losses.py

# coding=utf-8
# Copyright 2020 The Google Research Authors.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
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"""All functions related to loss computation and optimization.
"""

import torch
import torch.optim as optim
import numpy as np
import pickle
from models import utils as mutils
from sde_lib import VESDE, VPSDE
from flow_models.flow_model import flow_forward
from flow_models.resflow.utils import update_lipschitz
import likelihood


def get_optimizer(config, params, lr=None, beta1=None, eps=None, weight_decay=None):
  """Returns a flax optimizer object based on `config`."""
  if lr is None: lr = config.optim.lr
  if beta1 is None: beta1 = config.optim.beta1
  if eps is None: eps = config.optim.eps
  if weight_decay is None: weight_decay = config.optim.weight_decay

  if config.optim.optimizer == 'Adam':
    optimizer = optim.Adam(params, lr=lr, betas=(beta1, 0.999), eps=eps, weight_decay=weight_decay, amsgrad=config.optim.amsgrad)
  elif config.optim.optimizer == 'AdamW':
    optimizer = optim.AdamW(params, lr=lr, betas=(beta1, 0.99), eps=eps, weight_decay=weight_decay, amsgrad=config.optim.amsgrad)
  else:
    raise NotImplementedError(
      f'Optimizer {config.optim.optimizer} not supported yet!')

  return optimizer


def optimization_manager(config):
  """Returns an optimize_fn based on `config`."""

  def optimize_fn(optimizer, params, step, lr=config.optim.lr,
                  warmup=config.optim.warmup,
                  grad_clip=config.optim.grad_clip):
    """Optimizes with warmup and gradient clipping (disabled if negative)."""
    if warmup > 0:
      for g in optimizer.param_groups:
        g['lr'] = lr * np.minimum(step / warmup, 1.0)
    if grad_clip >= 0:
      torch.nn.utils.clip_grad_norm_(params, max_norm=grad_clip)
    optimizer.step()

  return optimize_fn


def get_sde_loss_fn(config, sde, train, variance='scoreflow'):
  """Create a loss function for training with arbirary SDEs.

  Args:
    sde: An `sde_lib.SDE` object that represents the forward SDE.
    train: `True` for training loss and `False` for evaluation loss.
    reduce_mean: If `True`, average the loss across data dimensions. Otherwise sum the loss across data dimensions.
    continuous: `True` indicates that the model is defined to take continuous time steps. Otherwise it requires
      ad-hoc interpolation to take continuous time steps.
    likelihood_weighting: If `True`, weight the mixture of score matching losses
      according to https://arxiv.org/abs/2101.09258; otherwise use the weighting recommended in our paper.
    eps: A `float` number. The smallest time step to sample from.

  Returns:
    A loss function.
  """
  reduce_op = torch.mean if config.training.reduce_mean else torch.sum

  def loss_fn(model, batch, st=False, recon_loss=None, importance_sampling=None):
    """Compute the loss function.

    Args:
      model: A score model.
      batch: A mini-batch of training data.

    Returns:
      loss: A scalar that represents the average loss value across the mini-batch.
    """
    if recon_loss is None:
      recon_loss = config.training.reconstruction_loss
    if importance_sampling is None:
      importance_sampling = config.training.importance_sampling
    # if st:
    #   assert not recon_loss
    t_min = sde.get_t_min(config, st)
    t, Z = sde.get_diffusion_time(config, batch.shape[0], batch.device, t_min, importance_sampling=importance_sampling)

    score_fn = mutils.get_score_fn(config, sde, model, None, train=train, continuous=config.training.continuous)
    z = torch.randn_like(batch)
    mean, std = sde.marginal_prob(batch, t)
    perturbed_data = mean + std[:, None, None, None] * z
    score = score_fn(perturbed_data, t)

    if importance_sampling:
      losses = torch.square(score * std[:, None, None, None] + z)
      losses = 0.5 * Z * reduce_op(losses.reshape(losses.shape[0], -1), dim=-1)
    else:
      if config.training.likelihood_weighting:
        g2 = sde.sde(torch.zeros_like(batch), t)[1] ** 2
        losses = torch.square(score + z / std[:, None, None, None])
        losses = 0.5 * Z * reduce_op(losses.reshape(losses.shape[0], -1), dim=-1) * g2
      else:
        losses = torch.square(score * std[:, None, None, None] + z)
        losses = 0.5 * Z * reduce_op(losses.reshape(losses.shape[0], -1), dim=-1)

