diff --git a/src/scanpy/_compat.py b/src/scanpy/_compat.py
index c5fa4dbe84..dca6c84c4e 100644
--- a/src/scanpy/_compat.py
+++ b/src/scanpy/_compat.py
@@ -9,15 +9,19 @@
 from pathlib import Path
 from typing import TYPE_CHECKING, Literal, ParamSpec, TypeVar, cast, overload
 
+import numpy as np
 from packaging.version import Version
 
 if TYPE_CHECKING:
     from collections.abc import Callable
     from importlib.metadata import PackageMetadata
 
+
 P = ParamSpec("P")
 R = TypeVar("R")
 
+_LegacyRandom = int | np.random.RandomState | None
+
 
 if TYPE_CHECKING:
     # type checkers are confused and can only see …core.Array
diff --git a/src/scanpy/_utils/__init__.py b/src/scanpy/_utils/__init__.py
index 150afe8311..67e2ae03c8 100644
--- a/src/scanpy/_utils/__init__.py
+++ b/src/scanpy/_utils/__init__.py
@@ -12,6 +12,7 @@
 import re
 import sys
 import warnings
+from collections.abc import Sequence
 from contextlib import contextmanager, suppress
 from enum import Enum
 from functools import partial, reduce, singledispatch, wraps
@@ -56,12 +57,13 @@
     from anndata import AnnData
     from numpy.typing import ArrayLike, DTypeLike, NDArray
 
+    from .._compat import _LegacyRandom
     from ..neighbors import NeighborsParams, RPForestDict
 
 
-# e.g. https://scikit-learn.org/stable/modules/generated/sklearn.decomposition.PCA.html
-# maybe in the future random.Generator
-AnyRandom = int | np.random.RandomState | None
+SeedLike = int | np.integer | Sequence[int] | np.random.SeedSequence
+RNGLike = np.random.Generator | np.random.BitGenerator
+
 LegacyUnionType = type(Union[int, str])  # noqa: UP007
 
 
@@ -493,7 +495,7 @@ def moving_average(a: np.ndarray, n: int):
     return ret[n - 1 :] / n
 
 
-def get_random_state(seed: AnyRandom) -> np.random.RandomState:
+def _get_legacy_random(seed: _LegacyRandom) -> np.random.RandomState:
     if isinstance(seed, np.random.RandomState):
         return seed
     return np.random.RandomState(seed)
diff --git a/src/scanpy/datasets/_datasets.py b/src/scanpy/datasets/_datasets.py
index 41b23160d6..df510b3209 100644
--- a/src/scanpy/datasets/_datasets.py
+++ b/src/scanpy/datasets/_datasets.py
@@ -18,7 +18,7 @@
 if TYPE_CHECKING:
     from typing import Literal
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
     VisiumSampleID = Literal[
         "V1_Breast_Cancer_Block_A_Section_1",
@@ -63,7 +63,7 @@ def blobs(
     n_centers: int = 5,
     cluster_std: float = 1.0,
     n_observations: int = 640,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
 ) -> AnnData:
     """\
     Gaussian Blobs.
diff --git a/src/scanpy/external/pp/_dca.py b/src/scanpy/external/pp/_dca.py
index 14842c8071..c47fff90f2 100644
--- a/src/scanpy/external/pp/_dca.py
+++ b/src/scanpy/external/pp/_dca.py
@@ -11,7 +11,7 @@
 
     from anndata import AnnData
 
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
 
     _AEType = Literal["zinb-conddisp", "zinb", "nb-conddisp", "nb"]
 
@@ -62,7 +62,7 @@ def dca(
     early_stop: int = 15,
     batch_size: int = 32,
     optimizer: str = "RMSprop",
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     threads: int | None = None,
     learning_rate: float | None = None,
     verbose: bool = False,
diff --git a/src/scanpy/external/pp/_magic.py b/src/scanpy/external/pp/_magic.py
index fd4b19667d..132d2a6448 100644
--- a/src/scanpy/external/pp/_magic.py
+++ b/src/scanpy/external/pp/_magic.py
@@ -19,7 +19,7 @@
 
     from anndata import AnnData
 
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
 
 MIN_VERSION = "2.0"
 
