diff --git a/CHANGELOG.md b/CHANGELOG.md
index a9f13288b59..6ae4db7ede7 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -51,6 +51,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed bug in `Metric._reduce_states(...)` when using `dist_sync_fn="cat"` ([#2226](https://github.com/Lightning-AI/torchmetrics/pull/2226))
 
 
+- Fixed bug in `MetricCollection` when using compute groups and `compute` is called more than once ([#2211](https://github.com/Lightning-AI/torchmetrics/pull/2211))
+
 ## [1.2.0] - 2023-09-22
 
 ### Added
diff --git a/src/torchmetrics/collections.py b/src/torchmetrics/collections.py
index 3a5650b0cae..06b9b7b4c4e 100644
--- a/src/torchmetrics/collections.py
+++ b/src/torchmetrics/collections.py
@@ -304,6 +304,7 @@ def _compute_groups_create_state_ref(self, copy: bool = False) -> None:
                         # Determine if we just should set a reference or a full copy
                         setattr(mi, state, deepcopy(m0_state) if copy else m0_state)
                     mi._update_count = deepcopy(m0._update_count) if copy else m0._update_count
+                    mi._computed = deepcopy(m0._computed) if copy else m0._computed
         self._state_is_copy = copy
 
     def compute(self) -> Dict[str, Any]:
diff --git a/tests/unittests/bases/test_collections.py b/tests/unittests/bases/test_collections.py
index ce4bb1ba8c8..caea6091c28 100644
--- a/tests/unittests/bases/test_collections.py
+++ b/tests/unittests/bases/test_collections.py
@@ -411,7 +411,8 @@ class TestComputeGroups:
             ("prefix_", "_postfix"),
         ],
     )
-    def test_check_compute_groups_correctness(self, metrics, expected, preds, target, prefix, postfix):
+    @pytest.mark.parametrize("with_reset", [True, False])
+    def test_check_compute_groups_correctness(self, metrics, expected, preds, target, prefix, postfix, with_reset):
         """Check that compute groups are formed after initialization and that metrics are correctly computed."""
         if isinstance(metrics, MetricCollection):
             prefix, postfix = None, None  # disable for nested collections
@@ -445,8 +446,9 @@ def test_check_compute_groups_correctness(self, metrics, expected, preds, target
             for key in res_cg:
                 assert torch.allclose(res_cg[key], res_without_cg[key])
 
-            m.reset()
-            m2.reset()
+            if with_reset:
+                m.reset()
+                m2.reset()
 
     @pytest.mark.parametrize("method", ["items", "values", "keys"])
     def test_check_compute_groups_items_and_values(self, metrics, expected, preds, target, method):