[2905]: Add Karras pattern to discrete euler (huggingface#2956)

* [2905]: Add Karras pattern to discrete euler

* [2905]: Add Karras pattern to discrete euler

* Review comments

* Review comments

* Review comments

* Review comments

---------

Co-authored-by: njindal <[email protected]>

Author: nipunjindal

schedulers/scheduling_euler_discrete.py

@@ -103,6 +103,10 @@ class EulerDiscreteScheduler(SchedulerMixin, ConfigMixin):
         interpolation_type (`str`, default `"linear"`, optional):
             interpolation type to compute intermediate sigmas for the scheduler denoising steps. Should be one of
             [`"linear"`, `"log_linear"`].
+        use_karras_sigmas (`bool`, *optional*, defaults to `False`):
+             This parameter controls whether to use Karras sigmas (Karras et al. (2022) scheme) for step sizes in the
+             noise schedule during the sampling process. If True, the sigmas will be determined according to a sequence
+             of noise levels {σi} as defined in Equation (5) of the paper https://arxiv.org/pdf/2206.00364.pdf.
     """
 
     _compatibles = [e.name for e in KarrasDiffusionSchedulers]
@@ -118,6 +122,7 @@ def __init__(
         trained_betas: Optional[Union[np.ndarray, List[float]]] = None,
         prediction_type: str = "epsilon",
         interpolation_type: str = "linear",
+        use_karras_sigmas: Optional[bool] = False,
     ):
         if trained_betas is not None:
             self.betas = torch.tensor(trained_betas, dtype=torch.float32)
@@ -149,6 +154,7 @@ def __init__(
         timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
         self.timesteps = torch.from_numpy(timesteps)
         self.is_scale_input_called = False
+        self.use_karras_sigmas = use_karras_sigmas
 
     def scale_model_input(
         self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
@@ -187,6 +193,7 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
 
         timesteps = np.linspace(0, self.config.num_train_timesteps - 1, num_inference_steps, dtype=float)[::-1].copy()
         sigmas = np.array(((1 - self.alphas_cumprod) / self.alphas_cumprod) ** 0.5)
+        log_sigmas = np.log(sigmas)
 
         if self.config.interpolation_type == "linear":
             sigmas = np.interp(timesteps, np.arange(0, len(sigmas)), sigmas)
@@ -198,6 +205,10 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
                 " 'linear' or 'log_linear'"
             )
 
+        if self.use_karras_sigmas:
+            sigmas = self._convert_to_karras(in_sigmas=sigmas)
+            timesteps = np.array([self._sigma_to_t(sigma, log_sigmas) for sigma in sigmas])
+
         sigmas = np.concatenate([sigmas, [0.0]]).astype(np.float32)
         self.sigmas = torch.from_numpy(sigmas).to(device=device)
         if str(device).startswith("mps"):
@@ -206,6 +217,43 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
         else:
             self.timesteps = torch.from_numpy(timesteps).to(device=device)
 
+    def _sigma_to_t(self, sigma, log_sigmas):
+        # get log sigma
+        log_sigma = np.log(sigma)
+
+        # get distribution
+        dists = log_sigma - log_sigmas[:, np.newaxis]
+
+        # get sigmas range
+        low_idx = np.cumsum((dists >= 0), axis=0).argmax(axis=0).clip(max=log_sigmas.shape[0] - 2)
+        high_idx = low_idx + 1
+
+        low = log_sigmas[low_idx]
+        high = log_sigmas[high_idx]
+
+        # interpolate sigmas
+        w = (low - log_sigma) / (low - high)
+        w = np.clip(w, 0, 1)
+
+        # transform interpolation to time range
+        t = (1 - w) * low_idx + w * high_idx
+        t = t.reshape(sigma.shape)
+        return t
+
+    # Copied from https://github.com/crowsonkb/k-diffusion/blob/686dbad0f39640ea25c8a8c6a6e56bb40eacefa2/k_diffusion/sampling.py#L17
+    def _convert_to_karras(self, in_sigmas: torch.FloatTensor) -> torch.FloatTensor:
+        """Constructs the noise schedule of Karras et al. (2022)."""
+
+        sigma_min: float = in_sigmas[-1].item()
+        sigma_max: float = in_sigmas[0].item()
+
+        rho = 7.0  # 7.0 is the value used in the paper
+        ramp = np.linspace(0, 1, self.num_inference_steps)
+        min_inv_rho = sigma_min ** (1 / rho)
+        max_inv_rho = sigma_max ** (1 / rho)
+        sigmas = (max_inv_rho + ramp * (min_inv_rho - max_inv_rho)) ** rho
+        return sigmas
+
     def step(
         self,
         model_output: torch.FloatTensor,