diff --git a/spacy/tests/parser/test_ner.py b/spacy/tests/parser/test_ner.py
index b657ae2e8..b4c22b48d 100644
--- a/spacy/tests/parser/test_ner.py
+++ b/spacy/tests/parser/test_ner.py
@@ -1,4 +1,7 @@
 import pytest
+from numpy.testing import assert_equal
+from spacy.attrs import ENT_IOB
+
 from spacy import util
 from spacy.lang.en import English
 from spacy.language import Language
@@ -332,6 +335,19 @@ def test_overfitting_IO():
         assert ents2[0].text == "London"
         assert ents2[0].label_ == "LOC"
 
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Just a sentence.",
+        "Then one more sentence about London.",
+        "Here is another one.",
+        "I like London.",
+    ]
+    batch_deps_1 = [doc.to_array([ENT_IOB]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([ENT_IOB]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.to_array([ENT_IOB]) for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
+
 
 def test_ner_warns_no_lookups(caplog):
     nlp = English()
diff --git a/spacy/tests/parser/test_parse.py b/spacy/tests/parser/test_parse.py
index ffb6f23f1..a914eb17a 100644
--- a/spacy/tests/parser/test_parse.py
+++ b/spacy/tests/parser/test_parse.py
@@ -1,4 +1,7 @@
 import pytest
+from numpy.testing import assert_equal
+from spacy.attrs import DEP
+
 from spacy.lang.en import English
 from spacy.training import Example
 from spacy.tokens import Doc
@@ -210,3 +213,16 @@ def test_overfitting_IO():
         assert doc2[0].dep_ == "nsubj"
         assert doc2[2].dep_ == "dobj"
         assert doc2[3].dep_ == "punct"
+
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Just a sentence.",
+        "Then one more sentence about London.",
+        "Here is another one.",
+        "I like London.",
+    ]
+    batch_deps_1 = [doc.to_array([DEP]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([DEP]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.to_array([DEP]) for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
diff --git a/spacy/tests/pipeline/test_entity_linker.py b/spacy/tests/pipeline/test_entity_linker.py
index f2e6defcb..8ba2d0d3e 100644
--- a/spacy/tests/pipeline/test_entity_linker.py
+++ b/spacy/tests/pipeline/test_entity_linker.py
@@ -1,5 +1,7 @@
 from typing import Callable, Iterable
 import pytest
+from numpy.testing import assert_equal
+from spacy.attrs import ENT_KB_ID
 
 from spacy.kb import KnowledgeBase, get_candidates, Candidate
 from spacy.vocab import Vocab
@@ -496,6 +498,19 @@ def test_overfitting_IO():
                 predictions.append(ent.kb_id_)
         assert predictions == GOLD_entities
 
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Russ Cochran captured his first major title with his son as caddie.",
+        "Russ Cochran his reprints include EC Comics.",
+        "Russ Cochran has been publishing comic art.",
+        "Russ Cochran was a member of University of Kentucky's golf team.",
+    ]
+    batch_deps_1 = [doc.to_array([ENT_KB_ID]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([ENT_KB_ID]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.to_array([ENT_KB_ID]) for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
+
 
