)
self.weight_init_offset = weight_init_offset
self.reset_parameters()
def reset_parameters(self) -> None:
torch.nn.init.kaiming_uniform_(self.weight, a=math.sqrt(5))
with torch.no_grad():
self.weight.add_(self.weight_init_offset)
if self.bias is not None:
fan_in, _ = torch.nn.init._calculate_fan_in_and_fan_out(self.weight)
bound = 1 / math.sqrt(fan_in) if fan_in > 0 else 0
torch.nn.init.uniform_(self.bias, -bound, bound)
def forward(self, input):
positive_weight = F.softplus(self.weight)
return F.linear(input, positive_weight, self.bias)
class GammaNetwork(torch.nn.Module):
"""The gamma network models a monotonic increasing function.
Construction as in the VDM paper."""
def __init__(self):
super().__init__()
self.l1 = PositiveLinear(1, 1)
self.l2 = PositiveLinear(1, 1024)
self.l3 = PositiveLinear(1024, 1)
self.gamma_0 = torch.nn.Parameter(torch.tensor([-5.]))
self.gamma_1 = torch.nn.Parameter(torch.tensor([10.]))
self.show_schedule()
def show_schedule(self, num_steps=50):
t = torch.linspace(0, 1, num_steps).view(num_steps, 1)
gamma = self.forward(t)
print('Gamma schedule:')
print(gamma.detach().cpu().numpy().reshape(num_steps))
def gamma_tilde(self, t):
l1_t = self.l1(t)
return l1_t + self.l3(torch.sigmoid(self.l2(l1_t)))
def forward(self, t):
zeros, ones = torch.zeros_like(t), torch.ones_like(t)
# Not super efficient.
gamma_tilde_0 = self.gamma_tilde(zeros)
gamma_tilde_1 = self.gamma_tilde(ones)
gamma_tilde_t = self.gamma_tilde(t)
# Normalize to [0, 1]
normalized_gamma = (gamma_tilde_t - gamma_tilde_0) / (
gamma_tilde_1 - gamma_tilde_0)
# Rescale to [gamma_0, gamma_1]
gamma = self.gamma_0 + (self.gamma_1 - self.gamma_0) * normalized_gamma
return gamma
def cosine_beta_schedule(timesteps, s=0.008, raise_to_power: float = 1):
"""
cosine schedule
as proposed in https://openreview.net/forum?id=-NEXDKk8gZ
"""
steps = timesteps + 2
x = np.linspace(0, steps, steps)
alphas_cumprod = np.cos(((x / steps) + s) / (1 + s) * np.pi * 0.5) ** 2
alphas_cumprod = alphas_cumprod / alphas_cumprod[0]
betas = 1 - (alphas_cumprod[1:] / alphas_cumprod[:-1])
betas = np.clip(betas, a_min=0, a_max=0.999)
alphas = 1. - betas
alphas_cumprod = np.cumprod(alphas, axis=0)
if raise_to_power != 1:
alphas_cumprod = np.power(alphas_cumprod, raise_to_power)
return alphas_cumprod
def clip_noise_schedule(alphas2, clip_value=0.001):
"""
For a noise schedule given by alpha^2, this clips alpha_t / alpha_t-1.
This may help improve stability during
sampling.
"""
alphas2 = np.concatenate([np.ones(1), alphas2], axis=0)
alphas_step = (alphas2[1:] / alphas2[:-1])
alphas_step = np.clip(alphas_step, a_min=clip_value, a_max=1.)
alphas2 = np.cumprod(alphas_step, axis=0)
return alphas2
def polynomial_schedule(timesteps: int, s=1e-4, power=3.):
"""
A noise schedule based on a simple polynomial equation: 1 - x^power.
"""
steps = timesteps + 1
x = np.linspace(0, steps, steps)
alphas2 = (1 - np.power(x / steps, power))**2
alphas2 = clip_noise_schedule(alphas2, clip_value=0.001)
precision = 1 - 2 * s
alphas2 = precision * alphas2 + s
return alphas2
class PredefinedNoiseSchedule(torch.nn.Module):
"""
Predefined noise schedule. Essentially creates a lookup array for predefined
(non-learned) noise schedules.
"""
def __init__(self, noise_schedule, timesteps, precision):
super(PredefinedNoiseSchedule, self).__init__()
self.timesteps = timesteps
if noise_schedule == 'cosine':
alphas2 = cosine_beta_schedule(timesteps)
elif 'polynomial' in noise_schedule:
splits = noise_schedule.split('_')
assert len(splits) == 2
power = float(splits[1])
alphas2 = polynomial_schedule(timesteps, s=precision, power=power)
else:
raise ValueError(noise_schedule)
sigmas2 = 1 - alphas2
log_alphas2 = np.log(alphas2)
log_sigmas2 = np.log(sigmas2)
log_alphas2_to_sigmas2 = log_alphas2 - log_sigmas2
self.gamma = torch.nn.Parameter(
torch.from_numpy(-log_alphas2_to_sigmas2).float(),
requires_grad=False)
def forward(self, t):
t_int = torch.round(t * self.timesteps).long()
return self.gamma[t_int]
Datasets
Models
