diff --git a/src/diffusers/pipelines/score_sde_ve/pipeline_score_sde_ve.py b/src/diffusers/pipelines/score_sde_ve/pipeline_score_sde_ve.py
index 1907fc7d50d8..7f63820eec28 100644
--- a/src/diffusers/pipelines/score_sde_ve/pipeline_score_sde_ve.py
+++ b/src/diffusers/pipelines/score_sde_ve/pipeline_score_sde_ve.py
@@ -57,7 +57,7 @@ def __call__(
 
         model = self.unet
 
-        sample = torch.randn(*shape, generator=generator) * self.scheduler.config.sigma_max
+        sample = torch.randn(*shape, generator=generator) * self.scheduler.init_noise_sigma
         sample = sample.to(self.device)
 
         self.scheduler.set_timesteps(num_inference_steps)
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
index 614367aea77e..b7dd8035402b 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion.py
@@ -281,9 +281,8 @@ def __call__(
         # It's more optimized to move all timesteps to correct device beforehand
         timesteps_tensor = self.scheduler.timesteps.to(self.device)
 
-        # if we use LMSDiscreteScheduler, let's make sure latents are multiplied by sigmas
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            latents = latents * self.scheduler.sigmas[0]
+        # scale the initial noise by the standard deviation required by the scheduler
+        latents = latents * self.scheduler.init_noise_sigma
 
         # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
         # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
@@ -297,10 +296,7 @@ def __call__(
         for i, t in enumerate(self.progress_bar(timesteps_tensor)):
             # expand the latents if we are doing classifier free guidance
             latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[i]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -311,10 +307,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, i, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
             # call the callback, if provided
             if callback is not None and i % callback_steps == 0:
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
index 23661b4bdaaa..4d706f2510b3 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_img2img.py
@@ -226,13 +226,9 @@ def __call__(
         offset = self.scheduler.config.get("steps_offset", 0)
         init_timestep = int(num_inference_steps * strength) + offset
         init_timestep = min(init_timestep, num_inference_steps)
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            timesteps = torch.tensor(
-                [num_inference_steps - init_timestep] * batch_size, dtype=torch.long, device=self.device
-            )
-        else:
-            timesteps = self.scheduler.timesteps[-init_timestep]
-            timesteps = torch.tensor([timesteps] * batch_size, dtype=torch.long, device=self.device)
+
+        timesteps = self.scheduler.timesteps[-init_timestep]
+        timesteps = torch.tensor([timesteps] * batch_size, device=self.device)
 
         # add noise to latents using the timesteps
         noise = torch.randn(init_latents.shape, generator=generator, device=self.device)
@@ -310,16 +306,9 @@ def __call__(
         timesteps = self.scheduler.timesteps[t_start:].to(self.device)
 
         for i, t in enumerate(self.progress_bar(timesteps)):
-            t_index = t_start + i
-
             # expand the latents if we are doing classifier free guidance
             latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
-
-            # if we use LMSDiscreteScheduler, let's make sure latents are multiplied by sigmas
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[t_index]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -330,10 +319,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, t_index, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
 
             # call the callback, if provided
             if callback is not None and i % callback_steps == 0:
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
index 493cb91bcb29..24dba21a167f 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_inpaint.py
@@ -260,13 +260,9 @@ def __call__(
         offset = self.scheduler.config.get("steps_offset", 0)
         init_timestep = int(num_inference_steps * strength) + offset
         init_timestep = min(init_timestep, num_inference_steps)
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            timesteps = torch.tensor(
-                [num_inference_steps - init_timestep] * batch_size, dtype=torch.long, device=self.device
-            )
-        else:
-            timesteps = self.scheduler.timesteps[-init_timestep]
-            timesteps = torch.tensor([timesteps] * batch_size, dtype=torch.long, device=self.device)
+
+        timesteps = self.scheduler.timesteps[-init_timestep]
+        timesteps = torch.tensor([timesteps] * batch_size, device=self.device)
 
