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,
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"""All functions related to loss computation and optimization.
"""

import flax
import jax
import jax.numpy as jnp
import jax.random as random
from models import utils as mutils
from sde_lib import VESDE, VPSDE
from utils import batch_mul


def get_optimizer(config):
  """Returns a flax optimizer object based on `config`."""
  if config.optim.optimizer == 'Adam':
    optimizer = flax.optim.Adam(beta1=config.optim.beta1, eps=config.optim.eps,
                                weight_decay=config.optim.weight_decay)
  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(state,
                  grad,
                  warmup=config.optim.warmup,
                  grad_clip=config.optim.grad_clip):
    """Optimizes with warmup and gradient clipping (disabled if negative)."""
    lr = state.lr
    if warmup > 0:
      lr = lr * jnp.minimum(state.step / warmup, 1.0)
    if grad_clip >= 0:
      # Compute global gradient norm
      grad_norm = jnp.sqrt(
        sum([jnp.sum(jnp.square(x)) for x in jax.tree_leaves(grad)]))
      # Clip gradient
      clipped_grad = jax.tree_map(
        lambda x: x * grad_clip / jnp.maximum(grad_norm, grad_clip), grad)
    else:  # disabling gradient clipping if grad_clip < 0
      clipped_grad = grad
    return state.optimizer.apply_gradient(clipped_grad, learning_rate=lr)

  return optimize_fn


def get_sde_loss_fn(sde, model, train, reduce_mean=True, continuous=True, likelihood_weighting=True, eps=1e-5):
  """Create a loss function for training with arbirary SDEs.

  Args:
    sde: An `sde_lib.SDE` object that represents the forward SDE.
    model: A `flax.linen.Module` object that represents the architecture of the score-based model.
    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 = jnp.mean if reduce_mean else lambda *args, **kwargs: 0.5 * jnp.sum(*args, **kwargs)

  def loss_fn(rng, params, states, batch):
    """Compute the loss function.

    Args:
      rng: A JAX random state.
      params: A dictionary that contains trainable parameters of the score-based model.
      states: A dictionary that contains mutable states of the score-based model.
      batch: A mini-batch of training data.

    Returns:
      loss: A scalar that represents the average loss value across the mini-batch.
      new_model_state: A dictionary that contains the mutated states of the score-based model.
    """

    score_fn = mutils.get_score_fn(sde, model, params, states, train=train, continuous=continuous, return_state=True)
    data = batch['image']

    rng, step_rng = random.split(rng)
    t = random.uniform(step_rng, (data.shape[0],), minval=eps, maxval=sde.T)
    rng, step_rng = random.split(rng)
    z = random.normal(step_rng, data.shape)
    mean, std = sde.marginal_prob(data, t)
    perturbed_data = mean + batch_mul(std, z)
    rng, step_rng = random.split(rng)
    score, new_model_state = score_fn(perturbed_data, t, rng=step_rng)

    if not likelihood_weighting:
      losses = jnp.square(batch_mul(score, std) + z)
      losses = reduce_op(losses.reshape((losses.shape[0], -1)), axis=-1)
    else:
      g2 = sde.sde(jnp.zeros_like(data), t)[1] ** 2
      losses = jnp.square(score + batch_mul(z, 1. / std))
      losses = reduce_op(losses.reshape((losses.shape[0], -1)), axis=-1) * g2

    loss = jnp.mean(losses)
    return loss, new_model_state

  return loss_fn


def get_smld_loss_fn(vesde, model, train, reduce_mean=False):
  """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 = vesde.discrete_sigmas[::-1]
  reduce_op = jnp.mean if reduce_mean else lambda *args, **kwargs: 0.5 * jnp.sum(*args, **kwargs)

  def loss_fn(rng, params, states, batch):
    model_fn = mutils.get_model_fn(model, params, states, train=train)
    data = batch['image']
    rng, step_rng = random.split(rng)
    labels = random.choice(step_rng, vesde.N, shape=(data.shape[0],))
    sigmas = smld_sigma_array[labels]
    rng, step_rng = random.split(rng)
    noise = batch_mul(random.normal(step_rng, data.shape), sigmas)
    perturbed_data = noise + data
    rng, step_rng = random.split(rng)
    score, new_model_state = model_fn(perturbed_data, labels, rng=step_rng)
    target = -batch_mul(noise, 1. / (sigmas ** 2))
    losses = jnp.square(score - target)
    losses = reduce_op(losses.reshape((losses.shape[0], -1)), axis=-1) * sigmas ** 2
    loss = jnp.mean(losses)
    return loss, new_model_state

