diff --git a/internal/knn/knn.go b/internal/knn/knn.go
index ad5ef7e..ea07d1c 100644
--- a/internal/knn/knn.go
+++ b/internal/knn/knn.go
@@ -38,7 +38,7 @@ func path(n *node.N, v vector.V) []*node.N {
 // slice.
 func KNN(n *node.N, p vector.V, k int) []*node.N {
 	q := pq.New(k)
-	knn(n, p, q)
+	knn(n, p, q, make([]float64, p.Dimension()))
 
 	// q.Pop() returns furthest distance first, so we need to reverse the
 	// queue for the KNN output.
@@ -50,15 +50,34 @@ func KNN(n *node.N, p vector.V, k int) []*node.N {
 	return ns
 }
 
+// sub uses the scratch space to calculate the difference between two vectors.
+//
+// Care should be taken that the scratch space is not used concurrently, as
+// subsequent calls will modify the slice.
+func sub(v vector.V, u vector.V, scratch []float64) vector.V {
+	for i := vector.D(0); i < v.Dimension(); i++ {
+		scratch[i] = v.X(i) - u.X(i)
+	}
+	return vector.V(scratch)
+}
+
 // knn recursively searches for the k-nearest neighbors of a node. The priority
 // queue input q in effect tracks the searched space.
-func knn(n *node.N, p vector.V, q *pq.Q) {
+//
+// The scratch input is used to reduce the amount of vector.Sub operations, as
+// the returned vector is copy-constructed.
+//
+// This does not seem have a significant impact relative to the overall
+// execution time, but we do see the overall allocs cut in half.
+//
+// TODO(minkezhang): Determine if this optimization is actually useful.
+func knn(n *node.N, p vector.V, q *pq.Q, scratch []float64) {
 	if n == nil {
 		return
 	}
 
 	for _, n := range path(n, p) {
-		if d := vector.Magnitude(vector.Sub(p, n.P())); !q.Full() || d < q.Priority() {
+		if d := vector.Magnitude(sub(p, n.P(), scratch)); !q.Full() || d < q.Priority() {
 			q.Push(n, d)
 		}
 
@@ -84,7 +103,7 @@ func knn(n *node.N, p vector.V, q *pq.Q) {
 				c = n.L()
 			}
 
-			knn(c, p, q)
+			knn(c, p, q, scratch)
 		}
 	}
 }