diff --git a/monai/networks/nets/regunet.py b/monai/networks/nets/regunet.py
index 4d6150ea1b..9b659b21e1 100644
--- a/monai/networks/nets/regunet.py
+++ b/monai/networks/nets/regunet.py
@@ -294,8 +294,19 @@ def affine_transform(self, theta: torch.Tensor):
         return grid_warped
 
     def forward(self, x: list[torch.Tensor], image_size: list[int]) -> torch.Tensor:
+        """
+        Predict an affine transform from the first feature map and return it as a displacement field.
+
+        Args:
+            x: feature maps from the network; only the first, ``x[0]``, is used. The reference grid is moved to its
+                device and dtype, so a network cast to half precision stays in half precision.
+            image_size: spatial size of the input image; not used by this head.
+
+        Returns:
+            The displacement field, the warped reference grid minus the reference grid.
+        """
         f = x[0]
-        self.grid = self.grid.to(device=f.device)
+        self.grid = self.grid.to(device=f.device, dtype=f.dtype)
         theta = self.fc(f.reshape(f.shape[0], -1))
         if self.save_theta:
             self.theta = theta.detach()
diff --git a/tests/networks/nets/test_globalnet.py b/tests/networks/nets/test_globalnet.py
index ecb0243a1b..84e3d466de 100644
--- a/tests/networks/nets/test_globalnet.py
+++ b/tests/networks/nets/test_globalnet.py
@@ -98,6 +98,26 @@ def test_script(self, input_param, input_shape, _):
         test_data = torch.randn(input_shape)
         test_script_save(net, test_data)
 
+    @parameterized.expand(TEST_CASES_GLOBAL_NET)
+    def test_half_precision_forward(self, input_param, input_shape, expected_shape):
+        """Check that a GlobalNet cast to half precision can run a forward pass and returns float16.
+
+        `AffineHead.grid` used to be moved by device only, so casting the network left it at float32 while theta
+        became float16, and the einsum in `affine_transform` raised `RuntimeError: expected scalar type Half but
+        found Float` on the first half-precision forward call.
+
+        Args:
+            input_param: keyword arguments used to build the GlobalNet.
+            input_shape: shape of the random float16 input.
+            expected_shape: shape the returned displacement field must have.
+        """
+        net = GlobalNet(**input_param).half()
+        with eval_mode(net):
+            img = torch.randn(input_shape, dtype=torch.float16)
+            result = net(img)
+            self.assertEqual(result.dtype, torch.float16)
+            self.assertEqual(result.shape, expected_shape)
+
 
 if __name__ == "__main__":
     unittest.main()