         # add noise to latents using the timesteps
         noise = torch.randn(init_latents.shape, generator=generator, device=self.device)
@@ -348,13 +344,9 @@ def __call__(
         timesteps = self.scheduler.timesteps[t_start:].to(self.device)
 
         for i, t in tqdm(enumerate(timesteps)):
-            t_index = t_start + i
             # expand the latents if we are doing classifier free guidance
             latent_model_input = torch.cat([latents] * 2) if do_classifier_free_guidance else latents
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[t_index]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
 
             # predict the noise residual
             noise_pred = self.unet(latent_model_input, t, encoder_hidden_states=text_embeddings).sample
@@ -365,14 +357,9 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, t_index, latents, **extra_step_kwargs).prev_sample
-                # masking
-                init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.LongTensor([t_index]))
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
-                # masking
-                init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.LongTensor([t]))
+            latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
+            # masking
+            init_latents_proper = self.scheduler.add_noise(init_latents_orig, noise, torch.tensor([t]))
 
             latents = (init_latents_proper * mask) + (latents * (1 - mask))
 
diff --git a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
index 0bb0ce440d90..4bd6c2c8bb3e 100644
--- a/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
+++ b/src/diffusers/pipelines/stable_diffusion/pipeline_stable_diffusion_onnx.py
@@ -147,9 +147,7 @@ def __call__(
         # set timesteps
         self.scheduler.set_timesteps(num_inference_steps)
 
-        # if we use LMSDiscreteScheduler, let's make sure latents are multiplied by sigmas
-        if isinstance(self.scheduler, LMSDiscreteScheduler):
-            latents = latents * self.scheduler.sigmas[0]
+        latents = latents * self.scheduler.init_noise_sigma
 
         # prepare extra kwargs for the scheduler step, since not all schedulers have the same signature
         # eta (η) is only used with the DDIMScheduler, it will be ignored for other schedulers.
@@ -163,10 +161,7 @@ def __call__(
         for i, t in enumerate(self.progress_bar(self.scheduler.timesteps)):
             # expand the latents if we are doing classifier free guidance
             latent_model_input = np.concatenate([latents] * 2) if do_classifier_free_guidance else latents
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                sigma = self.scheduler.sigmas[i]
-                # the model input needs to be scaled to match the continuous ODE formulation in K-LMS
-                latent_model_input = latent_model_input / ((sigma**2 + 1) ** 0.5)
+            latent_model_input = self.scheduler.scale_model_input(latent_model_input, t)
 
             # predict the noise residual
             noise_pred = self.unet(
@@ -180,11 +175,7 @@ def __call__(
                 noise_pred = noise_pred_uncond + guidance_scale * (noise_pred_text - noise_pred_uncond)
 
             # compute the previous noisy sample x_t -> x_t-1
-            if isinstance(self.scheduler, LMSDiscreteScheduler):
-                latents = self.scheduler.step(noise_pred, i, latents, **extra_step_kwargs).prev_sample
-            else:
-                latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
-
+            latents = self.scheduler.step(noise_pred, t, latents, **extra_step_kwargs).prev_sample
             latents = np.array(latents)
 
             # call the callback, if provided
diff --git a/src/diffusers/pipelines/stochastic_karras_ve/pipeline_stochastic_karras_ve.py b/src/diffusers/pipelines/stochastic_karras_ve/pipeline_stochastic_karras_ve.py
index 35d06106869e..9e8864b4ca76 100644
--- a/src/diffusers/pipelines/stochastic_karras_ve/pipeline_stochastic_karras_ve.py
+++ b/src/diffusers/pipelines/stochastic_karras_ve/pipeline_stochastic_karras_ve.py
@@ -69,7 +69,7 @@ def __call__(
         model = self.unet
 
         # sample x_0 ~ N(0, sigma_0^2 * I)
-        sample = torch.randn(*shape) * self.scheduler.config.sigma_max
+        sample = torch.randn(*shape) * self.scheduler.init_noise_sigma
         sample = sample.to(self.device)
 
         self.scheduler.set_timesteps(num_inference_steps)
diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 44c7b268cb68..2dc85a93adc9 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -152,10 +152,27 @@ def __init__(
         # whether we use the final alpha of the "non-previous" one.
         self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
         # setable values
         self.num_inference_steps = None
         self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())
 
