From 55cc97ce72199cd49a6fa8678dcdb9c2676ee959 Mon Sep 17 00:00:00 2001
From: "Esmail A.Gumaan" <113830751+Esmail-ibraheem@users.noreply.github.com>
Date: Sun, 14 Apr 2024 09:36:12 +0300
Subject: [PATCH] Create Gaussing_Diffusion.py

---
 Gaussing_Diffusion.py | 731 ++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 731 insertions(+)
 create mode 100644 Gaussing_Diffusion.py

diff --git a/Gaussing_Diffusion.py b/Gaussing_Diffusion.py
new file mode 100644
index 0000000..41853f8
--- /dev/null
+++ b/Gaussing_Diffusion.py
@@ -0,0 +1,731 @@
+
+class GaussianDiffusion:
+    """
+    Utilities for training and sampling diffusion models.
+    Original ported from this codebase:
+    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.
+    """
+
+    def __init__(
+        self,
+        *,
+        betas,
+        model_mean_type,
+        model_var_type,
+        loss_type
+    ):
+
+        self.model_mean_type = model_mean_type
+        self.model_var_type = model_var_type
+        self.loss_type = loss_type
+
+        # 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)
+
+        # 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)
+        )
+        # below: 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:])
+        ) if len(self.posterior_variance) > 1 else np.array([])
+
+        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):
+        """
+        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 = torch.randn_like(x_start)
+        assert noise.shape == x_start.shape
+        return (
+            _extract_into_tensor(self.sqrt_alphas_cumprod, t, x_start.shape) * x_start
+            + _extract_into_tensor(self.sqrt_one_minus_alphas_cumprod, t, x_start.shape) * noise
+        )
+
+    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, clip_denoised=True, denoised_fn=None, model_kwargs=None):
+        """
+        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.
+        """
+        if model_kwargs is None:
+            model_kwargs = {}
+
+        B, C = x.shape[:2]
+        assert t.shape == (B,)
+        model_output = model(x, t, **model_kwargs)
+        if isinstance(model_output, tuple):
+            model_output, extra = model_output
+        else:
+            extra = None
+
+        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 = torch.split(model_output, C, dim=1)
+            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 = torch.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: (
+                    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.START_X:
+            pred_xstart = process_xstart(model_output)
+        else:
+            pred_xstart = process_xstart(
+                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)
+
+        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,
+            "extra": extra,
+        }
+
+    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_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)
+
+    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, 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, 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,
+        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.
+        """
+        out = self.p_mean_variance(
+            model,
+            x,
+            t,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            model_kwargs=model_kwargs,
+        )
+        noise = torch.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 * torch.exp(0.5 * out["log_variance"]) * noise
+        return {"sample": sample, "pred_xstart": out["pred_xstart"]}
+
+    def p_sample_loop(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=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,
+            noise=noise,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            cond_fn=cond_fn,
+            model_kwargs=model_kwargs,
+            device=device,
+            progress=progress,
+        ):
+            final = sample
+        return final["sample"]
+
+    def p_sample_loop_progressive(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=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 = next(model.parameters()).device
+        assert isinstance(shape, (tuple, list))
+        if noise is not None:
+            img = noise
+        else:
+            img = torch.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 = torch.tensor([i] * shape[0], device=device)
+            with torch.no_grad():
+                out = self.p_sample(
+                    model,
+                    img,
+                    t,
+                    clip_denoised=clip_denoised,
+                    denoised_fn=denoised_fn,
+                    cond_fn=cond_fn,
+                    model_kwargs=model_kwargs,
+                )
+                yield out
+                img = out["sample"]
+
+    def ddim_sample(
+        self,
+        model,
+        x,
+        t,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        eta=0.0,
+    ):
+        """
+        Sample x_{t-1} from the model using DDIM.
+        Same usage as p_sample().
+        """
+        out = self.p_mean_variance(
+            model,
+            x,
+            t,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            model_kwargs=model_kwargs,
+        )
+        if cond_fn is not None:
+            out = self.condition_score(cond_fn, out, x, t, 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 = self._predict_eps_from_xstart(x, t, out["pred_xstart"])
+
+        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
+            * torch.sqrt((1 - alpha_bar_prev) / (1 - alpha_bar))
+            * torch.sqrt(1 - alpha_bar / alpha_bar_prev)
+        )
+        # Equation 12.
+        noise = torch.randn_like(x)
+        mean_pred = (
+            out["pred_xstart"] * torch.sqrt(alpha_bar_prev)
+            + torch.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": out["pred_xstart"]}
+
+    def ddim_reverse_sample(
+        self,
+        model,
+        x,
+        t,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_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,
+        )
+        if cond_fn is not None:
+            out = self.condition_score(cond_fn, out, x, t, 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"] * torch.sqrt(alpha_bar_next) + torch.sqrt(1 - alpha_bar_next) * eps
+
+        return {"sample": mean_pred, "pred_xstart": out["pred_xstart"]}
+
+    def ddim_sample_loop(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+        eta=0.0,
+    ):
+        """
+        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,
+            noise=noise,
+            clip_denoised=clip_denoised,
+            denoised_fn=denoised_fn,
+            cond_fn=cond_fn,
+            model_kwargs=model_kwargs,
+            device=device,
+            progress=progress,
+            eta=eta,
+        ):
+            final = sample
+        return final["sample"]
+
+    def ddim_sample_loop_progressive(
+        self,
+        model,
+        shape,
+        noise=None,
+        clip_denoised=True,
+        denoised_fn=None,
+        cond_fn=None,
+        model_kwargs=None,
+        device=None,
+        progress=False,
+        eta=0.0,
+    ):
+        """
+        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 = torch.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 = torch.tensor([i] * shape[0], device=device)
+            with torch.no_grad():
+                out = self.ddim_sample(
+                    model,
+                    img,
+                    t,
+                    clip_denoised=clip_denoised,
+                    denoised_fn=denoised_fn,
+                    cond_fn=cond_fn,
+                    model_kwargs=model_kwargs,
+                    eta=eta,
+                )
+                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 = torch.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):
+        """
+        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:
+            model_kwargs = {}
+        if noise is None:
+            noise = torch.randn_like(x_start)
+        x_t = self.q_sample(x_start, t, noise=noise)
+
+        terms = {}
+
+        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, t, **model_kwargs)
+
+            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 = torch.split(model_output, C, dim=1)
+                # Learn the variance using the variational bound, but don't let
+                # it affect our mean prediction.
+                frozen_out = torch.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]
+            assert model_output.shape == target.shape == x_start.shape
+            terms["mse"] = mean_flat((target - model_output) ** 2)
+            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 = torch.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 = torch.tensor([t] * batch_size, device=device)
+            noise = torch.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 torch.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 = torch.stack(vb, dim=1)
+        xstart_mse = torch.stack(xstart_mse, dim=1)
+        mse = torch.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 = torch.from_numpy(arr).to(device=timesteps.device)[timesteps].float()
+    while len(res.shape) < len(broadcast_shape):
+        res = res[..., None]
+    return res + torch.zeros(broadcast_shape, device=timesteps.device)