diff --git a/ignite/metrics/epoch_metric.py b/ignite/metrics/epoch_metric.py
index 672f843d1697..b9a30ddaad0b 100644
--- a/ignite/metrics/epoch_metric.py
+++ b/ignite/metrics/epoch_metric.py
@@ -1,6 +1,6 @@
 import warnings
-from collections.abc import Callable
-from typing import cast
+from collections.abc import Callable, Mapping, Sequence
+from typing import Union, cast
 
 import torch
 
@@ -8,6 +8,9 @@
 from ignite.exceptions import NotComputableError
 from ignite.metrics.metric import Metric, reinit__is_reduced
 
+# Supported return types for ``EpochMetric``'s ``compute_fn``.
+EpochMetricOutput = Union[int, float, torch.Tensor, Sequence, Mapping]
+
 __all__ = ["EpochMetric"]
 
 
@@ -30,7 +33,13 @@ class EpochMetric(Metric):
 
     Args:
         compute_fn: a callable which receives two tensors as the `predictions` and `targets`
-            and returns a scalar. Input tensors will be on specified ``device`` (see arg below).
+            and returns the computed metric. Supported return types are: ``int``, ``float``,
+            ``torch.Tensor``, a ``Sequence`` (tuple/list) of these, or a ``Mapping`` (dict) with
+            string keys and these values. An unsupported return type raises a ``TypeError``.
+            Note: in distributed configuration (``world_size > 1``), only scalar and
+            ``torch.Tensor`` outputs are broadcast across processes; tuple/list/mapping outputs
+            are supported only when ``world_size == 1``. Input tensors will be on specified
+            ``device`` (see arg below).
         output_transform: a callable that is used to transform the
             :class:`~ignite.engine.engine.Engine`'s ``process_function``'s output into the
             form expected by the metric. This can be useful if, for example, you have a multi-output model and
@@ -93,7 +102,7 @@ def __init__(
     def reset(self) -> None:
         self._predictions: list[torch.Tensor] = []
         self._targets: list[torch.Tensor] = []
-        self._result: float | None = None
+        self._result: EpochMetricOutput | None = None
 
     def _check_shape(self, output: tuple[torch.Tensor, torch.Tensor]) -> None:
         y_pred, y = output
@@ -142,7 +151,27 @@ def update(self, output: tuple[torch.Tensor, torch.Tensor]) -> None:
             except Exception as e:
                 warnings.warn(f"Probably, there can be a problem with `compute_fn`:\n {e}.", EpochMetricWarning)
 
-    def compute(self) -> float:
+    def _check_output_type(self, result: EpochMetricOutput) -> None:
+        # Recursively validate that compute_fn's output is a supported type. ``str``/``bytes``
+        # are rejected explicitly since ``str`` is itself a ``Sequence``.
+        if isinstance(result, (int, float, torch.Tensor)):
+            return
+        if isinstance(result, Mapping):
+            for key, value in result.items():
+                if not isinstance(key, str):
+                    raise TypeError(f"compute_fn output mapping keys should be str, but given {type(key)}.")
+                self._check_output_type(value)
+            return
+        if isinstance(result, Sequence) and not isinstance(result, (str, bytes)):
+            for value in result:
+                self._check_output_type(value)
+            return
+        raise TypeError(
+            f"compute_fn output type {type(result)} is not supported. Supported types are: "
+            "int, float, torch.Tensor, a Sequence of these, or a Mapping with str keys and these values."
+        )
+
+    def compute(self) -> EpochMetricOutput:
         if len(self._predictions) < 1 or len(self._targets) < 1:
             raise NotComputableError(f"{type(self).__name__} must have at least one example before it can be computed.")
 