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+            timestep (`int`, optional): current timestep
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
     def _get_variance(self, timestep, prev_timestep):
         alpha_prod_t = self.alphas_cumprod[timestep]
         alpha_prod_t_prev = self.alphas_cumprod[prev_timestep] if prev_timestep >= 0 else self.final_alpha_cumprod
diff --git a/src/diffusers/schedulers/scheduling_ddpm.py b/src/diffusers/schedulers/scheduling_ddpm.py
index e5a7abfc3797..e1db9079d149 100644
--- a/src/diffusers/schedulers/scheduling_ddpm.py
+++ b/src/diffusers/schedulers/scheduling_ddpm.py
@@ -140,12 +140,29 @@ def __init__(
         self.alphas_cumprod = torch.cumprod(self.alphas, dim=0)
         self.one = torch.tensor(1.0)
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
         # setable values
         self.num_inference_steps = None
         self.timesteps = torch.from_numpy(np.arange(0, num_train_timesteps)[::-1].copy())
 
         self.variance_type = variance_type
 
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+            timestep (`int`, optional): current timestep
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
         Sets the discrete timesteps used for the diffusion chain. Supporting function to be run before inference.
diff --git a/src/diffusers/schedulers/scheduling_karras_ve.py b/src/diffusers/schedulers/scheduling_karras_ve.py
index f8a7d9fe995e..28aad4a65f6f 100644
--- a/src/diffusers/schedulers/scheduling_karras_ve.py
+++ b/src/diffusers/schedulers/scheduling_karras_ve.py
@@ -95,11 +95,28 @@ def __init__(
             take_from=kwargs,
         )
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = sigma_max
+
         # setable values
         self.num_inference_steps: int = None
         self.timesteps: np.IntTensor = None
         self.schedule: torch.FloatTensor = None  # sigma(t_i)
 
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+            timestep (`int`, optional): current timestep
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
     def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.device] = None):
         """
         Sets the continuous timesteps used for the diffusion chain. Supporting function to be run before inference.
diff --git a/src/diffusers/schedulers/scheduling_lms_discrete.py b/src/diffusers/schedulers/scheduling_lms_discrete.py
index 33e9558d9c38..a55811a0629f 100644
--- a/src/diffusers/schedulers/scheduling_lms_discrete.py
+++ b/src/diffusers/schedulers/scheduling_lms_discrete.py
@@ -11,7 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
-
+import warnings
 from dataclasses import dataclass
 from typing import Optional, Tuple, Union
 
@@ -102,11 +102,36 @@ def __init__(
         sigmas = np.concatenate([sigmas[::-1], [0.0]]).astype(np.float32)
         self.sigmas = torch.from_numpy(sigmas)
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = self.sigmas.max()
+
         # setable values
         self.num_inference_steps = None
         timesteps = np.linspace(0, num_train_timesteps - 1, num_train_timesteps, dtype=float)[::-1].copy()
         self.timesteps = torch.from_numpy(timesteps)
         self.derivatives = []
+        self.is_scale_input_called = False
+
+    def scale_model_input(
+        self, sample: torch.FloatTensor, timestep: Union[float, torch.FloatTensor]
+    ) -> torch.FloatTensor:
+        """
+        Scales the denoising model input by `(sigma**2 + 1) ** 0.5` to match the K-LMS algorithm.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+            timestep (`float` or `torch.FloatTensor`): the current timestep in the diffusion chain
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        if isinstance(timestep, torch.Tensor):
+            timestep = timestep.to(self.timesteps.device)
+        step_index = (self.timesteps == timestep).nonzero().item()
+        sigma = self.sigmas[step_index]
+        sample = sample / ((sigma**2 + 1) ** 0.5)
+        self.is_scale_input_called = True
+        return sample
 
     def get_lms_coefficient(self, order, t, current_order):
         """
@@ -154,7 +179,7 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
     def step(
         self,
         model_output: torch.FloatTensor,
-        timestep: int,
+        timestep: Union[float, torch.FloatTensor],
         sample: torch.FloatTensor,
         order: int = 4,
         return_dict: bool = True,
@@ -165,7 +190,7 @@ def step(
 
