diff --git a/src/lightning/fabric/plugins/precision/amp.py b/src/lightning/fabric/plugins/precision/amp.py
index d5fc1f0c1cc2a..429d891a9169e 100644
--- a/src/lightning/fabric/plugins/precision/amp.py
+++ b/src/lightning/fabric/plugins/precision/amp.py
@@ -88,9 +88,11 @@ def optimizer_step(
             return super().optimizer_step(optimizer, **kwargs)
         if isinstance(optimizer, LBFGS):
             raise TypeError("AMP and the LBFGS optimizer are not compatible.")
+        previous_scale = self.scaler.get_scale()
         # note: the scaler will skip the `optimizer.step` if nonfinite gradients are found
         step_output = self.scaler.step(optimizer, **kwargs)  # type: ignore[arg-type]
         self.scaler.update()
+        optimizer._skip_next_scheduler_step = self.scaler.get_scale() < previous_scale
         return step_output
 
     @override
diff --git a/src/lightning/pytorch/loops/training_epoch_loop.py b/src/lightning/pytorch/loops/training_epoch_loop.py
index 3d01780b705fe..86d9f4819d93c 100644
--- a/src/lightning/pytorch/loops/training_epoch_loop.py
+++ b/src/lightning/pytorch/loops/training_epoch_loop.py
@@ -498,6 +498,9 @@ def _update_learning_rates(self, interval: str, update_plateau_schedulers: bool)
                         )
                         continue
 
+                if getattr(self.trainer.optimizers[config.opt_idx], "_skip_next_scheduler_step", False):
+                    continue
+
                 self.scheduler_progress.increment_ready()
 
                 # update LR
diff --git a/src/lightning/pytorch/plugins/precision/amp.py b/src/lightning/pytorch/plugins/precision/amp.py
index 5ea62233e1f69..5b63f59ee7b44 100644
--- a/src/lightning/pytorch/plugins/precision/amp.py
+++ b/src/lightning/pytorch/plugins/precision/amp.py
@@ -92,8 +92,10 @@ def optimizer_step(  # type: ignore[override]
         # in manual optimization, the closure does not return a value
         if not skip_unscaling:
             # note: the scaler will skip the `optimizer.step` if nonfinite gradients are found
-            step_output = self.scaler.step(optimizer, **kwargs)  # type: ignore[arg-type]
+            previous_scale = self.scaler.get_scale()
+            step_output = self.scaler.step(optimizer, **kwargs)
             self.scaler.update()
+            optimizer._skip_next_scheduler_step = self.scaler.get_scale() < previous_scale
             return step_output
         return closure_result
 
diff --git a/tests/tests_fabric/plugins/precision/test_amp.py b/tests/tests_fabric/plugins/precision/test_amp.py
index 73507f085936b..e3ca8fc013255 100644
--- a/tests/tests_fabric/plugins/precision/test_amp.py
+++ b/tests/tests_fabric/plugins/precision/test_amp.py
@@ -70,6 +70,7 @@ def test_amp_precision_backward():
 def test_amp_precision_optimizer_step_with_scaler():
     precision = MixedPrecision(precision="16-mixed", device="cuda")
     precision.scaler = Mock()
+    precision.scaler.get_scale = Mock(return_value=1.0)
     optimizer = Mock()
 
     precision.optimizer_step(optimizer, keyword="arg")
diff --git a/tests/tests_pytorch/models/test_hooks.py b/tests/tests_pytorch/models/test_hooks.py
index e943d0533cab5..8aff09e76bc54 100644
--- a/tests/tests_pytorch/models/test_hooks.py
+++ b/tests/tests_pytorch/models/test_hooks.py
@@ -303,11 +303,7 @@ def _auto_train_batch(trainer, model, batches, device, current_epoch=0, current_
                     "name": "optimizer_step",
                     "args": (current_epoch, i, ANY, ANY),
                 },
-                *(
-                    [{"name": "lr_scheduler_step", "args": (ANY, None)}]
-                    if i == (trainer.num_training_batches - 1)
-                    else []
-                ),
+                *([{"name": "lr_scheduler_step", "args": ANY}] if i == (trainer.num_training_batches - 1) else []),
                 {"name": "Callback.on_train_batch_end", "args": (trainer, model, {"loss": ANY}, ANY, i)},
                 {"name": "on_train_batch_end", "args": ({"loss": ANY}, ANY, i)},
             ])