scheduler: add remove noise

aka original sample prediction (or predict x0)

E.g. useful for methods like self-attention guidance (see equation (2)
in https://arxiv.org/pdf/2210.00939.pdf)

src/refiners/foundationals/latent_diffusion/schedulers/scheduler.py

@@ -78,11 +78,20 @@ class Scheduler(ABC):
         step: int,
     ) -> Tensor:
         timestep = self.timesteps[step]
-        cumulative_scale_factors = self.cumulative_scale_factors[timestep].unsqueeze(-1).unsqueeze(-1)
-        noise_stds = self.noise_std[timestep].unsqueeze(-1).unsqueeze(-1)
+        cumulative_scale_factors = self.cumulative_scale_factors[timestep]
+        noise_stds = self.noise_std[timestep]
         noised_x = cumulative_scale_factors * x + noise_stds * noise
         return noised_x
 
+    def remove_noise(self, x: Tensor, noise: Tensor, step: int) -> Tensor:
+        timestep = self.timesteps[step]
+        cumulative_scale_factors = self.cumulative_scale_factors[timestep]
+        noise_stds = self.noise_std[timestep]
+        # See equation (15) from https://arxiv.org/pdf/2006.11239.pdf. Useful to preview progress or for guidance like
+        # in https://arxiv.org/pdf/2210.00939.pdf (self-attention guidance)
+        denoised_x = (x - noise_stds * noise) / cumulative_scale_factors
+        return denoised_x
+
     def to(self: T, device: Device | str | None = None, dtype: DType | None = None) -> T:  # type: ignore
         if device is not None:
             self.device = Device(device)

tests/foundationals/latent_diffusion/test_schedulers.py

@@ -71,6 +71,31 @@ def test_ddim_solver_diffusers():
         assert allclose(diffusers_output, refiners_output, rtol=0.01), f"outputs differ at step {step}"
 
 
+def test_scheduler_remove_noise():
+    from diffusers import DDIMScheduler  # type: ignore
+
+    diffusers_scheduler = DDIMScheduler(
+        beta_end=0.012,
+        beta_schedule="scaled_linear",
+        beta_start=0.00085,
+        num_train_timesteps=1000,
+        set_alpha_to_one=False,
+        steps_offset=1,
+        clip_sample=False,
+    )
+    diffusers_scheduler.set_timesteps(30)
+    refiners_scheduler = DDIM(num_inference_steps=30)
+
+    sample = randn(1, 4, 32, 32)
+    noise = randn(1, 4, 32, 32)
+
+    for step, timestep in enumerate(diffusers_scheduler.timesteps):
+        diffusers_output = cast(Tensor, diffusers_scheduler.step(noise, timestep, sample).pred_original_sample)  # type: ignore
+        refiners_output = refiners_scheduler.remove_noise(x=sample, noise=noise, step=step)
+
+        assert allclose(diffusers_output, refiners_output, rtol=0.01), f"outputs differ at step {step}"
+
+
 def test_scheduler_device(test_device: Device):
     if test_device.type == "cpu":
         warn("not running on CPU, skipping")