add diffusion utils

README.md

@@ -5,10 +5,24 @@ colorFrom: red
 colorTo: pink
 sdk: gradio
 sdk_version: 5.9.1
+python_version: 3.11
 app_file: app.py
 pinned: false
 license: mit
+models:
+    - ntt123/diffusion-speech-360h
+preload_from_hub: true
+    - ntt123/diffusion-speech-360h acoustic_model_0140000.pt,duration_model_0120000.pt
 short_description: A simple diffusion-based text to speech model
 ---
 
-Check out the configuration reference at https://huggingface.co/docs/hub/spaces-config-reference
+```
+uv run synthesize.py \
+--duration-model-config ./train_duration_dit_s.yaml \
+--acoustic-model-config ./train_acoustic_dit_b.yaml \
+--duration-model-checkpoint ./duration_model_0120000.pt \
+--acoustic-model-checkpoint ./acoustic_model_0140000.pt \
+--speaker-id 1914 \
+--output-file ./audio.wav \
+--text "Ilya has made several major contributions to the field of deep learning."
+```

app.py

@@ -24,7 +24,7 @@ sampling_steps = [100, 250, 500, 1000]
 demo = gr.Interface(
     fn=text_to_speech,
     inputs=[
-        gr.Textbox(label="Text"),
+        gr.Textbox(label="Text", value="Text to Speech with Diffusion Transformer"),
         gr.Dropdown(choices=speaker_ids, label="Speaker ID", value="0"),
         gr.Slider(minimum=0, maximum=10, value=4.0, label="CFG Scale"),
         gr.Dropdown(choices=sampling_steps, label="Sampling Steps", value=100),

diffusion.py

@@ -0,0 +1,46 @@
+# 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 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_utils.py

@@ -0,0 +1,90 @@
+# 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 numpy as np
+import torch as th
+
+
+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

gaussian_diffusion.py

@@ -0,0 +1,917 @@
+# 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 enum
+import math
+
+import numpy as np
+import torch as th
+
+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)
+        )
+
+        # convert all numpy arrays to torch tensors
+        DEVICE = th.device("cpu")
+        self.betas = th.from_numpy(self.betas).to(DEVICE)
+        self.alphas_cumprod = th.from_numpy(self.alphas_cumprod).to(DEVICE)
+        self.alphas_cumprod_prev = th.from_numpy(self.alphas_cumprod_prev).to(DEVICE)
+        self.alphas_cumprod_next = th.from_numpy(self.alphas_cumprod_next).to(DEVICE)
+        self.sqrt_alphas_cumprod = th.from_numpy(self.sqrt_alphas_cumprod).to(DEVICE)
+        self.sqrt_one_minus_alphas_cumprod = th.from_numpy(self.sqrt_one_minus_alphas_cumprod).to(DEVICE)
+        self.log_one_minus_alphas_cumprod = th.from_numpy(self.log_one_minus_alphas_cumprod).to(DEVICE)
+        self.sqrt_recip_alphas_cumprod = th.from_numpy(self.sqrt_recip_alphas_cumprod).to(DEVICE)
+        self.sqrt_recipm1_alphas_cumprod = th.from_numpy(self.sqrt_recipm1_alphas_cumprod).to(DEVICE)
+        self.posterior_variance = th.from_numpy(self.posterior_variance).to(DEVICE)
+        self.posterior_log_variance_clipped = th.from_numpy(self.posterior_log_variance_clipped).to(DEVICE)
+        self.posterior_mean_coef1 = th.from_numpy(self.posterior_mean_coef1).to(DEVICE)
+        self.posterior_mean_coef2 = th.from_numpy(self.posterior_mean_coef2).to(DEVICE)
+        
+
+
+    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(th.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: (
+                    th.cat([self.posterior_variance[1], self.betas[1:]]),
+                    th.log(th.cat([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 = 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,
+        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
+        samples = []
+        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
+            samples.append(final["sample"])
+        return samples
+
+    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 = 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,
+                    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
+            * 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 = (
+            out["pred_xstart"] * 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": 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"] * 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,
+        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 = 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,
+                    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 = kl / math.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 = decoder_nll / math.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[:, None, None] == 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 = th.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 = 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]
+            assert model_output.shape == target.shape == x_start.shape
+            terms["mse"] = (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 = 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) / math.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 = arr.to(device=timesteps.device)[timesteps].float()
+    while len(res.shape) < len(broadcast_shape):
+        res = res[..., None]
+    return res + th.zeros(broadcast_shape, device=timesteps.device)

