diff --git a/CHANGELOG.md b/CHANGELOG.md
index ddaf4288a0202..6ca4a599978d9 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -297,6 +297,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 - Fixed training loop total batch counter when accumulate grad batches was enabled ([#7692](https://github.com/PyTorchLightning/pytorch-lightning/pull/7692))
 
 
+- Fixed a bug where skipping an optimizer while using amp causes amp to trigger an assertion error ([#7975](https://github.com/PyTorchLightning/pytorch-lightning/pull/7975))
+
+
 ## [1.3.2] - 2021-05-18
 
 ### Changed
diff --git a/pytorch_lightning/plugins/precision/native_amp.py b/pytorch_lightning/plugins/precision/native_amp.py
index 9f2b63f014da1..e25f46d9ec239 100644
--- a/pytorch_lightning/plugins/precision/native_amp.py
+++ b/pytorch_lightning/plugins/precision/native_amp.py
@@ -83,19 +83,21 @@ def pre_optimizer_step(
                 f"native PyTorch amp and lbfgs are not compatible (optimizer {optimizer_idx})."
                 " To request, please file a Github issue in PyTorch and tag @mcarilli"
             )
-        lambda_closure()
 
         if not pl_module.automatic_optimization:
             self.scaler.unscale_(optimizer)
             pl_module.trainer.call_hook("on_after_backward")
+            self.scaler.step(optimizer)
+            self.scaler.update()
+        else:
+            result = lambda_closure()
+            # lambda_closure returning None indicates that backward has been skipped
+            if result is not None:
+                self.scaler.step(optimizer)
+                self.scaler.update()
 
         return False
 
-    def post_optimizer_step(self, optimizer: Optimizer, optimizer_idx: int) -> None:
-        """Updates the GradScaler"""
-        self.scaler.step(optimizer)
-        self.scaler.update()
-
     @contextmanager
     def train_step_context(self) -> Generator[None, None, None]:
         """Enable autocast context"""
diff --git a/tests/plugins/test_amp_plugins.py b/tests/plugins/test_amp_plugins.py
index 6d0dbed2cf88b..cf58427b071ce 100644
--- a/tests/plugins/test_amp_plugins.py
+++ b/tests/plugins/test_amp_plugins.py
@@ -99,6 +99,47 @@ def test_amp_gradient_unscale(tmpdir, accum: int):
     trainer.fit(model)
 
 
+@RunIf(min_gpus=1, amp_native=True)
+def test_amp_skip_optimizer(tmpdir):
+    """
+    Test that optimizers can be skipped when using amp
+    """
+
+    class CustomBoringModel(BoringModel):
+
+        def __init__(self):
+            super().__init__()
+            self.layer1 = torch.nn.Linear(32, 32)
+            self.layer2 = torch.nn.Linear(32, 2)
+
+        def forward(self, x: torch.Tensor):
+            x = self.layer1(x)
+            x = self.layer2(x)
+            return x
+
+        def training_step(self, batch, batch_idx, optimizer_idx):
+            if optimizer_idx == 1:
+                return None
+            output = self(batch)
+            return self.loss(batch, output)
+
+        def configure_optimizers(self):
+            return [
+                torch.optim.SGD(self.layer1.parameters(), lr=0.1),
+                torch.optim.SGD(self.layer2.parameters(), lr=0.1),
+            ]
+
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        gpus=1,
+        fast_dev_run=1,
+        amp_backend='native',
+        precision=16,
+    )
+    model = CustomBoringModel()
+    trainer.fit(model)
+
+
 @RunIf(min_gpus=2, amp_apex=True, special=True)
 @pytest.mark.parametrize("amp_level", ['O2'])
 def test_amp_apex_ddp_fit(amp_level, tmpdir):