diff --git a/dvc/dependency/param.py b/dvc/dependency/param.py
index eb4faf176..f5ce0a5fb 100644
--- a/dvc/dependency/param.py
+++ b/dvc/dependency/param.py
@@ -39,12 +39,13 @@ class ParamsDependency(Dependency):
 
     def __init__(self, stage, path, params=None, repo=None):
         self.params = list(params) if params else []
-        info = (
-            {self.PARAM_PARAMS: params} if isinstance(params, dict) else None
-        )
+        hash_info = HashInfo()
+        if isinstance(params, dict):
+            hash_info = HashInfo(self.PARAM_PARAMS, params)
         repo = repo or stage.repo
         path = path or os.path.join(repo.root_dir, self.DEFAULT_PARAMS_FILE)
-        super().__init__(stage, path, info=info, repo=repo)
+        super().__init__(stage, path, repo=repo)
+        self.hash_info = hash_info
 
     def dumpd(self):
         ret = super().dumpd()
diff --git a/dvc/fs/git.py b/dvc/fs/git.py
index a80e3ced1..f1fc6ddc2 100644
--- a/dvc/fs/git.py
+++ b/dvc/fs/git.py
@@ -15,6 +15,7 @@ class GitFileSystem(FileSystem):  # pylint:disable=abstract-method
     """Proxies the repo file access methods to Git objects"""
 
     protocol = "local"
+    PARAM_CHECKSUM = "md5"
 
     def __init__(
         self,
diff --git a/dvc/output.py b/dvc/output.py
index f90e11b27..def18eb2d 100644
--- a/dvc/output.py
+++ b/dvc/output.py
@@ -330,7 +330,6 @@ class Output:
         # should be absolute and don't contain remote:// refs.
         self.stage = stage
         self.meta = meta
-        self.hash_info = HashInfo.from_dict(info)
         self.use_cache = False if self.IS_DEPENDENCY else cache
         self.metric = False if self.IS_DEPENDENCY else metric
         self.plot = False if self.IS_DEPENDENCY else plot
@@ -350,6 +349,16 @@ class Output:
             )
             self.meta.version_id = version_id
 
+        if self.is_in_repo:
+            self.hash_name = "md5"
+        else:
+            self.hash_name = self.fs.PARAM_CHECKSUM
+
+        self.hash_info = HashInfo(
+            name=self.hash_name,
+            value=getattr(self.meta, self.hash_name, None),
+        )
+
     def _parse_path(self, fs, fs_path):
         parsed = urlparse(self.def_path)
         if (
@@ -440,15 +449,13 @@ class Output:
     def _get_hash_meta(self):
         if self.use_cache:
             odb = self.odb
-            name = self.odb.fs.PARAM_CHECKSUM
         else:
             odb = self.repo.odb.local
-            name = self.fs.PARAM_CHECKSUM
         _, meta, obj = build(
             odb,
             self.fs_path,
             self.fs,
-            name,
+            self.hash_name,
             ignore=self.dvcignore,
             dry_run=not self.use_cache,
         )
@@ -579,7 +586,7 @@ class Output:
                 self.repo.odb.local,
                 self.fs_path,
                 self.fs,
-                self.fs.PARAM_CHECKSUM,
+                self.hash_name,
                 ignore=self.dvcignore,
                 dry_run=True,
             )
@@ -596,7 +603,7 @@ class Output:
             self.odb,
             self.fs_path,
             self.fs,
-            self.odb.fs.PARAM_CHECKSUM,
+            self.hash_name,
             ignore=self.dvcignore,
         )
         self.hash_info = self.obj.hash_info
@@ -638,7 +645,7 @@ class Output:
                     self.odb,
                     filter_info or self.fs_path,
                     self.fs,
-                    self.odb.fs.PARAM_CHECKSUM,
+                    self.hash_name,
                     ignore=self.dvcignore,
                 )
                 otransfer(
@@ -667,7 +674,7 @@ class Output:
             self.odb,
             self.fs_path,
             self.fs,
-            self.odb.fs.PARAM_CHECKSUM,
+            self.hash_name,
             ignore=self.dvcignore,
         )
         save_obj = save_obj.filter(prefix)
@@ -1048,7 +1055,7 @@ class Output:
         other = out.dumpd()
 
         ignored = [
-            self.fs.PARAM_CHECKSUM,
+            self.hash_name,
             Meta.PARAM_SIZE,
             Meta.PARAM_NFILES,
         ]
diff --git a/dvc/stage/loader.py b/dvc/stage/loader.py
index 8d498e471..ca9a62038 100644
--- a/dvc/stage/loader.py
+++ b/dvc/stage/loader.py
@@ -69,7 +69,8 @@ class StageLoader(Mapping):
             info = info.copy()
             info.pop("path", None)
             item.meta = Meta.from_dict(info)
-            item.hash_info = HashInfo.from_dict(info)
+            hash_value = getattr(item.meta, item.hash_name, None)
+            item.hash_info = HashInfo(item.hash_name, hash_value)
 
     @classmethod
     def load_stage(cls, dvcfile, name, stage_data, lock_data=None):
diff --git a/setup.cfg b/setup.cfg
index 6d6f1248b..2d2af511f 100644
--- a/setup.cfg
+++ b/setup.cfg
@@ -66,7 +66,7 @@ install_requires =
     dvc-render==0.0.10
     dvc-task==0.1.2
     dvclive>=0.10.0
-    dvc-data==0.6.1
+    dvc-data==0.6.3
     dvc-http==2.19.1
     hydra-core>=1.1.0
 
diff --git a/tests/func/test_import_url.py b/tests/func/test_import_url.py
index 8c6cd09c7..50dcf881c 100644
--- a/tests/func/test_import_url.py
+++ b/tests/func/test_import_url.py
@@ -281,8 +281,7 @@ def test_import_url_no_download(tmp_dir, dvc, local_workspace):
     assert not dst.exists()
 
     out = stage.outs[0]
-    assert out.hash_info.value is None
-    assert out.hash_info.name is None
+    assert not out.hash_info
     assert out.meta.size is None
 
     status = dvc.status()
diff --git a/tests/unit/output/test_output.py b/tests/unit/output/test_output.py
index fb728124e..bcf821098 100644
--- a/tests/unit/output/test_output.py
+++ b/tests/unit/output/test_output.py
@@ -91,6 +91,7 @@ def test_get_used_objs(exists, expected_message, mocker, caplog):
         stage.repo.dvcignore, "check_ignore", return_value=_no_match("path")
     )
     stage.repo.fs.version_aware = False
+    stage.repo.fs.PARAM_CHECKSUM = "md5"
 
     output = Output(stage, "path")