diff --git a/lucene/CHANGES.txt b/lucene/CHANGES.txt
index 39d7403a11c..de350ab0406 100644
--- a/lucene/CHANGES.txt
+++ b/lucene/CHANGES.txt
@@ -76,6 +76,8 @@ Optimizations
 * GITHUB#14133: Dense blocks of postings are now encoded as bit sets.
   (Adrien Grand)
 
+* GITHUB#14094: Early terminate when HNSW nearest neighbor queue saturates (Tommaso Teofili)
+
 Bug Fixes
 ---------------------
 
diff --git a/lucene/core/src/java/org/apache/lucene/codecs/lucene99/Lucene99HnswVectorsReader.java b/lucene/core/src/java/org/apache/lucene/codecs/lucene99/Lucene99HnswVectorsReader.java
index b29f9da5b41..3ce538eccbb 100644
--- a/lucene/core/src/java/org/apache/lucene/codecs/lucene99/Lucene99HnswVectorsReader.java
+++ b/lucene/core/src/java/org/apache/lucene/codecs/lucene99/Lucene99HnswVectorsReader.java
@@ -36,6 +36,7 @@
 import org.apache.lucene.index.VectorEncoding;
 import org.apache.lucene.index.VectorSimilarityFunction;
 import org.apache.lucene.internal.hppc.IntObjectHashMap;
+import org.apache.lucene.search.HnswQueueSaturationCollector;
 import org.apache.lucene.search.KnnCollector;
 import org.apache.lucene.store.ChecksumIndexInput;
 import org.apache.lucene.store.DataInput;
@@ -314,10 +315,16 @@ private void search(
       return;
     }
     final RandomVectorScorer scorer = scorerSupplier.get();
-    final KnnCollector collector =
-        new OrdinalTranslatedKnnCollector(knnCollector, scorer::ordToDoc);
     final Bits acceptedOrds = scorer.getAcceptOrds(acceptDocs);
     if (knnCollector.k() < scorer.maxOrd()) {
+      final KnnCollector collector;
+      OrdinalTranslatedKnnCollector ordinalTranslatedKnnCollector =
+          new OrdinalTranslatedKnnCollector(knnCollector, scorer::ordToDoc);
+      if (scorer.maxOrd() > 1000) {
+        collector = new HnswQueueSaturationCollector(ordinalTranslatedKnnCollector);
+      } else {
+        collector = ordinalTranslatedKnnCollector;
+      }
       HnswGraphSearcher.search(scorer, collector, getGraph(fieldEntry), acceptedOrds);
     } else {
       // if k is larger than the number of vectors, we can just iterate over all vectors
diff --git a/lucene/core/src/java/org/apache/lucene/search/HnswKnnCollector.java b/lucene/core/src/java/org/apache/lucene/search/HnswKnnCollector.java
new file mode 100644
index 00000000000..e145ea99dd6
--- /dev/null
+++ b/lucene/core/src/java/org/apache/lucene/search/HnswKnnCollector.java
@@ -0,0 +1,24 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.lucene.search;
+
+/** {@link KnnCollector} that exposes methods to hook into specific parts of the HNSW algorithm. */
+public interface HnswKnnCollector extends KnnCollector {
+
+  /** Indicates exploration of the next HNSW candidate graph node. */
+  void nextCandidate();
+}
diff --git a/lucene/core/src/java/org/apache/lucene/search/HnswQueueSaturationCollector.java b/lucene/core/src/java/org/apache/lucene/search/HnswQueueSaturationCollector.java
new file mode 100644
index 00000000000..b2af5cbd685
--- /dev/null
+++ b/lucene/core/src/java/org/apache/lucene/search/HnswQueueSaturationCollector.java
@@ -0,0 +1,130 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+
+package org.apache.lucene.search;
+
+/**
+ * A {@link HnswKnnCollector} that early exits when nearest neighbor queue keeps saturating beyond a
+ * 'patience' parameter. This records the rate of collection of new nearest neighbors in the {@code
+ * delegate} KnnCollector queue, at each HNSW node candidate visit. Once it saturates for a number
+ * of consecutive node visits (e.g., the patience parameter), this early terminates.
