DiT demo

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.gitignore

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+pretrained_models

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README.md

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+---
+title: Diffusion Transformers (DiT)
+emoji: 🚀
+colorFrom: yellow
+colorTo: green
+sdk: gradio
+sdk_version: 3.6
+app_file: app.py
+pinned: false
+license: cc-by-nc-4.0
+---
+
+The code and model weights are licensed under CC-BY-NC. See LICENSE.txt for details.

app.py

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+import torch
+from torchvision.utils import make_grid
+import math
+from PIL import Image
+from diffusion import create_diffusion
+from diffusers.models import AutoencoderKL
+import gradio as gr
+from imagenet_class_data import IMAGENET_1K_CLASSES
+from download import find_model
+from models import DiT_XL_2
+
+
+def load_model(image_size=256):
+    assert image_size in [256, 512]
+    latent_size = image_size // 8
+    model = DiT_XL_2(input_size=latent_size).to(device)
+    state_dict = find_model(f"DiT-XL-2-{image_size}x{image_size}.pt")
+    model.load_state_dict(state_dict)
+    model.eval()
+    return model
+
+
+torch.set_grad_enabled(False)
+device = "cuda" if torch.cuda.is_available() else "cpu"
+model = load_model(image_size=256)
+vae = AutoencoderKL.from_pretrained("stabilityai/sd-vae-ft-mse").to(device)
+current_image_size = 256
+current_vae_model = "stabilityai/sd-vae-ft-mse"
+
+
+def generate(image_size, vae_model, class_label, cfg_scale, num_sampling_steps, n, seed):
+    image_size = int(image_size.split("x")[0])
+    global current_image_size
+    if image_size != current_image_size:
+        global model
+        del model
+        # if device == "cuda":
+        #     torch.cuda.empty_cache()
+        model = load_model(image_size=image_size)
+    current_image_size = image_size
+
+    global current_vae_model
+    if vae_model != current_vae_model:
+        global vae
+        if device == "cuda":
+            vae.to("cpu")
+        del vae
+        vae = AutoencoderKL.from_pretrained(vae_model).to(device)
+
+    # Seed PyTorch:
+    torch.manual_seed(seed)
+
+    # Setup diffusion
+    diffusion = create_diffusion(str(num_sampling_steps))
+
+    # Create sampling noise:
+    latent_size = image_size // 8
+    z = torch.randn(n, 4, latent_size, latent_size, device=device)
+    y = torch.tensor([class_label] * n, device=device)
+
+    # Setup classifier-free guidance:
+    z = torch.cat([z, z], 0)
+    y_null = torch.tensor([1000] * n, device=device)
+    y = torch.cat([y, y_null], 0)
+    model_kwargs = dict(y=y, cfg_scale=cfg_scale)
+
+    # Sample images:
+    samples = diffusion.p_sample_loop(
+        model.forward_with_cfg, z.shape, z, clip_denoised=False, model_kwargs=model_kwargs, progress=True, device=device
+    )
+    samples, _ = samples.chunk(2, dim=0)  # Remove null class samples
+    samples = vae.decode(samples / 0.18215).sample
+
+    # Convert to PIL.Image format:
+    samples = samples.mul(127.5).add_(128.0).clamp_(0, 255).permute(0, 2, 3, 1).to("cpu", torch.uint8).numpy()
+    samples = [Image.fromarray(sample) for sample in samples]
+    return samples
+
+
+description = '''This is a demo of our DiT image generation models. DiTs are a new class of diffusion models with
+transformer backbones. They are class-conditional models trained on ImageNet-1K, and they outperform prior DDPMs.'''
+
+project_links = '''
+<p style="text-align: center">
+<a href="https://www.wpeebles.com/DiT.html">Project Page</a> &#183;
+<a href="http://colab.research.google.com/github/facebookresearch/DiT/blob/main/run_DiT.ipynb">Colab</a> &#183;
+<a href="http://arxiv.org/abs/2212.09748">Paper</a> &#183;
+<a href="https://github.com/facebookresearch/DiT">GitHub</a></p>'''
+
+examples = [
+    ["512x512", "stabilityai/sd-vae-ft-mse", "golden retriever", 4.0, 200, 4, 1000],
+    ["512x512", "stabilityai/sd-vae-ft-mse", "macaw", 4.0, 200, 4, 1],
+    ["512x512", "stabilityai/sd-vae-ft-mse", "balloon", 4.0, 200, 4, 1],
+    ["512x512", "stabilityai/sd-vae-ft-mse", "cliff, drop, drop-off", 4.0, 200, 4, 7],
+    ["512x512", "stabilityai/sd-vae-ft-mse", "Pembroke, Pembroke Welsh corgi", 4.0, 200, 4, 0],
+    ["256x256", "stabilityai/sd-vae-ft-mse", "sulphur-crested cockatoo, Kakatoe galerita, Cacatua galerita", 4.0, 200,
+     4, 1],
+    ["256x256", "stabilityai/sd-vae-ft-mse", "teddy, teddy bear", 4.0, 200, 4, 3],
+    ["256x256", "stabilityai/sd-vae-ft-mse", "cheeseburger", 4.0, 200, 4, 2],
+
+]
+
+with gr.Blocks() as demo:
+    gr.Markdown("<h1 style='text-align: center'>Scalable Diffusion Models with Transformers (DiT)</h1>")
+    gr.Markdown(project_links)
+    gr.Markdown(description)
+
+    with gr.Tabs():
+        with gr.TabItem('Generate'):
+            with gr.Row():
+                with gr.Column():
+                    with gr.Row():
+                        image_size = gr.inputs.Radio(choices=["256x256", "512x512"], default="256x256", label='DiT Model Resolution')
+                        vae_model = gr.inputs.Radio(choices=["stabilityai/sd-vae-ft-mse", "stabilityai/sd-vae-ft-ema"],
+                                                    default="stabilityai/sd-vae-ft-mse", label='VAE Decoder')
+                    with gr.Row():
+                        i1k_class = gr.inputs.Dropdown(
+                            list(IMAGENET_1K_CLASSES.values()),
+                            default='golden retriever',
+                            type="index", label='ImageNet-1K Class'
+                        )
+                    cfg_scale = gr.inputs.Slider(minimum=1, maximum=25, step=0.1, default=4.0, label='Classifier-free Guidance Scale')
+                    steps = gr.inputs.Slider(minimum=4, maximum=1000, step=1, default=75, label='Sampling Steps')
+                    n = gr.inputs.Slider(minimum=1, maximum=16, step=1, default=1, label='Number of Samples')
+                    seed = gr.inputs.Number(default=0, label='Seed')
+                    button = gr.Button("Generate", variant="primary")
+                with gr.Column():
+                    output = gr.Gallery(label='Generated Images').style(grid=[2], height="auto")
+                    button.click(generate, inputs=[image_size, vae_model, i1k_class, cfg_scale, steps, n, seed], outputs=[output])
+            with gr.Row():
+                ex = gr.Examples(examples=examples, fn=generate,
+                                 inputs=[image_size, vae_model, i1k_class, cfg_scale, steps, n, seed],
+                                 outputs=[output],
+                                 cache_examples=True)
+
+    demo.launch()

