diff --git a/src/lightning/pytorch/CHANGELOG.md b/src/lightning/pytorch/CHANGELOG.md
index 3558fe3cadc66..4b25fd8061837 100644
--- a/src/lightning/pytorch/CHANGELOG.md
+++ b/src/lightning/pytorch/CHANGELOG.md
@@ -20,6 +20,10 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 -
 
+### Fixed
+
+- Fix `StochasticWeightAveraging` with infinite epochs ([#21396](https://github.com/Lightning-AI/pytorch-lightning/pull/21396))
+
 
 ## [2.6.0] - 2025-11-28
 
diff --git a/src/lightning/pytorch/callbacks/stochastic_weight_avg.py b/src/lightning/pytorch/callbacks/stochastic_weight_avg.py
index 79c5423c54084..9b051b96d0027 100644
--- a/src/lightning/pytorch/callbacks/stochastic_weight_avg.py
+++ b/src/lightning/pytorch/callbacks/stochastic_weight_avg.py
@@ -139,6 +139,8 @@ def swa_start(self) -> int:
 
     @property
     def swa_end(self) -> int:
+        if self._max_epochs == -1:
+            return float("inf")  # type: ignore[return-value]
         return self._max_epochs - 1  # 0-based
 
     @staticmethod
@@ -163,12 +165,17 @@ def on_fit_start(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule") -
 
         assert trainer.max_epochs is not None
         if isinstance(self._swa_epoch_start, float):
+            if trainer.max_epochs == -1:
+                raise MisconfigurationException(
+                    "SWA with `swa_epoch_start` as a float is not supported when `max_epochs=-1`. "
+                    "Please provide `swa_epoch_start` as an integer."
+                )
             self._swa_epoch_start = int(trainer.max_epochs * self._swa_epoch_start)
 
         self._model_contains_batch_norm = self.pl_module_contains_batch_norm(pl_module)
 
         self._max_epochs = trainer.max_epochs
-        if self._model_contains_batch_norm:
+        if self._model_contains_batch_norm and trainer.max_epochs != -1:
             # virtually increase max_epochs to perform batch norm update on latest epoch.
             assert trainer.fit_loop.max_epochs is not None
             trainer.fit_loop.max_epochs += 1
@@ -243,7 +250,7 @@ def on_train_epoch_start(self, trainer: "pl.Trainer", pl_module: "pl.LightningMo
             self._latest_update_epoch = trainer.current_epoch
 
         # Note: No > here in case the callback is saved with the model and training continues
-        if trainer.current_epoch == self.swa_end + 1:
+        if self._max_epochs != -1 and trainer.current_epoch == self.swa_end + 1:
             # Transfer weights from average model to pl_module
             assert self._average_model is not None
             self.transfer_weights(self._average_model, pl_module)
@@ -267,17 +274,17 @@ def on_train_epoch_end(self, trainer: "pl.Trainer", *args: Any) -> None:
     @override
     def on_train_end(self, trainer: "pl.Trainer", pl_module: "pl.LightningModule") -> None:
         # the trainer increases the current epoch before this hook is called
-        if self._model_contains_batch_norm and trainer.current_epoch - 1 == self.swa_end + 1:
+        if self._model_contains_batch_norm and self._max_epochs != -1 and trainer.current_epoch - 1 == self.swa_end + 1:
             # BatchNorm epoch update. Reset state
             trainer.accumulate_grad_batches = self._accumulate_grad_batches
             trainer.fit_loop.max_batches -= 1
             assert trainer.fit_loop.max_epochs is not None
             trainer.fit_loop.max_epochs -= 1
             self.reset_momenta()
-        elif trainer.current_epoch - 1 == self.swa_end:
-            # Last SWA epoch. Transfer weights from average model to pl_module
-            assert self._average_model is not None
-            self.transfer_weights(self._average_model, pl_module)
+        elif trainer.current_epoch - 1 == self.swa_end or self._max_epochs == -1:
+            # Last SWA epoch or infinite training. Transfer weights from average model to pl_module
+            if self._average_model is not None:
+                self.transfer_weights(self._average_model, pl_module)
 
     @staticmethod
     def transfer_weights(src_pl_module: "pl.LightningModule", dst_pl_module: "pl.LightningModule") -> None:
diff --git a/tests/tests_pytorch/callbacks/test_stochastic_weight_avg.py b/tests/tests_pytorch/callbacks/test_stochastic_weight_avg.py
index c63dd4e5c2ac9..242679b7d559c 100644
--- a/tests/tests_pytorch/callbacks/test_stochastic_weight_avg.py
+++ b/tests/tests_pytorch/callbacks/test_stochastic_weight_avg.py
@@ -387,5 +387,35 @@ def test_misconfiguration_error_with_sharded_model(tmp_path, strategy: str):
         trainer.fit(model)
 
 
+def test_swa_with_infinite_epochs_and_batchnorm(tmp_path):
+    """Test that SWA works correctly with max_epochs=-1 (infinite training) and BatchNorm."""
+    model = SwaTestModel(batchnorm=True)
+    swa_callback = StochasticWeightAveraging(swa_lrs=0.1, swa_epoch_start=2)
+
+    trainer = Trainer(
+        default_root_dir=tmp_path,
+        enable_progress_bar=False,
+        enable_model_summary=False,
+        max_epochs=-1,
+        max_steps=30,  # Use max_steps as stopping condition
+        limit_train_batches=5,
+        limit_val_batches=0,
+        callbacks=[swa_callback],
+        logger=False,
+    )
+    assert trainer.max_epochs == -1
+    assert trainer.fit_loop.max_epochs == -1
+
+    trainer.fit(model)
+    assert trainer.current_epoch >= 5
+    assert trainer.global_step == 30
+    assert trainer.max_epochs == -1
+
+    # Verify SWA was actually applied (update_parameters should have been called)
+    # SWA starts at epoch 2, so with 6 epochs (0-5), we should have 4 updates (epochs 2, 3, 4, 5)
+    assert swa_callback.n_averaged is not None
+    assert swa_callback.n_averaged > 0, "SWA should have updated parameters"
+
+
 def _backward_patch(trainer: Trainer) -> AbstractContextManager:
     return mock.patch.object(Strategy, "backward", wraps=trainer.strategy.backward)