diff --git a/numpyro/distributions/discrete.py b/numpyro/distributions/discrete.py
index a41702a29..bce6c692f 100644
--- a/numpyro/distributions/discrete.py
+++ b/numpyro/distributions/discrete.py
@@ -29,9 +29,11 @@
 
 import numpy as np
 
+import jax
 from jax import lax
 from jax.nn import softmax, softplus
 import jax.numpy as jnp
+from jax.ops import index_add
 import jax.random as random
 from jax.scipy.special import expit, gammaln, logsumexp, xlog1py, xlogy
 
@@ -608,8 +610,9 @@ class Poisson(Distribution):
     support = constraints.nonnegative_integer
     is_discrete = True
 
-    def __init__(self, rate, validate_args=None):
+    def __init__(self, rate, *, is_sparse=False, validate_args=None):
         self.rate = rate
+        self.is_sparse = is_sparse
         super(Poisson, self).__init__(jnp.shape(rate), validate_args=validate_args)
 
     def sample(self, key, sample_shape=()):
@@ -620,6 +623,23 @@ def sample(self, key, sample_shape=()):
     def log_prob(self, value):
         if self._validate_args:
             self._validate_sample(value)
+        value = jax.device_get(value)
+        if (
+            self.is_sparse
+            and not isinstance(value, jax.core.Tracer)
+            and jnp.size(value) > 1
+        ):
+            shape = lax.broadcast_shapes(self.batch_shape, jnp.shape(value))
+            rate = jnp.broadcast_to(self.rate, shape).reshape(-1)
+            value = jnp.broadcast_to(value, shape).reshape(-1)
+            nonzero = value > 0
+            sparse_value = value[nonzero]
+            sparse_rate = rate[nonzero]
+            return index_add(
+                -rate,
+                nonzero,
+                jnp.log(sparse_rate) * sparse_value - gammaln(sparse_value + 1),
+            ).reshape(shape)
         return (jnp.log(self.rate) * value) - gammaln(value + 1) - self.rate
 
     @property
diff --git a/test/test_distributions.py b/test/test_distributions.py
index 500d62d9e..7e791c0a4 100644
--- a/test/test_distributions.py
+++ b/test/test_distributions.py
@@ -47,9 +47,7 @@ def _identity(x):
 
 class T(namedtuple("TestCase", ["jax_dist", "sp_dist", "params"])):
     def __new__(cls, jax_dist, *params):
-        sp_dist = None
-        if jax_dist in _DIST_MAP:
-            sp_dist = _DIST_MAP[jax_dist]
+        sp_dist = get_sp_dist(jax_dist)
         return super(cls, T).__new__(cls, jax_dist, sp_dist, params)
 
 
@@ -98,6 +96,11 @@ def sample(self, key, sample_shape=()):
         return transform(unconstrained_samples)
 
 
+class SparsePoisson(dist.Poisson):
+    def __init__(self, rate, *, validate_args=None):
+        super().__init__(rate, is_sparse=True, validate_args=validate_args)
+
+
 _DIST_MAP = {
     dist.BernoulliProbs: lambda probs: osp.bernoulli(p=probs),
     dist.BernoulliLogits: lambda logits: osp.bernoulli(p=_to_probs_bernoulli(logits)),
@@ -141,6 +144,14 @@ def sample(self, key, sample_shape=()):
     _TruncatedNormal: _truncnorm_to_scipy,
 }
 
+
+def get_sp_dist(jax_dist):
+    classes = jax_dist.mro() if isinstance(jax_dist, type) else [jax_dist]
+    for cls in classes:
+        if cls in _DIST_MAP:
+            return _DIST_MAP[cls]
+
+
 CONTINUOUS = [
     T(dist.Beta, 0.2, 1.1),
     T(dist.Beta, 1.0, jnp.array([2.0, 2.0])),
@@ -331,6 +342,8 @@ def sample(self, key, sample_shape=()):
     T(dist.OrderedLogistic, jnp.array([-4, 3, 4, 5]), jnp.array([-1.5])),
     T(dist.Poisson, 2.0),
     T(dist.Poisson, jnp.array([2.0, 3.0, 5.0])),
+    T(SparsePoisson, 2.0),
+    T(SparsePoisson, jnp.array([2.0, 3.0, 5.0])),
     T(dist.ZeroInflatedPoisson, 0.6, 2.0),
     T(dist.ZeroInflatedPoisson, jnp.array([0.2, 0.7, 0.3]), jnp.array([2.0, 3.0, 5.0])),
 ]
@@ -652,6 +665,29 @@ def test_pathwise_gradient(jax_dist, sp_dist, params):
         assert_allclose(actual_grad[i], expected_grad, rtol=0.005)
 
 
+@pytest.mark.parametrize(
+    "jax_dist, sp_dist, params", CONTINUOUS + DISCRETE + DIRECTIONAL
+)
+def test_jit_log_likelihood(jax_dist, sp_dist, params):
+    if jax_dist.__name__ in (
+        "GaussianRandomWalk",
+        "_ImproperWrapper",
+        "LKJ",
+        "LKJCholesky",
+    ):
+        pytest.xfail(reason="non-jittable params")
+
+    rng_key = random.PRNGKey(0)
+    samples = jax_dist(*params).sample(key=rng_key, sample_shape=(2, 3))
+
+    def log_likelihood(*params):
+        return jax_dist(*params).log_prob(samples)
+
+    expected = log_likelihood(*params)
+    actual = jax.jit(log_likelihood)(*params)
+    assert_allclose(actual, expected, atol=1e-5)
+
+
 @pytest.mark.parametrize(
     "jax_dist, sp_dist, params", CONTINUOUS + DISCRETE + DIRECTIONAL
 )
@@ -688,7 +724,7 @@ def test_log_prob(jax_dist, sp_dist, params, prepend_shape, jit):
                 # old api
                 low, loc, scale = params
                 high = jnp.inf
-            sp_dist = _DIST_MAP[type(jax_dist.base_dist)](loc, scale)
+            sp_dist = get_sp_dist(type(jax_dist.base_dist))(loc, scale)
             expected = sp_dist.logpdf(samples) - jnp.log(
                 sp_dist.cdf(high) - sp_dist.cdf(low)
             )