@@ -36,7 +36,7 @@ def magic(
     n_pca: int | None = 100,
     solver: Literal["exact", "approximate"] = "exact",
     knn_dist: str = "euclidean",
-    random_state: AnyRandom = None,
+    random_state: _LegacyRandom = None,
     n_jobs: int | None = None,
     verbose: bool = False,
     copy: bool | None = None,
diff --git a/src/scanpy/external/tl/_phate.py b/src/scanpy/external/tl/_phate.py
index 78b50327a9..ff50a1e6f7 100644
--- a/src/scanpy/external/tl/_phate.py
+++ b/src/scanpy/external/tl/_phate.py
@@ -16,7 +16,7 @@
 
     from anndata import AnnData
 
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
 
 
 @old_positionals(
@@ -49,7 +49,7 @@ def phate(
     mds_dist: str = "euclidean",
     mds: Literal["classic", "metric", "nonmetric"] = "metric",
     n_jobs: int | None = None,
-    random_state: AnyRandom = None,
+    random_state: _LegacyRandom = None,
     verbose: bool | int | None = None,
     copy: bool = False,
     **kwargs,
diff --git a/src/scanpy/neighbors/__init__.py b/src/scanpy/neighbors/__init__.py
index 379f34227b..ec5957b325 100644
--- a/src/scanpy/neighbors/__init__.py
+++ b/src/scanpy/neighbors/__init__.py
@@ -33,7 +33,7 @@
     from igraph import Graph
     from scipy.sparse import csr_matrix
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
     from ._types import KnnTransformerLike, _Metric, _MetricFn
 
 
@@ -54,13 +54,13 @@ class KwdsForTransformer(TypedDict):
     n_neighbors: int
     metric: _Metric | _MetricFn
     metric_params: Mapping[str, Any]
-    random_state: AnyRandom
+    random_state: _LegacyRandom
 
 
 class NeighborsParams(TypedDict):
     n_neighbors: int
     method: _Method
-    random_state: AnyRandom
+    random_state: _LegacyRandom
     metric: _Metric | _MetricFn
     metric_kwds: NotRequired[Mapping[str, Any]]
     use_rep: NotRequired[str]
@@ -79,7 +79,7 @@ def neighbors(
     transformer: KnnTransformerLike | _KnownTransformer | None = None,
     metric: _Metric | _MetricFn = "euclidean",
     metric_kwds: Mapping[str, Any] = MappingProxyType({}),
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     key_added: str | None = None,
     copy: bool = False,
 ) -> AnnData | None:
@@ -521,7 +521,7 @@ def compute_neighbors(
         transformer: KnnTransformerLike | _KnownTransformer | None = None,
         metric: _Metric | _MetricFn = "euclidean",
         metric_kwds: Mapping[str, Any] = MappingProxyType({}),
-        random_state: AnyRandom = 0,
+        random_state: _LegacyRandom = 0,
     ) -> None:
         """\
         Compute distances and connectivities of neighbors.
@@ -757,7 +757,7 @@ def compute_eigen(
         n_comps: int = 15,
         sym: bool | None = None,
         sort: Literal["decrease", "increase"] = "decrease",
-        random_state: AnyRandom = 0,
+        random_state: _LegacyRandom = 0,
     ):
         """\
         Compute eigen decomposition of transition matrix.
diff --git a/src/scanpy/plotting/_tools/paga.py b/src/scanpy/plotting/_tools/paga.py
index 7e62d46eac..ff14a19989 100644
--- a/src/scanpy/plotting/_tools/paga.py
+++ b/src/scanpy/plotting/_tools/paga.py
@@ -33,6 +33,7 @@
     from matplotlib.colors import Colormap
     from scipy.sparse import spmatrix
 
+    from ..._compat import _LegacyRandom
     from ...tools._draw_graph import _Layout as _LayoutWithoutEqTree
     from .._utils import _FontSize, _FontWeight, _LegendLoc
 
