diff --git a/src/fugw/mappings/dense.py b/src/fugw/mappings/dense.py
index f3ede0f..18fe2de 100644
--- a/src/fugw/mappings/dense.py
+++ b/src/fugw/mappings/dense.py
@@ -270,7 +270,9 @@ def fit(
 
         return self
 
-    def transform(self, source_features, device="auto"):
+    def transform(
+        self, source_features, id_interpolation=False, device="auto"
+    ):
         """
         Transport source feature maps using fitted OT plan.
         Use GPUs if available.
@@ -279,6 +281,9 @@ def transform(self, source_features, device="auto"):
         ----------
         source_features: ndarray(n_samples, n) or ndarray(n)
             Contrast map for source subject
+        id_interpolation: bool, optional, defaults to False
+            If True and source/target share the same geometry,
+            interpolate the transport plan with the identity.
         device: "auto" or torch.device
             If "auto": use first available GPU if it's available,
             CPU otherwise.
@@ -312,11 +317,37 @@ def transform(self, source_features, device="auto"):
         source_features_tensor = _make_tensor(source_features, device=device)
 
         # Transform data
-        transformed_data = (
-            (pi.T @ source_features_tensor.T / pi.sum(dim=0).reshape(-1, 1))
-            .T.detach()
-            .cpu()
-        )
+        if id_interpolation:
+            if pi.shape[0] != pi.shape[1]:
+                raise ValueError(
+                    "Cannot interpolate with identity if source and target"
+                    " have different geometries."
+                )
+            transformed_data = (
+                (
+                    (
+                        (
+                            pi.T
+                            @ source_features_tensor.T
+                            / pi.sum(dim=0).reshape(-1, 1)
+                        )
+                        + source_features_tensor.T
+                    )
+                    / 2
+                )
+                .T.detach()
+                .cpu()
+            )
+        else:
+            transformed_data = (
+                (
+                    pi.T
+                    @ source_features_tensor.T
+                    / pi.sum(dim=0).reshape(-1, 1)
+                )
+                .T.detach()
+                .cpu()
+            )
 
         # Free allocated GPU memory
         del pi, source_features_tensor