@@ -156,14 +185,48 @@ def compute(self) -> float:
                 _prediction_tensor = cast(torch.Tensor, idist.all_gather(_prediction_tensor))
                 _target_tensor = cast(torch.Tensor, idist.all_gather(_target_tensor))
 
-            self._result = 0.0
+            result: EpochMetricOutput = 0.0
             if idist.get_rank() == 0:
                 # Run compute_fn on zero rank only
-                self._result = self.compute_fn(_prediction_tensor, _target_tensor)
+                result = self.compute_fn(_prediction_tensor, _target_tensor)
 
             if ws > 1:
-                # broadcast result to all processes
-                self._result = cast(float, idist.broadcast(self._result, src=0))
+                # All ranks must take the same path through the collective calls below, otherwise
+                # they would deadlock on mismatched broadcasts. Only rank 0 holds the real result,
+                # so it classifies the result and shares a status code with every rank *before*
+                # broadcasting the result itself. Type/validation problems are surfaced through the
+                # same mechanism so that every rank raises the same exception.
+                _BROADCASTABLE, _UNSUPPORTED_CONTAINER, _UNSUPPORTED_TYPE = 0, 1, 2
+                status = _BROADCASTABLE
+                if idist.get_rank() == 0 and not isinstance(result, (int, float, torch.Tensor)):
+                    try:
+                        self._check_output_type(result)
+                        status = _UNSUPPORTED_CONTAINER
+                    except TypeError:
+                        status = _UNSUPPORTED_TYPE
+                status = int(idist.broadcast(status, src=0))
+
+                if status == _UNSUPPORTED_TYPE:
+                    # Every rank raises the same error; no result broadcast is attempted.
+                    raise TypeError(
+                        "compute_fn output type is not supported. Supported types are: int, float, "
+                        "torch.Tensor, a Sequence of these, or a Mapping with str keys and these values."
+                    )
+                if status == _UNSUPPORTED_CONTAINER:
+                    # Every rank raises the same error; no result broadcast is attempted.
+                    raise NotImplementedError(
+                        "Distributed broadcast of tuple/list/mapping compute_fn outputs is not supported yet. "
+                        "Such outputs are currently supported only in non-distributed (world_size == 1) "
+                        "configuration."
+                    )
+
+                # status == _BROADCASTABLE: every rank performs the matching result broadcast.
+                result = cast(EpochMetricOutput, idist.broadcast(result, src=0, safe_mode=True))
+            else:
+                # Single process: validate directly and surface unsupported types as TypeError.
+                self._check_output_type(result)
+
+            self._result = result
 