@@ -210,7 +211,7 @@ def _compute_pos(
     adjacency_solid: spmatrix | np.ndarray,
     *,
     layout: _Layout | None = None,
-    random_state: _sc_utils.AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     init_pos: np.ndarray | None = None,
     adj_tree=None,
     root: int = 0,
diff --git a/src/scanpy/preprocessing/_pca/__init__.py b/src/scanpy/preprocessing/_pca/__init__.py
index dba47d821c..3fd288ad93 100644
--- a/src/scanpy/preprocessing/_pca/__init__.py
+++ b/src/scanpy/preprocessing/_pca/__init__.py
@@ -30,7 +30,8 @@
     from scipy import sparse
     from scipy.sparse import spmatrix
 
-    from ..._utils import AnyRandom, Empty
+    from ..._compat import _LegacyRandom
+    from ..._utils import Empty
 
     CSMatrix = sparse.csr_matrix | sparse.csc_matrix
 
@@ -70,7 +71,7 @@ def pca(
     layer: str | None = None,
     zero_center: bool | None = True,
     svd_solver: SvdSolver | None = None,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     return_info: bool = False,
     mask_var: NDArray[np.bool_] | str | None | Empty = _empty,
     use_highly_variable: bool | None = None,
diff --git a/src/scanpy/preprocessing/_pca/_compat.py b/src/scanpy/preprocessing/_pca/_compat.py
index 23cb60a2e9..28eef2ba1a 100644
--- a/src/scanpy/preprocessing/_pca/_compat.py
+++ b/src/scanpy/preprocessing/_pca/_compat.py
@@ -18,7 +18,7 @@
     from scipy import sparse
     from sklearn.decomposition import PCA
 
-    from .._utils import AnyRandom
+    from ..._compat import _LegacyRandom
 
     CSMatrix = sparse.csr_matrix | sparse.csc_matrix
 
@@ -29,7 +29,7 @@ def _pca_compat_sparse(
     *,
     solver: Literal["arpack", "lobpcg"],
     mu: NDArray[np.floating] | None = None,
-    random_state: AnyRandom = None,
+    random_state: _LegacyRandom = None,
 ) -> tuple[NDArray[np.floating], PCA]:
     """Sparse PCA for scikit-learn <1.4"""
     random_state = check_random_state(random_state)
diff --git a/src/scanpy/preprocessing/_recipes.py b/src/scanpy/preprocessing/_recipes.py
index 4579739939..4b97405df9 100644
--- a/src/scanpy/preprocessing/_recipes.py
+++ b/src/scanpy/preprocessing/_recipes.py
@@ -16,7 +16,7 @@
 if TYPE_CHECKING:
     from anndata import AnnData
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
 
 @old_positionals(
@@ -36,7 +36,7 @@ def recipe_weinreb17(
     cv_threshold: int = 2,
     n_pcs: int = 50,
     svd_solver="randomized",
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     copy: bool = False,
 ) -> AnnData | None:
     """\
diff --git a/src/scanpy/preprocessing/_scrublet/__init__.py b/src/scanpy/preprocessing/_scrublet/__init__.py
index d57eb81750..68b7f59526 100644
--- a/src/scanpy/preprocessing/_scrublet/__init__.py
+++ b/src/scanpy/preprocessing/_scrublet/__init__.py
@@ -15,7 +15,7 @@
 from .core import Scrublet
 
 if TYPE_CHECKING:
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
     from ...neighbors import _Metric, _MetricFn
 
