diff --git a/pymc/sampling_jax.py b/pymc/sampling_jax.py
index 795050e5aa6..6fdbd64e730 100644
--- a/pymc/sampling_jax.py
+++ b/pymc/sampling_jax.py
@@ -26,7 +26,8 @@
 from aesara.link.jax.dispatch import jax_funcify
 
 from pymc import Model, modelcontext
-from pymc.aesaraf import compile_rv_inplace
+from pymc.aesaraf import compile_rv_inplace, inputvars
+from pymc.util import get_default_varnames
 
 warnings.warn("This module is experimental.")
 
@@ -101,6 +102,7 @@ def sample_numpyro_nuts(
     target_accept=0.8,
     random_seed=10,
     model=None,
+    var_names=None,
     progress_bar=True,
     keep_untransformed=False,
 ):
@@ -108,6 +110,11 @@ def sample_numpyro_nuts(
 
     model = modelcontext(model)
 
+    if var_names is None:
+        var_names = model.unobserved_value_vars
+
+    vars_to_sample = list(get_default_varnames(var_names, include_transformed=keep_untransformed))
+
     tic1 = pd.Timestamp.now()
     print("Compiling...", file=sys.stdout)
 
@@ -143,45 +150,28 @@ def sample_numpyro_nuts(
     seed = jax.random.PRNGKey(random_seed)
     map_seed = jax.random.split(seed, chains)
 
-    pmap_numpyro.run(map_seed, init_params=init_state_batched, extra_fields=("num_steps",))
+    if chains == 1:
+        pmap_numpyro.run(seed, init_params=init_state, extra_fields=("num_steps",))
+    else:
+        pmap_numpyro.run(map_seed, init_params=init_state_batched, extra_fields=("num_steps",))
+
     raw_mcmc_samples = pmap_numpyro.get_samples(group_by_chain=True)
 
     tic3 = pd.Timestamp.now()
     print("Sampling time = ", tic3 - tic2, file=sys.stdout)
 
     print("Transforming variables...", file=sys.stdout)
-    mcmc_samples = []
-    for i, (value_var, raw_samples) in enumerate(zip(model.value_vars, raw_mcmc_samples)):
-        raw_samples = at.constant(np.asarray(raw_samples))
-
-        rv = model.values_to_rvs[value_var]
-        transform = getattr(value_var.tag, "transform", None)
-
-        if transform is not None:
-            # TODO: This will fail when the transformation depends on another variable
-            #  such as in interval transform with RVs as edges
-            trans_samples = transform.backward(raw_samples, *rv.owner.inputs)
-            trans_samples.name = rv.name
-            mcmc_samples.append(trans_samples)
-
-            if keep_untransformed:
-                raw_samples.name = value_var.name
-                mcmc_samples.append(raw_samples)
-        else:
-            raw_samples.name = rv.name
-            mcmc_samples.append(raw_samples)
-
-    mcmc_varnames = [var.name for var in mcmc_samples]
-    mcmc_samples = compile_rv_inplace(
-        [],
-        mcmc_samples,
-        mode="JAX",
-    )()
+    mcmc_samples = {}
+    for v in vars_to_sample:
+        fgraph = FunctionGraph(model.value_vars, [v], clone=False)
+        jax_fn = jax_funcify(fgraph)
+        result = jax.vmap(jax.vmap(jax_fn))(*raw_mcmc_samples)[0]
+        mcmc_samples[v.name] = result
 
     tic4 = pd.Timestamp.now()
     print("Transformation time = ", tic4 - tic3, file=sys.stdout)
 
-    posterior = {k: v for k, v in zip(mcmc_varnames, mcmc_samples)}
+    posterior = mcmc_samples
     az_trace = az.from_dict(posterior=posterior)
 
     return az_trace
diff --git a/pymc/tests/test_sampling_jax.py b/pymc/tests/test_sampling_jax.py
index e5180e19f8d..3fd04059c09 100644
--- a/pymc/tests/test_sampling_jax.py
+++ b/pymc/tests/test_sampling_jax.py
@@ -44,6 +44,23 @@ def test_transform_samples():
     assert 1.5 < trace.posterior["sigma"].mean() < 2.5
 
 
+def test_deterministic_samples():
+    aesara.config.on_opt_error = "raise"
+    np.random.seed(13244)
+
+    obs = np.random.normal(10, 2, size=100)
+    obs_at = aesara.shared(obs, borrow=True, name="obs")
+    with pm.Model() as model:
+        a = pm.Uniform("a", -20, 20)
+        b = pm.Deterministic("b", a / 2.0)
+        c = pm.Normal("c", a, sigma=1.0, observed=obs_at)
+
+        trace = sample_numpyro_nuts(chains=2, random_seed=1322, keep_untransformed=True)
+
+    assert 8 < trace.posterior["a"].mean() < 11
+    assert np.allclose(trace.posterior["b"].values, trace.posterior["a"].values / 2)
+
+
 def test_replace_shared_variables():
     x = aesara.shared(5, name="shared_x")