diff --git a/pytensor/compile/builders.py b/pytensor/compile/builders.py
index a4a3d1840a..e8a6eb86b2 100644
--- a/pytensor/compile/builders.py
+++ b/pytensor/compile/builders.py
@@ -6,8 +6,11 @@
 from functools import partial
 from typing import Union, cast
 
-from pytensor.compile.function import function
-from pytensor.compile.function.pfunc import rebuild_collect_shared
+from pytensor.compile import get_default_mode, insert_deepcopy
+from pytensor.compile.function.pfunc import pfunc, rebuild_collect_shared
+from pytensor.compile.function.types import add_supervisor_to_fgraph
+from pytensor.compile.io import In, Out
+from pytensor.compile.mode import Mode
 from pytensor.compile.sharedvalue import SharedVariable
 from pytensor.configdefaults import config
 from pytensor.gradient import DisconnectedType, Rop, grad
@@ -21,7 +24,7 @@
 )
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.null_type import NullType
-from pytensor.graph.op import HasInnerGraph, Op
+from pytensor.graph.op import ComputeMapType, HasInnerGraph, Op, StorageMapType
 from pytensor.graph.replace import clone_replace
 from pytensor.graph.utils import MissingInputError
 
@@ -433,6 +436,9 @@ def __init__(
             assert isinstance(name, str), "name must be None or string object"
         self.name = name
         self.destroy_map = destroy_map if destroy_map is not None else {}
+        self._rewritten_fgraph = {}
+        self._wrapped_inputs = {}
+        self._wrapped_outputs = {}
 
     def __eq__(self, other):
         # TODO: recognize a copy
@@ -847,14 +853,58 @@ def infer_shape(self, fgraph, node, shapes):
 
         return ret
 
+    def _rewrite_fgraph(self, impl):
+        if self._rewritten_fgraph.get(impl, None) is None:
+            mode = get_default_mode()
+            if impl == "py":
+                mode = mode.excluding("cxx")
+            rewriter = mode.optimizer
+
+            # We are cloning fgraph too many times, but one of the existing tests checks for this
+            # TestOpFromGraph.test_outputs_consistency
+            fgraph = self.fgraph.clone()
+            self._wrapped_inputs[impl] = temp_wrapped_inputs = [
+                In(inp, borrow=False, mutable=False) for inp in fgraph.inputs
+            ]
+            # These are just temporary because the graph rewirite may change them
+            temp_wrapped_outputs = [
+                Out(out, borrow=True) for out in self.fgraph.outputs
+            ]
+            add_supervisor_to_fgraph(
+                fgraph,
+                temp_wrapped_inputs,
+                accept_inplace=False,
+            )
+            with config.change_flags(compute_test_value="off"):
+                rewriter(fgraph)
+            insert_deepcopy(fgraph, temp_wrapped_inputs, temp_wrapped_outputs)
+            self._wrapped_outputs[impl] = [
+                Out(out, borrow=True) for out in fgraph.outputs
+            ]
+            self._rewritten_fgraph[impl] = fgraph
+
+        return (
+            self._rewritten_fgraph[impl],
+            self._wrapped_inputs[impl],
+            self._wrapped_outputs[impl],
+        )
+
     @property
     def fn(self):
-        """Lazily compile the inner function graph."""
         if getattr(self, "_fn", None) is not None:
             return self._fn
 
-        self._fn = function(self.inner_inputs, self.inner_outputs, **self.kwargs)
-        self._fn.trust_input = True
+        fgraph, wrapped_inputs, wrapped_outputs = self._rewrite_fgraph(impl=None)
+
+        self._fn = pfunc(
+            wrapped_inputs,
+            wrapped_outputs,
+            mode=Mode(linker=get_default_mode().linker, optimizer=None),
+            accept_inplace=True,
+            on_unused_input="ignore",
+            fgraph=fgraph,
+            trust_input=True,
+        )
 
         return self._fn
 
@@ -871,6 +921,58 @@ def clone(self):
         res.fgraph = res.fgraph.clone()
         return res
 
