diff --git a/pyro/nn/module.py b/pyro/nn/module.py
index afa1ac5851..b84a17875b 100644
--- a/pyro/nn/module.py
+++ b/pyro/nn/module.py
@@ -163,6 +163,7 @@ class PyroSample:
         assert isinstance(my_module, PyroModule)
         my_module.x = PyroSample(Normal(0, 1))                    # independent
         my_module.y = PyroSample(lambda self: Normal(self.x, 1))  # dependent
+        my_module.z = PyroSample(lambda self: self.y ** 2)        # deterministic dependent
 
     or EXPERIMENTALLY as a decorator on lazy initialization methods::
 
@@ -175,16 +176,22 @@ def x(self):
             def y(self):
                 return Normal(self.x, 1)  # dependent
 
+            @PyroSample
+            def z(self):
+                return self.y ** 2        # deterministic dependent
+
             def forward(self):
-                return self.y             # accessed like a @property
+                return self.z             # accessed like a @property
 
     :param prior: distribution object or function that inputs the
         :class:`PyroModule` instance ``self`` and returns a distribution
-        object.
+        object or a deterministic value.
     """
 
     prior: Union[
-        "TorchDistributionMixin", Callable[["PyroModule"], "TorchDistributionMixin"]
+        "TorchDistributionMixin",
+        Callable[["PyroModule"], "TorchDistributionMixin"],
+        Callable[["PyroModule"], torch.Tensor],
     ]
 
     def __post_init__(self) -> None:
@@ -605,13 +612,17 @@ def __getattr__(self, name: str) -> Any:
                     if value is None:
                         if not hasattr(prior, "sample"):  # if not a distribution
                             prior = prior(self)
-                        value = pyro.sample(fullname, prior)
+                        value = (
+                            pyro.deterministic(fullname, prior)
+                            if isinstance(prior, torch.Tensor)
+                            else pyro.sample(fullname, prior)
+                        )
                         context.set(fullname, value)
                     return value
                 else:  # Cannot determine supermodule and hence cannot compute fullname.
                     if not hasattr(prior, "sample"):  # if not a distribution
                         prior = prior(self)
-                    return prior()
+                    return prior if isinstance(prior, torch.Tensor) else prior()
 
         result = super().__getattr__(name)
 
diff --git a/tests/nn/test_module.py b/tests/nn/test_module.py
index dda5fb03e3..07c4daedd1 100644
--- a/tests/nn/test_module.py
+++ b/tests/nn/test_module.py
@@ -491,9 +491,10 @@ def __init__(self, size):
         )
         self.s = PyroSample(dist.Normal(0, 1))
         self.t = PyroSample(lambda self: dist.Normal(self.s, self.z))
+        self.u = PyroSample(lambda self: self.t**2)
 
     def forward(self):
-        return self.x + self.y + self.t
+        return self.x + self.y + self.u
 
 
 class DecoratorModel(PyroModule):
@@ -521,8 +522,12 @@ def s(self):
     def t(self):
         return dist.Normal(self.s, self.z).to_event(1)
 
+    @PyroSample
+    def u(self):
+        return self.t**2
+
     def forward(self):
-        return self.x + self.y + self.t
+        return self.x + self.y + self.u
 
 
 @pytest.mark.parametrize("Model", [AttributeModel, DecoratorModel])
@@ -531,19 +536,32 @@ def test_decorator(Model, size):
     model = Model(size)
     for i in range(2):
         trace = poutine.trace(model).get_trace()
-        assert set(trace.nodes.keys()) == {"_INPUT", "x", "y", "z", "s", "t", "_RETURN"}
+        assert set(trace.nodes.keys()) == {
+            "_INPUT",
+            "x",
+            "y",
+            "z",
+            "s",
+            "t",
+            "u",
+            "_RETURN",
+        }
 
         assert trace.nodes["x"]["type"] == "param"
         assert trace.nodes["y"]["type"] == "param"
         assert trace.nodes["z"]["type"] == "param"
         assert trace.nodes["s"]["type"] == "sample"
         assert trace.nodes["t"]["type"] == "sample"
+        assert trace.nodes["u"]["type"] == "sample"
 
         assert trace.nodes["x"]["value"].shape == (size,)
         assert trace.nodes["y"]["value"].shape == (size,)
         assert trace.nodes["z"]["value"].shape == (size,)
         assert trace.nodes["s"]["value"].shape == ()
         assert trace.nodes["t"]["value"].shape == (size,)
+        assert trace.nodes["u"]["value"].shape == (size,)
+
+        assert trace.nodes["u"]["infer"] == {"_deterministic": True}
 
 
 def test_mixin_factory():