diff --git a/CHANGELOG.md b/CHANGELOG.md
index 3085994c4d..0770e5ef09 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -12,8 +12,10 @@ You may also find the [Upgrade Guide](https://rust-random.github.io/book/update.
 
 ### Fixes
 - Fix `WeightedIndex` panic when the sum of float weights is infinite; return `Error::Overflow` instead ([#1808])
+- Fix spurious `Error::NonFinite` from `Uniform::new_inclusive` on large finite float ranges such as `0.0..=f64::MAX` ([#1809])
 
 [#1808]: https://github.com/rust-random/rand/pull/1808
+[#1809]: https://github.com/rust-random/rand/pull/1809
 
 ## [0.10.2] — 2026-07-02
 
diff --git a/src/distr/uniform_float.rs b/src/distr/uniform_float.rs
index 3e91c0f3a0..b4351db511 100644
--- a/src/distr/uniform_float.rs
+++ b/src/distr/uniform_float.rs
@@ -66,7 +66,10 @@ macro_rules! uniform_float_impl {
                 let max_rand = <$ty>::splat(1.0 as $f_scalar - $f_scalar::EPSILON);
 
                 loop {
-                    let mask = (scale * max_rand + low).gt_mask(high);
+                    // `not_le_mask` rather than `gt_mask` so that a non-finite
+                    // product (which compares `false` under `>`) is also
+                    // reduced instead of being silently accepted.
+                    let mask = (scale * max_rand + low).not_le_mask(high);
                     if !mask.any() {
                         break;
                     }
@@ -126,12 +129,18 @@ macro_rules! uniform_float_impl {
                     return Err(Error::EmptyRange);
                 }
 
-                let max_rand = <$ty>::splat(1.0 as $f_scalar - $f_scalar::EPSILON);
-                let scale = (high - low) / max_rand;
-                if !scale.all_finite() {
+                let range = high - low;
+                if !range.all_finite() {
                     return Err(Error::NonFinite);
                 }
 
+                let max_rand = <$ty>::splat(1.0 as $f_scalar - $f_scalar::EPSILON);
+                // This division may overflow to infinity even where `range` is
+                // finite (e.g. `low = 0.0`, `high = f64::MAX`). `new_bounded`
+                // reduces `scale` until samples cannot exceed `high`, which
+                // handles the infinite case in a single step.
+                let scale = range / max_rand;
+
                 Ok(Self::new_bounded(low, high, scale))
             }
 
@@ -238,6 +247,8 @@ mod tests {
                     (-<$f_scalar>::from_bits(7), -0.0),
                     (0.1 * $f_scalar::MAX, $f_scalar::MAX),
                     (-$f_scalar::MAX * 0.2, $f_scalar::MAX * 0.7),
+                    (0.0, $f_scalar::MAX),
+                    (-$f_scalar::MAX, 0.0),
                 ];
                 for &(low_scalar, high_scalar) in v.iter() {
                     for lane in 0..<$ty>::LEN {
@@ -360,6 +371,10 @@ mod tests {
     #[test]
     fn test_float_overflow() {
         assert_eq!(Uniform::try_from(f64::MIN..f64::MAX), Err(Error::NonFinite));
+        assert_eq!(
+            Uniform::try_from(f64::MIN..=f64::MAX),
+            Err(Error::NonFinite)
+        );
     }
 
     #[test]
diff --git a/src/distr/utils.rs b/src/distr/utils.rs
index d3cfbf6a0f..1a74bdca1d 100644
--- a/src/distr/utils.rs
+++ b/src/distr/utils.rs
@@ -219,7 +219,11 @@ pub(crate) trait FloatSIMDUtils {
     fn all_finite(self) -> bool;
 
     type Mask;
-    fn gt_mask(self, other: Self) -> Self::Mask;
+
+    // The negation of `<=`, which (unlike `>`) is also `true` for lanes which
+    // are not-a-number. This lets callers treat NaN like an out-of-bounds
+    // value rather than silently accepting it.
+    fn not_le_mask(self, other: Self) -> Self::Mask;
 
     // Decrease all lanes where the mask is `true` to the next lower value
     // representable by the floating-point type. At least one of the lanes
@@ -294,8 +298,8 @@ macro_rules! scalar_float_impl {
             }
 
             #[inline(always)]
-            fn gt_mask(self, other: Self) -> Self::Mask {
-                self > other
+            fn not_le_mask(self, other: Self) -> Self::Mask {
+                !(self <= other)
             }
 
             #[inline(always)]
@@ -357,8 +361,8 @@ macro_rules! simd_impl {
             }
 
             #[inline(always)]
-            fn gt_mask(self, other: Self) -> Self::Mask {
-                self.simd_gt(other)
+            fn not_le_mask(self, other: Self) -> Self::Mask {
+                !self.simd_le(other)
             }
 
             #[inline(always)]