respace.py

@@ -0,0 +1,127 @@
+# 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 numpy as np
+import torch as th
+
+from gaussian_diffusion import GaussianDiffusion
+
+
+def space_timesteps(num_timesteps, section_counts):
+    """
+    Create a list of timesteps to use from an original diffusion process,
+    given the number of timesteps we want to take from equally-sized portions
+    of the original process.
+    For example, if there's 300 timesteps and the section counts are [10,15,20]
+    then the first 100 timesteps are strided to be 10 timesteps, the second 100
+    are strided to be 15 timesteps, and the final 100 are strided to be 20.
+    If the stride is a string starting with "ddim", then the fixed striding
+    from the DDIM paper is used, and only one section is allowed.
+    :param num_timesteps: the number of diffusion steps in the original
+                          process to divide up.
+    :param section_counts: either a list of numbers, or a string containing
+                           comma-separated numbers, indicating the step count
+                           per section. As a special case, use "ddimN" where N
+                           is a number of steps to use the striding from the
+                           DDIM paper.
+    :return: a set of diffusion steps from the original process to use.
+    """
+    if isinstance(section_counts, str):
+        if section_counts.startswith("ddim"):
+            desired_count = int(section_counts[len("ddim") :])
+            for i in range(1, num_timesteps):
+                if len(range(0, num_timesteps, i)) == desired_count:
+                    return set(range(0, num_timesteps, i))
+            raise ValueError(
+                f"cannot create exactly {num_timesteps} steps with an integer stride"
+            )
+        section_counts = [int(x) for x in section_counts.split(",")]
+    size_per = num_timesteps // len(section_counts)
+    extra = num_timesteps % len(section_counts)
+    start_idx = 0
+    all_steps = []
+    for i, section_count in enumerate(section_counts):
+        size = size_per + (1 if i < extra else 0)
+        if size < section_count:
+            raise ValueError(
+                f"cannot divide section of {size} steps into {section_count}"
+            )
+        if section_count <= 1:
+            frac_stride = 1
+        else:
+            frac_stride = (size - 1) / (section_count - 1)
+        cur_idx = 0.0
+        taken_steps = []
+        for _ in range(section_count):
+            taken_steps.append(start_idx + round(cur_idx))
+            cur_idx += frac_stride
+        all_steps += taken_steps
+        start_idx += size
+    return set(all_steps)
+
+
+class SpacedDiffusion(GaussianDiffusion):
+    """
+    A diffusion process which can skip steps in a base diffusion process.
+    :param use_timesteps: a collection (sequence or set) of timesteps from the
+                          original diffusion process to retain.
+    :param kwargs: the kwargs to create the base diffusion process.
+    """
+
+    def __init__(self, use_timesteps, **kwargs):
+        self.use_timesteps = set(use_timesteps)
+        self.timestep_map = []
+        self.original_num_steps = len(kwargs["betas"])
+
+        base_diffusion = GaussianDiffusion(**kwargs)  # pylint: disable=missing-kwoa
+        last_alpha_cumprod = 1.0
+        new_betas = []
+        for i, alpha_cumprod in enumerate(base_diffusion.alphas_cumprod):
+            if i in self.use_timesteps:
+                new_betas.append(1 - alpha_cumprod / last_alpha_cumprod)
+                last_alpha_cumprod = alpha_cumprod
+                self.timestep_map.append(i)
+        kwargs["betas"] = th.tensor(new_betas)
+        super().__init__(**kwargs)
+
+    def p_mean_variance(
+        self, model, *args, **kwargs
+    ):  # pylint: disable=signature-differs
+        return super().p_mean_variance(self._wrap_model(model), *args, **kwargs)
+
+    def training_losses(
+        self, model, *args, **kwargs
+    ):  # pylint: disable=signature-differs
+        return super().training_losses(self._wrap_model(model), *args, **kwargs)
+
+    def condition_mean(self, cond_fn, *args, **kwargs):
+        return super().condition_mean(self._wrap_model(cond_fn), *args, **kwargs)
+
+    def condition_score(self, cond_fn, *args, **kwargs):
+        return super().condition_score(self._wrap_model(cond_fn), *args, **kwargs)
+
+    def _wrap_model(self, model):
+        if isinstance(model, _WrappedModel):
+            return model
+        return _WrappedModel(model, self.timestep_map, self.original_num_steps)
+
+    def _scale_timesteps(self, t):
+        # Scaling is done by the wrapped model.
+        return t
+
+
+class _WrappedModel:
+    def __init__(self, model, timestep_map, original_num_steps):
+        self.model = model
+        self.timestep_map = timestep_map
+        # self.rescale_timesteps = rescale_timesteps
+        self.original_num_steps = original_num_steps
+
+    def __call__(self, x, ts, **kwargs):
+        map_tensor = th.tensor(self.timestep_map, device=ts.device, dtype=ts.dtype)
+        new_ts = map_tensor[ts]
+        # if self.rescale_timesteps:
+        #     new_ts = new_ts.float() * (1000.0 / self.original_num_steps)
+        return self.model(x, new_ts, **kwargs)

