diff --git a/src/diffusers/schedulers/scheduling_ddim.py b/src/diffusers/schedulers/scheduling_ddim.py
index 89d90ba60a..5945b0c1ea 100644
--- a/src/diffusers/schedulers/scheduling_ddim.py
+++ b/src/diffusers/schedulers/scheduling_ddim.py
@@ -129,6 +129,10 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
             an offset added to the inference steps. You can use a combination of `offset=1` and
             `set_alpha_to_one=False`, to make the last step use step 0 for the previous alpha product, as done in
             stable diffusion.
+        prediction_type (`Literal["epsilon", "sample", "v"]`, optional):
+                prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
+                process), `sample` (directly predicting the noisy sample`) or `v` (see section 2.4
+                https://imagen.research.google/video/paper.pdf)
 
     """
 
@@ -181,8 +185,12 @@ class DDIMScheduler(SchedulerMixin, ConfigMixin):
         # For the final step, there is no previous alphas_cumprod because we are already at 0
         # `set_alpha_to_one` decides whether we set this parameter simply to one or
         # 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]
-        self.final_sigma = torch.tensor(0.0) if set_alpha_to_one else self.sigmas[0]
+        if set_alpha_to_one:
+            self.final_alpha_cumprod = torch.tensor(1.0)
+            self.final_sigma = torch.tensor(0.0)  # TODO rename set_alpha_to_one for something general with sigma=0
+        else:
+            self.final_alpha_cumprod = self.alphas_cumprod[0]
+            self.final_sigma = self.sigmas[0] if prediction_type == "v" else None
 
         # standard deviation of the initial noise distribution
         self.init_noise_sigma = 1.0
diff --git a/src/diffusers/schedulers/scheduling_ddpm.py b/src/diffusers/schedulers/scheduling_ddpm.py
index d403c4f595..9931d8c143 100644
--- a/src/diffusers/schedulers/scheduling_ddpm.py
+++ b/src/diffusers/schedulers/scheduling_ddpm.py
@@ -114,6 +114,8 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
                 prediction type of the scheduler function, one of `epsilon` (predicting the noise of the diffusion
                 process), `sample` (directly predicting the noisy sample`) or `v` (see section 2.4
                 https://imagen.research.google/video/paper.pdf)
+        predict_epsilon (`bool`, default `True`):
+            depreciated flag (removing v0.10.0) for epsilon vs. direct sample prediction.
     """
 
     _compatible_classes = [
@@ -136,6 +138,7 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         variance_type: str = "fixed_small",
         clip_sample: bool = True,
         prediction_type: Literal["epsilon", "sample", "v"] = "epsilon",
+        predict_epsilon: bool = True,
     ):
         if trained_betas is not None:
             self.betas = torch.from_numpy(trained_betas)
@@ -265,8 +268,8 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
         if self.variance_type == "v_diffusion":
             assert self.prediction_type == "v", "Need to use v prediction with v_diffusion"
         message = (
-            "Please make sure to instantiate your scheduler with `predict_epsilon` instead. E.g. `scheduler ="
-            " DDPMScheduler.from_config(<model_id>, predict_epsilon=True)`."
+            "Please make sure to instantiate your scheduler with `prediction_type=epsilon` instead. E.g. `scheduler ="
+            " DDPMScheduler.from_config(<model_id>, prediction_type=epsilon)`."
         )
         predict_epsilon = deprecate("predict_epsilon", "0.10.0", message, take_from=kwargs)
         if predict_epsilon is not None and predict_epsilon != self.config.predict_epsilon:
@@ -293,11 +296,14 @@ class DDPMScheduler(SchedulerMixin, ConfigMixin):
                 sample * self.sqrt_alphas_cumprod[timestep]
                 - model_output * self.sqrt_one_minus_alphas_cumprod[timestep]
             )
+
+        # not check on predict_epsilon for depreciation flag above
+        elif self.prediction_type == "sample" or not self.config.predict_epsilon:
+            pred_original_sample = model_output
+
         elif self.prediction_type == "epsilon" or self.config.predict_epsilon:
             pred_original_sample = (sample - beta_prod_t ** (0.5) * model_output) / alpha_prod_t ** (0.5)
 
-        elif self.prediction_type == "sample":
-            pred_original_sample = model_output
         else:
             raise ValueError(
                 f"prediction_type given as {self.prediction_type} must be one of `epsilon`, `sample`, or `v`"
diff --git a/tests/test_scheduler.py b/tests/test_scheduler.py
index ab52171511..5a19d1059c 100755
--- a/tests/test_scheduler.py
+++ b/tests/test_scheduler.py
@@ -393,9 +393,9 @@ class DDPMSchedulerTest(SchedulerCommonTest):
         for clip_sample in [True, False]:
             self.check_over_configs(clip_sample=clip_sample)
 
-    def test_predict_epsilon(self):
-        for predict_epsilon in [True, False]:
-            self.check_over_configs(predict_epsilon=predict_epsilon)
+    def test_prediction_type(self):
+        for prediction_type in ["epsilon", "sample", "v"]:
+            self.check_over_configs(prediction_type=prediction_type)
 
     def test_deprecated_epsilon(self):
         deprecate("remove this test", "0.10.0", "remove")
@@ -407,7 +407,7 @@ class DDPMSchedulerTest(SchedulerCommonTest):
         time_step = 4
 
         scheduler = scheduler_class(**scheduler_config)
-        scheduler_eps = scheduler_class(predict_epsilon=False, **scheduler_config)
+        scheduler_eps = scheduler_class(prediction_type="sample", **scheduler_config)
 
         kwargs = {}
         if "generator" in set(inspect.signature(scheduler.step).parameters.keys()):