+    def prepare_node(
+        self,
+        node: Apply,
+        storage_map: StorageMapType | None,
+        compute_map: ComputeMapType | None,
+        impl: str | None,
+    ) -> None:
+        self._rewrite_fgraph(impl)
+        self.fn
+
+    def make_thunk(self, node, storage_map, compute_map, no_recycling, impl=None):
+        from pytensor.link.vm import VMLinker
+
+        self.prepare_node(node, storage_map, compute_map, impl)
+        fg, _, _ = self._rewrite_fgraph(impl)
+        fg_no_recycling = [
+            new_o
+            for (new_o, old_o) in zip(fg.outputs, node.outputs, strict=True)
+            if old_o in no_recycling
+        ]
+
+        node_input_storage = [storage_map[r] for r in node.inputs]
+        node_output_storage = [storage_map[r] for r in node.outputs]
+        node_compute_map = [compute_map[r] for r in node.outputs]
+
+        def create_thunk(linker):
+            linker.accept(fg, no_recycling=fg_no_recycling)
+            thunk, _, _ = linker.make_thunk(
+                input_storage=node_input_storage,
+                output_storage=node_output_storage,
+            )
+            return thunk
+
+            def thunk_wrapper(thunk=thunk, node_compute_map=node_compute_map):
+                thunk()
+                for cm in node_compute_map:
+                    cm[0] = True
+
+            return thunk_wrapper
+
+        if impl != "py":
+            # try:
+            #     # We default to CLinker because it generates code for the whole graph that the compiler can reason about.
+            #     # Whereas the VMLinker will compile each node separately and call them in a pre-defined VM.
+            #     # It also has less overhead
+            #     return create_thunk(linker=CLinker())
+            # except NotImplementedError:
+            #     # Some Op doesn't have a C implementation, VM it is
+            return create_thunk(VMLinker(use_cloop=True, c_thunks=True))
+        else:
+            return create_thunk(VMLinker(use_cloop=False, c_thunks=False))
+
     def perform(self, node, inputs, outputs):
         variables = self.fn(*inputs)
         assert len(variables) == len(outputs)
diff --git a/pytensor/link/c/c_code/lazylinker_c.c b/pytensor/link/c/c_code/lazylinker_c.c
index 08f3e4d0fb..b1b0f9ee37 100644
--- a/pytensor/link/c/c_code/lazylinker_c.c
+++ b/pytensor/link/c/c_code/lazylinker_c.c
@@ -676,20 +676,7 @@ static int lazy_rec_eval(CLazyLinker *self, Py_ssize_t var_idx, PyObject *one,
       // rval is new ref
       if (rval) // pycall returned normally (no exception)
       {
-        if (rval == Py_None) {
-          Py_DECREF(rval); // ignore a return of None
-        } else if (PyList_Check(rval)) {
-          PyErr_SetString(PyExc_TypeError,
-                          "non-lazy thunk should return None, not list");
-          err = 1;
-          goto pyfail;
-        } else // don't know what it returned, but it wasn't right.
-        {
-          PyErr_SetObject(PyExc_TypeError, rval);
-          err = 1;
-          // We don't release rval since we put it in the error above
-          goto fail;
-        }
+        Py_DECREF(rval); // ignore whatever was returned
       } else // pycall returned NULL (internal error)
       {
         err = 1;
@@ -981,7 +968,7 @@ static PyTypeObject lazylinker_ext_CLazyLinkerType = {
 };
 
 static PyObject *get_version(PyObject *dummy, PyObject *args) {
-  PyObject *result = PyFloat_FromDouble(0.3);
+  PyObject *result = PyFloat_FromDouble(0.4);
   return result;
 }
 
diff --git a/pytensor/link/c/lazylinker_c.py b/pytensor/link/c/lazylinker_c.py
index ce67190342..f03f1cc008 100644
--- a/pytensor/link/c/lazylinker_c.py
+++ b/pytensor/link/c/lazylinker_c.py
@@ -14,7 +14,7 @@
 _logger = logging.getLogger(__file__)
 
 force_compile = False
-version = 0.3  # must match constant returned in function get_version()
+version = 0.4  # must match constant returned in function get_version()
 lazylinker_ext: ModuleType | None = None
 
 
diff --git a/pytensor/tensor/rewriting/basic.py b/pytensor/tensor/rewriting/basic.py
index 59148fae3b..6d559bff7d 100644
--- a/pytensor/tensor/rewriting/basic.py
+++ b/pytensor/tensor/rewriting/basic.py
@@ -1120,15 +1120,11 @@ def unconditional_constant_folding(fgraph, node):
         compute_map[o] = [False]
 
     thunk = node.op.make_thunk(node, storage_map, compute_map, no_recycling=[])
-    required = thunk()
-
-    # A node whose inputs are all provided should always return successfully
-    assert not required
+    thunk()
 
     rval = []
     for output in node.outputs:
         data = storage_map[output][0]
-        assert compute_map[output][0], (output, data)
 
