guided_diffusion/gaussian_diffusion.py

"""
This code started out as a PyTorch port of Ho et al's diffusion models:
https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py

Docstrings have been added, as well as DDIM sampling and a new collection of beta schedules.
"""

from pdb import set_trace as st
import enum
import math

import numpy as np
import torch as th

from .nn import mean_flat
from .losses import normal_kl, discretized_gaussian_log_likelihood
from . import dist_util


def get_named_beta_schedule(schedule_name, num_diffusion_timesteps):
    """
    Get a pre-defined beta schedule for the given name.

    The beta schedule library consists of beta schedules which remain similar
    in the limit of num_diffusion_timesteps.
    Beta schedules may be added, but should not be removed or changed once
    they are committed to maintain backwards compatibility.
    """
    if schedule_name == "linear":  # * used here
        # Linear schedule from Ho et al, extended to work for any number of
        # diffusion steps.
        scale = 1000 / num_diffusion_timesteps
        beta_start = scale * 0.0001
        beta_end = scale * 0.02
        return np.linspace(beta_start,
                           beta_end,
                           num_diffusion_timesteps,
                           dtype=np.float64)

    elif schedule_name == "linear_simple":
        return betas_for_alpha_bar_linear_simple(num_diffusion_timesteps,
                                                 lambda t: 0.001 / (1.001 - t))

    elif schedule_name == "cosine":
        return betas_for_alpha_bar(
            num_diffusion_timesteps,
            lambda t: math.cos((t + 0.008) / 1.008 * math.pi / 2)**2,
        )

    else:
        raise NotImplementedError(f"unknown beta schedule: {schedule_name}")


def betas_for_alpha_bar_linear_simple(num_diffusion_timesteps,
                                      alpha_bar,
                                      max_beta=0.999):
    """proposed by Chen Ting, on the importance of noise schedule, arXiv 2023. 
    gamma = 1-t
    """
    betas = []
    for i in range(num_diffusion_timesteps):
        t = i / num_diffusion_timesteps
        betas.append(min(max_beta, alpha_bar(t)))

    return betas


def betas_for_alpha_bar(num_diffusion_timesteps, alpha_bar, max_beta=0.999):
    """
    Create a beta schedule that discretizes the given alpha_t_bar function,
    which defines the cumulative product of (1-beta) over time from t = [0,1].

    :param num_diffusion_timesteps: the number of betas to produce.
    :param alpha_bar: a lambda that takes an argument t from 0 to 1 and
                      produces the cumulative product of (1-beta) up to that
                      part of the diffusion process.
    :param max_beta: the maximum beta to use; use values lower than 1 to
                     prevent singularities.
    """
    betas = []
    for i in range(num_diffusion_timesteps):
        t1 = i / num_diffusion_timesteps
        t2 = (i + 1) / num_diffusion_timesteps
        betas.append(min(1 - alpha_bar(t2) / alpha_bar(t1), max_beta))
    return np.array(betas)


class ModelMeanType(enum.Enum):
    """
    Which type of output the model predicts.
    """

    PREVIOUS_X = enum.auto()  # the model predicts x_{t-1}
    START_X = enum.auto()  # the model predicts x_0
    EPSILON = enum.auto()  # the model predicts epsilon
    V = enum.auto()  # the model predicts velosity


class ModelVarType(enum.Enum):
    """
    What is used as the model's output variance.

    The LEARNED_RANGE option has been added to allow the model to predict
    values between FIXED_SMALL and FIXED_LARGE, making its job easier.
    """

    LEARNED = enum.auto()
    FIXED_SMALL = enum.auto()
    FIXED_LARGE = enum.auto()
    LEARNED_RANGE = enum.auto()


class LossType(enum.Enum):
    MSE = enum.auto()  # use raw MSE loss (and KL when learning variances)
    RESCALED_MSE = (
        enum.auto()
    )  # use raw MSE loss (with RESCALED_KL when learning variances)
    KL = enum.auto()  # use the variational lower-bound
    RESCALED_KL = enum.auto()  # like KL, but rescale to estimate the full VLB

    def is_vb(self):
        return self == LossType.KL or self == LossType.RESCALED_KL


class GaussianDiffusion:
    """
    Utilities for training and sampling diffusion models.

    Ported directly from here, and then adapted over time to further experimentation.
    https://github.com/hojonathanho/diffusion/blob/1e0dceb3b3495bbe19116a5e1b3596cd0706c543/diffusion_tf/diffusion_utils_2.py#L42

    :param betas: a 1-D numpy array of betas for each diffusion timestep,
                  starting at T and going to 1.
    :param model_mean_type: a ModelMeanType determining what the model outputs.
    :param model_var_type: a ModelVarType determining how variance is output.
    :param loss_type: a LossType determining the loss function to use.
    :param rescale_timesteps: if True, pass floating point timesteps into the
                              model so that they are always scaled like in the
                              original paper (0 to 1000).
    """
    '''
    defaults: 
        learn_sigma=False,
        diffusion_steps=1000,
        noise_schedule="linear",
        timestep_respacing="",
        use_kl=False,
        predict_xstart=False,
        rescale_timesteps=False,
        rescale_learned_sigmas=False, 
    '''

    def __init__(
        self,
        *,
        betas,
        model_mean_type,
        model_var_type,
        loss_type,
        rescale_timesteps=False,
        standarization_xt=False,
    ):
        self.model_mean_type = model_mean_type
        self.model_var_type = model_var_type
        self.loss_type = loss_type
        self.rescale_timesteps = rescale_timesteps
        self.standarization_xt = standarization_xt

