diff --git a/pymc_experimental/model/transforms/autoreparam.py b/pymc_experimental/model/transforms/autoreparam.py
index cc1f78289..bb3996459 100644
--- a/pymc_experimental/model/transforms/autoreparam.py
+++ b/pymc_experimental/model/transforms/autoreparam.py
@@ -246,6 +246,44 @@ def _(
     return vip_rep
 
 
+@_vip_reparam_node.register
+def _(
+    op: pm.Exponential,
+    node: Apply,
+    name: str,
+    dims: List[Variable],
+    transform: Optional[Transform],
+    lam: pt.TensorVariable,
+) -> ModelDeterministic:
+    rng, size, scale = node.inputs
+    scale_centered = scale**lam
+    scale_noncentered = scale ** (1 - lam)
+    vip_rv_ = pm.Exponential.dist(
+        scale=scale_centered,
+        size=size,
+        rng=rng,
+    )
+    vip_rv_value_ = vip_rv_.clone()
+    vip_rv_.name = f"{name}::tau_"
+    if transform is not None:
+        vip_rv_value_.name = f"{vip_rv_.name}_{transform.name}__"
+    else:
+        vip_rv_value_.name = vip_rv_.name
+    vip_rv = model_free_rv(
+        vip_rv_,
+        vip_rv_value_,
+        transform,
+        *dims,
+    )
+
+    vip_rep_ = scale_noncentered * vip_rv
+
+    vip_rep_.name = name
+
+    vip_rep = model_deterministic(vip_rep_, *dims)
+    return vip_rep
+
+
 def vip_reparametrize(
     model: pm.Model,
     var_names: Sequence[str],
diff --git a/tests/model/transforms/test_autoreparam.py b/tests/model/transforms/test_autoreparam.py
index b2ea245ae..1d2173066 100644
--- a/tests/model/transforms/test_autoreparam.py
+++ b/tests/model/transforms/test_autoreparam.py
@@ -11,6 +11,7 @@ def model_c():
         m = pm.Normal("m")
         s = pm.LogNormal("s")
         pm.Normal("g", m, s, shape=5)
+        pm.Exponential("e", scale=s, shape=7)
     return mod
 
 
@@ -20,31 +21,34 @@ def model_nc():
         m = pm.Normal("m")
         s = pm.LogNormal("s")
         pm.Deterministic("g", pm.Normal("z", shape=5) * s + m)
+        pm.Deterministic("e", pm.Exponential("z_e", 1, shape=7) * s)
     return mod
 
 
-def test_reparametrize_created(model_c: pm.Model):
-    model_reparam, vip = vip_reparametrize(model_c, ["g"])
-    assert "g" in vip.get_lambda()
-    assert "g::lam_logit__" in model_reparam.named_vars
-    assert "g::tau_" in model_reparam.named_vars
+@pytest.mark.parametrize("var", ["g", "e"])
+def test_reparametrize_created(model_c: pm.Model, var):
+    model_reparam, vip = vip_reparametrize(model_c, [var])
+    assert f"{var}" in vip.get_lambda()
+    assert f"{var}::lam_logit__" in model_reparam.named_vars
+    assert f"{var}::tau_" in model_reparam.named_vars
     vip.set_all_lambda(1)
-    assert ~np.isfinite(model_reparam["g::lam_logit__"].get_value()).any()
+    assert ~np.isfinite(model_reparam[f"{var}::lam_logit__"].get_value()).any()
 
 
-def test_random_draw(model_c: pm.Model, model_nc):
+@pytest.mark.parametrize("var", ["g", "e"])
+def test_random_draw(model_c: pm.Model, model_nc, var):
     model_c = pm.do(model_c, {"m": 3, "s": 2})
     model_nc = pm.do(model_nc, {"m": 3, "s": 2})
-    model_v, vip = vip_reparametrize(model_c, ["g"])
-    assert "g" in [v.name for v in model_v.deterministics]
-    c = pm.draw(model_c["g"], random_seed=42, draws=1000)
-    nc = pm.draw(model_nc["g"], random_seed=42, draws=1000)
+    model_v, vip = vip_reparametrize(model_c, [var])
+    assert var in [v.name for v in model_v.deterministics]
+    c = pm.draw(model_c[var], random_seed=42, draws=1000)
+    nc = pm.draw(model_nc[var], random_seed=42, draws=1000)
     vip.set_all_lambda(1)
-    v_1 = pm.draw(model_v["g"], random_seed=42, draws=1000)
+    v_1 = pm.draw(model_v[var], random_seed=42, draws=1000)
     vip.set_all_lambda(0)
-    v_0 = pm.draw(model_v["g"], random_seed=42, draws=1000)
+    v_0 = pm.draw(model_v[var], random_seed=42, draws=1000)
     vip.set_all_lambda(0.5)
-    v_05 = pm.draw(model_v["g"], random_seed=42, draws=1000)
+    v_05 = pm.draw(model_v[var], random_seed=42, draws=1000)
     np.testing.assert_allclose(c.mean(), nc.mean())
     np.testing.assert_allclose(c.mean(), v_0.mean())
     np.testing.assert_allclose(v_05.mean(), v_1.mean())
@@ -57,10 +61,12 @@ def test_random_draw(model_c: pm.Model, model_nc):
 
 
 def test_reparam_fit(model_c):
-    model_v, vip = vip_reparametrize(model_c, ["g"])
+    vars = ["g", "e"]
+    model_v, vip = vip_reparametrize(model_c, ["g", "e"])
     with model_v:
-        vip.fit(random_seed=42)
-    np.testing.assert_allclose(vip.get_lambda()["g"], 0, atol=0.01)
+        vip.fit(50000, random_seed=42)
+    for var in vars:
+        np.testing.assert_allclose(vip.get_lambda()[var], 0, atol=0.01)
 
 
 def test_multilevel():