timestep_sampler.py

@@ -0,0 +1,150 @@
+# 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 abc import ABC, abstractmethod
+
+import numpy as np
+import torch as th
+import torch.distributed as dist
+
+
+def create_named_schedule_sampler(name, diffusion):
+    """
+    Create a ScheduleSampler from a library of pre-defined samplers.
+    :param name: the name of the sampler.
+    :param diffusion: the diffusion object to sample for.
+    """
+    if name == "uniform":
+        return UniformSampler(diffusion)
+    elif name == "loss-second-moment":
+        return LossSecondMomentResampler(diffusion)
+    else:
+        raise NotImplementedError(f"unknown schedule sampler: {name}")
+
+
+class ScheduleSampler(ABC):
+    """
+    A distribution over timesteps in the diffusion process, intended to reduce
+    variance of the objective.
+    By default, samplers perform unbiased importance sampling, in which the
+    objective's mean is unchanged.
+    However, subclasses may override sample() to change how the resampled
+    terms are reweighted, allowing for actual changes in the objective.
+    """
+
+    @abstractmethod
+    def weights(self):
+        """
+        Get a numpy array of weights, one per diffusion step.
+        The weights needn't be normalized, but must be positive.
+        """
+
+    def sample(self, batch_size, device):
+        """
+        Importance-sample timesteps for a batch.
+        :param batch_size: the number of timesteps.
+        :param device: the torch device to save to.
+        :return: a tuple (timesteps, weights):
+                 - timesteps: a tensor of timestep indices.
+                 - weights: a tensor of weights to scale the resulting losses.
+        """
+        w = self.weights()
+        p = w / np.sum(w)
+        indices_np = np.random.choice(len(p), size=(batch_size,), p=p)
+        indices = th.from_numpy(indices_np).long().to(device)
+        weights_np = 1 / (len(p) * p[indices_np])
+        weights = th.from_numpy(weights_np).float().to(device)
+        return indices, weights
+
+
+class UniformSampler(ScheduleSampler):
+    def __init__(self, diffusion):
+        self.diffusion = diffusion
+        self._weights = np.ones([diffusion.num_timesteps])
+
+    def weights(self):
+        return self._weights
+
+
+class LossAwareSampler(ScheduleSampler):
+    def update_with_local_losses(self, local_ts, local_losses):
+        """
+        Update the reweighting using losses from a model.
+        Call this method from each rank with a batch of timesteps and the
+        corresponding losses for each of those timesteps.
+        This method will perform synchronization to make sure all of the ranks
+        maintain the exact same reweighting.
+        :param local_ts: an integer Tensor of timesteps.
+        :param local_losses: a 1D Tensor of losses.
+        """
+        batch_sizes = [
+            th.tensor([0], dtype=th.int32, device=local_ts.device)
+            for _ in range(dist.get_world_size())
+        ]
+        dist.all_gather(
+            batch_sizes,
+            th.tensor([len(local_ts)], dtype=th.int32, device=local_ts.device),
+        )
+
+        # Pad all_gather batches to be the maximum batch size.
+        batch_sizes = [x.item() for x in batch_sizes]
+        max_bs = max(batch_sizes)
+
+        timestep_batches = [th.zeros(max_bs).to(local_ts) for bs in batch_sizes]