 
@@ -58,7 +58,7 @@ def scrublet(
     threshold: float | None = None,
     verbose: bool = True,
     copy: bool = False,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
 ) -> AnnData | None:
     """\
     Predict doublets using Scrublet :cite:p:`Wolock2019`.
@@ -309,7 +309,7 @@ def _scrublet_call_doublets(
     knn_dist_metric: _Metric | _MetricFn = "euclidean",
     get_doublet_neighbor_parents: bool = False,
     threshold: float | None = None,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     verbose: bool = True,
 ) -> AnnData:
     """\
@@ -503,7 +503,7 @@ def scrublet_simulate_doublets(
     layer: str | None = None,
     sim_doublet_ratio: float = 2.0,
     synthetic_doublet_umi_subsampling: float = 1.0,
-    random_seed: AnyRandom = 0,
+    random_seed: _LegacyRandom = 0,
 ) -> AnnData:
     """\
     Simulate doublets by adding the counts of random observed transcriptome pairs.
diff --git a/src/scanpy/preprocessing/_scrublet/core.py b/src/scanpy/preprocessing/_scrublet/core.py
index 4c992b2b64..1236f42a7a 100644
--- a/src/scanpy/preprocessing/_scrublet/core.py
+++ b/src/scanpy/preprocessing/_scrublet/core.py
@@ -9,7 +9,7 @@
 from scipy import sparse
 
 from ... import logging as logg
-from ..._utils import get_random_state
+from ..._utils import _get_legacy_random
 from ...neighbors import (
     Neighbors,
     _get_indices_distances_from_sparse_matrix,
@@ -21,7 +21,7 @@
     from numpy.random import RandomState
     from numpy.typing import NDArray
 
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
     from ...neighbors import _Metric, _MetricFn
 
 __all__ = ["Scrublet"]
@@ -73,7 +73,7 @@ class Scrublet:
     n_neighbors: InitVar[int | None] = None
     expected_doublet_rate: float = 0.1
     stdev_doublet_rate: float = 0.02
-    random_state: InitVar[AnyRandom] = 0
+    random_state: InitVar[_LegacyRandom] = 0
 
     # private fields
 
@@ -174,7 +174,7 @@ def __post_init__(
         counts_obs: sparse.csr_matrix | sparse.csc_matrix | NDArray[np.integer],
         total_counts_obs: NDArray[np.integer] | None,
         n_neighbors: int | None,
-        random_state: AnyRandom,
+        random_state: _LegacyRandom,
     ) -> None:
         self._counts_obs = sparse.csc_matrix(counts_obs)
         self._total_counts_obs = (
@@ -187,7 +187,7 @@ def __post_init__(
             if n_neighbors is None
             else n_neighbors
         )
-        self._random_state = get_random_state(random_state)
+        self._random_state = _get_legacy_random(random_state)
 
     def simulate_doublets(
         self,
diff --git a/src/scanpy/preprocessing/_scrublet/pipeline.py b/src/scanpy/preprocessing/_scrublet/pipeline.py
index 5f6c62838c..586587e2cf 100644
--- a/src/scanpy/preprocessing/_scrublet/pipeline.py
+++ b/src/scanpy/preprocessing/_scrublet/pipeline.py
@@ -12,7 +12,7 @@
 if TYPE_CHECKING:
     from typing import Literal
 
-    from ..._utils import AnyRandom
+    from ..._compat import _LegacyRandom
     from .core import Scrublet
 
 
@@ -49,7 +49,7 @@ def truncated_svd(
     self: Scrublet,
     n_prin_comps: int = 30,
     *,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     algorithm: Literal["arpack", "randomized"] = "arpack",
 ) -> None:
     if self._counts_sim_norm is None:
@@ -68,7 +68,7 @@ def pca(
     self: Scrublet,
     n_prin_comps: int = 50,
     *,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     svd_solver: Literal["auto", "full", "arpack", "randomized"] = "arpack",
 ) -> None:
     if self._counts_sim_norm is None:
diff --git a/src/scanpy/preprocessing/_scrublet/sparse_utils.py b/src/scanpy/preprocessing/_scrublet/sparse_utils.py
index cc0b1bc815..795559583c 100644
--- a/src/scanpy/preprocessing/_scrublet/sparse_utils.py
+++ b/src/scanpy/preprocessing/_scrublet/sparse_utils.py
@@ -7,12 +7,12 @@
 
 from scanpy.preprocessing._utils import _get_mean_var
 
-from ..._utils import get_random_state
+from ..._utils import _get_legacy_random
 
