diff --git a/asdf_pydantic/converter.py b/asdf_pydantic/converter.py
index 89b54af..4be2684 100644
--- a/asdf_pydantic/converter.py
+++ b/asdf_pydantic/converter.py
@@ -1,37 +1,29 @@
 from __future__ import annotations
 
-from typing import Optional, Type
+from typing import Type
 
 from asdf.extension import Converter
 
 from asdf_pydantic.model import AsdfPydanticModel
 
-_ASDF_PYDANTIC_SINGLETON_CONVERTER: Optional[AsdfPydanticConverter] = None
-
 
 class AsdfPydanticConverter(Converter):
-    """Implements a converter compatible with all subclass of AsdfPydanticModel.
-
-    The instance is a singleton.
-    """
-
-    _tag_to_class: dict[str, Type[AsdfPydanticModel]] = {}
+    """Implements a converter compatible with all subclass of AsdfPydanticModel."""
 
+    _tag_to_class: dict[str, Type[AsdfPydanticModel]]
 
-    def __new__(cls, *args, **kwargs):
-        global _ASDF_PYDANTIC_SINGLETON_CONVERTER
-        if _ASDF_PYDANTIC_SINGLETON_CONVERTER is None:
-            _ASDF_PYDANTIC_SINGLETON_CONVERTER = super().__new__(cls)
+    def __init__(self, *model_classes: Type[AsdfPydanticModel]) -> None:
+        self._tag_to_class = {}
+        self.add_models(*model_classes)
+        super().__init__()
 
-        return _ASDF_PYDANTIC_SINGLETON_CONVERTER
-
-    @classmethod
     def add_models(
-        cls, *model_classes: Type[AsdfPydanticModel]
+        self, *model_classes: Type[AsdfPydanticModel]
     ) -> "AsdfPydanticConverter":
         for model_class in model_classes:
-            cls._tag_to_class[model_class.get_tag_uri()] = model_class
-        return cls()
+            self._tag_to_class[model_class.get_tag_uri()] = model_class
+
+        return self
 
     @property
     def tags(self) -> tuple[str]:
diff --git a/tests/test_converter.py b/tests/test_converter.py
new file mode 100644
index 0000000..5421296
--- /dev/null
+++ b/tests/test_converter.py
@@ -0,0 +1,13 @@
+import pytest
+
+from asdf_pydantic.converter import AsdfPydanticConverter
+from asdf_pydantic.model import AsdfPydanticModel
+
+
+class TestModel(AsdfPydanticModel):
+    _tag = "https://example.org/test_model"
+
+
+@pytest.mark.parametrize("args", [tuple(), (TestModel,)])
+def test_converter_is_unscoped_by_default(args):
+    assert AsdfPydanticConverter(*args) is not AsdfPydanticConverter(*args)