diff --git a/.github/workflows/ci.yaml b/.github/workflows/ci.yaml
index da758a4..3543102 100644
--- a/.github/workflows/ci.yaml
+++ b/.github/workflows/ci.yaml
@@ -2,10 +2,10 @@ name: CI
 
 on:
   push:
-    branches: ["main"]
+    branches: ["main", "beta"]
 
   pull_request:
-    branches: ["main"]
+    branches: ["main", "beta"]
 
 jobs:
   test:
diff --git a/replicate/use.py b/replicate/use.py
index 50c9ca6..2ea6783 100644
--- a/replicate/use.py
+++ b/replicate/use.py
@@ -1,10 +1,10 @@
 # TODO
 # - [ ] Support text streaming
 # - [ ] Support file streaming
+import copy
 import hashlib
 import os
 import tempfile
-from dataclasses import dataclass
 from functools import cached_property
 from pathlib import Path
 from typing import (
@@ -24,7 +24,6 @@
     cast,
     overload,
 )
-from urllib.parse import urlparse
 
 import httpx
 
@@ -61,36 +60,6 @@ def _has_concatenate_iterator_output_type(openapi_schema: dict) -> bool:
     return True
 
 
-def _has_iterator_output_type(openapi_schema: dict) -> bool:
-    """
-    Returns true if the model output type is an iterator (non-concatenate).
-    """
-    output = openapi_schema.get("components", {}).get("schemas", {}).get("Output", {})
-    return (
-        output.get("type") == "array" and output.get("x-cog-array-type") == "iterator"
-    )
-
-
-def _download_file(url: str) -> Path:
-    """
-    Download a file from URL to a temporary location and return the Path.
-    """
-    parsed_url = urlparse(url)
-    filename = os.path.basename(parsed_url.path)
-
-    if not filename or "." not in filename:
-        filename = "download"
-
-    _, ext = os.path.splitext(filename)
-    with tempfile.NamedTemporaryFile(delete=False, suffix=ext) as temp_file:
-        with httpx.stream("GET", url) as response:
-            response.raise_for_status()
-            for chunk in response.iter_bytes():
-                temp_file.write(chunk)
-
-    return Path(temp_file.name)
-
-
 def _process_iterator_item(item: Any, openapi_schema: dict) -> Any:
     """
     Process a single item from an iterator output based on schema.
@@ -177,6 +146,60 @@ def _process_output_with_schema(output: Any, openapi_schema: dict) -> Any:  # py
     return output
 
 
+def _dereference_schema(schema: dict[str, Any]) -> dict[str, Any]:
+    """
+    Performs basic dereferencing on an OpenAPI schema based on the current schemas generated
+    by Replicate. This code assumes that:
+
+    1) References will always point to a field within #/components/schemas and will error
+       if the reference is more deeply nested.
+    2) That the references when used can be discarded.
+
+    Should something more in-depth be required we could consider using the jsonref package.
+    """
+    dereferenced = copy.deepcopy(schema)
+    schemas = dereferenced.get("components", {}).get("schemas", {})
+    dereferenced_refs = set()
+
+    def _resolve_ref(obj: Any) -> Any:
+        if isinstance(obj, dict):
+            if "$ref" in obj:
+                ref_path = obj["$ref"]
+                if ref_path.startswith("#/components/schemas/"):
+                    parts = ref_path.replace("#/components/schemas/", "").split("/", 2)
+
+                    if len(parts) > 1:
+                        raise NotImplementedError(
+                            f"Unexpected nested $ref found in schema: {ref_path}"
+                        )
+
+                    (schema_name,) = parts
+                    if schema_name in schemas:
+                        dereferenced_refs.add(schema_name)
+                        return _resolve_ref(schemas[schema_name])
+                    else:
+                        return obj
+                else:
+                    return obj
+            else:
+                return {key: _resolve_ref(value) for key, value in obj.items()}
+        elif isinstance(obj, list):
+            return [_resolve_ref(item) for item in obj]
+        else:
+            return obj
+
+    result = _resolve_ref(dereferenced)
+
+    # Filter out any references that have now been referenced.
+    result["components"]["schemas"] = {
+        k: v
+        for k, v in result["components"]["schemas"].items()
+        if k not in dereferenced_refs
+    }
+
+    return result
+
+
 T = TypeVar("T")
 
 
@@ -302,7 +325,6 @@ class FunctionRef(Protocol, Generic[Input, Output]):
     __call__: Callable[Input, Output]
 
 
-@dataclass
 class Run[O]:
     """
     Represents a running prediction with access to the underlying schema.
@@ -361,13 +383,13 @@ def logs(self) -> Optional[str]:
         return self._prediction.logs
 
 
-@dataclass
 class Function(Generic[Input, Output]):
     """
     A wrapper for a Replicate model that can be called as a function.
     """
 
     _ref: str
+    _streaming: bool
 
     def __init__(self, ref: str, *, streaming: bool) -> None:
         self._ref = ref
@@ -405,7 +427,9 @@ def create(self, *_: Input.args, **inputs: Input.kwargs) -> Run[Output]:
             )
 
         return Run(
-            prediction=prediction, schema=self.openapi_schema, streaming=self._streaming
+            prediction=prediction,
+            schema=self.openapi_schema(),
+            streaming=self._streaming,
         )
 
     @property
@@ -415,20 +439,28 @@ def default_example(self) -> Optional[dict[str, Any]]:
         """
         raise NotImplementedError("This property has not yet been implemented")
 