    if recon_loss:
      eps_vec = torch.ones((batch.shape[0]), device=batch.device) * t_min
      mean, std = sde.marginal_prob(batch, eps_vec)
      z = torch.randn_like(batch)
      perturbed_data = mean + std[:, None, None, None] * z
      score = score_fn(perturbed_data, eps_vec)

      alpha, beta = sde.marginal_prob(torch.ones_like(batch), eps_vec)
      q_mean = perturbed_data / alpha + beta[:, None, None, None] ** 2 * score / alpha
      if variance == 'ddpm':
        q_std = beta
      elif variance == 'scoreflow':
        q_std = beta / torch.mean(alpha, axis=(1, 2, 3))

      n_dim = np.prod(batch.shape[1:])
      p_entropy = n_dim / 2. * (np.log(2 * np.pi) + 2 * torch.log(std) + 1.)
      q_recon = n_dim / 2. * (np.log(2 * np.pi) + 2 * torch.log(q_std)) + 0.5 / (q_std ** 2) * torch.square(batch - q_mean).sum(axis=(1, 2, 3))
      reconstruction_loss = q_recon - p_entropy
      if config.training.reduce_mean:
        reconstruction_loss = reconstruction_loss / n_dim
      losses = losses + reconstruction_loss

    return losses

  return loss_fn


def get_smld_loss_fn(config, vesde, train):
  """Legacy code to reproduce previous results on SMLD(NCSN). Not recommended for new work."""
  assert isinstance(vesde, VESDE), "SMLD training only works for VESDEs."

  # Previous SMLD models assume descending sigmas
  smld_sigma_array = torch.flip(vesde.discrete_sigmas, dims=(0,))
  reduce_op = torch.mean if config.training.reduce_mean else torch.sum

  def loss_fn(model, batch):
    model_fn = mutils.get_model_fn(model, train=train)
    labels = torch.randint(0, vesde.N, (batch.shape[0],), device=batch.device)
    sigmas = smld_sigma_array.to(batch.device)[labels]
    noise = torch.randn_like(batch) * sigmas[:, None, None, None]
    perturbed_data = noise + batch
    score = model_fn(perturbed_data, labels)
    target = -noise / (sigmas ** 2)[:, None, None, None]
    losses = torch.square(score - target)
    losses = reduce_op(losses.reshape(losses.shape[0], -1), dim=-1) * sigmas ** 2
    loss = torch.mean(losses)
    return loss

  return loss_fn


def get_ddpm_loss_fn(config, vpsde, train):
  """Legacy code to reproduce previous results on DDPM. Not recommended for new work."""
  assert isinstance(vpsde, VPSDE), "DDPM training only works for VPSDEs."

  reduce_op = torch.mean if config.training.reduce_mean else torch.sum

  def loss_fn(model, batch):
    model_fn = mutils.get_model_fn(model, train=train)
    labels = torch.randint(0, vpsde.N, (batch.shape[0],), device=batch.device)
    sqrt_alphas_cumprod = vpsde.sqrt_alphas_cumprod.to(batch.device)
    sqrt_1m_alphas_cumprod = vpsde.sqrt_1m_alphas_cumprod.to(batch.device)
    noise = torch.randn_like(batch)
    perturbed_data = sqrt_alphas_cumprod[labels, None, None, None] * batch + \
                     sqrt_1m_alphas_cumprod[labels, None, None, None] * noise
    score = model_fn(perturbed_data, labels)
    losses = torch.square(score - noise)
    losses = reduce_op(losses.reshape(losses.shape[0], -1), dim=-1)
    loss = torch.mean(losses)
    return loss

  return loss_fn


def get_step_fn(config, sde, train, optimize_fn=None, scaler=None):
  """Create a one-step training/evaluation function.

  Args:
    sde: An `sde_lib.SDE` object that represents the forward SDE.
    optimize_fn: An optimization function.
    reduce_mean: If `True`, average the loss across data dimensions. Otherwise sum the loss across data dimensions.
    continuous: `True` indicates that the model is defined to take continuous time steps.
    likelihood_weighting: If `True`, weight the mixture of score matching losses according to
      https://arxiv.org/abs/2101.09258; otherwise use the weighting recommended by our paper.