         Args:
             model_output (`torch.FloatTensor`): direct output from learned diffusion model.
-            timestep (`int`): current discrete timestep in the diffusion chain.
+            timestep (`float`): current timestep in the diffusion chain.
             sample (`torch.FloatTensor`):
                 current instance of sample being created by diffusion process.
             order: coefficient for multi-step inference.
@@ -177,7 +202,21 @@ def step(
             When returning a tuple, the first element is the sample tensor.
 
         """
-        sigma = self.sigmas[timestep]
+        if not isinstance(timestep, float) and not isinstance(timestep, torch.FloatTensor):
+            warnings.warn(
+                f"`LMSDiscreteScheduler` timesteps must be `float` or `torch.FloatTensor`, not {type(timestep)}. "
+                "Make sure to pass one of the `scheduler.timesteps`"
+            )
+        if not self.is_scale_input_called:
+            warnings.warn(
+                "The `scale_model_input` function should be called before `step` to ensure correct denoising. "
+                "See `StableDiffusionPipeline` for a usage example."
+            )
+
+        if isinstance(timestep, torch.Tensor):
+            timestep = timestep.to(self.timesteps.device)
+        step_index = (self.timesteps == timestep).nonzero().item()
+        sigma = self.sigmas[step_index]
 
         # 1. compute predicted original sample (x_0) from sigma-scaled predicted noise
         pred_original_sample = sample - sigma * model_output
@@ -189,8 +228,8 @@ def step(
             self.derivatives.pop(0)
 
         # 3. Compute linear multistep coefficients
-        order = min(timestep + 1, order)
-        lms_coeffs = [self.get_lms_coefficient(order, timestep, curr_order) for curr_order in range(order)]
+        order = min(step_index + 1, order)
+        lms_coeffs = [self.get_lms_coefficient(order, step_index, curr_order) for curr_order in range(order)]
 
         # 4. Compute previous sample based on the derivatives path
         prev_sample = sample + sum(
@@ -206,12 +245,14 @@ def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.IntTensor,
+        timesteps: torch.FloatTensor,
     ) -> torch.FloatTensor:
         sigmas = self.sigmas.to(original_samples.device)
+        schedule_timesteps = self.timesteps.to(original_samples.device)
         timesteps = timesteps.to(original_samples.device)
+        step_indices = [(schedule_timesteps == t).nonzero().item() for t in timesteps]
 
-        sigma = sigmas[timesteps].flatten()
+        sigma = sigmas[step_indices].flatten()
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
diff --git a/src/diffusers/schedulers/scheduling_pndm.py b/src/diffusers/schedulers/scheduling_pndm.py
index 86e9b35ccd8d..f6a6d6153be5 100644
--- a/src/diffusers/schedulers/scheduling_pndm.py
+++ b/src/diffusers/schedulers/scheduling_pndm.py
@@ -129,6 +129,9 @@ def __init__(
 
         self.final_alpha_cumprod = torch.tensor(1.0) if set_alpha_to_one else self.alphas_cumprod[0]
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = 1.0
+
         # For now we only support F-PNDM, i.e. the runge-kutta method
         # For more information on the algorithm please take a look at the paper: https://arxiv.org/pdf/2202.09778.pdf
         # mainly at formula (9), (12), (13) and the Algorithm 2.
@@ -342,6 +345,19 @@ def step_plms(
 
         return SchedulerOutput(prev_sample=prev_sample)
 
