diff --git a/src/diffusers/schedulers/scheduling_deis_multistep.py b/src/diffusers/schedulers/scheduling_deis_multistep.py
index c7a94bce88eb..af9b0381dcc4 100644
--- a/src/diffusers/schedulers/scheduling_deis_multistep.py
+++ b/src/diffusers/schedulers/scheduling_deis_multistep.py
@@ -243,8 +243,8 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
             sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
             sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
 
-        self.sigmas = torch.from_numpy(sigmas).to(device=device)
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.sigmas = torch.from_numpy(sigmas)
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
 
         self.num_inference_steps = len(timesteps)
 
@@ -707,12 +707,12 @@ def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch
         """
         return sample
 
-    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
     def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.FloatTensor,
+        timesteps: torch.IntTensor,
     ) -> torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
@@ -730,7 +730,8 @@ def add_noise(
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
     def __len__(self):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
index 264ee268ae17..726ad138ad84 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep.py
@@ -263,8 +263,8 @@ def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torc
             sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
             sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
 
-        self.sigmas = torch.from_numpy(sigmas).to(device=device)
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.sigmas = torch.from_numpy(sigmas)
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
 
         self.num_inference_steps = len(timesteps)
 
@@ -840,12 +840,11 @@ def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch
         """
         return sample
 
-    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
     def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.FloatTensor,
+        timesteps: torch.IntTensor,
     ) -> torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
@@ -863,7 +862,8 @@ def add_noise(
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
     def __len__(self):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
index 7c740234fa40..c0b286a37060 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_multistep_inverse.py
@@ -274,7 +274,7 @@ def set_timesteps(self, num_inference_steps: int = None, device: Union[str, torc
         _, unique_indices = np.unique(timesteps, return_index=True)
         timesteps = timesteps[np.sort(unique_indices)]
 
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
 
         self.num_inference_steps = len(timesteps)
 
@@ -858,12 +858,12 @@ def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch
         """
         return sample
 
-    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
     def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.FloatTensor,
+        timesteps: torch.IntTensor,
     ) -> torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
@@ -881,7 +881,8 @@ def add_noise(
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
     def __len__(self):
diff --git a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
index 10f7ab34e0a4..6744a68b4c4b 100644
--- a/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
+++ b/src/diffusers/schedulers/scheduling_dpmsolver_singlestep.py
@@ -275,7 +275,7 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
 
         self.sigmas = torch.from_numpy(sigmas).to(device=device)
 
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
         self.model_outputs = [None] * self.config.solver_order
         self.sample = None
 
@@ -870,12 +870,12 @@ def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch
         """
         return sample
 
-    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
     def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.FloatTensor,
+        timesteps: torch.IntTensor,
     ) -> torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
@@ -893,7 +893,8 @@ def add_noise(
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
     def __len__(self):
diff --git a/src/diffusers/schedulers/scheduling_unipc_multistep.py b/src/diffusers/schedulers/scheduling_unipc_multistep.py
index 2dcca2ecaece..2b5bd4fd60db 100644
--- a/src/diffusers/schedulers/scheduling_unipc_multistep.py
+++ b/src/diffusers/schedulers/scheduling_unipc_multistep.py
@@ -254,8 +254,8 @@ def set_timesteps(self, num_inference_steps: int, device: Union[str, torch.devic
             sigma_last = ((1 - self.alphas_cumprod[0]) / self.alphas_cumprod[0]) ** 0.5
             sigmas = np.concatenate([sigmas, [sigma_last]]).astype(np.float32)
 
-        self.sigmas = torch.from_numpy(sigmas).to(device=device)
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.sigmas = torch.from_numpy(sigmas)
+        self.timesteps = torch.from_numpy(timesteps).to(device=device, dtype=torch.int64)
 
         self.num_inference_steps = len(timesteps)
 
@@ -801,12 +801,12 @@ def scale_model_input(self, sample: torch.FloatTensor, *args, **kwargs) -> torch
         """
         return sample
 
-    # Copied from diffusers.schedulers.scheduling_euler_discrete.EulerDiscreteScheduler.add_noise
+    # Copied from diffusers.schedulers.scheduling_dpmsolver_multistep.DPMSolverMultistepScheduler.add_noise
     def add_noise(
         self,
         original_samples: torch.FloatTensor,
         noise: torch.FloatTensor,
-        timesteps: torch.FloatTensor,
+        timesteps: torch.IntTensor,
     ) -> torch.FloatTensor:
         # Make sure sigmas and timesteps have the same device and dtype as original_samples
         sigmas = self.sigmas.to(device=original_samples.device, dtype=original_samples.dtype)
@@ -824,7 +824,8 @@ def add_noise(
         while len(sigma.shape) < len(original_samples.shape):
             sigma = sigma.unsqueeze(-1)
 
-        noisy_samples = original_samples + noise * sigma
+        alpha_t, sigma_t = self._sigma_to_alpha_sigma_t(sigma)
+        noisy_samples = alpha_t * original_samples + sigma_t * noise
         return noisy_samples
 
     def __len__(self):