diffusion/__init__.py

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+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+from . import gaussian_diffusion as gd
+from .respace import SpacedDiffusion, space_timesteps
+
+
+def create_diffusion(
+    timestep_respacing,
+    noise_schedule="linear", 
+    use_kl=False,
+    sigma_small=False,
+    predict_xstart=False,
+    learn_sigma=True,
+    rescale_learned_sigmas=False,
+    diffusion_steps=1000
+):
+    betas = gd.get_named_beta_schedule(noise_schedule, diffusion_steps)
+    if use_kl:
+        loss_type = gd.LossType.RESCALED_KL
+    elif rescale_learned_sigmas:
+        loss_type = gd.LossType.RESCALED_MSE
+    else:
+        loss_type = gd.LossType.MSE
+    if timestep_respacing is None or timestep_respacing == "":
+        timestep_respacing = [diffusion_steps]
+    return SpacedDiffusion(
+        use_timesteps=space_timesteps(diffusion_steps, timestep_respacing),
+        betas=betas,
+        model_mean_type=(
+            gd.ModelMeanType.EPSILON if not predict_xstart else gd.ModelMeanType.START_X
+        ),
+        model_var_type=(
+            (
+                gd.ModelVarType.FIXED_LARGE
+                if not sigma_small
+                else gd.ModelVarType.FIXED_SMALL
+            )
+            if not learn_sigma
+            else gd.ModelVarType.LEARNED_RANGE
+        ),
+        loss_type=loss_type
+        # rescale_timesteps=rescale_timesteps,
+    )