 def test_kb_serialization():
     # Test that the KB can be used in a pipeline with a different vocab
diff --git a/spacy/tests/pipeline/test_models.py b/spacy/tests/pipeline/test_models.py
new file mode 100644
index 000000000..d04ac9cd4
--- /dev/null
+++ b/spacy/tests/pipeline/test_models.py
@@ -0,0 +1,107 @@
+from typing import List
+
+import numpy
+import pytest
+from numpy.testing import assert_almost_equal
+from spacy.vocab import Vocab
+from thinc.api import NumpyOps, Model, data_validation
+from thinc.types import Array2d, Ragged
+
+from spacy.lang.en import English
+from spacy.ml import FeatureExtractor, StaticVectors
+from spacy.ml._character_embed import CharacterEmbed
+from spacy.tokens import Doc
+
+
+OPS = NumpyOps()
+
+texts = ["These are 4 words", "Here just three"]
+l0 = [[1, 2], [3, 4], [5, 6], [7, 8]]
+l1 = [[9, 8], [7, 6], [5, 4]]
+list_floats = [OPS.xp.asarray(l0, dtype="f"), OPS.xp.asarray(l1, dtype="f")]
+list_ints = [OPS.xp.asarray(l0, dtype="i"), OPS.xp.asarray(l1, dtype="i")]
+array = OPS.xp.asarray(l1, dtype="f")
+ragged = Ragged(array, OPS.xp.asarray([2, 1], dtype="i"))
+
+
+def get_docs():
+    vocab = Vocab()
+    for t in texts:
+        for word in t.split():
+            hash_id = vocab.strings.add(word)
+            vector = numpy.random.uniform(-1, 1, (7,))
+            vocab.set_vector(hash_id, vector)
+    docs = [English(vocab)(t) for t in texts]
+    return docs
+
+
+# Test components with a model of type Model[List[Doc], List[Floats2d]]
+@pytest.mark.parametrize("name", ["tagger", "tok2vec", "morphologizer", "senter"])
+def test_components_batching_list(name):
+    nlp = English()
+    proc = nlp.create_pipe(name)
+    util_batch_unbatch_docs_list(proc.model, get_docs(), list_floats)
+
+
+# Test components with a model of type Model[List[Doc], Floats2d]
+@pytest.mark.parametrize("name", ["textcat"])
+def test_components_batching_array(name):
+    nlp = English()
+    proc = nlp.create_pipe(name)
+    util_batch_unbatch_docs_array(proc.model, get_docs(), array)
+
+
+LAYERS = [
+    (CharacterEmbed(nM=5, nC=3), get_docs(), list_floats),
+    (FeatureExtractor([100, 200]), get_docs(), list_ints),
+    (StaticVectors(), get_docs(), ragged),
+]
+
+
+@pytest.mark.parametrize("model,in_data,out_data", LAYERS)
+def test_layers_batching_all(model, in_data, out_data):
+    # In = List[Doc]
+    if isinstance(in_data, list) and isinstance(in_data[0], Doc):
+        if isinstance(out_data, OPS.xp.ndarray) and out_data.ndim == 2:
+            util_batch_unbatch_docs_array(model, in_data, out_data)
+        elif (
+            isinstance(out_data, list)
+            and isinstance(out_data[0], OPS.xp.ndarray)
+            and out_data[0].ndim == 2
+        ):
+            util_batch_unbatch_docs_list(model, in_data, out_data)
+        elif isinstance(out_data, Ragged):
+            util_batch_unbatch_docs_ragged(model, in_data, out_data)
+
+
+def util_batch_unbatch_docs_list(
+    model: Model[List[Doc], List[Array2d]], in_data: List[Doc], out_data: List[Array2d]
+):
+    with data_validation(True):
+        model.initialize(in_data, out_data)
+        Y_batched = model.predict(in_data)
+        Y_not_batched = [model.predict([u])[0] for u in in_data]
+        for i in range(len(Y_batched)):
+            assert_almost_equal(Y_batched[i], Y_not_batched[i], decimal=4)
+
+
+def util_batch_unbatch_docs_array(
+    model: Model[List[Doc], Array2d], in_data: List[Doc], out_data: Array2d
+):
+    with data_validation(True):
+        model.initialize(in_data, out_data)
+        Y_batched = model.predict(in_data).tolist()
+        Y_not_batched = [model.predict([u])[0] for u in in_data]
+        assert_almost_equal(Y_batched, Y_not_batched, decimal=4)
+
+
+def util_batch_unbatch_docs_ragged(
+    model: Model[List[Doc], Ragged], in_data: List[Doc], out_data: Ragged
+):
+    with data_validation(True):
+        model.initialize(in_data, out_data)
+        Y_batched = model.predict(in_data)
+        Y_not_batched = []
+        for u in in_data:
+            Y_not_batched.extend(model.predict([u]).data.tolist())
+        assert_almost_equal(Y_batched.data, Y_not_batched, decimal=4)
diff --git a/spacy/tests/pipeline/test_morphologizer.py b/spacy/tests/pipeline/test_morphologizer.py
index fd7aa05be..85d1d6c8b 100644
--- a/spacy/tests/pipeline/test_morphologizer.py
+++ b/spacy/tests/pipeline/test_morphologizer.py
@@ -1,4 +1,5 @@
 import pytest
+from numpy.testing import assert_equal
 