         # TODO: `Type` itself should provide an interface for constructing
         # instances appropriate for a given constant.
diff --git a/tests/compile/test_builders.py b/tests/compile/test_builders.py
index ba0257cdda..6017bc7a60 100644
--- a/tests/compile/test_builders.py
+++ b/tests/compile/test_builders.py
@@ -4,6 +4,7 @@
 import pytest
 
 import pytensor.tensor as pt
+from pytensor import scan
 from pytensor.compile import shared
 from pytensor.compile.builders import OpFromGraph
 from pytensor.compile.function import function
@@ -15,9 +16,10 @@
     grad,
     verify_grad,
 )
-from pytensor.graph.basic import equal_computations
+from pytensor.graph.basic import Apply, equal_computations
 from pytensor.graph.fg import FunctionGraph
 from pytensor.graph.null_type import NullType, null_type
+from pytensor.graph.op import Op
 from pytensor.graph.rewriting.utils import rewrite_graph
 from pytensor.graph.utils import MissingInputError
 from pytensor.printing import debugprint
@@ -622,14 +624,15 @@ def test_outputs_consistency(self):
         """Make sure that `OpFromGraph.fn` doesn't change the value of `OpFromGraph.inner_outputs`."""
 
         x = scalar("x")
-        op = OpFromGraph([x], [x**2 / x], mode="FAST_RUN")
+        op = OpFromGraph([x], [x**2 / x])
 
         # Confirm that the inner-graph is as expected
         assert equal_computations(op.inner_outputs, [x**2 / x], op.inner_inputs, [x])
 
         # These outputs of the compiled `op.fgraph` should differ from the
         # original, uncompiled `op.fgraph` outputs
-        fn = op.fn
+        with config.change_flags(mode="FAST_RUN"):
+            fn = op.fn
         new_inputs = fn.maker.fgraph.inputs
         new_outputs = fn.maker.fgraph.outputs
         assert not equal_computations(new_outputs, [x**2 / x], new_inputs, [x])
@@ -740,3 +743,58 @@ def test_debugprint():
 
     for truth, out in zip(exp_res.split("\n"), lines, strict=True):
         assert truth.strip() == out.strip()
+
+
+@pytest.mark.parametrize("kind", ("ofg", "inlined", "scan"))
+@pytest.mark.parametrize("c_op", (True, False), ids=lambda x: f"c_op={x}")
+def test_benchmark(c_op, kind, benchmark):
+    class ExpWithoutC(Op):
+        def make_node(self, x):
+            return Apply(self, [x], [x.type()])
+
+        def perform(self, node, inputs, output_storage):
+            output_storage[0][0] = np.exp(inputs[0])
+
+    exp_without_c = ExpWithoutC()
+
+    n = 25
+
+    def _f(x):
+        if isinstance(x, np.ndarray):
+            y = np.exp(x)
+        else:
+            if c_op:
+                y = pt.exp(x)
+            else:
+                y = exp_without_c(x)
+        y /= y.sum()
+        return y
+
+    x = pt.vector("x")
+
+    if kind == "ofg":
+        f = OpFromGraph([x], [_f(x)])
+    else:
+        f = _f
+
+    if kind == "scan":
+        # Scan is included for a reference of how bad the overhead can be
+        outs, _ = scan(fn=f, outputs_info=[x], n_steps=n)
+        out = outs[-1]
+    else:
+        out = x
+        for i in range(n):
+            out = f(out)
+
+    compiled_fn = function([x], out, trust_input=True, mode="FAST_RUN")
+    compiled_fn.vm.allow_gc = False
+
+    rng = np.random.default_rng(1)
+    x_test = rng.normal(size=(10,))
+
+    res = benchmark(compiled_fn, x_test)
+
+    expected_res = x_test
+    for i in range(n):
+        expected_res = _f(expected_res)
+    np.testing.assert_allclose(res, expected_res)