+ */
+public class HnswQueueSaturationCollector implements HnswKnnCollector {
+
+  private static final double DEFAULT_SATURATION_THRESHOLD = 0.995d;
+
+  private final KnnCollector delegate;
+  private final double saturationThreshold;
+  private final int patience;
+  private boolean patienceFinished;
+  private int countSaturated;
+  private int previousQueueSize;
+  private int currentQueueSize;
+
+  HnswQueueSaturationCollector(
+      KnnCollector delegate, double saturationThreshold, int patience) {
+    this.delegate = delegate;
+    this.previousQueueSize = 0;
+    this.currentQueueSize = 0;
+    this.countSaturated = 0;
+    this.patienceFinished = false;
+    this.saturationThreshold = saturationThreshold;
+    this.patience = patience;
+  }
+
+  public HnswQueueSaturationCollector(KnnCollector delegate) {
+    this.delegate = delegate;
+    this.previousQueueSize = 0;
+    this.currentQueueSize = 0;
+    this.countSaturated = 0;
+    this.patienceFinished = false;
+    this.saturationThreshold = DEFAULT_SATURATION_THRESHOLD;
+    this.patience = defaultPatience();
+  }
+
+  private int defaultPatience() {
+    return Math.max(7, (int) (k() * 0.3));
+  }
+
+  @Override
+  public boolean earlyTerminated() {
+    return delegate.earlyTerminated() || patienceFinished;
+  }
+
+  @Override
+  public void incVisitedCount(int count) {
+    delegate.incVisitedCount(count);
+  }
+
+  @Override
+  public long visitedCount() {
+    return delegate.visitedCount();
+  }
+
+  @Override
+  public long visitLimit() {
+    return delegate.visitLimit();
+  }
+
+  @Override
+  public int k() {
+    return delegate.k();
+  }
+
+  @Override
+  public boolean collect(int docId, float similarity) {
+    boolean collect = delegate.collect(docId, similarity);
+    if (collect) {
+      currentQueueSize++;
+    }
+    return collect;
+  }
+
+  @Override
+  public float minCompetitiveSimilarity() {
+    return delegate.minCompetitiveSimilarity();
+  }
+
+  @Override
+  public TopDocs topDocs() {
+    TopDocs topDocs;
+    if (patienceFinished && delegate.earlyTerminated() == false) {
+      TopDocs delegateDocs = delegate.topDocs();
+      TotalHits totalHits =
+          new TotalHits(delegateDocs.totalHits.value(), TotalHits.Relation.EQUAL_TO);
+      topDocs = new TopDocs(totalHits, delegateDocs.scoreDocs);
+    } else {
+      topDocs = delegate.topDocs();
+    }
+    return topDocs;
+  }
+
+  @Override
+  public void nextCandidate() {
+    double queueSaturation =
+        (double) Math.min(currentQueueSize, previousQueueSize) / currentQueueSize;
+    previousQueueSize = currentQueueSize;
+    if (queueSaturation >= saturationThreshold) {
+      countSaturated++;
+    } else {
+      countSaturated = 0;
+    }
+    if (countSaturated > patience) {
+      patienceFinished = true;
+    }
+  }
+}
diff --git a/lucene/core/src/java/org/apache/lucene/util/hnsw/HnswGraphSearcher.java b/lucene/core/src/java/org/apache/lucene/util/hnsw/HnswGraphSearcher.java
index e8f0d316fd8..fb93398d159 100644
--- a/lucene/core/src/java/org/apache/lucene/util/hnsw/HnswGraphSearcher.java
+++ b/lucene/core/src/java/org/apache/lucene/util/hnsw/HnswGraphSearcher.java
@@ -21,6 +21,7 @@
 
 import java.io.IOException;
 import org.apache.lucene.search.DocIdSetIterator;
+import org.apache.lucene.search.HnswKnnCollector;
 import org.apache.lucene.search.KnnCollector;
 import org.apache.lucene.search.TopKnnCollector;
 import org.apache.lucene.search.knn.EntryPointProvider;
@@ -272,6 +273,9 @@ void searchLevel(
           }
         }
       }
+      if (results instanceof HnswKnnCollector hnswKnnCollector) {
+        hnswKnnCollector.nextCandidate();
+      }
     }
   }
 
diff --git a/lucene/core/src/test/org/apache/lucene/search/TestHnswQueueSaturationCollector.java b/lucene/core/src/test/org/apache/lucene/search/TestHnswQueueSaturationCollector.java
new file mode 100644
index 00000000000..1ef29845016
--- /dev/null
+++ b/lucene/core/src/test/org/apache/lucene/search/TestHnswQueueSaturationCollector.java
@@ -0,0 +1,108 @@
+/*
+ * Licensed to the Apache Software Foundation (ASF) under one or more
+ * contributor license agreements.  See the NOTICE file distributed with
+ * this work for additional information regarding copyright ownership.
