diff --git a/pytensor/tensor/rewriting/linalg.py b/pytensor/tensor/rewriting/linalg.py
index 2831ab02ab..c02d3f5a23 100644
--- a/pytensor/tensor/rewriting/linalg.py
+++ b/pytensor/tensor/rewriting/linalg.py
@@ -11,7 +11,7 @@
     register_specialize,
     register_stabilize,
 )
-from pytensor.tensor.slinalg import Cholesky, Solve, cholesky, solve
+from pytensor.tensor.slinalg import Cholesky, Solve, SolveTriangular, cholesky, solve
 
 
 logger = logging.getLogger(__name__)
@@ -50,31 +50,30 @@ def inv_as_solve(fgraph, node):
 @register_stabilize
 @register_canonicalize
 @node_rewriter([Solve])
-def tag_solve_triangular(fgraph, node):
+def generic_solve_to_solve_triangular(fgraph, node):
     """
-    If a general solve() is applied to the output of a cholesky op, then
+    If any solve() is applied to the output of a cholesky op, then
     replace it with a triangular solve.
 
     """
     if isinstance(node.op, Solve):
-        if node.op.assume_a == "gen":
-            A, b = node.inputs  # result is solution Ax=b
-            if A.owner and isinstance(A.owner.op, Cholesky):
-                if A.owner.op.lower:
-                    return [Solve(assume_a="sym", lower=True)(A, b)]
+        A, b = node.inputs  # result is solution Ax=b
+        if A.owner and isinstance(A.owner.op, Cholesky):
+            if A.owner.op.lower:
+                return [SolveTriangular(lower=True)(A, b)]
+            else:
+                return [SolveTriangular(lower=False)(A, b)]
+        if (
+            A.owner
+            and isinstance(A.owner.op, DimShuffle)
+            and A.owner.op.new_order == (1, 0)
+        ):
+            (A_T,) = A.owner.inputs
+            if A_T.owner and isinstance(A_T.owner.op, Cholesky):
+                if A_T.owner.op.lower:
+                    return [SolveTriangular(lower=False)(A, b)]
                 else:
-                    return [Solve(assume_a="sym", lower=False)(A, b)]
-            if (
-                A.owner
-                and isinstance(A.owner.op, DimShuffle)
-                and A.owner.op.new_order == (1, 0)
-            ):
-                (A_T,) = A.owner.inputs
-                if A_T.owner and isinstance(A_T.owner.op, Cholesky):
-                    if A_T.owner.op.lower:
-                        return [Solve(assume_a="sym", lower=False)(A, b)]
-                    else:
-                        return [Solve(assume_a="sym", lower=True)(A, b)]
+                    return [SolveTriangular(lower=True)(A, b)]
 
 
 @register_canonicalize
diff --git a/tests/tensor/rewriting/test_linalg.py b/tests/tensor/rewriting/test_linalg.py
index 9ec182cb21..c28388d11c 100644
--- a/tests/tensor/rewriting/test_linalg.py
+++ b/tests/tensor/rewriting/test_linalg.py
@@ -2,6 +2,7 @@
 import numpy.linalg
 import pytest
 import scipy.linalg
+from numpy.testing import assert_allclose
 
 import pytensor
 from pytensor import function
@@ -12,7 +13,7 @@
 from pytensor.tensor.math import _allclose
 from pytensor.tensor.nlinalg import MatrixInverse, matrix_inverse
 from pytensor.tensor.rewriting.linalg import inv_as_solve
-from pytensor.tensor.slinalg import Cholesky, Solve, solve
+from pytensor.tensor.slinalg import Cholesky, Solve, SolveTriangular, solve
 from pytensor.tensor.type import dmatrix, matrix, vector
 from tests import unittest_tools as utt
 from tests.test_rop import break_op
@@ -81,25 +82,46 @@ def test_transinv_to_invtrans():
                 assert node.inputs[0].name == "X"
 
 
-def test_tag_solve_triangular():
+def test_generic_solve_to_solve_triangular():
     cholesky_lower = Cholesky(lower=True)
     cholesky_upper = Cholesky(lower=False)
     A = matrix("A")
-    x = vector("x")
+    x = matrix("x")
+
     L = cholesky_lower(A)
     U = cholesky_upper(A)
     b1 = solve(L, x)
     b2 = solve(U, x)
     f = pytensor.function([A, x], b1)
+
+    X = np.random.normal(size=(10, 10)).astype(config.floatX)
+    X = X @ X.T
+    X_chol = np.linalg.cholesky(X)
+    eye = np.eye(10, dtype=config.floatX)
+
     if config.mode != "FAST_COMPILE":
-        for node in f.maker.fgraph.toposort():
-            if isinstance(node.op, Solve):
-                assert node.op.assume_a != "gen" and node.op.lower
+        toposort = f.maker.fgraph.toposort()
+        op_list = [node.op for node in toposort]
+
+        assert not any(isinstance(op, Solve) for op in op_list)
+        assert any(isinstance(op, SolveTriangular) for op in op_list)
+
+        assert_allclose(
+            f(X, eye) @ X_chol, eye, atol=1e-8 if config.floatX.endswith("64") else 1e-4
+        )
+
     f = pytensor.function([A, x], b2)
+
     if config.mode != "FAST_COMPILE":
-        for node in f.maker.fgraph.toposort():
-            if isinstance(node.op, Solve):
-                assert node.op.assume_a != "gen" and not node.op.lower
+        toposort = f.maker.fgraph.toposort()
+        op_list = [node.op for node in toposort]
+        assert not any(isinstance(op, Solve) for op in op_list)
+        assert any(isinstance(op, SolveTriangular) for op in op_list)
+        assert_allclose(
+            f(X, eye).T @ X_chol,
+            eye,
+            atol=1e-8 if config.floatX.endswith("64") else 1e-4,
+        )
 
 
 def test_matrix_inverse_solve():