+        loss_batches = [th.zeros(max_bs).to(local_losses) for bs in batch_sizes]
+        dist.all_gather(timestep_batches, local_ts)
+        dist.all_gather(loss_batches, local_losses)
+        timesteps = [
+            x.item() for y, bs in zip(timestep_batches, batch_sizes) for x in y[:bs]
+        ]
+        losses = [x.item() for y, bs in zip(loss_batches, batch_sizes) for x in y[:bs]]
+        self.update_with_all_losses(timesteps, losses)
+
+    @abstractmethod
+    def update_with_all_losses(self, ts, losses):
+        """
+        Update the reweighting using losses from a model.
+        Sub-classes should override this method to update the reweighting
+        using losses from the model.
+        This method directly updates the reweighting without synchronizing
+        between workers. It is called by update_with_local_losses from all
+        ranks with identical arguments. Thus, it should have deterministic
+        behavior to maintain state across workers.
+        :param ts: a list of int timesteps.
+        :param losses: a list of float losses, one per timestep.
+        """
+
+
+class LossSecondMomentResampler(LossAwareSampler):
+    def __init__(self, diffusion, history_per_term=10, uniform_prob=0.001):
+        self.diffusion = diffusion
+        self.history_per_term = history_per_term
+        self.uniform_prob = uniform_prob
+        self._loss_history = np.zeros(
+            [diffusion.num_timesteps, history_per_term], dtype=np.float64
+        )
+        self._loss_counts = np.zeros([diffusion.num_timesteps], dtype=np.int)
+
+    def weights(self):
+        if not self._warmed_up():
+            return np.ones([self.diffusion.num_timesteps], dtype=np.float64)
+        weights = np.sqrt(np.mean(self._loss_history**2, axis=-1))
+        weights /= np.sum(weights)
+        weights *= 1 - self.uniform_prob
+        weights += self.uniform_prob / len(weights)
+        return weights
+
+    def update_with_all_losses(self, ts, losses):
+        for t, loss in zip(ts, losses):
+            if self._loss_counts[t] == self.history_per_term:
+                # Shift out the oldest loss term.
+                self._loss_history[t, :-1] = self._loss_history[t, 1:]
+                self._loss_history[t, -1] = loss
+            else:
+                self._loss_history[t, self._loss_counts[t]] = loss
+                self._loss_counts[t] += 1
+
+    def _warmed_up(self):
+        return (self._loss_counts == self.history_per_term).all()

uv.lock

@@ -1,8 +1,10 @@
 version = 1
 requires-python = ">=3.12"
 resolution-markers = [
-    "python_full_version < '3.13'",
-    "python_full_version >= '3.13'",
+    "python_full_version < '3.13' and platform_system != 'Darwin'",
+    "python_full_version < '3.13' and platform_system == 'Darwin'",
+    "python_full_version >= '3.13' and platform_system != 'Darwin'",
+    "python_full_version >= '3.13' and platform_system == 'Darwin'",
 ]
 
 [[package]]
@@ -188,7 +190,8 @@ dependencies = [
     { name = "gradio" },
     { name = "nltk" },
     { name = "soundfile" },
-    { name = "torch" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://download.pytorch.org/whl/cpu" }, marker = "platform_system != 'Darwin'" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://pypi.org/simple" }, marker = "platform_system == 'Darwin'" },
     { name = "vocos" },
 ]
 
