diff --git a/pytorch_lightning/loops/batch/training_batch_loop.py b/pytorch_lightning/loops/batch/training_batch_loop.py
index 180bd5889251e..9328ddd9080f6 100644
--- a/pytorch_lightning/loops/batch/training_batch_loop.py
+++ b/pytorch_lightning/loops/batch/training_batch_loop.py
@@ -14,6 +14,7 @@
 
 from collections import OrderedDict
 from contextlib import contextmanager
+from copy import copy
 from functools import partial, update_wrapper
 from typing import Any, Callable, Dict, Generator, List, Mapping, Optional, Tuple
 
@@ -146,12 +147,12 @@ def advance(self, batch, batch_idx, dataloader_idx):
 
                 result = self._run_optimization(batch_idx, split_batch, opt_idx, optimizer)
                 if result:
-                    self.batch_outputs[opt_idx].append(result.training_step_output)
+                    self.batch_outputs[opt_idx].append(copy(result.training_step_output))
         else:
             # in manual optimization, there is no looping over optimizers
             result = self._run_optimization(batch_idx, split_batch)
             if result:
-                self.batch_outputs[0].append(result.training_step_output)
+                self.batch_outputs[0].append(copy(result.training_step_output))
 
     def teardown(self) -> None:
         # release memory
diff --git a/tests/trainer/loops/test_training_loop_flow_dict.py b/tests/trainer/loops/test_training_loop_flow_dict.py
index f064dacb78844..ab4d7979bbf39 100644
--- a/tests/trainer/loops/test_training_loop_flow_dict.py
+++ b/tests/trainer/loops/test_training_loop_flow_dict.py
@@ -108,7 +108,7 @@ def training_step(self, batch, batch_idx):
             acc = acc + batch_idx
 
             self.training_step_called = True
-            out = {"loss": acc, "random_things": [1, "a", torch.tensor(2)]}
+            out = {"loss": acc, "random_things": [1, "a", torch.tensor(2)], "batch_idx": batch_idx}
             return out
 
         def training_epoch_end(self, outputs):
@@ -116,11 +116,13 @@ def training_epoch_end(self, outputs):
 
             # verify we saw the current num of batches
             assert len(outputs) == 2
+            assert len({id(output) for output in outputs}) == 2
+            assert [output["batch_idx"] for output in outputs] == [0, 1]
 
             for b in outputs:
                 assert isinstance(b, dict)
                 assert self.count_num_graphs(b) == 0
-                assert {"random_things", "loss"} == set(b.keys())
+                assert {"random_things", "loss", "batch_idx"} == set(b.keys())
 
         def backward(self, loss, optimizer, optimizer_idx):
             return LightningModule.backward(self, loss, optimizer, optimizer_idx)
@@ -155,7 +157,7 @@ def training_step(self, batch, batch_idx):
             acc = acc + batch_idx
 
             self.training_step_called = True
-            self.out = {"loss": acc, "random_things": [1, "a", torch.tensor(2)]}
+            self.out = {"loss": acc, "random_things": [1, "a", torch.tensor(2)], "batch_idx": batch_idx}
             return self.out
 
         def training_step_end(self, tr_step_output):
@@ -169,11 +171,13 @@ def training_epoch_end(self, outputs):
 
             # verify we saw the current num of batches
             assert len(outputs) == 2
+            assert len({id(output) for output in outputs}) == 2
+            assert [output["batch_idx"] for output in outputs] == [0, 1]
 
             for b in outputs:
                 assert isinstance(b, dict)
                 assert self.count_num_graphs(b) == 0
-                assert {"random_things", "loss"} == set(b.keys())
+                assert {"random_things", "loss", "batch_idx"} == set(b.keys())
 
         def backward(self, loss, optimizer, optimizer_idx):
             return LightningModule.backward(self, loss, optimizer, optimizer_idx)
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index e0f909a7b8b35..ed7a274569d79 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -11,6 +11,7 @@
 # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 # See the License for the specific language governing permissions and
 # limitations under the License.
+import gc
 import logging
 import math
 import os
@@ -1872,13 +1873,22 @@ def on_epoch_start(self, trainer, *_):
     assert list(trainer.optimizers[0].state.values())[0]["exp_avg_sq"].device == torch.device("cpu")
     assert trainer.callback_metrics["train_loss"].device == torch.device("cpu")
 
+    # before measuring the memory force release any leftover allocations, including CUDA tensors
+    gc.collect()
     memory_1 = torch.cuda.memory_allocated(0)
+    assert memory_1 == initial
+
     deepcopy(trainer)
+
+    # before measuring the memory force release any leftover allocations, including CUDA tensors
+    gc.collect()
     memory_2 = torch.cuda.memory_allocated(0)
-    assert memory_1 == memory_2 == initial
+    assert memory_2 == initial
 
     trainer_2 = Trainer(**trainer_kwargs)
     trainer_2.fit(model)
-    memory_3 = torch.cuda.memory_allocated(0)
 
-    assert initial == memory_1 == memory_3
+    # before measuring the memory force release any leftover allocations, including CUDA tensors
+    gc.collect()
+    memory_3 = torch.cuda.memory_allocated(0)
+    assert memory_3 == initial