diff --git a/pyro/infer/autoguide/effect.py b/pyro/infer/autoguide/effect.py
index d7abe537b0..6de36a87b3 100644
--- a/pyro/infer/autoguide/effect.py
+++ b/pyro/infer/autoguide/effect.py
@@ -157,12 +157,16 @@ def __init__(
         self.init_loc_fn = init_loc_fn
         self._init_scale = init_scale
         self._computing_median = False
+        self._computing_quantiles = False
+        self._quantile_values = None
 
     def get_posterior(
         self, name: str, prior: Distribution
     ) -> Union[Distribution, torch.Tensor]:
         if self._computing_median:
             return self._get_posterior_median(name, prior)
+        if self._computing_quantiles:
+            return self._get_posterior_quantiles(name, prior)
 
         with helpful_support_errors({"name": name, "fn": prior}):
             transform = biject_to(prior.support)
@@ -205,11 +209,30 @@ def median(self, *args, **kwargs):
         finally:
             self._computing_median = False
 
+    @torch.no_grad()
     def _get_posterior_median(self, name, prior):
         transform = biject_to(prior.support)
         loc, scale = self._get_params(name, prior)
         return transform(loc)
 
+    def quantiles(self, quantiles, *args, **kwargs):
+        self._computing_quantiles = True
+        self._quantile_values = quantiles
+        try:
+            return self(*args, **kwargs)
+        finally:
+            self._computing_quantiles = False
+
+    @torch.no_grad()
+    def _get_posterior_quantiles(self, name, prior):
+        transform = biject_to(prior.support)
+        loc, scale = self._get_params(name, prior)
+        site_quantiles = torch.tensor(
+            self._quantile_values, dtype=loc.dtype, device=loc.device
+        )
+        site_quantiles_values = dist.Normal(loc, scale).icdf(site_quantiles)
+        return transform(site_quantiles_values)
+
 
 class AutoHierarchicalNormalMessenger(AutoNormalMessenger):
     """
@@ -263,12 +286,16 @@ def __init__(
         self._init_weight = init_weight
         self._hierarchical_sites = hierarchical_sites
         self._computing_median = False
+        self._computing_quantiles = False
+        self._quantile_values = None
 
     def get_posterior(
         self, name: str, prior: Distribution
     ) -> Union[Distribution, torch.Tensor]:
         if self._computing_median:
             return self._get_posterior_median(name, prior)
+        if self._computing_quantiles:
+            return self._get_posterior_quantiles(name, prior)
 
         with helpful_support_errors({"name": name, "fn": prior}):
             transform = biject_to(prior.support)
@@ -351,6 +378,7 @@ def median(self, *args, **kwargs):
         finally:
             self._computing_median = False
 
+    @torch.no_grad()
     def _get_posterior_median(self, name, prior):
         transform = biject_to(prior.support)
         if (self._hierarchical_sites is None) or (name in self._hierarchical_sites):
@@ -360,6 +388,29 @@ def _get_posterior_median(self, name, prior):
             loc, scale = self._get_params(name, prior)
         return transform(loc)
 
+    def quantiles(self, quantiles, *args, **kwargs):
+        self._computing_quantiles = True
+        self._quantile_values = quantiles
+        try:
+            return self(*args, **kwargs)
+        finally:
+            self._computing_quantiles = False
+
+    @torch.no_grad()
+    def _get_posterior_quantiles(self, name, prior):
+        transform = biject_to(prior.support)
+        if (self._hierarchical_sites is None) or (name in self._hierarchical_sites):
+            loc, scale, weight = self._get_params(name, prior)
+            loc = loc + transform.inv(prior.mean) * weight
+        else:
+            loc, scale = self._get_params(name, prior)
+
+        site_quantiles = torch.tensor(
+            self._quantile_values, dtype=loc.dtype, device=loc.device
+        )
+        site_quantiles_values = dist.Normal(loc, scale).icdf(site_quantiles)
+        return transform(site_quantiles_values)
+
 
 class AutoRegressiveMessenger(AutoMessenger):
     """
diff --git a/tests/infer/test_autoguide.py b/tests/infer/test_autoguide.py
index f316ee049d..d3d7a7d7e9 100644
--- a/tests/infer/test_autoguide.py
+++ b/tests/infer/test_autoguide.py
@@ -522,10 +522,13 @@ def AutoGuideList_x(model):
         AutoLowRankMultivariateNormal,
         AutoLaplaceApproximation,
         AutoGuideList_x,
+        AutoNormalMessenger,
+        AutoHierarchicalNormalMessenger,
     ],
 )
 @pytest.mark.parametrize("Elbo", [Trace_ELBO, TraceGraph_ELBO, TraceEnum_ELBO])
 def test_quantiles(auto_class, Elbo):
+    xfail_messenger(auto_class, Elbo)
     def model():
         pyro.sample("y", dist.LogNormal(0.0, 1.0))
         pyro.sample("z", dist.Beta(2.0, 2.0).expand([2]).to_event(1))