diff --git a/mart/attack/composer.py b/mart/attack/composer.py
index 6b40950a..524ef9d5 100644
--- a/mart/attack/composer.py
+++ b/mart/attack/composer.py
@@ -10,10 +10,14 @@
 from typing import Any, Iterable
 
 import torch
+import torchvision
+import torchvision.transforms as T
+import torchvision.transforms.functional as F
+from torchvision.transforms.functional import InterpolationMode
 
 
-class Composer(abc.ABC):
-    def __call__(
+class Composer(torch.nn.Module):
+    def forward(
         self,
         perturbation: torch.Tensor | Iterable[torch.Tensor],
         *,
@@ -24,6 +28,17 @@ def __call__(
         if isinstance(perturbation, torch.Tensor) and isinstance(input, torch.Tensor):
             return self.compose(perturbation, input=input, target=target)
 
+        elif (
+            isinstance(perturbation, torch.Tensor)
+            and isinstance(input, Iterable)  # noqa: W503
+            and isinstance(target, Iterable)  # noqa: W503
+        ):
+            # FIXME: replace tuple with whatever input's type is
+            return tuple(
+                self.compose(perturbation, input=input_i, target=target_i)
+                for input_i, target_i in zip(input, target)
+            )
+
         elif (
             isinstance(perturbation, Iterable)
             and isinstance(input, Iterable)  # noqa: W503
@@ -56,8 +71,13 @@ def compose(self, perturbation, *, input, target):
         return input + perturbation
 
 
-class Overlay(Composer):
-    """We assume an adversary overlays a patch to the input."""
+class Composite(Composer):
+    """We assume an adversary underlays a patch to the input."""
+
+    def __init__(self, premultiplied_alpha=False):
+        super().__init__()
+
+        self.premultiplied_alpha = premultiplied_alpha
 
     def compose(self, perturbation, *, input, target):
         # True is mutable, False is immutable.
@@ -67,14 +87,7 @@ def compose(self, perturbation, *, input, target):
         #   because some data modules (e.g. Armory) gives binary mask.
         mask = mask.to(input)
 
-        return input * (1 - mask) + perturbation * mask
-
-
-class MaskAdditive(Composer):
-    """We assume an adversary adds masked perturbation to the input."""
-
-    def compose(self, perturbation, *, input, target):
-        mask = target["perturbable_mask"]
-        masked_perturbation = perturbation * mask
+        if not self.premultiplied_alpha:
+            perturbation = perturbation * mask
 
-        return input + masked_perturbation
+        return input * (1 - mask) + perturbation
diff --git a/mart/configs/attack/composer/composite.yaml b/mart/configs/attack/composer/composite.yaml
new file mode 100644
index 00000000..c75347ff
--- /dev/null
+++ b/mart/configs/attack/composer/composite.yaml
@@ -0,0 +1 @@
+_target_: mart.attack.composer.Composite
diff --git a/mart/configs/attack/composer/mask_additive.yaml b/mart/configs/attack/composer/mask_additive.yaml
deleted file mode 100644
index 4bca36f8..00000000
--- a/mart/configs/attack/composer/mask_additive.yaml
+++ /dev/null
@@ -1 +0,0 @@
-_target_: mart.attack.composer.MaskAdditive
diff --git a/mart/configs/attack/composer/overlay.yaml b/mart/configs/attack/composer/overlay.yaml
deleted file mode 100644
index 469f7245..00000000
--- a/mart/configs/attack/composer/overlay.yaml
+++ /dev/null
@@ -1 +0,0 @@
-_target_: mart.attack.composer.Overlay
diff --git a/mart/configs/attack/object_detection_mask_adversary.yaml b/mart/configs/attack/object_detection_mask_adversary.yaml
index ad99dda0..580493a7 100644
--- a/mart/configs/attack/object_detection_mask_adversary.yaml
+++ b/mart/configs/attack/object_detection_mask_adversary.yaml
@@ -3,7 +3,7 @@ defaults:
   - perturber: default
   - perturber/initializer: constant
   - perturber/projector: mask_range
-  - composer: overlay
+  - composer: composite
   - /optimizer@optimizer: sgd
   - gain: rcnn_training_loss
   - gradient_modifier: sign
diff --git a/tests/test_composer.py b/tests/test_composer.py
index 9fc15cf8..dbe26d74 100644
--- a/tests/test_composer.py
+++ b/tests/test_composer.py
@@ -6,7 +6,7 @@
 
 import torch
 
-from mart.attack.composer import Additive, MaskAdditive, Overlay
+from mart.attack.composer import Additive, Composite
 
 
 def test_additive_composer_forward(input_data, target_data, perturbation):
@@ -17,22 +17,11 @@ def test_additive_composer_forward(input_data, target_data, perturbation):
     torch.testing.assert_close(output, expected_output, equal_nan=True)
 
 
-def test_overlay_composer_forward(input_data, target_data, perturbation):
-    composer = Overlay()
+def test_composite_composer_forward(input_data, target_data, perturbation):
+    composer = Composite()
 
     output = composer(perturbation, input=input_data, target=target_data)
     mask = target_data["perturbable_mask"]
     mask = mask.to(input_data)
     expected_output = input_data * (1 - mask) + perturbation
     torch.testing.assert_close(output, expected_output, equal_nan=True)
-
-
-def test_mask_additive_composer_forward():
-    input = torch.zeros((2, 2))
-    perturbation = torch.ones((2, 2))
-    target = {"perturbable_mask": torch.eye(2)}
-    expected_output = torch.eye(2)
-
-    composer = MaskAdditive()
-    output = composer(perturbation, input=input, target=target)
-    torch.testing.assert_close(output, expected_output, equal_nan=True)