-    @cached_property
     def openapi_schema(self) -> dict[str, Any]:
         """
         Get the OpenAPI schema for this model version.
         """
-        latest_version = self._model.latest_version
-        if latest_version is None:
-            msg = f"Model {self._model.owner}/{self._model.name} has no latest version"
+        return self._openapi_schema
+
+    @cached_property
+    def _openapi_schema(self) -> dict[str, Any]:
+        _, _, model_version = self._parsed_ref
+        model = self._model
+
+        version = (
+            model.versions.get(model_version) if model_version else model.latest_version
+        )
+        if version is None:
+            msg = f"Model {self._model.owner}/{self._model.name} has no version"
             raise ValueError(msg)
 
-        schema = latest_version.openapi_schema
-        if cog_version := latest_version.cog_version:
+        schema = version.openapi_schema
+        if cog_version := version.cog_version:
             schema = make_schema_backwards_compatible(schema, cog_version)
-        return schema
+        return _dereference_schema(schema)
 
     def _client(self) -> Client:
         return Client()
@@ -469,7 +501,6 @@ def _version(self) -> Version | None:
         return version
 
 
-@dataclass
 class AsyncRun[O]:
     """
     Represents a running prediction with access to its version (async version).
@@ -528,21 +559,25 @@ async def logs(self) -> Optional[str]:
         return self._prediction.logs
 
 
-@dataclass
 class AsyncFunction(Generic[Input, Output]):
     """
     An async wrapper for a Replicate model that can be called as a function.
     """
 
-    function_ref: str
-    streaming: bool
+    _ref: str
+    _streaming: bool
+    _openapi_schema: dict[str, Any] | None = None
+
+    def __init__(self, ref: str, *, streaming: bool) -> None:
+        self._ref = ref
+        self._streaming = streaming
 
     def _client(self) -> Client:
         return Client()
 
     @cached_property
     def _parsed_ref(self) -> Tuple[str, str, Optional[str]]:
-        return ModelVersionIdentifier.parse(self.function_ref)
+        return ModelVersionIdentifier.parse(self._ref)
 
     async def _model(self) -> Model:
         client = self._client()
@@ -607,7 +642,7 @@ async def create(self, *_: Input.args, **inputs: Input.kwargs) -> AsyncRun[Outpu
         return AsyncRun(
             prediction=prediction,
             schema=await self.openapi_schema(),
-            streaming=self.streaming,
+            streaming=self._streaming,
         )
 
     @property
@@ -621,16 +656,26 @@ async def openapi_schema(self) -> dict[str, Any]:
         """
         Get the OpenAPI schema for this model version asynchronously.
         """
-        model = await self._model()
-        latest_version = model.latest_version
-        if latest_version is None:
-            msg = f"Model {model.owner}/{model.name} has no latest version"
-            raise ValueError(msg)
+        if not self._openapi_schema:
+            _, _, model_version = self._parsed_ref
 
-        schema = latest_version.openapi_schema
-        if cog_version := latest_version.cog_version:
-            schema = make_schema_backwards_compatible(schema, cog_version)
-        return schema
+            model = await self._model()
+            if model_version:
+                version = await model.versions.async_get(model_version)
+            else:
+                version = model.latest_version
+
+            if version is None:
+                msg = f"Model {model.owner}/{model.name} has no version"
+                raise ValueError(msg)
+
+            schema = version.openapi_schema
+            if cog_version := version.cog_version:
+                schema = make_schema_backwards_compatible(schema, cog_version)
+
+            self._openapi_schema = _dereference_schema(schema)
+
+        return self._openapi_schema
 
 
 @overload
diff --git a/tests/test_use.py b/tests/test_use.py
index 70270f7..734c832 100644
--- a/tests/test_use.py
+++ b/tests/test_use.py
@@ -334,6 +334,61 @@ async def test_use_function_create_method(client_mode):
     assert run._prediction.input == {"prompt": "hello world"}
 
 
+@pytest.mark.asyncio
+@pytest.mark.parametrize("client_mode", [ClientMode.DEFAULT, ClientMode.ASYNC])
+@respx.mock
+async def test_use_function_openapi_schema_dereferenced(client_mode):
+    mock_model_endpoints(
+        versions=[
+            create_mock_version(
+                {
+                    "openapi_schema": {
+                        "components": {
+                            "schemas": {
+                                "Output": {"$ref": "#/components/schemas/ModelOutput"},
+                                "ModelOutput": {
+                                    "type": "object",
+                                    "properties": {
+                                        "text": {"type": "string"},
+                                        "image": {
+                                            "type": "string",
+                                            "format": "uri",
+                                        },
+                                        "count": {"type": "integer"},
+                                    },
+                                },
+                            }
+                        }
+                    }
+                }
+            )
+        ]
+    )
+
+    hotdog_detector = replicate.use(
+        "acme/hotdog-detector", use_async=client_mode == ClientMode.ASYNC
+    )
+
+    if client_mode == ClientMode.ASYNC:
+        schema = await hotdog_detector.openapi_schema()
+    else:
+        schema = hotdog_detector.openapi_schema()
+
+    assert schema["components"]["schemas"]["Output"] == {
+        "type": "object",
+        "properties": {
+            "text": {"type": "string"},
+            "image": {
+                "type": "string",
+                "format": "uri",
+            },
+            "count": {"type": "integer"},
+        },
+    }
+
+    assert "ModelOutput" not in schema["components"]["schemas"]
+
+
 @pytest.mark.asyncio
 @pytest.mark.parametrize("client_mode", [ClientMode.DEFAULT, ClientMode.ASYNC])
 @respx.mock
diff --git a/uv.lock b/uv.lock
index bcfad2f..30c17f9 100644
--- a/uv.lock
+++ b/uv.lock
@@ -1282,7 +1282,7 @@ wheels = [
 
 [[package]]
 name = "replicate"
-version = "1.0.7"
+version = "1.1.0b1"
 source = { editable = "." }
 dependencies = [
     { name = "httpx" },