diff --git a/distributed/shuffle/_rechunk.py b/distributed/shuffle/_rechunk.py
index 738c8034f79..e58d0608f99 100644
--- a/distributed/shuffle/_rechunk.py
+++ b/distributed/shuffle/_rechunk.py
@@ -1,7 +1,8 @@
 from __future__ import annotations
 
+import math
 from collections import defaultdict
-from itertools import product
+from itertools import compress, product
 from typing import TYPE_CHECKING, NamedTuple
 
 import dask
@@ -72,6 +73,34 @@ def rechunk_p2p(x: da.Array, chunks: ChunkedAxes) -> da.Array:
         # Special case for empty array, as the algorithm below does not behave correctly
         return da.empty(x.shape, chunks=chunks, dtype=x.dtype)
 
+    old_chunks = x.chunks
+    new_chunks = chunks
+
+    def is_unknown(dim: ChunkedAxis) -> bool:
+        return any(math.isnan(chunk) for chunk in dim)
+
+    old_is_unknown = [is_unknown(dim) for dim in old_chunks]
+    new_is_unknown = [is_unknown(dim) for dim in new_chunks]
+
+    if old_is_unknown != new_is_unknown or any(
+        new != old for new, old in compress(zip(old_chunks, new_chunks), old_is_unknown)
+    ):
+        raise ValueError(
+            "Chunks must be unchanging along dimensions with missing values.\n\n"
+            "A possible solution:\n  x.compute_chunk_sizes()"
+        )
+
+    old_known = [dim for dim, unknown in zip(old_chunks, old_is_unknown) if not unknown]
+    new_known = [dim for dim, unknown in zip(new_chunks, new_is_unknown) if not unknown]
+
+    old_sizes = [sum(o) for o in old_known]
+    new_sizes = [sum(n) for n in new_known]
+
+    if old_sizes != new_sizes:
+        raise ValueError(
+            f"Cannot change dimensions from {old_sizes!r} to {new_sizes!r}"
+        )
+
     dsk: dict = {}
     token = tokenize(x, chunks)
     _barrier_key = barrier_key(ShuffleId(token))
diff --git a/distributed/shuffle/_worker_extension.py b/distributed/shuffle/_worker_extension.py
index 90b6b5f2d5f..30a031fc46a 100644
--- a/distributed/shuffle/_worker_extension.py
+++ b/distributed/shuffle/_worker_extension.py
@@ -301,7 +301,7 @@ def __init__(
         memory_limiter_disk: ResourceLimiter,
         memory_limiter_comms: ResourceLimiter,
     ):
-        from dask.array.rechunk import _old_to_new
+        from dask.array.rechunk import old_to_new
 
         super().__init__(
             id=id,
@@ -315,6 +315,14 @@ def __init__(
             memory_limiter_comms=memory_limiter_comms,
             memory_limiter_disk=memory_limiter_disk,
         )
+        from dask.array.core import normalize_chunks
+
+        # We rely on a canonical `np.nan` in `dask.array.rechunk.old_to_new`
+        # that passes an implicit identity check when testing for list equality.
+        # This does not work with (de)serialization, so we have to normalize the chunks
+        # here again to canonicalize `nan`s.
+        old = normalize_chunks(old)
+        new = normalize_chunks(new)
         self.old = old
         self.new = new
         partitions_of = defaultdict(list)
@@ -323,7 +331,7 @@ def __init__(
         self.partitions_of = dict(partitions_of)
         self.worker_for = worker_for
         self._slicing = rechunk_slicing(old, new)
-        self._old_to_new = _old_to_new(old, new)
+        self._old_to_new = old_to_new(old, new)
 
     async def _receive(self, data: list[tuple[ArrayRechunkShardID, bytes]]) -> None:
         self.raise_if_closed()
diff --git a/distributed/shuffle/tests/test_rechunk.py b/distributed/shuffle/tests/test_rechunk.py
index 609b7a04711..a9e5996ff97 100644
--- a/distributed/shuffle/tests/test_rechunk.py
+++ b/distributed/shuffle/tests/test_rechunk.py
@@ -1,6 +1,7 @@
 from __future__ import annotations
 
 import asyncio
+import math
 import random
 import warnings
 
@@ -83,7 +84,9 @@ async def test_lowlevel_rechunk(
 
     ind_chunks = [[(i, x) for i, x in enumerate(dim)] for dim in old]
     ind_chunks = [list(zip(x, y)) for x, y in product(*ind_chunks)]
-    old_chunks = {idx: np.random.random(chunk) for idx, chunk in ind_chunks}
+    old_chunks = {
+        idx: np.random.default_rng().random(chunk) for idx, chunk in ind_chunks
+    }
 
     workers = list("abcdefghijklmn")[:n_workers]
 
