diff --git a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
index 7b207f782079..1e285183c9bf 100644
--- a/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
+++ b/src/diffusers/schedulers/scheduling_flow_match_euler_discrete.py
@@ -407,6 +407,15 @@ def index_for_timestep(
 
         indices = (schedule_timesteps == timestep).nonzero()
 
+        if indices.numel() == 0:
+            # `schedule_timesteps` is derived from `sigmas * num_train_timesteps` and is stored in float32,
+            # so values that are conceptually integers (e.g. `254`) can carry a small rounding error
+            # (e.g. `254.00001`). An exact `==` lookup then misses them, which happens in particular for the
+            # training path of `scale_noise`/`add_noise` where integer timesteps are passed in. Fall back to a
+            # tolerance-based match so these timesteps resolve to their index instead of raising an `IndexError`.
+            timestep = torch.as_tensor(timestep, dtype=schedule_timesteps.dtype, device=schedule_timesteps.device)
+            indices = torch.isclose(schedule_timesteps, timestep).nonzero()
+
         # The sigma index that is taken for the **very** first `step`
         # is always the second index (or the last index if there is only 1)
         # This way we can ensure we don't accidentally skip a sigma in
diff --git a/tests/schedulers/test_scheduler_flow_match_euler.py b/tests/schedulers/test_scheduler_flow_match_euler.py
new file mode 100644
index 000000000000..34dbc0d1f0ca
--- /dev/null
+++ b/tests/schedulers/test_scheduler_flow_match_euler.py
@@ -0,0 +1,58 @@
+import unittest
+
+import torch
+
+from diffusers import FlowMatchEulerDiscreteScheduler
+
+from ..testing_utils import torch_device
+
+
+class FlowMatchEulerDiscreteSchedulerTest(unittest.TestCase):
+    def test_index_for_timestep_handles_float_precision(self):
+        # `timesteps` is derived from `sigmas * num_train_timesteps` in float32, so conceptually integer
+        # timesteps can carry a small rounding error (e.g. `254.00001`). `index_for_timestep` must still
+        # resolve them instead of raising an `IndexError` from an empty exact-equality lookup. See
+        # https://github.com/huggingface/diffusers/issues/11749.
+        scheduler = FlowMatchEulerDiscreteScheduler()
+        timesteps = scheduler.timesteps.to(torch_device)
+
+        # locate an entry that is not bit-exact to its rounded integer value
+        rounded = timesteps.round()
+        mismatched = (timesteps != rounded).nonzero()
+        self.assertGreater(mismatched.numel(), 0, "expected at least one timestep with float rounding error")
+        index = int(mismatched[0])
+        integer_timestep = rounded[index]
+
+        self.assertFalse(torch.equal(timesteps[index], integer_timestep))
+        self.assertEqual(scheduler.index_for_timestep(integer_timestep, timesteps), index)
+
+    def test_index_for_timestep_matches_exact_value(self):
+        # an exact element of the schedule must still resolve to its own index (no drift to a neighbor).
+        scheduler = FlowMatchEulerDiscreteScheduler()
+        timesteps = scheduler.timesteps.to(torch_device)
+
+        for index in (0, len(timesteps) // 2, len(timesteps) - 1):
+            self.assertEqual(scheduler.index_for_timestep(timesteps[index], timesteps), index)
+
+    def test_index_for_timestep_rejects_unknown_timestep(self):
+        # a value that is not in the schedule (beyond float tolerance) must not be silently matched.
+        scheduler = FlowMatchEulerDiscreteScheduler()
+        timesteps = scheduler.timesteps.to(torch_device)
+
+        unknown = (timesteps[0] + timesteps[1]) / 2  # halfway between two steps
+        with self.assertRaises(IndexError):
+            scheduler.index_for_timestep(unknown, timesteps)
+
+    def test_scale_noise_with_integer_timesteps(self):
+        # the training path of `scale_noise` (`begin_index is None`) is commonly called with integer
+        # timesteps; it must not raise from the float-precision lookup. See issue #11749.
+        scheduler = FlowMatchEulerDiscreteScheduler()
+        self.assertIsNone(scheduler.begin_index)
+
+        sample = torch.randn(2, 4, 8, 8).to(torch_device)
+        noise = torch.randn_like(sample)
+        timesteps = torch.tensor([254, 500], device=torch_device)
+
+        scaled = scheduler.scale_noise(sample, timesteps, noise)
+        self.assertEqual(scaled.shape, sample.shape)
+        self.assertTrue(torch.isfinite(scaled).all())