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 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, get_div_fn, get_value_div_fn
import functools
import numpy as np
from bound_likelihood import get_likelihood_offset_fn


def get_optimizer(config, beta2=0.999):
  """Returns a flax optimizer object based on `config`."""
  if config.optim.optimizer == 'Adam':
    optimizer = flax.optim.Adam(beta1=config.optim.beta1, beta2=beta2, 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, deq_score_joint=False):
  """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)

  def optimize_deq_score_fn(state,
                            grad,
                            warmup=config.optim.warmup,
                            grad_clip=config.optim.grad_clip):
    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.deq_optimizer.apply_gradient(clipped_grad['deq'], learning_rate=lr),
            state.score_optimizer.apply_gradient(clipped_grad['score'], learning_rate=lr))

  if deq_score_joint:
    return optimize_deq_score_fn
  else:
    return optimize_fn


def get_score_t(score_fn):
  def score_t(x, t, rng):
    tangent = jnp.ones_like(t)
    return jax.jvp(lambda time: score_fn(x, time, rng=rng), (t,), (tangent,))

  return score_t


def get_sde_loss_fn(sde, model, train, reduce_mean=True, continuous=True, likelihood_weighting=True,
                    importance_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.
    importance_weighting: If `True`, use importance weighting to reduce the variance of likelihood weighting.
    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)
    if likelihood_weighting and importance_weighting:
      t = sde.sample_importance_weighted_time_for_likelihood(step_rng, (data.shape[0],), eps=eps)
    else:
      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 likelihood_weighting:
      if importance_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

    else:
      losses = jnp.square(batch_mul(score, std) + z)
      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,
                importance_weighting=False, smallest_time=1e-5):
  """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,
                              importance_weighting=importance_weighting,
                              eps=smallest_time)
  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


def get_dequantization_loss_fn(sde, score_fn, deq_model, scaler, inverse_scaler,
                               train=True, importance_weighting=True, eps=1e-5,
                               eps_offset=True):
  def div_drift_fn(x, t, eps):
    div_fn = get_div_fn(lambda x, t: sde.sde(x, t)[0])
    return div_fn(x, t, eps)

  def loss_fn(rng, params, batch):
    dequantizer = mutils.get_dequantizer(deq_model, params, train=train)

    data = batch['image']
    shape = data.shape
    rng, step_rng = random.split(rng)
    u = random.normal(step_rng, shape)
    if train:
      rng, step_rng = random.split(rng)
      deq_noise, sldj = dequantizer(u, inverse_scaler(data), rng=step_rng)
    else:
      deq_noise, sldj = dequantizer(u, inverse_scaler(data))

    data = scaler((inverse_scaler(data) * 255. + deq_noise) / 256.)

    mean, std = sde.marginal_prob(data, jnp.ones((shape[0],)) * sde.T)
    rng, step_rng = jax.random.split(rng)
    z = jax.random.normal(step_rng, shape)
    neg_prior_logp = -sde.prior_logp(mean + batch_mul(std, z))

    rng, step_rng = random.split(rng)
    if importance_weighting:
      t = sde.sample_importance_weighted_time_for_likelihood(step_rng, (shape[0],), eps=eps)
      Z = sde.likelihood_importance_cum_weight(sde.T, eps=eps)
    else:
      t = random.uniform(step_rng, (shape[0],), minval=eps, maxval=sde.T)

    rng, step_rng = random.split(rng)
    z = random.normal(step_rng, shape)
    mean, std = sde.marginal_prob(data, t)
    perturbed_data = mean + batch_mul(std, z)

    score = score_fn(perturbed_data, t)
    if importance_weighting:
      losses = jnp.square(batch_mul(score, std) + z)
      losses = jnp.sum(losses.reshape((losses.shape[0], -1)), axis=-1)
      grad_norm = jnp.square(z).reshape((z.shape[0], -1)).sum(axis=-1)
      losses = (losses - grad_norm) * Z
    else:
      g2 = sde.sde(jnp.zeros_like(data), t)[1] ** 2
      losses = jnp.square(score + batch_mul(z, 1. / std))
      losses = jnp.sum(losses.reshape((losses.shape[0], -1)), axis=-1) * g2
      grad_norm = jnp.square(z).reshape((z.shape[0], -1)).sum(axis=-1)
      grad_norm = grad_norm * g2 / (std ** 2)
      losses = losses - grad_norm

    rng, step_rng = random.split(rng)
    z = random.normal(step_rng, shape)
    rng, step_rng = random.split(rng)
    t = random.uniform(step_rng, (shape[0],), minval=eps, maxval=sde.T)
    mean, std = sde.marginal_prob(data, t)
    noisy_data = mean + batch_mul(std, z)
    rng, step_rng = random.split(rng)
    epsilon = random.rademacher(step_rng, shape, dtype=jnp.float32)
    drift_div = div_drift_fn(noisy_data, t, epsilon)

    losses = neg_prior_logp + 0.5 * (losses - 2 * drift_div) - sldj
    if eps_offset:
      offset_fn = get_likelihood_offset_fn(sde, score_fn, eps)
      rng, step_rng = random.split(rng)
      losses = losses + offset_fn(step_rng, data)

    dim = np.prod(shape[1:])
    bpd = losses / np.log(2.)
    bpd = bpd / dim
    offset = jnp.log2(jax.grad(inverse_scaler)(0.)) + 8.
    bpd += offset
    bpd = bpd.mean()

    loss = jnp.mean(losses)

    return loss, bpd

  return loss_fn


def get_dequantizer_step_fn(sde, score_fn, deq_model, scaler, inverse_scaler,
                            train, optimize_fn=None, importance_weighting=False, smallest_time=1e-5,
                            eps_offset=True):
  loss_fn = get_dequantization_loss_fn(sde, score_fn, deq_model, scaler, inverse_scaler, train,
                                       importance_weighting=importance_weighting, eps=smallest_time,
                                       eps_offset=eps_offset)

  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
      (loss, bpd), grad = grad_fn(step_rng, params, 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,
        params_ema=new_params_ema
      )
    else:
      loss, bpd = loss_fn(step_rng, state.params_ema, batch)
      new_state = state

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

  return step_fn