diff --git a/cellrank/tl/_lineage.py b/cellrank/tl/_lineage.py
index 655ab6d7d..da00f5afd 100644
--- a/cellrank/tl/_lineage.py
+++ b/cellrank/tl/_lineage.py
@@ -1,4 +1,14 @@
-from typing import List, Tuple, Union, Mapping, TypeVar, Callable, Iterable, Optional
+from typing import (
+    Any,
+    List,
+    Tuple,
+    Union,
+    Mapping,
+    TypeVar,
+    Callable,
+    Iterable,
+    Optional,
+)
 from typing_extensions import Literal
 
 from copy import copy
@@ -20,6 +30,8 @@
     _compute_mean_color,
     _create_categorical_colors,
 )
+from anndata._io.specs.methods import H5Group, ZarrGroup, write_basic
+from anndata._io.specs.registry import _REGISTRY, IOSpec
 
 import numpy as np
 import pandas as pd
@@ -1303,3 +1315,19 @@ def _mutual_info(reference, query):
         weights[i, :] = mutual_info_regression(reference, target)
 
     return weights
+
+
+_SPEC = IOSpec("array", "0.2.0")
+
+
+@_REGISTRY.register_write(H5Group, Lineage, _SPEC)
+@_REGISTRY.register_write(H5Group, LineageView, _SPEC)
+@_REGISTRY.register_write(ZarrGroup, Lineage, _SPEC)
+@_REGISTRY.register_write(ZarrGroup, LineageView, _SPEC)
+def _write_lineage(
+    f: Any,
+    k: str,
+    elem: Union[Lineage, LineageView],
+    dataset_kwargs: Mapping[str, Any] = MappingProxyType({}),
+) -> None:
+    write_basic(f, k, elem=elem.X, dataset_kwargs=dataset_kwargs)
diff --git a/cellrank/tl/estimators/terminal_states/_gpcca.py b/cellrank/tl/estimators/terminal_states/_gpcca.py
index f92e1f970..ee8b37ce9 100644
--- a/cellrank/tl/estimators/terminal_states/_gpcca.py
+++ b/cellrank/tl/estimators/terminal_states/_gpcca.py
@@ -1,7 +1,6 @@
 from typing import Any, Dict, Tuple, Union, Mapping, Optional, Sequence
 from typing_extensions import Literal
 
-from copy import deepcopy
 from enum import auto
 from types import MappingProxyType
 from pathlib import Path
@@ -1042,7 +1041,7 @@ def _write_macrostates(
             self._set("_coarse_tmat", value=tmat, shadow_only=True)
             self._set("_coarse_init_dist", value=init_dist, shadow_only=True)
             self._set("_coarse_stat_dist", value=stat_dist, shadow_only=True)
-            self._set(obj=self.adata.uns, key=Key.uns.coarse(self.backward), value={"coarse_tmat": tmat, **dists})
+            self._set(obj=self.adata.uns, key=Key.uns.coarse(self.backward), value=AnnData(tmat, obs=dists))
         else:
             for attr in ["_schur_vectors", "_schur_matrix", "_coarse_tmat", "_coarse_init_dist", "_coarse_stat_dist"]:
                 self._set(attr, value=None, shadow_only=True)
@@ -1104,14 +1103,14 @@ def _read_from_adata(self, adata: AnnData, **kwargs: Any) -> bool:
             self._macrostates_colors = self.macrostates_memberships.colors.copy()
             self.params[key] = self._read_params(key)
 
-            tmat = deepcopy(self.adata.uns[Key.uns.coarse(self.backward)])
-            if not isinstance(tmat, dict):
+            tmat = self.adata.uns[Key.uns.coarse(self.backward)].copy()
+            if not isinstance(tmat, AnnData):
                 raise TypeError(f"Expected coarse-grained transition matrix to be stored "
-                                f"as `dict`, found `{type(tmat).__name__}`.")
+                                f"as `AnnData`, found `{type(tmat).__name__}`.")
 
-            self._coarse_tmat = tmat["coarse_tmat"]
-            self._coarse_init_dist = tmat["coarse_init_dist"]
-            self._coarse_stat_dist = tmat.get("coarse_stat_dist", None)
+            self._coarse_tmat = pd.DataFrame(tmat.X, index=tmat.obs_names, columns=tmat.obs_names)
+            self._coarse_init_dist = tmat.obs["coarse_init_dist"]
+            self._coarse_stat_dist = tmat.obs.get("coarse_stat_dist", None)
 
             self._set(obj=self._shadow_adata.uns, key=Key.uns.coarse(self.backward), value=tmat)
 
diff --git a/requirements.txt b/requirements.txt
index e32024ae3..432616ff7 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -1,4 +1,4 @@
-anndata<0.8  # TODO(mihalk8): remove me after #777
+anndata>=0.8,<0.9
 docrep>=0.3.0
 joblib>=0.13.1
 matplotlib>=3.3.0