@@ -161,7 +164,7 @@ async def test_rechunk_configuration(c, s, *ws, config_value, keyword):
     --------
     dask.array.tests.test_rechunk.test_rechunk_1d
     """
-    a = np.random.uniform(0, 1, 30)
+    a = np.random.default_rng().uniform(0, 1, 30)
     x = da.from_array(a, chunks=((10,) * 3,))
     new = ((6,) * 5,)
     config = {"array.rechunk.method": config_value} if config_value is not None else {}
@@ -185,7 +188,7 @@ async def test_rechunk_2d(c, s, *ws):
     --------
     dask.array.tests.test_rechunk.test_rechunk_2d
     """
-    a = np.random.uniform(0, 1, 300).reshape((10, 30))
+    a = np.random.default_rng().uniform(0, 1, 300).reshape((10, 30))
     x = da.from_array(a, chunks=((1, 2, 3, 4), (5,) * 6))
     new = ((5, 5), (15,) * 2)
     x2 = rechunk(x, chunks=new, method="p2p")
@@ -202,7 +205,7 @@ async def test_rechunk_4d(c, s, *ws):
     dask.array.tests.test_rechunk.test_rechunk_4d
     """
     old = ((5, 5),) * 4
-    a = np.random.uniform(0, 1, 10000).reshape((10,) * 4)
+    a = np.random.default_rng().uniform(0, 1, 10000).reshape((10,) * 4)
     x = da.from_array(a, chunks=old)
     new = (
         (10,),
@@ -225,7 +228,7 @@ async def test_rechunk_with_single_output_chunk_raises(c, s, *ws):
     dask.array.tests.test_rechunk.test_rechunk_4d
     """
     old = ((5, 5),) * 4
-    a = np.random.uniform(0, 1, 10000).reshape((10,) * 4)
+    a = np.random.default_rng().uniform(0, 1, 10000).reshape((10,) * 4)
     x = da.from_array(a, chunks=old)
     new = ((10,),) * 4
     x2 = rechunk(x, chunks=new, method="p2p")
@@ -244,7 +247,7 @@ async def test_rechunk_expand(c, s, *ws):
     --------
     dask.array.tests.test_rechunk.test_rechunk_expand
     """
-    a = np.random.uniform(0, 1, 100).reshape((10, 10))
+    a = np.random.default_rng().uniform(0, 1, 100).reshape((10, 10))
     x = da.from_array(a, chunks=(5, 5))
     y = x.rechunk(chunks=((3, 3, 3, 1), (3, 3, 3, 1)), method="p2p")
     assert np.all(await c.compute(y) == a)
@@ -258,7 +261,7 @@ async def test_rechunk_expand2(c, s, *ws):
     dask.array.tests.test_rechunk.test_rechunk_expand2
     """
     (a, b) = (3, 2)
-    orig = np.random.uniform(0, 1, a**b).reshape((a,) * b)
+    orig = np.random.default_rng().uniform(0, 1, a**b).reshape((a,) * b)
     for off, off2 in product(range(1, a - 1), range(1, a - 1)):
         old = ((a - off, off),) * b
         x = da.from_array(orig, chunks=old)
@@ -280,7 +283,7 @@ async def test_rechunk_method(c, s, *ws):
     """
     old = ((5, 2, 3),) * 4
     new = ((3, 3, 3, 1),) * 4
-    a = np.random.uniform(0, 1, 10000).reshape((10,) * 4)
+    a = np.random.default_rng().uniform(0, 1, 10000).reshape((10,) * 4)
     x = da.from_array(a, chunks=old)
     x2 = x.rechunk(chunks=new, method="p2p")
     assert x2.chunks == new
@@ -298,7 +301,7 @@ async def test_rechunk_blockshape(c, s, *ws):
     new_shape, new_chunks = (10, 10), (4, 3)
     new_blockdims = normalize_chunks(new_chunks, new_shape)
     old_chunks = ((4, 4, 2), (3, 3, 3, 1))
-    a = np.random.uniform(0, 1, 100).reshape((10, 10))
+    a = np.random.default_rng().uniform(0, 1, 100).reshape((10, 10))
     x = da.from_array(a, chunks=old_chunks)
     check1 = rechunk(x, chunks=new_chunks, method="p2p")
     assert check1.chunks == new_blockdims
@@ -463,6 +466,56 @@ async def test_rechunk_same(c, s, *ws):
     assert x is y
 