  Returns:
    A one-step function for training or evaluation.
  """
  if config.training.continuous:
    loss_fn = get_sde_loss_fn(config, sde, train)
  else:
    assert not config.training.likelihood_weighting, "Likelihood weighting is not supported for original SMLD/DDPM training."
    if isinstance(sde, VESDE):
      loss_fn = get_smld_loss_fn(config, sde, train)
    elif isinstance(sde, VPSDE):
      loss_fn = get_ddpm_loss_fn(config, sde, train)
    else:
      raise ValueError(f"Discrete training for {sde.__class__.__name__} is not recommended.")

  def calculate_logp(batch):
    Ts = torch.ones(batch.shape[0], device=config.device) * sde.T
    meanT, stdT = sde.marginal_prob(batch, Ts)
    z = torch.randn_like(batch)
    yT = meanT + stdT[:, None, None, None] * z
    log_p = sde.prior_logp(yT)
    return log_p

  def step_fn(state, flow_state, batch):
    """Running one step of training or evaluation.

    This function will undergo `jax.lax.scan` so that multiple steps can be pmapped and jit-compiled together
    for faster execution.

    Args:
      state: A dictionary of training information, containing the score model, optimizer,
       EMA status, and number of optimization steps.
      batch: A mini-batch of training/evaluation data.

    Returns:
      losses: The list of loss values of this state and batch.
    """
    model = state['model']
    optimizer = state['optimizer']

    optimizer.zero_grad()
    batch_size = batch.shape[0]
    num_micro_batch = config.optim.num_micro_batch
    losses_ = torch.zeros(batch_size)
    for k in range(num_micro_batch):
      losses = loss_fn(model, batch[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)])
      torch.mean(losses).backward(retain_graph=True)
      losses_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses.cpu().detach()
    optimize_fn(optimizer, model.parameters(), step=state['step'])
    state['step'] += 1
    state['ema'].update(model.parameters())

    return losses_, None, None, None, None

  def flow_step_fn_nll(state, flow_state, batch):
    """Running one step of training or evaluation.

    This function will undergo `jax.lax.scan` so that multiple steps can be pmapped and jit-compiled together
    for faster execution.

    Args:
      state: A dictionary of training information, containing the score model, optimizer,
       EMA status, and number of optimization steps.
      flow_state: A dictionary of training information, containing the flow model, optimizer,
       EMA status, and number of optimization steps.
      batch: A mini-batch of training/evaluation data.

    Returns:
      losses: The list of loss values of this state and batch.
    """
    model = state['model']
    flow_model = flow_state['model']
    optimizer = state['optimizer']
    flow_optimizer = flow_state['optimizer']

    batch_size = batch.shape[0]
    num_micro_batch = config.optim.num_micro_batch
    losses_ = torch.zeros(batch_size)
    losses_score_ = torch.zeros(batch_size)
    losses_flow_ = torch.zeros(batch_size)
    losses_logp_ = torch.zeros(batch_size)

    optimizer.zero_grad()
    flow_optimizer.zero_grad()

    if train:
      for k in range(num_micro_batch):
        mini_batch = batch[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)]
        transformed_mini_batch, losses_flow = flow_forward(config, flow_model, mini_batch, reverse=False)

        losses_score = loss_fn(model, transformed_mini_batch, st=config.training.st)
        losses_logp = calculate_logp(transformed_mini_batch)
        if config.training.reduce_mean:
          losses_flow = - losses_flow / np.prod(batch.shape[1:])
          losses_logp = - losses_logp / np.prod(batch.shape[1:])
        else:
          losses_flow = - losses_flow
          losses_logp = - losses_logp
        assert losses_score.shape == losses_flow.shape == losses_logp.shape == torch.Size([transformed_mini_batch.shape[0]])
        losses = losses_score + losses_flow + losses_logp
        torch.mean(losses).backward(retain_graph=True)
        # save losses
        losses_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses.cpu().detach()
        losses_score_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_score.cpu().detach()
        losses_flow_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_flow.cpu().detach()
        losses_logp_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_logp.cpu().detach()

      optimize_fn(optimizer, model.parameters(), step=state['step'])
      optimize_fn(flow_optimizer, flow_model.parameters(), step=flow_state['step'])

    update_lipschitz(flow_model)
    state['step'] += 1
    state['ema'].update(model.parameters())
    flow_state['step'] += 1
    flow_state['ema'].update(flow_model.parameters())

    return losses_, losses_score_, losses_flow_, losses_logp_

  def flow_step_fn_fid(state, flow_state, batch):
    """Running one step of training or evaluation.

