diff --git a/pyro/distributions/transforms/spline.py b/pyro/distributions/transforms/spline.py
index ba7d240a1b..2f32f61aac 100644
--- a/pyro/distributions/transforms/spline.py
+++ b/pyro/distributions/transforms/spline.py
@@ -254,6 +254,8 @@ def _monotonic_rational_spline(
             c = -input_delta * (inputs - input_cumheights)
 
             discriminant = b.pow(2) - 4 * a * c
+            # Make sure outside_interval input can be reversed as identity.
+            discriminant = discriminant.masked_fill(outside_interval_mask, 0)
             assert (discriminant >= 0).all()
 
             root = (2 * c) / (-b - torch.sqrt(discriminant))