 
+@gen_cluster(client=True)
+async def test_rechunk_same_fully_unknown(c, s, *ws):
+    """
+    See Also
+    --------
+    dask.array.tests.test_rechunk.test_rechunk_same_fully_unknown
+    """
+    dd = pytest.importorskip("dask.dataframe")
+    x = da.ones(shape=(10, 10), chunks=(5, 10))
+    y = dd.from_array(x).values
+    new_chunks = ((np.nan, np.nan), (10,))
+    assert y.chunks == new_chunks
+    result = y.rechunk(new_chunks, method="p2p")
+    assert y is result
+
+
+@gen_cluster(client=True)
+async def test_rechunk_same_fully_unknown_floats(c, s, *ws):
+    """Similar to test_rechunk_same_fully_unknown but testing the behavior if
+    ``float("nan")`` is used instead of the recommended ``np.nan``
+
+    See Also
+    --------
+    dask.array.tests.test_rechunk.test_rechunk_same_fully_unknown_floats
+    """
+    dd = pytest.importorskip("dask.dataframe")
+    x = da.ones(shape=(10, 10), chunks=(5, 10))
+    y = dd.from_array(x).values
+    new_chunks = ((float("nan"), float("nan")), (10,))
+    result = y.rechunk(new_chunks, method="p2p")
+    assert y is result
+
+
+@gen_cluster(client=True)
+async def test_rechunk_same_partially_unknown(c, s, *ws):
+    """
+    See Also
+    --------
+    dask.array.tests.test_rechunk.test_rechunk_same_partially_unknown
+    """
+    dd = pytest.importorskip("dask.dataframe")
+    x = da.ones(shape=(10, 10), chunks=(5, 10))
+    y = dd.from_array(x).values
+    z = da.concatenate([x, y])
+    new_chunks = ((5, 5, np.nan, np.nan), (10,))
+    assert z.chunks == new_chunks
+    result = z.rechunk(new_chunks, method="p2p")
+    assert z is result
+
+
 @gen_cluster(client=True)
 async def test_rechunk_with_zero_placeholders(c, s, *ws):
     """
@@ -513,7 +566,7 @@ async def test_rechunk_unknown_from_pandas(c, s, *ws):
     dd = pytest.importorskip("dask.dataframe")
     pd = pytest.importorskip("pandas")
 
-    arr = np.random.randn(50, 10)
+    arr = np.random.default_rng().standard_normal((50, 10))
     x = dd.from_pandas(pd.DataFrame(arr), 2).values
     result = x.rechunk((None, (5, 5)), method="p2p")
     assert np.isnan(x.chunks[0]).all()
@@ -559,11 +612,11 @@ async def test_rechunk_unknown_from_array(c, s, *ws):
     ],
 )
 @gen_cluster(client=True)
-async def test_rechunk_unknown(c, s, *ws, x, chunks):
+async def test_rechunk_with_fully_unknown_dimension(c, s, *ws, x, chunks):
     """
     See Also
     --------
-    dask.array.tests.test_rechunk.test_rechunk_unknown
+    dask.array.tests.test_rechunk.test_rechunk_with_fully_unknown_dimension
     """
     dd = pytest.importorskip("dask.dataframe")
     y = dd.from_array(x).values
@@ -574,28 +627,79 @@ async def test_rechunk_unknown(c, s, *ws, x, chunks):
     assert_eq(await c.compute(result), await c.compute(expected))
 