 if TYPE_CHECKING:
     from numpy.typing import NDArray
 
-    from ..._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
 
 def sparse_multiply(
@@ -47,10 +47,10 @@ def subsample_counts(
     *,
     rate: float,
     original_totals,
-    random_seed: AnyRandom = 0,
+    random_seed: _LegacyRandom = 0,
 ) -> tuple[sparse.csr_matrix | sparse.csc_matrix, NDArray[np.int64]]:
     if rate < 1:
-        random_seed = get_random_state(random_seed)
+        random_seed = _get_legacy_random(random_seed)
         E.data = random_seed.binomial(np.round(E.data).astype(int), rate)
         current_totals = np.asarray(E.sum(1)).squeeze()
         unsampled_orig_totals = original_totals - current_totals
diff --git a/src/scanpy/preprocessing/_simple.py b/src/scanpy/preprocessing/_simple.py
index 4d540ef931..01936414a5 100644
--- a/src/scanpy/preprocessing/_simple.py
+++ b/src/scanpy/preprocessing/_simple.py
@@ -50,8 +50,7 @@
     import pandas as pd
     from numpy.typing import NDArray
 
-    from .._compat import DaskArray
-    from .._utils import AnyRandom
+    from .._compat import DaskArray, _LegacyRandom
 
 
 @old_positionals(
@@ -831,7 +830,7 @@ def subsample(
     fraction: float | None = None,
     *,
     n_obs: int | None = None,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     copy: bool = False,
 ) -> AnnData | tuple[np.ndarray | spmatrix, NDArray[np.int64]] | None:
     """\
@@ -894,7 +893,7 @@ def downsample_counts(
     counts_per_cell: int | Collection[int] | None = None,
     total_counts: int | None = None,
     *,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     replace: bool = False,
     copy: bool = False,
 ) -> AnnData | None:
@@ -1030,7 +1029,7 @@ def _downsample_array(
     col: np.ndarray,
     target: int,
     *,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     replace: bool = True,
     inplace: bool = False,
 ):
diff --git a/src/scanpy/preprocessing/_utils.py b/src/scanpy/preprocessing/_utils.py
index 9c02f7e636..b200e89ce8 100644
--- a/src/scanpy/preprocessing/_utils.py
+++ b/src/scanpy/preprocessing/_utils.py
@@ -16,8 +16,8 @@
 
     from numpy.typing import DTypeLike, NDArray
 
-    from .._compat import DaskArray
-    from .._utils import AnyRandom, _SupportedArray
+    from .._compat import DaskArray, _LegacyRandom
+    from .._utils import _SupportedArray
 
 
 @singledispatch
@@ -150,7 +150,7 @@ def sample_comb(
     dims: tuple[int, ...],
     nsamp: int,
     *,
-    random_state: AnyRandom = None,
+    random_state: _LegacyRandom = None,
     method: Literal[
         "auto", "tracking_selection", "reservoir_sampling", "pool"
     ] = "auto",
diff --git a/src/scanpy/tools/_diffmap.py b/src/scanpy/tools/_diffmap.py
index dee643c39b..d2bdcc647b 100644
--- a/src/scanpy/tools/_diffmap.py
+++ b/src/scanpy/tools/_diffmap.py
@@ -8,7 +8,7 @@
 if TYPE_CHECKING:
     from anndata import AnnData
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
 
 @old_positionals("neighbors_key", "random_state", "copy")
@@ -17,7 +17,7 @@ def diffmap(
     n_comps: int = 15,
     *,
     neighbors_key: str | None = None,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     copy: bool = False,
 ) -> AnnData | None:
     """\
diff --git a/src/scanpy/tools/_draw_graph.py b/src/scanpy/tools/_draw_graph.py
index 3f0e65c061..aedd41f3d3 100644
--- a/src/scanpy/tools/_draw_graph.py
+++ b/src/scanpy/tools/_draw_graph.py
@@ -18,7 +18,7 @@
     from anndata import AnnData
     from scipy.sparse import spmatrix
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
     S = TypeVar("S", bound=LiteralString)
 