        # Use float64 for accuracy.
        betas = np.array(betas, dtype=np.float64)
        self.betas = betas
        assert len(betas.shape) == 1, "betas must be 1-D"
        assert (betas > 0).all() and (betas <= 1).all()

        self.num_timesteps = int(betas.shape[0])

        alphas = 1.0 - betas
        self.alphas_cumprod = np.cumprod(alphas, axis=0)
        self.alphas_cumprod_prev = np.append(1.0, self.alphas_cumprod[:-1])
        self.alphas_cumprod_next = np.append(self.alphas_cumprod[1:], 0.0)
        assert self.alphas_cumprod_prev.shape == (self.num_timesteps, )

        # calculations for diffusion q(x_t | x_{t-1}) and others
        self.sqrt_alphas_cumprod = np.sqrt(self.alphas_cumprod)
        self.sqrt_one_minus_alphas_cumprod = np.sqrt(1.0 - self.alphas_cumprod)
        self.log_one_minus_alphas_cumprod = np.log(1.0 - self.alphas_cumprod)
        self.sqrt_recip_alphas_cumprod = np.sqrt(1.0 / self.alphas_cumprod)
        self.sqrt_recipm1_alphas_cumprod = np.sqrt(
            1.0 / self.alphas_cumprod -
            1)  # sqrt(1/cumprod(alphas) - 1), for calculating x_0 from x_t

        # calculations for posterior q(x_{t-1} | x_t, x_0)
        self.posterior_variance = (betas * (1.0 - self.alphas_cumprod_prev) /
                                   (1.0 - self.alphas_cumprod))
        # log calculation clipped because the posterior variance is 0 at the
        # beginning of the diffusion chain.
        self.posterior_log_variance_clipped = np.log(
            np.append(self.posterior_variance[1], self.posterior_variance[1:]))
        self.posterior_mean_coef1 = (betas *
                                     np.sqrt(self.alphas_cumprod_prev) /
                                     (1.0 - self.alphas_cumprod))
        self.posterior_mean_coef2 = ((1.0 - self.alphas_cumprod_prev) *
                                     np.sqrt(alphas) /
                                     (1.0 - self.alphas_cumprod))

    def q_mean_variance(self, x_start, t):
        """
        Get the distribution q(x_t | x_0).

        :param x_start: the [N x C x ...] tensor of noiseless inputs.
        :param t: the number of diffusion steps (minus 1). Here, 0 means one step.
        :return: A tuple (mean, variance, log_variance), all of x_start's shape.
        """
        mean = (
            _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) *
            x_start)
        variance = _extract_into_tensor(1.0 - self.alphas_cumprod, t,
                                        x_start.shape)
        log_variance = _extract_into_tensor(self.log_one_minus_alphas_cumprod,
                                            t, x_start.shape)
        return mean, variance, log_variance

    def q_sample(self, x_start, t, noise=None, return_detail=False):
        """
        Diffuse the data for a given number of diffusion steps.

        In other words, sample from q(x_t | x_0).

        :param x_start: the initial data batch.
        :param t: the number of diffusion steps (minus 1). Here, 0 means one step.
        :param noise: if specified, the split-out normal noise.
        :return: A noisy version of x_start.
        """
        if noise is None:
            noise = th.randn_like(x_start)
        assert noise.shape == x_start.shape
        alpha_bar = _extract_into_tensor(self.sqrt_alphas_cumprod, t,
                                         x_start.shape)
        one_minus_alpha_bar = _extract_into_tensor(
            self.sqrt_one_minus_alphas_cumprod, t, x_start.shape)
        xt = (alpha_bar * x_start + one_minus_alpha_bar * noise)

        if self.standarization_xt:
            xt = xt / (1e-5 + xt.std(dim=list(range(1, xt.ndim)), keepdim=True)
                       )  # B 1 1 1 #

        if return_detail:
            return xt, alpha_bar, one_minus_alpha_bar

        return xt

    def q_posterior_mean_variance(self, x_start, x_t, t):
        """
        Compute the mean and variance of the diffusion posterior:

            q(x_{t-1} | x_t, x_0)

        """
        assert x_start.shape == x_t.shape
        posterior_mean = (
            _extract_into_tensor(self.posterior_mean_coef1, t, x_t.shape) *
            x_start +
            _extract_into_tensor(self.posterior_mean_coef2, t, x_t.shape) *
            x_t)
        posterior_variance = _extract_into_tensor(self.posterior_variance, t,
                                                  x_t.shape)
        posterior_log_variance_clipped = _extract_into_tensor(
            self.posterior_log_variance_clipped, t, x_t.shape)
        assert (posterior_mean.shape[0] == posterior_variance.shape[0] ==
                posterior_log_variance_clipped.shape[0] == x_start.shape[0])
        return posterior_mean, posterior_variance, posterior_log_variance_clipped

    def p_mean_variance(self,
                        model,
                        x,
                        t,
                        c=None,
                        clip_denoised=True,
                        denoised_fn=None,
                        model_kwargs=None,
                        mixing_normal=False,
                        direct_return_model_output=False):
        """
        Apply the model to get p(x_{t-1} | x_t), as well as a prediction of
        the initial x, x_0.