diffusion/diffusion_utils.py

@@ -0,0 +1,88 @@
+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+import torch as th
+import numpy as np
+
+
+def normal_kl(mean1, logvar1, mean2, logvar2):
+    """
+    Compute the KL divergence between two gaussians.
+    Shapes are automatically broadcasted, so batches can be compared to
+    scalars, among other use cases.
+    """
+    tensor = None
+    for obj in (mean1, logvar1, mean2, logvar2):
+        if isinstance(obj, th.Tensor):
+            tensor = obj
+            break
+    assert tensor is not None, "at least one argument must be a Tensor"
+
+    # Force variances to be Tensors. Broadcasting helps convert scalars to
+    # Tensors, but it does not work for th.exp().
+    logvar1, logvar2 = [
+        x if isinstance(x, th.Tensor) else th.tensor(x).to(tensor)
+        for x in (logvar1, logvar2)
+    ]
+
+    return 0.5 * (
+        -1.0
+        + logvar2
+        - logvar1
+        + th.exp(logvar1 - logvar2)
+        + ((mean1 - mean2) ** 2) * th.exp(-logvar2)
+    )
+
+
+def approx_standard_normal_cdf(x):
+    """
+    A fast approximation of the cumulative distribution function of the
+    standard normal.
+    """
+    return 0.5 * (1.0 + th.tanh(np.sqrt(2.0 / np.pi) * (x + 0.044715 * th.pow(x, 3))))
+
+
+def continuous_gaussian_log_likelihood(x, *, means, log_scales):
+    """
+    Compute the log-likelihood of a continuous Gaussian distribution.
+    :param x: the targets
+    :param means: the Gaussian mean Tensor.
+    :param log_scales: the Gaussian log stddev Tensor.
+    :return: a tensor like x of log probabilities (in nats).
+    """
+    centered_x = x - means
+    inv_stdv = th.exp(-log_scales)
+    normalized_x = centered_x * inv_stdv
+    log_probs = th.distributions.Normal(th.zeros_like(x), th.ones_like(x)).log_prob(normalized_x)
+    return log_probs
+
+
+def discretized_gaussian_log_likelihood(x, *, means, log_scales):
+    """
+    Compute the log-likelihood of a Gaussian distribution discretizing to a
+    given image.
+    :param x: the target images. It is assumed that this was uint8 values,
+              rescaled to the range [-1, 1].
+    :param means: the Gaussian mean Tensor.
+    :param log_scales: the Gaussian log stddev Tensor.
+    :return: a tensor like x of log probabilities (in nats).
+    """
+    assert x.shape == means.shape == log_scales.shape
+    centered_x = x - means
+    inv_stdv = th.exp(-log_scales)
+    plus_in = inv_stdv * (centered_x + 1.0 / 255.0)
+    cdf_plus = approx_standard_normal_cdf(plus_in)
+    min_in = inv_stdv * (centered_x - 1.0 / 255.0)
+    cdf_min = approx_standard_normal_cdf(min_in)
+    log_cdf_plus = th.log(cdf_plus.clamp(min=1e-12))
+    log_one_minus_cdf_min = th.log((1.0 - cdf_min).clamp(min=1e-12))
+    cdf_delta = cdf_plus - cdf_min
+    log_probs = th.where(
+        x < -0.999,
+        log_cdf_plus,
+        th.where(x > 0.999, log_one_minus_cdf_min, th.log(cdf_delta.clamp(min=1e-12))),
+    )
+    assert log_probs.shape == x.shape
+    return log_probs

diffusion/gaussian_diffusion.py

@@ -0,0 +1,873 @@
+# Modified from OpenAI's diffusion repos
+#     GLIDE: https://github.com/openai/glide-text2im/blob/main/glide_text2im/gaussian_diffusion.py
+#     ADM:   https://github.com/openai/guided-diffusion/blob/main/guided_diffusion
+#     IDDPM: https://github.com/openai/improved-diffusion/blob/main/improved_diffusion/gaussian_diffusion.py
+
+
+import math
+
+import numpy as np
+import torch as th
+import enum
+
+from .diffusion_utils import discretized_gaussian_log_likelihood, normal_kl
+
+
+def mean_flat(tensor):
+    """
+    Take the mean over all non-batch dimensions.
+    """
+    return tensor.mean(dim=list(range(1, len(tensor.shape))))
+
+
+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
+
+
+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
+
+
+def _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, warmup_frac):
+    betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64)
+    warmup_time = int(num_diffusion_timesteps * warmup_frac)
+    betas[:warmup_time] = np.linspace(beta_start, beta_end, warmup_time, dtype=np.float64)
+    return betas
+
+
+def get_beta_schedule(beta_schedule, *, beta_start, beta_end, num_diffusion_timesteps):
+    """
+    This is the deprecated API for creating beta schedules.
+    See get_named_beta_schedule() for the new library of schedules.
+    """
+    if beta_schedule == "quad":
+        betas = (
+            np.linspace(
+                beta_start ** 0.5,
+                beta_end ** 0.5,
+                num_diffusion_timesteps,
+                dtype=np.float64,
+            )
+            ** 2
+        )
+    elif beta_schedule == "linear":
+        betas = np.linspace(beta_start, beta_end, num_diffusion_timesteps, dtype=np.float64)
+    elif beta_schedule == "warmup10":
+        betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.1)
+    elif beta_schedule == "warmup50":
+        betas = _warmup_beta(beta_start, beta_end, num_diffusion_timesteps, 0.5)
+    elif beta_schedule == "const":
+        betas = beta_end * np.ones(num_diffusion_timesteps, dtype=np.float64)
+    elif beta_schedule == "jsd":  # 1/T, 1/(T-1), 1/(T-2), ..., 1
+        betas = 1.0 / np.linspace(
+            num_diffusion_timesteps, 1, num_diffusion_timesteps, dtype=np.float64
+        )
+    else:
+        raise NotImplementedError(beta_schedule)
+    assert betas.shape == (num_diffusion_timesteps,)
+    return betas
+
+
+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":
+        # Linear schedule from Ho et al, extended to work for any number of
+        # diffusion steps.
+        scale = 1000 / num_diffusion_timesteps
+        return get_beta_schedule(
+            "linear",
+            beta_start=scale * 0.0001,
+            beta_end=scale * 0.02,
+            num_diffusion_timesteps=num_diffusion_timesteps,
+        )
+    elif schedule_name == "squaredcos_cap_v2":
+        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(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 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 = th.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 = th.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 = 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: (
+                    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
+
+