diff --git a/include/mitsuba/core/distr_1d.h b/include/mitsuba/core/distr_1d.h
index 5772ca005..57a8c1447 100644
--- a/include/mitsuba/core/distr_1d.h
+++ b/include/mitsuba/core/distr_1d.h
@@ -21,6 +21,7 @@ template <typename Value> struct DiscreteDistribution {
     using Float = std::conditional_t<dr::is_static_array_v<Value>,
                                      dr::value_t<Value>, Value>;
     using FloatStorage   = DynamicBuffer<Float>;
+    using UInt32         = dr::uint32_array_t<Float>;
     using Index          = dr::uint32_array_t<Value>;
     using Mask           = dr::mask_t<Value>;
 
@@ -46,17 +47,15 @@ template <typename Value> struct DiscreteDistribution {
     /// Initialize from a given floating point array
     DiscreteDistribution(const ScalarFloat *values, size_t size)
         : m_pmf(dr::load<FloatStorage>(values, size)) {
-        compute_cdf(values, size);
+        compute_cdf_scalar(values, size);
     }
 
     /// Update the internal state. Must be invoked when changing the pmf.
     void update() {
         if constexpr (dr::is_jit_v<Float>) {
-            FloatStorage temp = dr::migrate(m_pmf, AllocType::Host);
-            dr::sync_thread();
-            compute_cdf(temp.data(), temp.size());
+            compute_cdf();
         } else {
-            compute_cdf(m_pmf.data(), m_pmf.size());
+            compute_cdf_scalar(m_pmf.data(), m_pmf.size());
         }
     }
 
@@ -108,21 +107,28 @@ template <typename Value> struct DiscreteDistribution {
      * \brief %Transform a uniformly distributed sample to the stored
      * distribution
      *
-     * \param value
+     * \param sample
      *     A uniformly distributed sample on the interval [0, 1].
      *
      * \return
      *     The discrete index associated with the sample
      */
-    Index sample(Value value, Mask active = true) const {
+    Index sample(Value sample, Mask active = true) const {
         MI_MASK_ARGUMENT(active);
 
-        value *= m_sum;
+        sample *= m_sum;
 
         return dr::binary_search<Index>(
             m_valid.x(), m_valid.y(),
             [&](Index index) DRJIT_INLINE_LAMBDA {
-                return dr::gather<Value>(m_cdf, index, active) < value;
+                Value value = dr::gather<Value>(m_cdf, index, active);
+                if constexpr (!dr::is_jit_v<Float>) {
+                    return value < sample;
+                } else {
+                    // `m_valid` is not computed in JIT variants
+                    return ((value < sample) || (dr::eq(value, 0))) &&
+                           dr::neq(value, m_sum);
+                }
             }
         );
     }
@@ -209,7 +215,21 @@ template <typename Value> struct DiscreteDistribution {
     }
 
 private:
-    void compute_cdf(const ScalarFloat *pmf, size_t size) {
+    void compute_cdf() {
+        if (m_pmf.empty())
+            Throw("DiscreteDistribution: empty distribution!");
+        if (!dr::all(m_pmf >= 0.f))
+            Throw("DiscreteDistribution: entries must be non-negative!");
+        if (!dr::any(m_pmf > 0.f))
+            Throw("DiscreteDistribution: no probability mass found!");
+
+        m_cdf = dr::prefix_sum(m_pmf, false);
+        m_valid = ScalarVector2u(0, m_pmf.size() - 1);
+        m_sum = dr::gather<Float>(m_cdf, UInt32(m_pmf.size() - 1));
+        m_normalization = 1.0 / m_sum;
+    }
+
+    void compute_cdf_scalar(const ScalarFloat *pmf, size_t size) {
         if (size == 0)
             Throw("DiscreteDistribution: empty distribution!");
 
@@ -225,7 +245,7 @@ template <typename Value> struct DiscreteDistribution {
             if (value < 0.0) {
                 Throw("DiscreteDistribution: entries must be non-negative!");
             } else if (value > 0.0) {
-                // Determine the first and last wavelength bin with nonzero density
+                // Determine the first and last bin with nonzero density
                 if (m_valid.x() == (uint32_t) -1)
                     m_valid.x() = i;
                 m_valid.y() = i;