diff --git a/pymc/distributions/truncated.py b/pymc/distributions/truncated.py
index 45f77574d6..1ef4a1da32 100644
--- a/pymc/distributions/truncated.py
+++ b/pymc/distributions/truncated.py
@@ -106,28 +106,34 @@ def rv_op(cls, dist, lower, upper, max_n_steps, *, size=None):
         ]
         graph_inputs = [*rv_inputs, lower, upper]
 
-        rv = dist.owner.op.make_node(*rv_inputs).default_output()
+        # Variables with `_` suffix identify dummy inputs for the OpFromGraph
+        graph_inputs_ = [
+            inp.type() if not isinstance(inp.type, RandomType) else inp for inp in graph_inputs
+        ]
+        *rv_inputs_, lower_, upper_ = graph_inputs_
+
+        rv_ = dist.owner.op.make_node(*rv_inputs_).default_output()
 
         # Try to use inverted cdf sampling
         # truncated_rv = icdf(rv, draw(uniform(cdf(lower), cdf(upper))))
         try:
-            logcdf_lower, logcdf_upper = cls._create_logcdf_exprs(rv, rv, lower, upper)
+            logcdf_lower_, logcdf_upper_ = TruncatedRV._create_logcdf_exprs(
+                rv_, rv_, lower_, upper_
+            )
             # We use the first RNG from the base RV, so we don't have to introduce a new one
             # This is not problematic because the RNG won't be used in the RV logcdf graph
-            uniform_rng = next(inp for inp in rv_inputs if isinstance(inp.type, RandomType))
-            uniform_next_rng, uniform = pt.random.uniform(
-                pt.exp(logcdf_lower),
-                pt.exp(logcdf_upper),
-                rng=uniform_rng,
-                size=rv.shape,
+            uniform_rng_ = next(inp_ for inp_ in rv_inputs_ if isinstance(inp_.type, RandomType))
+            uniform_next_rng_, uniform_ = pt.random.uniform(
+                pt.exp(logcdf_lower_),
+                pt.exp(logcdf_upper_),
+                rng=uniform_rng_,
+                size=rv_.shape,
             ).owner.outputs
-            # 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})
+            truncated_rv_ = icdf(rv_, uniform_, warn_rvs=False)
             return TruncatedRV(
                 base_rv_op=dist.owner.op,
-                inputs=graph_inputs,
-                outputs=[truncated_rv, uniform_next_rng],
+                inputs=graph_inputs_,
+                outputs=[truncated_rv_, uniform_next_rng_],
                 ndim_supp=0,
                 max_n_steps=max_n_steps,
             )(*graph_inputs)
@@ -154,25 +160,25 @@ def loop_fn(truncated_rv, reject_draws, lower, upper, *rv_inputs):
 
             return (
                 (truncated_rv, reject_draws),
-                collect_default_updates(new_truncated_rv, inputs=rv_inputs),
+                collect_default_updates(new_truncated_rv),
                 until(~pt.any(reject_draws)),
             )
 
-        (truncated_rv, reject_draws_), updates = scan(
+        (truncated_rv_, reject_draws_), updates = scan(
             loop_fn,
             outputs_info=[
-                pt.zeros_like(rv),
-                pt.ones_like(rv, dtype=bool),
+                pt.zeros_like(rv_),
+                pt.ones_like(rv_, dtype=bool),
             ],
-            non_sequences=[lower, upper, *rv_inputs],
+            non_sequences=[lower_, upper_, *rv_inputs_],
             n_steps=max_n_steps,
             strict=True,
         )
 
-        truncated_rv = truncated_rv[-1]
-        convergence = ~pt.any(reject_draws_[-1])
-        truncated_rv = TruncationCheck(f"Truncation did not converge in {max_n_steps} steps")(
-            truncated_rv, convergence
+        truncated_rv_ = truncated_rv_[-1]
+        convergence_ = ~pt.any(reject_draws_[-1])
+        truncated_rv_ = TruncationCheck(f"Truncation did not converge in {max_n_steps} steps")(
+            truncated_rv_, convergence_
         )
 
         # Sort updates of each RNG so that they show in the same order as the input RNGs
@@ -184,8 +190,8 @@ def sort_updates(update):
 
         return TruncatedRV(
             base_rv_op=dist.owner.op,
-            inputs=graph_inputs,
-            outputs=[truncated_rv, *next_rngs],
+            inputs=graph_inputs_,
+            outputs=[truncated_rv_, *next_rngs],
             ndim_supp=0,
             max_n_steps=max_n_steps,
         )(*graph_inputs)
diff --git a/tests/distributions/test_truncated.py b/tests/distributions/test_truncated.py
index 4f748f0fbc..50ae98147f 100644
--- a/tests/distributions/test_truncated.py
+++ b/tests/distributions/test_truncated.py
@@ -585,3 +585,17 @@ def test_truncated_identity_input(dist_op):
 
     rv_out = Truncated.dist(dist=dist_op(mu_identity, 5), lower=0, upper=1)
     assert np.ptp(draw(rv_out, draws=500)) < 1
+
+
+@pytest.mark.parametrize("rv_op", [icdf_normal, rejection_normal])
+def test_truncated_custom_dist_indexed_argument(rv_op):
+    # Regression test for https://github.com/pymc-devs/pymc/issues/7312
+
+    def dist(scale, size):
+        return pt.exp(rv_op(scale=scale, size=size))
+
+    scale = Exponential.dist(scale=[1, 2, 3])
+    latent = CustomDist.dist(scale[[0, 0, 1, 1, 2, 2]], dist=dist)
+    rv_out = Truncated.dist(latent, upper=7)
+
+    assert np.ptp(draw(rv_out, draws=100)) < 7