@@ -43,7 +43,7 @@ def draw_graph(
     *,
     init_pos: str | bool | None = None,
     root: int | None = None,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     n_jobs: int | None = None,
     adjacency: spmatrix | None = None,
     key_added_ext: str | None = None,
diff --git a/src/scanpy/tools/_leiden.py b/src/scanpy/tools/_leiden.py
index 5a8ba00484..f73ec1fd7d 100644
--- a/src/scanpy/tools/_leiden.py
+++ b/src/scanpy/tools/_leiden.py
@@ -17,6 +17,8 @@
     from anndata import AnnData
     from scipy import sparse
 
+    from .._compat import _LegacyRandom
+
 try:
     from leidenalg.VertexPartition import MutableVertexPartition
 except ImportError:
@@ -32,7 +34,7 @@ def leiden(
     resolution: float = 1,
     *,
     restrict_to: tuple[str, Sequence[str]] | None = None,
-    random_state: _utils.AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     key_added: str = "leiden",
     adjacency: sparse.spmatrix | None = None,
     directed: bool | None = None,
diff --git a/src/scanpy/tools/_louvain.py b/src/scanpy/tools/_louvain.py
index d3e616a850..470858ff38 100644
--- a/src/scanpy/tools/_louvain.py
+++ b/src/scanpy/tools/_louvain.py
@@ -22,6 +22,8 @@
     from anndata import AnnData
     from scipy.sparse import spmatrix
 
+    from .._compat import _LegacyRandom
+
 try:
     from louvain.VertexPartition import MutableVertexPartition
 except ImportError:
@@ -50,7 +52,7 @@ def louvain(
     adata: AnnData,
     resolution: float | None = None,
     *,
-    random_state: _utils.AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     restrict_to: tuple[str, Sequence[str]] | None = None,
     key_added: str = "louvain",
     adjacency: spmatrix | None = None,
diff --git a/src/scanpy/tools/_score_genes.py b/src/scanpy/tools/_score_genes.py
index a3909b7a28..a40d9f3288 100644
--- a/src/scanpy/tools/_score_genes.py
+++ b/src/scanpy/tools/_score_genes.py
@@ -22,7 +22,7 @@
     from numpy.typing import DTypeLike, NDArray
     from scipy.sparse import csc_matrix, csr_matrix
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
     try:
         _StrIdx = pd.Index[str]
@@ -70,7 +70,7 @@ def score_genes(
     gene_pool: Sequence[str] | pd.Index[str] | None = None,
     n_bins: int = 25,
     score_name: str = "score",
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     copy: bool = False,
     use_raw: bool | None = None,
     layer: str | None = None,
diff --git a/src/scanpy/tools/_tsne.py b/src/scanpy/tools/_tsne.py
index ac0e6a6317..18e4a47f8e 100644
--- a/src/scanpy/tools/_tsne.py
+++ b/src/scanpy/tools/_tsne.py
@@ -15,7 +15,7 @@
 if TYPE_CHECKING:
     from anndata import AnnData
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
 
 @old_positionals(
@@ -38,7 +38,7 @@ def tsne(
     metric: str = "euclidean",
     early_exaggeration: float = 12,
     learning_rate: float = 1000,
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     use_fast_tsne: bool = False,
     n_jobs: int | None = None,
     key_added: str | None = None,
diff --git a/src/scanpy/tools/_umap.py b/src/scanpy/tools/_umap.py
index 4f225da2a1..902171d58c 100644
--- a/src/scanpy/tools/_umap.py
+++ b/src/scanpy/tools/_umap.py
@@ -17,7 +17,7 @@
 
     from anndata import AnnData
 
-    from .._utils import AnyRandom
+    from .._compat import _LegacyRandom
 
     _InitPos = Literal["paga", "spectral", "random"]
 
@@ -49,7 +49,7 @@ def umap(
     gamma: float = 1.0,
     negative_sample_rate: int = 5,
     init_pos: _InitPos | np.ndarray | None = "spectral",
-    random_state: AnyRandom = 0,
+    random_state: _LegacyRandom = 0,
     a: float | None = None,
     b: float | None = None,
     method: Literal["umap", "rapids"] = "umap",