diff --git a/normalizing_flows/bijections/finite/linear.py b/normalizing_flows/bijections/finite/linear.py
index 8b98c67..a009ba2 100644
--- a/normalizing_flows/bijections/finite/linear.py
+++ b/normalizing_flows/bijections/finite/linear.py
@@ -14,6 +14,19 @@
 from normalizing_flows.utils import get_batch_shape, flatten_event, unflatten_event, flatten_batch, unflatten_batch
 
 
+class Identity(Bijection):
+    def __init__(self, event_shape: Union[torch.Size, Tuple[int, ...]], **kwargs):
+        super().__init__(event_shape, **kwargs)
+
+    def forward(self, x: torch.Tensor, context: torch.Tensor = None) -> Tuple[torch.Tensor, torch.Tensor]:
+        batch_shape = get_batch_shape(x, self.event_shape)
+        return x, torch.zeros(size=batch_shape, device=x.device)
+
+    def inverse(self, z: torch.Tensor, context: torch.Tensor = None) -> Tuple[torch.Tensor, torch.Tensor]:
+        batch_shape = get_batch_shape(z, self.event_shape)
+        return z, torch.zeros(size=batch_shape, device=z.device)
+
+
 class LinearBijection(Bijection):
     def __init__(self, event_shape: Union[torch.Size, Tuple[int, ...]], matrix: InvertibleMatrix):
         super().__init__(event_shape)