+    def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
     def _get_prev_sample(self, sample, timestep, prev_timestep, model_output):
         # See formula (9) of PNDM paper https://arxiv.org/pdf/2202.09778.pdf
         # this function computes x_(t−δ) using the formula of (9)
diff --git a/src/diffusers/schedulers/scheduling_sde_ve.py b/src/diffusers/schedulers/scheduling_sde_ve.py
index 9dda30e360de..cb7f21e6189a 100644
--- a/src/diffusers/schedulers/scheduling_sde_ve.py
+++ b/src/diffusers/schedulers/scheduling_sde_ve.py
@@ -84,11 +84,28 @@ def __init__(
             take_from=kwargs,
         )
 
+        # standard deviation of the initial noise distribution
+        self.init_noise_sigma = sigma_max
+
         # setable values
         self.timesteps = None
 
         self.set_sigmas(num_train_timesteps, sigma_min, sigma_max, sampling_eps)
 
+    def scale_model_input(self, sample: torch.FloatTensor, timestep: Optional[int] = None) -> torch.FloatTensor:
+        """
+        Ensures interchangeability with schedulers that need to scale the denoising model input depending on the
+        current timestep.
+
+        Args:
+            sample (`torch.FloatTensor`): input sample
+            timestep (`int`, optional): current timestep
+
+        Returns:
+            `torch.FloatTensor`: scaled input sample
+        """
+        return sample
+
     def set_timesteps(
         self, num_inference_steps: int, sampling_eps: float = None, device: Union[str, torch.device] = None
     ):
diff --git a/tests/test_scheduler.py b/tests/test_scheduler.py
index 4e968aef70c4..c3d4b9bc76f9 100755
--- a/tests/test_scheduler.py
+++ b/tests/test_scheduler.py
@@ -201,7 +201,7 @@ def recursive_check(tuple_object, dict_object):
                 )
 
         kwargs = dict(self.forward_default_kwargs)
-        num_inference_steps = kwargs.pop("num_inference_steps", None)
+        num_inference_steps = kwargs.pop("num_inference_steps", 50)
 
         for scheduler_class in self.scheduler_classes:
             scheduler_config = self.get_scheduler_config()
@@ -226,6 +226,27 @@ def recursive_check(tuple_object, dict_object):
 
             recursive_check(outputs_tuple, outputs_dict)
 
+    def test_scheduler_public_api(self):
+        for scheduler_class in self.scheduler_classes:
+            scheduler_config = self.get_scheduler_config()
+            scheduler = scheduler_class(**scheduler_config)
+            self.assertTrue(
+                hasattr(scheduler, "init_noise_sigma"),
+                f"{scheduler_class} does not implement a required attribute `init_noise_sigma`",
+            )
+            self.assertTrue(
+                hasattr(scheduler, "scale_model_input"),
+                f"{scheduler_class} does not implement a required class method `scale_model_input(sample, timestep)`",
+            )
+            self.assertTrue(
+                hasattr(scheduler, "step"),
+                f"{scheduler_class} does not implement a required class method `step(...)`",
+            )
+
+            sample = self.dummy_sample
+            scaled_sample = scheduler.scale_model_input(sample, 0.0)
+            self.assertEqual(sample.shape, scaled_sample.shape)
+
 
 class DDPMSchedulerTest(SchedulerCommonTest):
     scheduler_classes = (DDPMScheduler,)
@@ -865,14 +886,14 @@ def test_full_loop_no_noise(self):
         scheduler.set_timesteps(self.num_inference_steps)
 
         model = self.dummy_model()
-        sample = self.dummy_sample_deter * scheduler.sigmas[0]
+        sample = self.dummy_sample_deter * scheduler.init_noise_sigma
 
         for i, t in enumerate(scheduler.timesteps):
-            sample = sample / ((scheduler.sigmas[i] ** 2 + 1) ** 0.5)
+            sample = scheduler.scale_model_input(sample, t)
 
             model_output = model(sample, t)
 
-            output = scheduler.step(model_output, i, sample)
+            output = scheduler.step(model_output, t, sample)
             sample = output.prev_sample
 
         result_sum = torch.sum(torch.abs(sample))