diff --git a/pymc/distributions/truncated.py b/pymc/distributions/truncated.py
index 45f44e01f0..45f77574d6 100644
--- a/pymc/distributions/truncated.py
+++ b/pymc/distributions/truncated.py
@@ -121,7 +121,9 @@ def rv_op(cls, dist, lower, upper, max_n_steps, *, size=None):
                 rng=uniform_rng,
                 size=rv.shape,
             ).owner.outputs
-            truncated_rv = icdf(rv, uniform, warn_rvs=False)
+            # So icdf does not see the random graph of uniform
+            uniform_type = uniform.type()
+            truncated_rv = graph_replace(icdf(rv, uniform_type), {uniform_type: uniform})
             return TruncatedRV(
                 base_rv_op=dist.owner.op,
                 inputs=graph_inputs,
diff --git a/tests/distributions/test_truncated.py b/tests/distributions/test_truncated.py
index a451051210..4f748f0fbc 100644
--- a/tests/distributions/test_truncated.py
+++ b/tests/distributions/test_truncated.py
@@ -17,6 +17,7 @@
 import pytest
 import scipy
 
+from pytensor.scalar import Identity
 from pytensor.tensor.random.basic import GeometricRV, NormalRV
 from pytensor.tensor.random.type import RandomType
 
@@ -573,3 +574,14 @@ def maxwell_dist(scale, size):
         logp(trunc_x, test_value).eval(),
         expected_logp,
     )
+
+
+@pytest.mark.parametrize("dist_op", [icdf_normal, rejection_normal])
+def test_truncated_identity_input(dist_op):
+    # Regression test for https://github.com/pymc-devs/pymc/issues/7312
+    mu = Exponential.dist(scale=0.5)
+    mu_identity = mu.copy()
+    assert isinstance(mu_identity.owner.op.scalar_op, Identity)
+
+    rv_out = Truncated.dist(dist=dist_op(mu_identity, 5), lower=0, upper=1)
+    assert np.ptp(draw(rv_out, draws=500)) < 1