    This function will undergo `jax.lax.scan` so that multiple steps can be pmapped and jit-compiled together
    for faster execution.

    Args:
      state: A dictionary of training information, containing the score model, optimizer,
       EMA status, and number of optimization steps.
      flow_state: A dictionary of training information, containing the flow model, optimizer,
       EMA status, and number of optimization steps.
      batch: A mini-batch of training/evaluation data.

    Returns:
      losses: The list of loss values of this state and batch.
    """
    model = state['model']
    flow_model = flow_state['model']
    optimizer = state['optimizer']
    flow_optimizer = flow_state['optimizer']

    batch_size = batch.shape[0]
    num_micro_batch = config.optim.num_micro_batch
    losses_ = torch.zeros(batch_size)
    losses_score_ = torch.zeros(batch_size)
    losses_flow_ = torch.zeros(batch_size)
    losses_logp_ = torch.zeros(batch_size)

    optimizer.zero_grad()
    flow_optimizer.zero_grad()

    if train:
      # flow training (all losses)
      for k in range(num_micro_batch):
        mini_batch = batch[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)]
        transformed_mini_batch, losses_flow = flow_forward(config, flow_model, mini_batch, reverse=False)

        losses_score = loss_fn(model, transformed_mini_batch, importance_sampling=True)
        losses_logp = calculate_logp(transformed_mini_batch)
        if config.training.reduce_mean:
          losses_flow = - losses_flow / np.prod(batch.shape[1:])
          losses_logp = - losses_logp / np.prod(batch.shape[1:])
        else:
          losses_flow = - losses_flow
          losses_logp = - losses_logp
        assert losses_score.shape == losses_flow.shape == losses_logp.shape == torch.Size([transformed_mini_batch.shape[0]])
        losses = losses_score + losses_flow + losses_logp
        torch.mean(losses).backward(retain_graph=True)
        # save losses
        losses_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses.cpu().detach()
        losses_flow_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_flow.cpu().detach()
        losses_logp_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_logp.cpu().detach()
      optimize_fn(flow_optimizer, flow_model.parameters(), step=flow_state['step'])
      update_lipschitz(flow_model)
      flow_state['ema'].update(flow_model.parameters())

      # diffusion training with st
      if not config.training.st:
        optimizer.zero_grad()
      for k in range(num_micro_batch):
        mini_batch = batch[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)]
        if not config.training.st:
          with torch.no_grad():
            transformed_mini_batch, _ = flow_forward(config, flow_model, mini_batch, log_det=None, reverse=False)
        transformed_mini_batch = transformed_mini_batch.detach()
        losses_add_score = loss_fn(model, transformed_mini_batch, st=config.training.st, recon_loss=False)

        if config.training.st:
          const_adj = (losses_add_score.mean() / losses_score.mean()).detach()
          for p in model.parameters():
            if p.grad is None:
              continue
            else:
              p.grad = const_adj * p.grad

        torch.mean(losses_add_score).backward(retain_graph=True)
        # save losses
        losses_score_[batch_size // num_micro_batch * k: batch_size // num_micro_batch * (k + 1)] = losses_add_score.cpu().detach()
      optimize_fn(optimizer, model.parameters(), step=state['step'])
      state['ema'].update(model.parameters())

      state['step'] += 1
      flow_state['step'] += 1

    return losses_, losses_score_, losses_flow_, losses_logp_

  if config.flow.model == 'identity':
    print('Train only the score network.')
    return step_fn
  elif config.flow.model != 'identity':
    print('Train flow network with NLL.')
    if not config.training.likelihood_weighting:
      print('Train score network with FID-favorable setting (weighting function = variance weighting).')
      return flow_step_fn_fid
    else:
      print('Train score network with NLL-favorable setting (weighting function = likelihood weighting).')
      return flow_step_fn_nll
  else:
    raise NotImplementedError


def get_div_fn(fn):
  """Create the divergence function of `fn` using the Hutchinson-Skilling trace estimator."""

  def div_fn(x, t, eps):
    with torch.enable_grad():
      #x.requires_grad_(True)
      fn_eps = torch.sum(fn(x, t) * eps)
      grad_fn_eps = torch.autograd.grad(fn_eps, x)[0]
    #x.requires_grad_(False)
    return torch.sum(grad_fn_eps * eps, dim=tuple(range(1, len(x.shape))))

  return div_fn