        :param model: the model, which takes a signal and a batch of timesteps
                      as input.
        :param x: the [N x C x ...] tensor at time t.
        :param t: a 1-D Tensor of timesteps.
        :param clip_denoised: if True, clip the denoised signal into [-1, 1].
        :param denoised_fn: if not None, a function which applies to the
            x_start prediction before it is used to sample. Applies before
            clip_denoised.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.
        :return: a dict with the following keys:
                 - 'mean': the model mean output.
                 - 'variance': the model variance output.
                 - 'log_variance': the log of 'variance'.
                 - 'pred_xstart': the prediction for x_0.
        """
        # lazy import to avoid partially initialized import
        from guided_diffusion.continuous_diffusion_utils import get_mixed_prediction

        if model_kwargs is None:
            model_kwargs = {}

        # if mixing_normal is not None:
        # t = t / self.num_timesteps  # [0,1] for SDE diffusion

        B, C = x.shape[:2]
        assert t.shape == (B, )
        model_output = model(x,
                             self._scale_timesteps(t),
                             c=c,
                             mixing_normal=mixing_normal,
                             **model_kwargs)

        if direct_return_model_output:
            return model_output

        if self.model_mean_type == ModelMeanType.V:
            v_transformed_to_eps_flag = False

        # st()
        if mixing_normal:  # directly change the model predicted eps logits
            if self.model_mean_type == ModelMeanType.START_X:
                mixing_component = self.get_mixing_component_x0(x,
                                                                t,
                                                                enabled=True)
            else:
                assert self.model_mean_type in [
                    ModelMeanType.EPSILON, ModelMeanType.V
                ]
                mixing_component = self.get_mixing_component(x,
                                                             t,
                                                             enabled=True)

                if self.model_mean_type == ModelMeanType.V:
                    model_output = self._predict_eps_from_z_and_v(
                        x, t, model_output)
                    v_transformed_to_eps_flag = True
            # ! transform result to v first?
            # model_output =
            model_output = get_mixed_prediction(True, model_output,
                                                model.mixing_logit,
                                                mixing_component)

        if self.model_var_type in [
                ModelVarType.LEARNED, ModelVarType.LEARNED_RANGE
        ]:
            assert model_output.shape == (B, C * 2, *x.shape[2:])
            model_output, model_var_values = th.split(model_output, C, dim=1)
            if self.model_var_type == ModelVarType.LEARNED:
                model_log_variance = model_var_values
                model_variance = th.exp(model_log_variance)
            else:
                min_log = _extract_into_tensor(
                    self.posterior_log_variance_clipped, t, x.shape)
                max_log = _extract_into_tensor(np.log(self.betas), t, x.shape)
                # The model_var_values is [-1, 1] for [min_var, max_var].
                frac = (model_var_values + 1) / 2
                model_log_variance = frac * max_log + (1 - frac) * min_log
                model_variance = th.exp(model_log_variance)
        else:
            model_variance, model_log_variance = {
                # for fixedlarge, we set the initial (log-)variance like so
                # to get a better decoder log likelihood.
                # ?
                ModelVarType.FIXED_LARGE: (  # * used here
                    np.append(self.posterior_variance[1], self.betas[1:]),
                    np.log(
                        np.append(self.posterior_variance[1], self.betas[1:])),
                ),
                ModelVarType.FIXED_SMALL: (
                    self.posterior_variance,
                    self.posterior_log_variance_clipped,
                ),
            }[self.model_var_type]
            model_variance = _extract_into_tensor(model_variance, t, x.shape)
            model_log_variance = _extract_into_tensor(model_log_variance, t,
                                                      x.shape)

        def process_xstart(x):
            if denoised_fn is not None:
                x = denoised_fn(x)
            if clip_denoised:
                return x.clamp(-1, 1)
            return x

        if self.model_mean_type == ModelMeanType.PREVIOUS_X:
            pred_xstart = process_xstart(
                self._predict_xstart_from_xprev(x_t=x, t=t,
                                                xprev=model_output))
            model_mean = model_output
        elif self.model_mean_type in [
                ModelMeanType.START_X, ModelMeanType.EPSILON, ModelMeanType.V
        ]:
            if self.model_mean_type == ModelMeanType.START_X:
                pred_xstart = process_xstart(model_output)
            else:  # * used here
                if self.model_mean_type == ModelMeanType.V:
                    assert v_transformed_to_eps_flag  # type: ignore
                pred_xstart = process_xstart(  # * return the x_0 using self._predict_xstart_from_eps as the denoised_fn
                    self._predict_xstart_from_eps(x_t=x, t=t,
                                                  eps=model_output))
            model_mean, _, _ = self.q_posterior_mean_variance(
                x_start=pred_xstart, x_t=x, t=t)
        else:
            raise NotImplementedError(self.model_mean_type)

        assert (model_mean.shape == model_log_variance.shape ==
                pred_xstart.shape == x.shape)
        return {
            "mean": model_mean,
            "variance": model_variance,
            "log_variance": model_log_variance,
            "pred_xstart": pred_xstart,
        }

    def _predict_xstart_from_eps(self, x_t, t, eps):
        assert x_t.shape == eps.shape
        return (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t,
                                     x_t.shape) * x_t -
                _extract_into_tensor(self.sqrt_recipm1_alphas_cumprod, t,
                                     x_t.shape) * eps)

    def _predict_xstart_from_xprev(self, x_t, t, xprev):
        assert x_t.shape == xprev.shape
        return (  # (xprev - coef2*x_t) / coef1
            _extract_into_tensor(1.0 / self.posterior_mean_coef1, t, x_t.shape)
            * xprev - _extract_into_tensor(
                self.posterior_mean_coef2 / self.posterior_mean_coef1, t,
                x_t.shape) * x_t)

    def _predict_eps_from_xstart(self, x_t, t, pred_xstart):
        return (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t,
                                     x_t.shape) * x_t -
                pred_xstart) / _extract_into_tensor(
                    self.sqrt_recipm1_alphas_cumprod, t, x_t.shape)

