timestep scheduling with np.linspace (#8623)

Fixes #8600 

### Description

The `np.linspace` approach generates a descending array that starts
exactly at 999 and ends exactly at 0 (after rounding), ensuring the
scheduler samples the entire intended trajectory.

### Types of changes
<!--- Put an `x` in all the boxes that apply, and remove the not
applicable items -->
- [x] Non-breaking change (fix or new feature that would not break
existing functionality).
- [ ] Breaking change (fix or new feature that would cause existing
functionality to change).
- [ ] New tests added to cover the changes.
- [ ] Integration tests passed locally by running `./runtests.sh -f -u
--net --coverage`.
- [ ] Quick tests passed locally by running `./runtests.sh --quick
--unittests --disttests`.
- [ ] In-line docstrings updated.
- [ ] Documentation updated, tested `make html` command in the `docs/`
folder.

---------

Signed-off-by: ytl0623 <[email protected]>
Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>

Author: ytl0623

monai/networks/schedulers/ddim.py

@@ -117,18 +117,14 @@ def set_timesteps(self, num_inference_steps: int, device: str | torch.device | N
             )
 
         self.num_inference_steps = num_inference_steps
-        step_ratio = self.num_train_timesteps // self.num_inference_steps
-        if self.steps_offset >= step_ratio:
-            raise ValueError(
-                f"`steps_offset`: {self.steps_offset} cannot be greater than or equal to "
-                f"`num_train_timesteps // num_inference_steps : {step_ratio}` as this will cause timesteps to exceed"
-                f" the max train timestep."
-            )
-
-        # creates integer timesteps by multiplying by ratio
-        # casting to int to avoid issues when num_inference_step is power of 3
-        timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].copy().astype(np.int64)
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        if self.steps_offset < 0 or self.steps_offset >= self.num_train_timesteps:
+            raise ValueError(f"`steps_offset`: {self.steps_offset} must be in range [0, {self.num_train_timesteps}).")
+
+        self.timesteps = (
+            torch.linspace((self.num_train_timesteps - 1) - self.steps_offset, 0, num_inference_steps, device=device)
+            .round()
+            .long()
+        )
         self.timesteps += self.steps_offset
 
     def _get_variance(self, timestep: int, prev_timestep: int) -> torch.Tensor:

monai/networks/schedulers/ddpm.py

@@ -31,7 +31,6 @@
 
 from __future__ import annotations
 
-import numpy as np
 import torch
 
 from monai.utils import StrEnum
@@ -122,11 +121,9 @@ def set_timesteps(self, num_inference_steps: int, device: str | torch.device | N
             )
 
         self.num_inference_steps = num_inference_steps
-        step_ratio = self.num_train_timesteps // self.num_inference_steps
-        # creates integer timesteps by multiplying by ratio
-        # casting to int to avoid issues when num_inference_step is power of 3
-        timesteps = (np.arange(0, num_inference_steps) * step_ratio).round()[::-1].astype(np.int64)
-        self.timesteps = torch.from_numpy(timesteps).to(device)
+        self.timesteps = (
+            torch.linspace(self.num_train_timesteps - 1, 0, self.num_inference_steps, device=device).round().long()
+        )
 
     def _get_mean(self, timestep: int, x_0: torch.Tensor, x_t: torch.Tensor) -> torch.Tensor:
         """