diff --git a/pymc/step_methods/mlda.py b/pymc/step_methods/mlda.py
index d66013189d..eb29244f2d 100644
--- a/pymc/step_methods/mlda.py
+++ b/pymc/step_methods/mlda.py
@@ -66,22 +66,14 @@ def __init__(self, *args, **kwargs):
             self.Q_last = np.nan
             self.Q_reg = [np.nan] * self.mlda_subsampling_rate_above
 
-            # extract some necessary variables
-            vars = kwargs.get("vars", None)
-            if vars is None:
-                vars = model.value_vars
-            else:
-                vars = [model.rvs_to_values.get(var, var) for var in vars]
-            vars = pm.inputvars(vars)
-            shared = pm.make_shared_replacements(initial_values, vars, model)
-
         # call parent class __init__
         super().__init__(*args, **kwargs)
 
         # modify the delta function and point to model if VR is used
         if self.mlda_variance_reduction:
-            self.delta_logp = delta_logp_inverse(initial_values, model.logpt, vars, shared)
             self.model = model
+            self.delta_logp_factory = self.delta_logp
+            self.delta_logp = lambda q, q0: -self.delta_logp_factory(q0, q)
 
     def reset_tuning(self):
         """
@@ -136,22 +128,14 @@ def __init__(self, *args, **kwargs):
             self.Q_last = np.nan
             self.Q_reg = [np.nan] * self.mlda_subsampling_rate_above
 
-            # extract some necessary variables
-            vars = kwargs.get("vars", None)
-            if vars is None:
-                vars = model.value_vars
-            else:
-                vars = [model.rvs_to_values.get(var, var) for var in vars]
-            vars = pm.inputvars(vars)
-            shared = pm.make_shared_replacements(initial_values, vars, model)
-
         # call parent class __init__
         super().__init__(*args, **kwargs)
 
         # modify the delta function and point to model if VR is used
         if self.mlda_variance_reduction:
-            self.delta_logp = delta_logp_inverse(initial_values, model.logpt, vars, shared)
             self.model = model
+            self.delta_logp_factory = self.delta_logp
+            self.delta_logp = lambda q, q0: -self.delta_logp_factory(q0, q)
 
     def reset_tuning(self):
         """Skips resetting of tuned sampler parameters
@@ -556,7 +540,7 @@ def __init__(
         # Construct Aesara function for current-level model likelihood
         # (for use in acceptance)
         shared = pm.make_shared_replacements(initial_values, vars, model)
-        self.delta_logp = delta_logp_inverse(initial_values, model.logpt, vars, shared)
+        self.delta_logp = delta_logp(initial_values, model.logpt, vars, shared)
 
         # Construct Aesara function for below-level model likelihood
         # (for use in acceptance)
@@ -749,7 +733,9 @@ def astep(self, q0: RaveledVars) -> Tuple[RaveledVars, List[Dict[str, Any]]]:
             accept = np.float64(0.0)
             skipped_logp = True
         else:
-            accept = self.delta_logp(q.data, q0.data) + self.delta_logp_below(q0.data, q.data)
+            # NB! The order and sign of the first term are swapped compared
+            # to the convention to make sure the proposal is evaluated last.
+            accept = -self.delta_logp(q0.data, q.data) + self.delta_logp_below(q0.data, q.data)
             skipped_logp = False
 
         # Accept/reject sample - next sample is stored in q_new
@@ -954,19 +940,6 @@ def update(self, x):
         self.t += 1
 
 
-def delta_logp_inverse(point, logp, vars, shared):
-    [logp0], inarray0 = pm.join_nonshared_inputs(point, [logp], vars, shared)
-
-    tensor_type = inarray0.type
-    inarray1 = tensor_type("inarray1")
-
-    logp1 = pm.CallableTensor(logp0)(inarray1)
-
-    f = compile_rv_inplace([inarray1, inarray0], -logp0 + logp1)
-    f.trust_input = True
-    return f
-
-
 def extract_Q_estimate(trace, levels):
     """
     Returns expectation and standard error of quantity of interest,