    # https://github.com/Stability-AI/stablediffusion/blob/cf1d67a6fd5ea1aa600c4df58e5b47da45f6bdbf/ldm/models/diffusion/ddpm.py#L288
    def _predict_start_from_z_and_v(self, x_t, t, v):
        # self.register_buffer('sqrt_alphas_cumprod', to_torch(np.sqrt(alphas_cumprod)))
        # self.register_buffer('sqrt_one_minus_alphas_cumprod', to_torch(np.sqrt(1. - alphas_cumprod)))
        return (_extract_into_tensor(self.sqrt_alphas_cumprod, t, x_t.shape) *
                x_t - _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod,
                                           t, x_t.shape) * v)

    def _predict_eps_from_z_and_v(self, x_t, t, v):
        return (
            _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_t.shape) * v +
            _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t,
                                 x_t.shape) * x_t)

    def _scale_timesteps(self, t):
        if self.rescale_timesteps:
            return t.float() * (1000.0 / self.num_timesteps)
        return t

    def condition_mean(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
        """
        Compute the mean for the previous step, given a function cond_fn that
        computes the gradient of a conditional log probability with respect to
        x. In particular, cond_fn computes grad(log(p(y|x))), and we want to
        condition on y.

        This uses the conditioning strategy from Sohl-Dickstein et al. (2015).
        """
        gradient = cond_fn(x, self._scale_timesteps(t), **model_kwargs)
        new_mean = (p_mean_var["mean"].float() +
                    p_mean_var["variance"] * gradient.float())
        return new_mean

    def condition_score(self, cond_fn, p_mean_var, x, t, model_kwargs=None):
        """
        Compute what the p_mean_variance output would have been, should the
        model's score function be conditioned by cond_fn.

        See condition_mean() for details on cond_fn.

        Unlike condition_mean(), this instead uses the conditioning strategy
        from Song et al (2020).
        """
        alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)

        eps = self._predict_eps_from_xstart(x, t, p_mean_var["pred_xstart"])
        eps = eps - (1 - alpha_bar).sqrt() * cond_fn(
            x, self._scale_timesteps(t), **model_kwargs)

        out = p_mean_var.copy()
        out["pred_xstart"] = self._predict_xstart_from_eps(x, t, eps)
        out["mean"], _, _ = self.q_posterior_mean_variance(
            x_start=out["pred_xstart"], x_t=x, t=t)
        return out

    def p_sample(
        self,
        model,
        x,
        t,
        cond=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        mixing_normal=False,
    ):
        """
        Sample x_{t-1} from the model at the given timestep.

        :param model: the model to sample from.
        :param x: the current tensor at x_{t-1}.
        :param t: the value of t, starting at 0 for the first diffusion step.
        :param clip_denoised: if True, clip the x_start prediction to [-1, 1].
        :param denoised_fn: if not None, a function which applies to the
            x_start prediction before it is used to sample.
        :param cond_fn: if not None, this is a gradient function that acts
                        similarly to the model.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.
        :return: a dict containing the following keys:
                 - 'sample': a random sample from the model.
                 - 'pred_xstart': a prediction of x_0.
        """
        out = self.p_mean_variance(model,
                                   x,
                                   t,
                                   c=cond,
                                   clip_denoised=clip_denoised,
                                   denoised_fn=denoised_fn,
                                   model_kwargs=model_kwargs,
                                   mixing_normal=mixing_normal)
        noise = th.randn_like(x)
        nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
                        )  # no noise when t == 0
        if cond_fn is not None:
            out["mean"] = self.condition_mean(cond_fn,
                                              out,
                                              x,
                                              t,
                                              model_kwargs=model_kwargs)
        sample = out["mean"] + nonzero_mask * th.exp(
            0.5 * out["log_variance"]) * noise
        return {"sample": sample, "pred_xstart": out["pred_xstart"]}

    def get_mixing_component(self, x_noisy, t, enabled):
        # alpha_bars = th.gather(self._alpha_bars, 0, timestep-1)
        if enabled:
            # one_minus_alpha_bars_sqrt = utils.view4D(th.sqrt(1.0 - alpha_bars), size)
            one_minus_alpha_bars_sqrt = _extract_into_tensor(
                self.sqrt_one_minus_alphas_cumprod, t, x_noisy.shape)
            mixing_component = one_minus_alpha_bars_sqrt * x_noisy
        else:
            mixing_component = None

        return mixing_component

    def get_mixing_component_x0(self, x_noisy, t, enabled):
        # alpha_bars = th.gather(self._alpha_bars, 0, timestep-1)
        if enabled:
            # one_minus_alpha_bars_sqrt = utils.view4D(th.sqrt(1.0 - alpha_bars), size)
            one_minus_alpha_bars_sqrt = _extract_into_tensor(
                self.sqrt_alphas_cumprod, t, x_noisy.shape)
            mixing_component = one_minus_alpha_bars_sqrt * x_noisy
        else:
            mixing_component = None

        return mixing_component

    def p_sample_mixing_component(
        self,
        model,
        x,
        t,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
    ):
        """
        Sample x_{t-1} from the model at the given timestep.