 
+@pytest.mark.parametrize(
+    "x, chunks",
+    [
+        (da.ones(shape=(50, 10), chunks=(25, 10)), (None, 5)),
+        (da.ones(shape=(50, 10), chunks=(25, 10)), {1: 5}),
+        (da.ones(shape=(50, 10), chunks=(25, 10)), (None, (5, 5))),
+        pytest.param(
+            da.ones(shape=(1000, 10), chunks=(5, 10)),
+            (None, 5),
+            marks=pytest.mark.skip(reason="distributed#7757"),
+        ),
+        pytest.param(
+            da.ones(shape=(1000, 10), chunks=(5, 10)),
+            {1: 5},
+            marks=pytest.mark.skip(reason="distributed#7757"),
+        ),
+        pytest.param(
+            da.ones(shape=(1000, 10), chunks=(5, 10)),
+            (None, (5, 5)),
+            marks=pytest.mark.skip(reason="distributed#7757"),
+        ),
+        (da.ones(shape=(10, 10), chunks=(10, 10)), (None, 5)),
+        (da.ones(shape=(10, 10), chunks=(10, 10)), {1: 5}),
+        (da.ones(shape=(10, 10), chunks=(10, 10)), (None, (5, 5))),
+        (da.ones(shape=(10, 10), chunks=(10, 2)), (None, 5)),
+        (da.ones(shape=(10, 10), chunks=(10, 2)), {1: 5}),
+        (da.ones(shape=(10, 10), chunks=(10, 2)), (None, (5, 5))),
+    ],
+)
+@gen_cluster(client=True)
+async def test_rechunk_with_partially_unknown_dimension(c, s, *ws, x, chunks):
+    """
+    See Also
+    --------
+    dask.array.tests.test_rechunk.test_rechunk_with_partially_unknown_dimension
+    """
+    dd = pytest.importorskip("dask.dataframe")
+    y = dd.from_array(x).values
+    z = da.concatenate([x, y])
+    xx = da.concatenate([x, x])
+    result = z.rechunk(chunks, method="p2p")
+    expected = xx.rechunk(chunks, method="p2p")
+    assert_chunks_match(result.chunks, expected.chunks)
+    assert_eq(await c.compute(result), await c.compute(expected))
+
+
+@pytest.mark.parametrize(
+    "new_chunks",
+    [
+        ((np.nan, np.nan), (5, 5)),
+        ((math.nan, math.nan), (5, 5)),
+        ((float("nan"), float("nan")), (5, 5)),
+    ],
+)
 @gen_cluster(client=True)
-async def test_rechunk_unknown_explicit(c, s, *ws):
+async def test_rechunk_with_fully_unknown_dimension_explicit(c, s, *ws, new_chunks):
     """
     See Also
     --------
-    dask.array.tests.test_rechunk.test_rechunk_unknown_explicit
+    dask.array.tests.test_rechunk.test_rechunk_with_fully_unknown_dimension_explicit
     """
     dd = pytest.importorskip("dask.dataframe")
     x = da.ones(shape=(10, 10), chunks=(5, 2))
     y = dd.from_array(x).values
-    result = y.rechunk(((float("nan"), float("nan")), (5, 5)), method="p2p")
+    result = y.rechunk(new_chunks, method="p2p")
     expected = x.rechunk((None, (5, 5)), method="p2p")
     assert_chunks_match(result.chunks, expected.chunks)
     assert_eq(await c.compute(result), await c.compute(expected))
 
 
 def assert_chunks_match(left, right):
-    for x, y in zip(left, right):
-        if np.isnan(x).any():
-            assert np.isnan(x).all()
-        else:
-            assert x == y
+    for ldim, rdim in zip(left, right):
+        assert all(np.isnan(l) or l == r for l, r in zip(ldim, rdim))
 
 
 @gen_cluster(client=True)
@@ -607,9 +711,17 @@ async def test_rechunk_unknown_raises(c, s, *ws):
     """
     dd = pytest.importorskip("dask.dataframe")
 
-    x = dd.from_array(da.ones(shape=(10, 10), chunks=(5, 5))).values
-    with pytest.raises(ValueError):
-        x.rechunk((None, (5, 5, 5)), method="p2p")
+    x = da.ones(shape=(10, 10), chunks=(5, 5))
+    y = dd.from_array(x).values
+    with pytest.raises(ValueError, match="Chunks do not add"):
+        y.rechunk((None, (5, 5, 5)), method="p2p")
+
+    with pytest.raises(ValueError, match="Chunks must be unchanging"):
+        y.rechunk(((5, 5), (5, 5)), method="p2p")
+
+    with pytest.raises(ValueError, match="Chunks must be unchanging"):
+        z = da.concatenate([x, y])
+        z.rechunk(((5, 3, 2, np.nan, np.nan), (5, 5)), method="p2p")
 
 
 @gen_cluster(client=True)
@@ -880,8 +992,8 @@ def test_rechunk_slicing_nan():
     --------
     dask.array.tests.test_rechunk.test_intersect_nan
     """
-    old_chunks = ((float("nan"), float("nan")), (8,))
-    new_chunks = ((float("nan"), float("nan")), (4, 4))
+    old_chunks = ((np.nan, np.nan), (8,))
+    new_chunks = ((np.nan, np.nan), (4, 4))
     result = rechunk_slicing(old_chunks, new_chunks)
     expected = {
         (0, 0): [
@@ -908,8 +1020,8 @@ def test_rechunk_slicing_nan_single():
     --------
     dask.array.tests.test_rechunk.test_intersect_nan_single
     """
-    old_chunks = ((float("nan"),), (10,))
-    new_chunks = ((float("nan"),), (5, 5))
+    old_chunks = ((np.nan,), (10,))
+    new_chunks = ((np.nan,), (5, 5))
 
     result = rechunk_slicing(old_chunks, new_chunks)
     expected = {
@@ -927,8 +1039,8 @@ def test_rechunk_slicing_nan_long():
     --------
     dask.array.tests.test_rechunk.test_intersect_nan_long
     """
-    old_chunks = (tuple([float("nan")] * 4), (10,))
-    new_chunks = (tuple([float("nan")] * 4), (5, 5))
+    old_chunks = (tuple([np.nan] * 4), (10,))
+    new_chunks = (tuple([np.nan] * 4), (5, 5))
     result = rechunk_slicing(old_chunks, new_chunks)
     expected = {
         (0, 0): [