@@ -198,7 +201,8 @@ requires-dist = [
     { name = "gradio", specifier = ">=5.9.1" },
     { name = "nltk", specifier = ">=3.9.1" },
     { name = "soundfile", specifier = ">=0.12.1" },
-    { name = "torch", specifier = ">=2.5.1" },
+    { name = "torch", marker = "platform_system != 'Darwin'", specifier = ">=2.5.1", index = "https://download.pytorch.org/whl/cpu" },
+    { name = "torch", marker = "platform_system == 'Darwin'", specifier = ">=2.5.1" },
     { name = "vocos", specifier = ">=0.1.0" },
 ]
 
@@ -224,7 +228,8 @@ source = { registry = "https://pypi.org/simple" }
 dependencies = [
     { name = "einops" },
     { name = "numpy" },
-    { name = "torch" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://download.pytorch.org/whl/cpu" }, marker = "platform_system != 'Darwin'" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://pypi.org/simple" }, marker = "platform_system == 'Darwin'" },
     { name = "torchaudio" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/62/59/e47bbd0542d0e6f4ce9983d5eb458a01d4b42c81e5c410cb9e159b1061ae/encodec-0.1.1.tar.gz", hash = "sha256:36dde98ccfe6c51a15576476cadfcb3b35a63507b8b8555abd69889a6fba6772", size = 3736037 }
@@ -598,7 +603,7 @@ name = "nvidia-cudnn-cu12"
 version = "9.1.0.70"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "nvidia-cublas-cu12" },
+    { name = "nvidia-cublas-cu12", marker = "platform_system != 'Darwin'" },
 ]
 wheels = [
     { url = "https://files.pythonhosted.org/packages/9f/fd/713452cd72343f682b1c7b9321e23829f00b842ceaedcda96e742ea0b0b3/nvidia_cudnn_cu12-9.1.0.70-py3-none-manylinux2014_x86_64.whl", hash = "sha256:165764f44ef8c61fcdfdfdbe769d687e06374059fbb388b6c89ecb0e28793a6f", size = 664752741 },
@@ -609,7 +614,7 @@ name = "nvidia-cufft-cu12"
 version = "11.2.1.3"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "nvidia-nvjitlink-cu12" },
+    { name = "nvidia-nvjitlink-cu12", marker = "platform_system != 'Darwin'" },
 ]
 wheels = [
     { url = "https://files.pythonhosted.org/packages/7a/8a/0e728f749baca3fbeffad762738276e5df60851958be7783af121a7221e7/nvidia_cufft_cu12-11.2.1.3-py3-none-manylinux2014_aarch64.whl", hash = "sha256:5dad8008fc7f92f5ddfa2101430917ce2ffacd86824914c82e28990ad7f00399", size = 211422548 },
@@ -630,9 +635,9 @@ name = "nvidia-cusolver-cu12"
 version = "11.6.1.9"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "nvidia-cublas-cu12" },
-    { name = "nvidia-cusparse-cu12" },
-    { name = "nvidia-nvjitlink-cu12" },
+    { name = "nvidia-cublas-cu12", marker = "platform_system != 'Darwin'" },
+    { name = "nvidia-cusparse-cu12", marker = "platform_system != 'Darwin'" },
+    { name = "nvidia-nvjitlink-cu12", marker = "platform_system != 'Darwin'" },
 ]
 wheels = [
     { url = "https://files.pythonhosted.org/packages/46/6b/a5c33cf16af09166845345275c34ad2190944bcc6026797a39f8e0a282e0/nvidia_cusolver_cu12-11.6.1.9-py3-none-manylinux2014_aarch64.whl", hash = "sha256:d338f155f174f90724bbde3758b7ac375a70ce8e706d70b018dd3375545fc84e", size = 127634111 },
@@ -644,7 +649,7 @@ name = "nvidia-cusparse-cu12"
 version = "12.3.1.170"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "nvidia-nvjitlink-cu12" },
+    { name = "nvidia-nvjitlink-cu12", marker = "platform_system != 'Darwin'" },
 ]
 wheels = [
     { url = "https://files.pythonhosted.org/packages/96/a9/c0d2f83a53d40a4a41be14cea6a0bf9e668ffcf8b004bd65633f433050c0/nvidia_cusparse_cu12-12.3.1.170-py3-none-manylinux2014_aarch64.whl", hash = "sha256:9d32f62896231ebe0480efd8a7f702e143c98cfaa0e8a76df3386c1ba2b54df3", size = 207381987 },
@@ -1153,12 +1158,16 @@ wheels = [
 [[package]]
 name = "torch"
 version = "2.5.1"
-source = { registry = "https://pypi.org/simple" }
+source = { registry = "https://download.pytorch.org/whl/cpu" }
+resolution-markers = [
+    "python_full_version < '3.13' and platform_system != 'Darwin'",