        :param model: the model to sample from.
        :param x: the current tensor at x_{t-1}.
        :param t: the value of t, starting at 0 for the first diffusion step.
        :param clip_denoised: if True, clip the x_start prediction to [-1, 1].
        :param denoised_fn: if not None, a function which applies to the
            x_start prediction before it is used to sample.
        :param cond_fn: if not None, this is a gradient function that acts
                        similarly to the model.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.
        :return: a dict containing the following keys:
                 - 'sample': a random sample from the model.
                 - 'pred_xstart': a prediction of x_0.
        """

        assert self.model_mean_type == ModelMeanType.EPSILON, 'currently LSGM only implemented for EPSILON prediction'

        out = self.p_mean_variance(
            model,
            x,
            t / self.
            num_timesteps,  # trained on SDE diffusion, normalize steps to (0,1]
            clip_denoised=clip_denoised,
            denoised_fn=denoised_fn,
            model_kwargs=model_kwargs,
        )
        # mixing_component = self.get_mixing_component(x, t, enabled=True)
        # out['mean'] = get_mixed_prediction(model.mixed_prediction, out['mean'], model.mixing_logit, mixing_component)

        noise = th.randn_like(x)
        nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
                        )  # no noise when t == 0
        if cond_fn is not None:
            out["mean"] = self.condition_mean(cond_fn,
                                              out,
                                              x,
                                              t,
                                              model_kwargs=model_kwargs)
        sample = out["mean"] + nonzero_mask * th.exp(
            0.5 * out["log_variance"]) * noise
        return {"sample": sample, "pred_xstart": out["pred_xstart"]}

    def p_sample_loop(
        self,
        model,
        shape,
        cond=None,
        noise=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        device=None,
        progress=False,
        mixing_normal=False,
    ):
        """
        Generate samples from the model.

        :param model: the model module.
        :param shape: the shape of the samples, (N, C, H, W).
        :param noise: if specified, the noise from the encoder to sample.
                      Should be of the same shape as `shape`.
        :param clip_denoised: if True, clip x_start predictions to [-1, 1].
        :param denoised_fn: if not None, a function which applies to the
            x_start prediction before it is used to sample.
        :param cond_fn: if not None, this is a gradient function that acts
                        similarly to the model.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.
        :param device: if specified, the device to create the samples on.
                       If not specified, use a model parameter's device.
        :param progress: if True, show a tqdm progress bar.
        :return: a non-differentiable batch of samples.
        """
        final = None
        for sample in self.p_sample_loop_progressive(
                model,
                shape,
                cond=cond,
                noise=noise,
                clip_denoised=clip_denoised,
                denoised_fn=denoised_fn,
                cond_fn=cond_fn,
                model_kwargs=model_kwargs,
                device=device,
                progress=progress,
                mixing_normal=mixing_normal):
            final = sample
        return final["sample"]

    def p_sample_loop_progressive(
        self,
        model,
        shape,
        cond=None,
        noise=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        device=None,
        progress=False,
        mixing_normal=False,
    ):
        """
        Generate samples from the model and yield intermediate samples from
        each timestep of diffusion.

        Arguments are the same as p_sample_loop().
        Returns a generator over dicts, where each dict is the return value of
        p_sample().
        """
        if device is None:
            device = dist_util.dev()
        #     device = next(model.parameters()).device
        assert isinstance(shape, (tuple, list))
        if noise is not None:
            img = noise
        else:
            img = th.randn(*shape, device=device)
        indices = list(range(self.num_timesteps))[::-1]

        if progress:
            # Lazy import so that we don't depend on tqdm.
            from tqdm.auto import tqdm

            indices = tqdm(indices)

        for i in indices:
            t = th.tensor([i] * shape[0], device=device)
            with th.no_grad():
                out = self.p_sample(model,
                                    img,
                                    t,
                                    cond=cond,
                                    clip_denoised=clip_denoised,
                                    denoised_fn=denoised_fn,
                                    cond_fn=cond_fn,
                                    model_kwargs=model_kwargs,
                                    mixing_normal=mixing_normal)
                yield out
                img = out["sample"]

    def ddim_sample(
        self,
        model,
        x,
        t,
        cond=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        eta=0.0,
        unconditional_guidance_scale=1.,
        unconditional_conditioning=None,
        mixing_normal=False,
        objv_inference=False,
    ):
        """
        Sample x_{t-1} from the model using DDIM.