  return loss_fn


def get_ddpm_loss_fn(vpsde, model, train, reduce_mean=True):
  """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 = jnp.mean if reduce_mean else lambda *args, **kwargs: 0.5 * jnp.sum(*args, **kwargs)

  def loss_fn(rng, params, states, batch):
    model_fn = mutils.get_model_fn(model, params, states, train=train)
    data = batch['image']
    rng, step_rng = random.split(rng)
    labels = random.choice(step_rng, vpsde.N, shape=(data.shape[0],))
    sqrt_alphas_cumprod = vpsde.sqrt_alphas_cumprod
    sqrt_1m_alphas_cumprod = vpsde.sqrt_1m_alphas_cumprod
    rng, step_rng = random.split(rng)
    noise = random.normal(step_rng, data.shape)
    perturbed_data = batch_mul(sqrt_alphas_cumprod[labels], data) + \
                     batch_mul(sqrt_1m_alphas_cumprod[labels], noise)
    rng, step_rng = random.split(rng)
    score, new_model_state = model_fn(perturbed_data, labels, rng=step_rng)
    losses = jnp.square(score - noise)
    losses = reduce_op(losses.reshape((losses.shape[0], -1)), axis=-1)
    loss = jnp.mean(losses)
    return loss, new_model_state

  return loss_fn


def get_step_fn(sde, model, train, optimize_fn=None, reduce_mean=False, continuous=True, likelihood_weighting=False):
  """Create a one-step training/evaluation function.

  Args:
    sde: An `sde_lib.SDE` object that represents the forward SDE.
    model: A `flax.linen.Module` object that represents the architecture of the score-based model.
    train: `True` for training and `False` for evaluation.
    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 continuous:
    loss_fn = get_sde_loss_fn(sde, model, train, reduce_mean=reduce_mean,
                              continuous=True, likelihood_weighting=likelihood_weighting)
  else:
    assert not likelihood_weighting, "Likelihood weighting is not supported for original SMLD/DDPM training."
    if isinstance(sde, VESDE):
      loss_fn = get_smld_loss_fn(sde, model, train, reduce_mean=reduce_mean)
    elif isinstance(sde, VPSDE):
      loss_fn = get_ddpm_loss_fn(sde, model, train, reduce_mean=reduce_mean)
    else:
      raise ValueError(f"Discrete training for {sde.__class__.__name__} is not recommended.")

  def step_fn(carry_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:
      carry_state: A tuple (JAX random state, `flax.struct.dataclass` containing the training state).
      batch: A mini-batch of training/evaluation data.

    Returns:
      new_carry_state: The updated tuple of `carry_state`.
      loss: The average loss value of this state.
    """

    (rng, state) = carry_state
    rng, step_rng = jax.random.split(rng)
    grad_fn = jax.value_and_grad(loss_fn, argnums=1, has_aux=True)
    if train:
      params = state.optimizer.target
      states = state.model_state
      (loss, new_model_state), grad = grad_fn(step_rng, params, states, batch)
      grad = jax.lax.pmean(grad, axis_name='batch')
      new_optimizer = optimize_fn(state, grad)
      new_params_ema = jax.tree_multimap(
        lambda p_ema, p: p_ema * state.ema_rate + p * (1. - state.ema_rate),
        state.params_ema, new_optimizer.target
      )
      step = state.step + 1
      new_state = state.replace(
        step=step,
        optimizer=new_optimizer,
        model_state=new_model_state,
        params_ema=new_params_ema
      )
    else:
      loss, _ = loss_fn(step_rng, state.params_ema, state.model_state, batch)
      new_state = state

    loss = jax.lax.pmean(loss, axis_name='batch')
    new_carry_state = (rng, new_state)
    return new_carry_state, loss

  return step_fn