 from spacy import util
 from spacy.training import Example
@@ -6,6 +7,7 @@ from spacy.lang.en import English
 from spacy.language import Language
 from spacy.tests.util import make_tempdir
 from spacy.morphology import Morphology
+from spacy.attrs import MORPH
 
 
 def test_label_types():
@@ -101,3 +103,16 @@ def test_overfitting_IO():
         doc2 = nlp2(test_text)
         assert [str(t.morph) for t in doc2] == gold_morphs
         assert [t.pos_ for t in doc2] == gold_pos_tags
+
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Just a sentence.",
+        "Then one more sentence about London.",
+        "Here is another one.",
+        "I like London.",
+    ]
+    batch_deps_1 = [doc.to_array([MORPH]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([MORPH]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.to_array([MORPH]) for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
diff --git a/spacy/tests/pipeline/test_senter.py b/spacy/tests/pipeline/test_senter.py
index c9722e5de..7a256f79b 100644
--- a/spacy/tests/pipeline/test_senter.py
+++ b/spacy/tests/pipeline/test_senter.py
@@ -1,4 +1,6 @@
 import pytest
+from numpy.testing import assert_equal
+from spacy.attrs import SENT_START
 
 from spacy import util
 from spacy.training import Example
@@ -80,3 +82,18 @@ def test_overfitting_IO():
         nlp2 = util.load_model_from_path(tmp_dir)
         doc2 = nlp2(test_text)
         assert [int(t.is_sent_start) for t in doc2] == gold_sent_starts
+
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Just a sentence.",
+        "Then one more sentence about London.",
+        "Here is another one.",
+        "I like London.",
+    ]
+    batch_deps_1 = [doc.to_array([SENT_START]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([SENT_START]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [
+        doc.to_array([SENT_START]) for doc in [nlp(text) for text in texts]
+    ]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
diff --git a/spacy/tests/pipeline/test_tagger.py b/spacy/tests/pipeline/test_tagger.py
index b9db76cdf..885bdbce1 100644
--- a/spacy/tests/pipeline/test_tagger.py
+++ b/spacy/tests/pipeline/test_tagger.py
@@ -1,4 +1,7 @@
 import pytest
+from numpy.testing import assert_equal
+from spacy.attrs import TAG
+
 from spacy import util
 from spacy.training import Example
 from spacy.lang.en import English
@@ -117,6 +120,19 @@ def test_overfitting_IO():
         assert doc2[2].tag_ is "J"
         assert doc2[3].tag_ is "N"
 
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = [
+        "Just a sentence.",
+        "I like green eggs.",
+        "Here is another one.",
+        "I eat ham.",
+    ]
+    batch_deps_1 = [doc.to_array([TAG]) for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.to_array([TAG]) for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.to_array([TAG]) for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
+
 
 def test_tagger_requires_labels():
     nlp = English()
diff --git a/spacy/tests/pipeline/test_textcat.py b/spacy/tests/pipeline/test_textcat.py
index dd2f1070b..91348b1b3 100644
--- a/spacy/tests/pipeline/test_textcat.py
+++ b/spacy/tests/pipeline/test_textcat.py
@@ -1,6 +1,7 @@
 import pytest
 import random
 import numpy.random
+from numpy.testing import assert_equal
 from thinc.api import fix_random_seed
 from spacy import util
 from spacy.lang.en import English
@@ -174,6 +175,14 @@ def test_overfitting_IO():
     assert scores["cats_score"] == 1.0
     assert "cats_score_desc" in scores
 
+    # Make sure that running pipe twice, or comparing to call, always amounts to the same predictions
+    texts = ["Just a sentence.", "I like green eggs.", "I am happy.", "I eat ham."]
+    batch_deps_1 = [doc.cats for doc in nlp.pipe(texts)]
+    batch_deps_2 = [doc.cats for doc in nlp.pipe(texts)]
+    no_batch_deps = [doc.cats for doc in [nlp(text) for text in texts]]
+    assert_equal(batch_deps_1, batch_deps_2)
+    assert_equal(batch_deps_1, no_batch_deps)
+
 
 # fmt: off
 @pytest.mark.parametrize(