        Same usage as p_sample().
        """

        if unconditional_guidance_scale != 1.0:
            assert cond is not None
            if unconditional_conditioning is None:
                unconditional_conditioning = th.zeros_like(
                    cond['c_crossattn']
                )  # ImageEmbedding adopts zero as the null embedding

        if unconditional_conditioning is None or unconditional_guidance_scale == 1.:
            # e_t = self.model.apply_model(x, t, c)
            out = self.p_mean_variance(
                model,
                x,
                t,
                c=cond,
                clip_denoised=clip_denoised,
                denoised_fn=denoised_fn,
                model_kwargs=model_kwargs,
                mixing_normal=mixing_normal,
            )
            eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"])

        elif objv_inference:
            assert cond is not None
            x_in = th.cat([x] * 2)
            t_in = th.cat([t] * 2)
            c_in = {}
            for k in cond:
                c_in[k] = th.cat([
                    unconditional_conditioning[k].repeat_interleave(
                        cond[k].shape[0], 0), cond[k]
                ])

            model_uncond, model_t = self.p_mean_variance(
                model,
                x_in,
                t_in,
                c=c_in,
                clip_denoised=clip_denoised,
                denoised_fn=denoised_fn,
                model_kwargs=model_kwargs,
                mixing_normal=mixing_normal,
                direct_return_model_output=True,  # ! compat with _wrapper
            ).chunk(2)
            # Usually our model outputs epsilon, but we re-derive it
            # model_uncond, model_t = model(x_in, self._scale_timesteps(t_in), c=c_in, mixing_normal=mixing_normal, **model_kwargs).chunk(2)

            # in case we used x_start or x_prev prediction.
            # st()

            # ! guidance
            # e_t_uncond, e_t = eps.chunk(2)
            model_out = model_uncond + unconditional_guidance_scale * (
                model_t - model_uncond)

            if self.model_mean_type == ModelMeanType.V:
                eps = self._predict_eps_from_z_and_v(x, t, model_out)

            # eps = self._predict_eps_from_xstart(x_in, t_in, out["pred_xstart"])

        else:
            assert cond is not None
            x_in = th.cat([x] * 2)
            t_in = th.cat([t] * 2)
            c_in = {
                'c_crossattn':
                th.cat([
                    unconditional_conditioning.repeat_interleave(
                        cond['c_crossattn'].shape[0], dim=0),
                    cond['c_crossattn']
                ])
            }

            # c_in = {}
            # for k in cond:
            #     c_in[k] = th.cat([unconditional_conditioning[k], cond[k]])

            out = self.p_mean_variance(
                model,
                x_in,
                t_in,
                c=c_in,
                clip_denoised=clip_denoised,
                denoised_fn=denoised_fn,
                model_kwargs=model_kwargs,
                mixing_normal=mixing_normal,
            )
            # Usually our model outputs epsilon, but we re-derive it
            # in case we used x_start or x_prev prediction.
            eps = self._predict_eps_from_xstart(x_in, t_in, out["pred_xstart"])

            # ! guidance
            e_t_uncond, e_t = eps.chunk(2)
            # st()
            eps = e_t_uncond + unconditional_guidance_scale * (e_t -
                                                               e_t_uncond)

        if cond_fn is not None:
            out = self.condition_score(cond_fn,
                                       out,
                                       x,
                                       t,
                                       model_kwargs=model_kwargs)

        # eps = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
        # ! re-derive xstart
        pred_x0 = self._predict_xstart_from_eps(x, t, eps)

        alpha_bar = _extract_into_tensor(self.alphas_cumprod, t, x.shape)
        alpha_bar_prev = _extract_into_tensor(self.alphas_cumprod_prev, t,
                                              x.shape)
        sigma = (eta * th.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar)) *
                 th.sqrt(1 - alpha_bar / alpha_bar_prev))
        # Equation 12.
        noise = th.randn_like(x)
        mean_pred = (pred_x0 * th.sqrt(alpha_bar_prev) +
                     th.sqrt(1 - alpha_bar_prev - sigma**2) * eps)
        nonzero_mask = ((t != 0).float().view(-1, *([1] * (len(x.shape) - 1)))
                        )  # no noise when t == 0
        sample = mean_pred + nonzero_mask * sigma * noise
        return {"sample": sample, "pred_xstart": pred_x0}

    def ddim_reverse_sample(
        self,
        model,
        x,
        t,
        clip_denoised=True,
        denoised_fn=None,
        model_kwargs=None,
        eta=0.0,
    ):
        """
        Sample x_{t+1} from the model using DDIM reverse ODE.
        """
        assert eta == 0.0, "Reverse ODE only for deterministic path"
        out = self.p_mean_variance(
            model,
            x,
            t,
            clip_denoised=clip_denoised,
            denoised_fn=denoised_fn,
            model_kwargs=model_kwargs,
        )
        # Usually our model outputs epsilon, but we re-derive it
        # in case we used x_start or x_prev prediction.
        eps = (_extract_into_tensor(self.sqrt_recip_alphas_cumprod, t, x.shape)
               * x - out["pred_xstart"]) / _extract_into_tensor(
                   self.sqrt_recipm1_alphas_cumprod, t, x.shape)
        alpha_bar_next = _extract_into_tensor(self.alphas_cumprod_next, t,
                                              x.shape)

        # Equation 12. reversed
        mean_pred = (out["pred_xstart"] * th.sqrt(alpha_bar_next) +
                     th.sqrt(1 - alpha_bar_next) * eps)

        return {"sample": mean_pred, "pred_xstart": out["pred_xstart"]}

    def ddim_sample_loop(
        self,
        model,
        shape,
        cond=None,
        noise=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        device=None,
        progress=False,
        eta=0.0,
        mixing_normal=False,
        unconditional_guidance_scale=1.0,
        unconditional_conditioning=None,
        objv_inference=False,
    ):
        """
        Generate samples from the model using DDIM.