         return self._result
 
diff --git a/tests/ignite/metrics/test_epoch_metric.py b/tests/ignite/metrics/test_epoch_metric.py
index 5bbb2e2307cc..0b11b11c68d3 100644
--- a/tests/ignite/metrics/test_epoch_metric.py
+++ b/tests/ignite/metrics/test_epoch_metric.py
@@ -211,3 +211,153 @@ def compute_fn(y_preds, y_targets):
     assert torch.equal(em._targets[0].cpu(), output1[1].cpu())
     assert torch.equal(em._targets[1].cpu(), output2[1].cpu())
     assert em.compute() == 0.0
+
+
+def test_epoch_metric_compute_fn_tensor_output():
+    """Test EpochMetric with compute_fn returning a tensor."""
+
+    def compute_fn(y_preds, y_targets):
+        return torch.mean(((y_preds - y_targets.type_as(y_preds)) ** 2), dim=0)
+
+    em = EpochMetric(compute_fn)
+    em.reset()
+    output1 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output1)
+    output2 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output2)
+
+    result = em.compute()
+    assert isinstance(result, torch.Tensor)
+    assert result.shape == (3,)
+
+    preds = torch.cat([output1[0], output2[0]], dim=0)
+    targets = torch.cat([output1[1], output2[1]], dim=0)
+    expected = compute_fn(preds, targets)
+    assert torch.allclose(result, expected)
+
+
+def test_epoch_metric_compute_fn_tuple_output():
+    """Test EpochMetric with compute_fn returning a tuple of tensors."""
+
+    def compute_fn(y_preds, y_targets):
+        mse = torch.mean(((y_preds - y_targets.type_as(y_preds)) ** 2))
+        mae = torch.mean(torch.abs(y_preds - y_targets.type_as(y_preds)))
+        return (mse, mae)
+
+    em = EpochMetric(compute_fn)
+    em.reset()
+    output1 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output1)
+    output2 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output2)
+
+    result = em.compute()
+    assert isinstance(result, tuple)
+    assert len(result) == 2
+
+    preds = torch.cat([output1[0], output2[0]], dim=0)
+    targets = torch.cat([output1[1], output2[1]], dim=0)
+    expected = compute_fn(preds, targets)
+    assert torch.allclose(result[0], expected[0])
+    assert torch.allclose(result[1], expected[1])
+
+
+def test_epoch_metric_compute_fn_invalid_output():
+    """Test EpochMetric raises TypeError for unsupported compute_fn output."""
+
+    def compute_fn(y_preds, y_targets):
+        return "invalid_output"
+
+    em = EpochMetric(compute_fn, check_compute_fn=False)
+    em.reset()
+    output1 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output1)
+    output2 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output2)
+
+    with pytest.raises(TypeError, match=r"compute_fn output type"):
+        em.compute()
+
+
+def test_epoch_metric_compute_fn_list_output():
+    """Test EpochMetric with compute_fn returning a list of tensors."""
+
+    def compute_fn(y_preds, y_targets):
+        mse = torch.mean(((y_preds - y_targets.type_as(y_preds)) ** 2))
+        mae = torch.mean(torch.abs(y_preds - y_targets.type_as(y_preds)))
+        return [mse, mae]
+
+    em = EpochMetric(compute_fn)
+    em.reset()
+    output1 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output1)
+    output2 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output2)
+
+    result = em.compute()
+    assert isinstance(result, list)
+    assert len(result) == 2
+
+    preds = torch.cat([output1[0], output2[0]], dim=0)
+    targets = torch.cat([output1[1], output2[1]], dim=0)
+    expected = compute_fn(preds, targets)
+    assert torch.allclose(result[0], expected[0])
+    assert torch.allclose(result[1], expected[1])
+
+
+def test_epoch_metric_compute_fn_dict_output():
+    """Test EpochMetric with compute_fn returning a dict of tensors."""
+
+    def compute_fn(y_preds, y_targets):
+        return {
+            "mse": torch.mean(((y_preds - y_targets.type_as(y_preds)) ** 2)),
+            "mae": torch.mean(torch.abs(y_preds - y_targets.type_as(y_preds))),
+        }
+
+    em = EpochMetric(compute_fn)
+    em.reset()
+    output1 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output1)
+    output2 = (torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long))
+    em.update(output2)
+
+    result = em.compute()
+    assert isinstance(result, dict)
+    assert "mse" in result
+    assert "mae" in result
+
+    preds = torch.cat([output1[0], output2[0]], dim=0)
+    targets = torch.cat([output1[1], output2[1]], dim=0)
+    expected = compute_fn(preds, targets)
+    assert torch.allclose(result["mse"], expected["mse"])
+    assert torch.allclose(result["mae"], expected["mae"])
+
+
+def test_epoch_metric_nested_invalid_output_raises():
+    """Test EpochMetric raises TypeError for container with invalid nested type."""
+
+    def compute_fn(y_preds, y_targets):
+        return [torch.tensor(1.0), "not-a-number"]
+
+    em = EpochMetric(compute_fn, check_compute_fn=False)
+    em.reset()
+    em.update((torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long)))
+    em.update((torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long)))
+
+    with pytest.raises(TypeError, match=r"compute_fn output type .* is not supported"):
+        em.compute()
+
+
+def test_epoch_metric_mapping_non_str_key_raises():
+    """Test EpochMetric raises TypeError for mapping with non-string keys."""
+
+    def compute_fn(y_preds, y_targets):
+        return {0: torch.tensor(1.0)}
+
+    em = EpochMetric(compute_fn, check_compute_fn=False)
+    em.reset()
+    em.update((torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long)))
+    em.update((torch.rand(4, 3), torch.randint(0, 2, size=(4, 3), dtype=torch.long)))
+
+    with pytest.raises(TypeError, match=r"mapping keys should be str"):
+        em.compute()
\ No newline at end of file