+    "python_full_version >= '3.13' and platform_system != 'Darwin'",
+]
 dependencies = [
-    { name = "filelock" },
-    { name = "fsspec" },
-    { name = "jinja2" },
-    { name = "networkx" },
+    { name = "filelock", marker = "platform_system != 'Darwin'" },
+    { name = "fsspec", marker = "platform_system != 'Darwin'" },
+    { name = "jinja2", marker = "platform_system != 'Darwin'" },
+    { name = "networkx", marker = "platform_system != 'Darwin'" },
     { name = "nvidia-cublas-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
     { name = "nvidia-cuda-cupti-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
     { name = "nvidia-cuda-nvrtc-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
@@ -1171,17 +1180,33 @@ dependencies = [
     { name = "nvidia-nccl-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
     { name = "nvidia-nvjitlink-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
     { name = "nvidia-nvtx-cu12", marker = "platform_machine == 'x86_64' and platform_system == 'Linux'" },
-    { name = "setuptools" },
-    { name = "sympy" },
-    { name = "triton", marker = "python_full_version < '3.13' and platform_machine == 'x86_64' and platform_system == 'Linux'" },
-    { name = "typing-extensions" },
+    { name = "setuptools", marker = "platform_system != 'Darwin'" },
+    { name = "sympy", marker = "platform_system != 'Darwin'" },
+    { name = "typing-extensions", marker = "platform_system != 'Darwin'" },
+]
+wheels = [
+    { url = "https://download.pytorch.org/whl/cpu/torch-2.5.1-cp312-cp312-manylinux_2_17_aarch64.manylinux2014_aarch64.whl", hash = "sha256:36d1be99281b6f602d9639bd0af3ee0006e7aab16f6718d86f709d395b6f262c" },
+]
+
+[[package]]
+name = "torch"
+version = "2.5.1"
+source = { registry = "https://pypi.org/simple" }
+resolution-markers = [
+    "python_full_version < '3.13' and platform_system == 'Darwin'",
+    "python_full_version >= '3.13' and platform_system == 'Darwin'",
+]
+dependencies = [
+    { name = "filelock", marker = "platform_system == 'Darwin'" },
+    { name = "fsspec", marker = "platform_system == 'Darwin'" },
+    { name = "jinja2", marker = "platform_system == 'Darwin'" },
+    { name = "networkx", marker = "platform_system == 'Darwin'" },
+    { name = "setuptools", marker = "platform_system == 'Darwin'" },
+    { name = "sympy", marker = "platform_system == 'Darwin'" },
+    { name = "typing-extensions", marker = "platform_system == 'Darwin'" },
 ]
 wheels = [
-    { url = "https://files.pythonhosted.org/packages/8b/5c/36c114d120bfe10f9323ed35061bc5878cc74f3f594003854b0ea298942f/torch-2.5.1-cp312-cp312-manylinux1_x86_64.whl", hash = "sha256:ed231a4b3a5952177fafb661213d690a72caaad97d5824dd4fc17ab9e15cec03", size = 906389343 },
-    { url = "https://files.pythonhosted.org/packages/6d/69/d8ada8b6e0a4257556d5b4ddeb4345ea8eeaaef3c98b60d1cca197c7ad8e/torch-2.5.1-cp312-cp312-manylinux2014_aarch64.whl", hash = "sha256:3f4b7f10a247e0dcd7ea97dc2d3bfbfc90302ed36d7f3952b0008d0df264e697", size = 91811673 },
-    { url = "https://files.pythonhosted.org/packages/5f/ba/607d013b55b9fd805db2a5c2662ec7551f1910b4eef39653eeaba182c5b2/torch-2.5.1-cp312-cp312-win_amd64.whl", hash = "sha256:73e58e78f7d220917c5dbfad1a40e09df9929d3b95d25e57d9f8558f84c9a11c", size = 203046841 },
     { url = "https://files.pythonhosted.org/packages/57/6c/bf52ff061da33deb9f94f4121fde7ff3058812cb7d2036c97bc167793bd1/torch-2.5.1-cp312-none-macosx_11_0_arm64.whl", hash = "sha256:8c712df61101964eb11910a846514011f0b6f5920c55dbf567bff8a34163d5b1", size = 63858109 },
-    { url = "https://files.pythonhosted.org/packages/69/72/20cb30f3b39a9face296491a86adb6ff8f1a47a897e4d14667e6cf89d5c3/torch-2.5.1-cp313-cp313-manylinux1_x86_64.whl", hash = "sha256:9b61edf3b4f6e3b0e0adda8b3960266b9009d02b37555971f4d1c8f7a05afed7", size = 906393265 },
 ]
 