        Same usage as p_sample_loop().
        """
        final = None
        for sample in self.ddim_sample_loop_progressive(
                model,
                shape,
                cond=cond,
                noise=noise,
                clip_denoised=clip_denoised,
                denoised_fn=denoised_fn,
                cond_fn=cond_fn,
                model_kwargs=model_kwargs,
                device=device,
                progress=progress,
                eta=eta,
                mixing_normal=mixing_normal,
                unconditional_guidance_scale=unconditional_guidance_scale,
                unconditional_conditioning=unconditional_conditioning,
                objv_inference=objv_inference,
        ):
            final = sample
        return final["sample"]

    def ddim_sample_loop_progressive(
        self,
        model,
        shape,
        cond=None,
        noise=None,
        clip_denoised=True,
        denoised_fn=None,
        cond_fn=None,
        model_kwargs=None,
        device=None,
        progress=False,
        eta=0.0,
        mixing_normal=False,
        unconditional_guidance_scale=1.0,
        unconditional_conditioning=None,
        objv_inference=False,
    ):
        """
        Use DDIM to sample from the model and yield intermediate samples from
        each timestep of DDIM.

        Same usage as p_sample_loop_progressive().
        """
        if device is None:
            device = next(model.parameters()).device
        assert isinstance(shape, (tuple, list))
        if noise is not None:
            img = noise
        else:
            img = th.randn(*shape, device=device)
        indices = list(range(self.num_timesteps))[::-1]

        if progress:
            # Lazy import so that we don't depend on tqdm.
            from tqdm.auto import tqdm

            indices = tqdm(indices)

        for i in indices:
            t = th.tensor([i] * shape[0], device=device)
            with th.no_grad():
                out = self.ddim_sample(
                    model,
                    img,
                    t,
                    cond=cond,
                    clip_denoised=clip_denoised,
                    denoised_fn=denoised_fn,
                    cond_fn=cond_fn,
                    model_kwargs=model_kwargs,
                    eta=eta,
                    mixing_normal=mixing_normal,
                    unconditional_guidance_scale=unconditional_guidance_scale,
                    unconditional_conditioning=unconditional_conditioning,
                    objv_inference=objv_inference,
                )
                yield out
                img = out["sample"]

    def _vb_terms_bpd(self,
                      model,
                      x_start,
                      x_t,
                      t,
                      clip_denoised=True,
                      model_kwargs=None):
        """
        Get a term for the variational lower-bound.

        The resulting units are bits (rather than nats, as one might expect).
        This allows for comparison to other papers.

        :return: a dict with the following keys:
                 - 'output': a shape [N] tensor of NLLs or KLs.
                 - 'pred_xstart': the x_0 predictions.
        """
        true_mean, _, true_log_variance_clipped = self.q_posterior_mean_variance(
            x_start=x_start, x_t=x_t, t=t)
        out = self.p_mean_variance(model,
                                   x_t,
                                   t,
                                   clip_denoised=clip_denoised,
                                   model_kwargs=model_kwargs)
        kl = normal_kl(true_mean, true_log_variance_clipped, out["mean"],
                       out["log_variance"])
        kl = mean_flat(kl) / np.log(2.0)

        decoder_nll = -discretized_gaussian_log_likelihood(
            x_start, means=out["mean"], log_scales=0.5 * out["log_variance"])
        assert decoder_nll.shape == x_start.shape
        decoder_nll = mean_flat(decoder_nll) / np.log(2.0)

        # At the first timestep return the decoder NLL,
        # otherwise return KL(q(x_{t-1}|x_t,x_0) || p(x_{t-1}|x_t))
        output = th.where((t == 0), decoder_nll, kl)
        return {"output": output, "pred_xstart": out["pred_xstart"]}

    def training_losses(self,
                        model,
                        x_start,
                        t,
                        model_kwargs=None,
                        noise=None,
                        return_detail=False):
        """
        Compute training losses for a single timestep.

        :param model: the model to evaluate loss on.
        :param x_start: the [N x C x ...] tensor of inputs.
        :param t: a batch of timestep indices.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.
        :param noise: if specified, the specific Gaussian noise to try to remove.
        :return: a dict with the key "loss" containing a tensor of shape [N].
                 Some mean or variance settings may also have other keys.
        """
        if model_kwargs is None:  # * micro_cond
            model_kwargs = {}
        if noise is None:
            noise = th.randn_like(x_start)  # x_start is the x0 image
        x_t = self.q_sample(x_start,
                            t,
                            noise=noise,
                            return_detail=return_detail
                            )  # * add noise according to predefined schedule
        if return_detail:
            x_t, alpha_bar, _ = x_t

        # terms = {}
        terms = {"x_t": x_t}

        if self.loss_type == LossType.KL or self.loss_type == LossType.RESCALED_KL:
            terms["loss"] = self._vb_terms_bpd(
                model=model,
                x_start=x_start,
                x_t=x_t,
                t=t,
                clip_denoised=False,
                model_kwargs=model_kwargs,
            )["output"]
            if self.loss_type == LossType.RESCALED_KL:
                terms["loss"] *= self.num_timesteps
        elif self.loss_type == LossType.MSE or self.loss_type == LossType.RESCALED_MSE:
            model_output = model(
                x_t, self._scale_timesteps(t), **model_kwargs
            )  # directly predict epsilon or x_0; no learned sigma

