diff --git a/dvc/repo/index.py b/dvc/repo/index.py
index a32a9c737a..011e751b9e 100644
--- a/dvc/repo/index.py
+++ b/dvc/repo/index.py
@@ -169,8 +169,9 @@ def _load_storage_from_out(storage_map, key, out):
                 FileStorage(
                     key=key,
                     fs=remote.fs,
-                    path=remote.fs.path.join(remote.path, *key),
+                    path=remote.path,
                     index=remote.index,
+                    prefix=(),
                 )
             )
         else:
diff --git a/pyproject.toml b/pyproject.toml
index 8b11aeaf77..70a2f1fe4a 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -34,7 +34,7 @@ dependencies = [
     "configobj>=5.0.6",
     "distro>=1.3",
     "dpath<3,>=2.1.0",
-    "dvc-data>=2.18.2,<2.19.0",
+    "dvc-data>=2.19.0,<2.20.0",
     "dvc-http>=2.29.0",
     "dvc-render>=0.3.1,<1",
     "dvc-studio-client>=0.13.0,<1",