+ * The ASF licenses this file to You under the Apache License, Version 2.0
+ * (the "License"); you may not use this file except in compliance with
+ * the License.  You may obtain a copy of the License at
+ *
+ *     http://www.apache.org/licenses/LICENSE-2.0
+ *
+ * Unless required by applicable law or agreed to in writing, software
+ * distributed under the License is distributed on an "AS IS" BASIS,
+ * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+ * See the License for the specific language governing permissions and
+ * limitations under the License.
+ */
+package org.apache.lucene.search;
+
+import java.util.Random;
+import org.apache.lucene.tests.util.LuceneTestCase;
+import org.junit.Test;
+
+/** Tests for {@link HnswQueueSaturationCollector} */
+public class TestHnswQueueSaturationCollector extends LuceneTestCase {
+
+  @Test
+  public void testDelegate() {
+    Random random = random();
+    int numDocs = 100;
+    int k = random.nextInt(1, 10);
+    KnnCollector delegate = new TopKnnCollector(k, numDocs);
+    HnswQueueSaturationCollector queueSaturationCollector =
+        new HnswQueueSaturationCollector(delegate);
+    for (int i = 0; i < random.nextInt(numDocs); i++) {
+      queueSaturationCollector.collect(random.nextInt(numDocs), random.nextFloat(1.0f));
+    }
+    assertEquals(delegate.k(), queueSaturationCollector.k());
+    assertEquals(delegate.visitedCount(), queueSaturationCollector.visitedCount());
+    assertEquals(delegate.visitLimit(), queueSaturationCollector.visitLimit());
+    assertEquals(
+        delegate.minCompetitiveSimilarity(),
+        queueSaturationCollector.minCompetitiveSimilarity(),
+        1e-3);
+  }
+
+  @Test
+  public void testEarlyExpectedExit() {
+    int numDocs = 1000;
+    int k = 10;
+    KnnCollector delegate = new TopKnnCollector(k, numDocs);
+    HnswQueueSaturationCollector queueSaturationCollector =
+        new HnswQueueSaturationCollector(delegate, 0.9, 10);
+    for (int i = 0; i < numDocs; i++) {
+      queueSaturationCollector.collect(i, 1.0f - i * 1e-3f);
+      if (i % 10 == 0) {
+        queueSaturationCollector.nextCandidate();
+      }
+      if (queueSaturationCollector.earlyTerminated()) {
+        assertEquals(120, i);
+        break;
+      }
+    }
+  }
+
+  @Test
+  public void testDelegateVsSaturateEarlyExit() {
+    Random random = random();
+    int numDocs = 10000;
+    int k = random.nextInt(1, 100);
+    KnnCollector delegate = new TopKnnCollector(k, numDocs);
+    HnswQueueSaturationCollector queueSaturationCollector =
+        new HnswQueueSaturationCollector(delegate);
+    for (int i = 0; i < random.nextInt(numDocs); i++) {
+      queueSaturationCollector.collect(random.nextInt(numDocs), random.nextFloat(1.0f));
+      if (i % 10 == 0) {
+        queueSaturationCollector.nextCandidate();
+      }
+      boolean earlyTerminatedSaturation = queueSaturationCollector.earlyTerminated();
+      boolean earlyTerminatedDelegate = delegate.earlyTerminated();
+      assertTrue(earlyTerminatedSaturation || !earlyTerminatedDelegate);
+    }
+  }
+
+  @Test
+  public void testEarlyExitRelation() {
+    Random random = random();
+    int numDocs = 10000;
+    int k = random.nextInt(100);
+    KnnCollector delegate = new TopKnnCollector(k, random.nextInt(numDocs));
+    HnswQueueSaturationCollector queueSaturationCollector =
+        new HnswQueueSaturationCollector(delegate);
+    for (int i = 0; i < random.nextInt(numDocs); i++) {
+      queueSaturationCollector.collect(random.nextInt(numDocs), random.nextFloat(1.0f));
+      if (i % 10 == 0) {
+        queueSaturationCollector.nextCandidate();
+      }
+      if (delegate.earlyTerminated()) {
+        TopDocs topDocs = queueSaturationCollector.topDocs();
+        assertEquals(TotalHits.Relation.GREATER_THAN_OR_EQUAL_TO, topDocs.totalHits.relation());
+      }
+      if (queueSaturationCollector.earlyTerminated()) {
+        TopDocs topDocs = queueSaturationCollector.topDocs();
+        assertEquals(TotalHits.Relation.EQUAL_TO, topDocs.totalHits.relation());
+        break;
+      }
+    }
+  }
+}