diff --git a/crates/content/src/lib.rs b/crates/content/src/lib.rs
index c52916d332..4957f86861 100644
--- a/crates/content/src/lib.rs
+++ b/crates/content/src/lib.rs
@@ -730,11 +730,14 @@ impl Matrix {
     pub fn invert(&self) -> Option<Matrix> {
         let [a, b, c, d, e, f] = self.0;
         let det = a * d - b * c;
-        if det.abs() < 1e-12 || !det.is_finite() {
+        if det == 0.0 || !det.is_finite() || det.abs() <= 1e-12 * ((a * d).abs() + (b * c).abs()) {
             return None;
         }
         let (ia, ib, ic, id) = (d / det, -b / det, -c / det, a / det);
-        Some(Matrix([ia, ib, ic, id, -(e * ia + f * ic), -(e * ib + f * id)]))
+        let inverse = [ia, ib, ic, id, -(e * ia + f * ic), -(e * ib + f * id)];
+        // A determinant that underflows toward zero can still pass the relative check above,
+        // and dividing by it overflows: such a matrix has no usable inverse.
+        inverse.iter().all(|v| v.is_finite()).then_some(Matrix(inverse))
     }
 
     /// The bounding box of a rectangle `[x0 y0 x1 y1]` after this transform.
diff --git a/crates/content/src/tests.rs b/crates/content/src/tests.rs
index c5c7a3aaac..9ac9297cd2 100644
--- a/crates/content/src/tests.rs
+++ b/crates/content/src/tests.rs
@@ -552,3 +552,17 @@ fn inline_images_end_where_the_renderer_ends_them() {
         assert_eq!((parsed.skipped, parsed.ambiguous_images), (0, 0), "{}", String::from_utf8_lossy(data));
     }
 }
+
+#[test]
+fn invert_accepts_small_scale_and_rejects_singular() {
+    let m = Matrix([1e-7, 0., 0., 1e-7, 0., 0.]);
+    let inv = m.invert().expect("a uniform 1e-7 scale is invertible");
+    let id = m.then(&inv).0;
+    for (got, want) in id.iter().zip(Matrix::IDENTITY.0) {
+        assert!((got - want).abs() < 1e-9, "{id:?}");
+    }
+    assert!(Matrix([1., 2., 2., 4., 0., 0.]).invert().is_none());
+    assert!(Matrix([f64::NAN, 0., 0., 1., 0., 0.]).invert().is_none());
+    // A subnormal scale passes the relative check but its inverse overflows (CodeRabbit on #5703).
+    assert!(Matrix([1e-310, 0., 0., 1., 0., 0.]).invert().is_none());
+}