diff --git a/pytensor/tensor/rewriting/linalg.py b/pytensor/tensor/rewriting/linalg.py
index 1de6dbb373..d76cc04ee9 100644
--- a/pytensor/tensor/rewriting/linalg.py
+++ b/pytensor/tensor/rewriting/linalg.py
@@ -611,3 +611,64 @@ def rewrite_inv_inv(fgraph, node):
     ):
         return None
     return [potential_inner_inv.inputs[0]]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_cholesky_eye_to_eye(fgraph, node):
+    """
+     This rewrite takes advantage of the fact that the cholesky decomposition of an identity matrix is the matrix itself
+
+    The presence of an identity matrix is identified by checking whether we have k = 0 for an Eye Op inside Cholesky.
+
+    Parameters
+    ----------
+    fgraph: FunctionGraph
+        Function graph being optimized
+    node: Apply
+        Node of the function graph to be optimized
+
+    Returns
+    -------
+    list of Variable, optional
+        List of optimized variables, or None if no optimization was performed
+    """
+    # Find whether cholesky op is being applied
+    if not isinstance(node.op.core_op, Cholesky):
+        return None
+
+    # Check whether input to Cholesky is Eye and the 1's are on main diagonal
+    eye_check = node.inputs[0]
+    if not (
+        eye_check.owner
+        and isinstance(eye_check.owner.op, Eye)
+        and getattr(eye_check.owner.inputs[-1], "data", -1).item() == 0
+    ):
+        return None
+    return [eye_check]
+
+
+@register_canonicalize
+@register_stabilize
+@node_rewriter([Blockwise])
+def rewrite_cholesky_diag_from_eye_mul(fgraph, node):
+    # Find whether cholesky op is being applied
+    if not isinstance(node.op.core_op, Cholesky):
+        return None
+
+    # Check whether input is diagonal from multiplcation of identity matrix with a tensor
+    inputs = node.inputs[0]
+    inputs_or_none = _find_diag_from_eye_mul(inputs)
+    if inputs_or_none is None:
+        return None
+
+    eye_input, non_eye_inputs = inputs_or_none
+
+    # Dealing with only one other input
+    if len(non_eye_inputs) != 1:
+        return None
+
+    eye_input, non_eye_input = eye_input[0], non_eye_inputs[0]
+
+    return [eye_input * (non_eye_input**0.5)]
diff --git a/tests/tensor/rewriting/test_linalg.py b/tests/tensor/rewriting/test_linalg.py
index 7353a82be0..605a81a3c1 100644
--- a/tests/tensor/rewriting/test_linalg.py
+++ b/tests/tensor/rewriting/test_linalg.py
@@ -568,3 +568,66 @@ def get_pt_function(x, op_name):
     op2 = get_pt_function(op1, inv_op_2)
     rewritten_out = rewrite_graph(op2)
     assert rewritten_out == x
+
+
+def test_cholesky_eye_rewrite():
+    x = pt.eye(10)
+    x_mat = pt.matrix("x")
+    L = pt.linalg.cholesky(x)
+    L_mat = pt.linalg.cholesky(x_mat)
+    f_rewritten = function([], L, mode="FAST_RUN")
+    f_rewritten_mat = function([x_mat], L_mat, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    nodes_mat = f_rewritten_mat.maker.fgraph.apply_nodes
+
+    # Rewrite Test
+    assert not any(isinstance(node.op, Cholesky) for node in nodes)
+    assert any(isinstance(node.op, Cholesky) for node in nodes_mat)
+
+    # Value Test
+    x_test = np.eye(10)
+    L = np.linalg.cholesky(x_test)
+    rewritten_val = f_rewritten()
+
+    assert_allclose(
+        L,
+        rewritten_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )
+
+
+@pytest.mark.parametrize(
+    "shape",
+    [(), (7,), (1, 7), (7, 1), (7, 7), (3, 7, 7)],
+    ids=["scalar", "vector", "row_vec", "col_vec", "matrix", "batched_input"],
+)
+def test_cholesky_diag_from_eye_mul(shape):
+    # Initializing x based on scalar/vector/matrix
+    x = pt.tensor("x", shape=shape)
+    y = pt.eye(7) * x
+    # Performing cholesky decomposition using pt.linalg.cholesky
+    z_cholesky = pt.linalg.cholesky(y)
+
+    # REWRITE TEST
+    f_rewritten = function([x], z_cholesky, mode="FAST_RUN")
+    nodes = f_rewritten.maker.fgraph.apply_nodes
+    assert not any(isinstance(node.op, Cholesky) for node in nodes)
+
+    # NUMERIC VALUE TEST
+    if len(shape) == 0:
+        x_test = np.array(np.random.rand()).astype(config.floatX)
+    elif len(shape) == 1:
+        x_test = np.random.rand(*shape).astype(config.floatX)
+    else:
+        x_test = np.random.rand(*shape).astype(config.floatX)
+    x_test_matrix = np.eye(7) * x_test
+    cholesky_val = np.linalg.cholesky(x_test_matrix)
+    rewritten_val = f_rewritten(x_test)
+
+    assert_allclose(
+        cholesky_val,
+        rewritten_val,
+        atol=1e-3 if config.floatX == "float32" else 1e-8,
+        rtol=1e-3 if config.floatX == "float32" else 1e-8,
+    )