 [[package]]
@@ -1189,7 +1214,8 @@ name = "torchaudio"
 version = "2.5.1"
 source = { registry = "https://pypi.org/simple" }
 dependencies = [
-    { name = "torch" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://download.pytorch.org/whl/cpu" }, marker = "platform_system != 'Darwin'" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://pypi.org/simple" }, marker = "platform_system == 'Darwin'" },
 ]
 wheels = [
     { url = "https://files.pythonhosted.org/packages/03/ab/151037a41e2cf4a5d489dfe5e7196b755e0fd83958d5ca7ad8ed85afcb1c/torchaudio-2.5.1-cp312-cp312-macosx_11_0_arm64.whl", hash = "sha256:f1cbfdfd1bbdfbe7289d47a74f36ff6c5d87c3205606202fef5a7fb693f61cf0", size = 1798042 },
@@ -1210,17 +1236,6 @@ wheels = [
     { url = "https://files.pythonhosted.org/packages/d0/30/dc54f88dd4a2b5dc8a0279bdd7270e735851848b762aeb1c1184ed1f6b14/tqdm-4.67.1-py3-none-any.whl", hash = "sha256:26445eca388f82e72884e0d580d5464cd801a3ea01e63e5601bdff9ba6a48de2", size = 78540 },
 ]
 
-[[package]]
-name = "triton"
-version = "3.1.0"
-source = { registry = "https://pypi.org/simple" }
-dependencies = [
-    { name = "filelock", marker = "python_full_version < '3.13'" },
-]
-wheels = [
-    { url = "https://files.pythonhosted.org/packages/78/eb/65f5ba83c2a123f6498a3097746607e5b2f16add29e36765305e4ac7fdd8/triton-3.1.0-cp312-cp312-manylinux_2_17_x86_64.manylinux2014_x86_64.whl", hash = "sha256:c8182f42fd8080a7d39d666814fa36c5e30cc00ea7eeeb1a2983dbb4c99a0fdc", size = 209551444 },
-]
-
 [[package]]
 name = "typeguard"
 version = "4.4.1"
@@ -1299,7 +1314,8 @@ dependencies = [
     { name = "numpy" },
     { name = "pyyaml" },
     { name = "scipy" },
-    { name = "torch" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://download.pytorch.org/whl/cpu" }, marker = "platform_system != 'Darwin'" },
+    { name = "torch", version = "2.5.1", source = { registry = "https://pypi.org/simple" }, marker = "platform_system == 'Darwin'" },
     { name = "torchaudio" },
 ]
 sdist = { url = "https://files.pythonhosted.org/packages/db/48/1e4d3a4a97292e47ebaa18e3eae6ecb2f57bde47693ccab0e7acb23f9ffe/vocos-0.1.0.tar.gz", hash = "sha256:b488224dbe398ff7d4790a027ad659478b4bc02e465db992c62c12b32ca043d8", size = 21107 }