            if self.model_var_type in [
                    ModelVarType.LEARNED,
                    ModelVarType.LEARNED_RANGE,
            ]:
                B, C = x_t.shape[:2]
                assert model_output.shape == (B, C * 2, *x_t.shape[2:])
                model_output, model_var_values = th.split(model_output,
                                                          C,
                                                          dim=1)
                # Learn the variance using the variational bound, but don't let
                # it affect our mean prediction.
                frozen_out = th.cat([model_output.detach(), model_var_values],
                                    dim=1)
                terms["vb"] = self._vb_terms_bpd(
                    model=lambda *args, r=frozen_out: r,
                    x_start=x_start,
                    x_t=x_t,
                    t=t,
                    clip_denoised=False,
                )["output"]
                if self.loss_type == LossType.RESCALED_MSE:
                    # Divide by 1000 for equivalence with initial implementation.
                    # Without a factor of 1/1000, the VB term hurts the MSE term.
                    terms["vb"] *= self.num_timesteps / 1000.0

            target = {
                ModelMeanType.PREVIOUS_X:
                self.q_posterior_mean_variance(x_start=x_start, x_t=x_t,
                                               t=t)[0],
                ModelMeanType.START_X:
                x_start,
                ModelMeanType.EPSILON:
                noise,
            }[self.model_mean_type]  # ModelMeanType.EPSILON
            # st()
            assert model_output.shape == target.shape == x_start.shape
            terms["mse"] = mean_flat((target - model_output)**2)

            terms['model_output'] = model_output
            # terms['target'] = target # TODO, flag.
            if return_detail:
                terms.update({
                    'diffusion_target': target,
                    'alpha_bar': alpha_bar,
                    # 'one_minus_alpha':one_minus_alpha
                    # 'noise': noise
                })

            if "vb" in terms:
                terms["loss"] = terms["mse"] + terms["vb"]
            else:
                terms["loss"] = terms["mse"]
        else:
            raise NotImplementedError(self.loss_type)

        return terms

    def _prior_bpd(self, x_start):
        """
        Get the prior KL term for the variational lower-bound, measured in
        bits-per-dim.

        This term can't be optimized, as it only depends on the encoder.

        :param x_start: the [N x C x ...] tensor of inputs.
        :return: a batch of [N] KL values (in bits), one per batch element.
        """
        batch_size = x_start.shape[0]
        t = th.tensor([self.num_timesteps - 1] * batch_size,
                      device=x_start.device)
        qt_mean, _, qt_log_variance = self.q_mean_variance(x_start, t)
        kl_prior = normal_kl(mean1=qt_mean,
                             logvar1=qt_log_variance,
                             mean2=0.0,
                             logvar2=0.0)
        return mean_flat(kl_prior) / np.log(2.0)

    def calc_bpd_loop(self,
                      model,
                      x_start,
                      clip_denoised=True,
                      model_kwargs=None):
        """
        Compute the entire variational lower-bound, measured in bits-per-dim,
        as well as other related quantities.

        :param model: the model to evaluate loss on.
        :param x_start: the [N x C x ...] tensor of inputs.
        :param clip_denoised: if True, clip denoised samples.
        :param model_kwargs: if not None, a dict of extra keyword arguments to
            pass to the model. This can be used for conditioning.

        :return: a dict containing the following keys:
                 - total_bpd: the total variational lower-bound, per batch element.
                 - prior_bpd: the prior term in the lower-bound.
                 - vb: an [N x T] tensor of terms in the lower-bound.
                 - xstart_mse: an [N x T] tensor of x_0 MSEs for each timestep.
                 - mse: an [N x T] tensor of epsilon MSEs for each timestep.
        """
        device = x_start.device
        batch_size = x_start.shape[0]

        vb = []
        xstart_mse = []
        mse = []
        for t in list(range(self.num_timesteps))[::-1]:
            t_batch = th.tensor([t] * batch_size, device=device)
            noise = th.randn_like(x_start)
            x_t = self.q_sample(x_start=x_start, t=t_batch, noise=noise)
            # Calculate VLB term at the current timestep
            with th.no_grad():
                out = self._vb_terms_bpd(
                    model,
                    x_start=x_start,
                    x_t=x_t,
                    t=t_batch,
                    clip_denoised=clip_denoised,
                    model_kwargs=model_kwargs,
                )
            vb.append(out["output"])
            xstart_mse.append(mean_flat((out["pred_xstart"] - x_start)**2))
            eps = self._predict_eps_from_xstart(x_t, t_batch,
                                                out["pred_xstart"])
            mse.append(mean_flat((eps - noise)**2))

        vb = th.stack(vb, dim=1)
        xstart_mse = th.stack(xstart_mse, dim=1)
        mse = th.stack(mse, dim=1)

        prior_bpd = self._prior_bpd(x_start)
        total_bpd = vb.sum(dim=1) + prior_bpd
        return {
            "total_bpd": total_bpd,
            "prior_bpd": prior_bpd,
            "vb": vb,
            "xstart_mse": xstart_mse,
            "mse": mse,
        }


def _extract_into_tensor(arr, timesteps, broadcast_shape):
    """
    Extract values from a 1-D numpy array for a batch of indices.

    :param arr: the 1-D numpy array.
    :param timesteps: a tensor of indices into the array to extract.
    :param broadcast_shape: a larger shape of K dimensions with the batch
                            dimension equal to the length of timesteps.
    :return: a tensor of shape [batch_size, 1, ...] where the shape has K dims.
    """
    res = th.from_numpy(arr).to(device=timesteps.device)[timesteps].float()
    while len(res.shape) < len(broadcast_shape):
        res = res[..., None]
    return res.expand(broadcast_shape)