diff --git a/python/cog/files.py b/python/cog/files.py
index 2470cbc9f5..698ef57748 100644
--- a/python/cog/files.py
+++ b/python/cog/files.py
@@ -8,8 +8,9 @@
 import requests
 
 
-def upload_file(fh: io.IOBase, output_file_prefix: str = None) -> str:
-    fh.seek(0)
+def upload_file(fh: io.IOBase, output_file_prefix: Optional[str] = None) -> str:
+    if fh.seekable():
+        fh.seek(0)
 
     if output_file_prefix is not None:
         name = getattr(fh, "name", "output")
@@ -42,7 +43,8 @@ def guess_filename(obj: io.IOBase) -> str:
 def put_file_to_signed_endpoint(
     fh: io.IOBase, endpoint: str, client: requests.Session, prediction_id: Optional[str]
 ) -> str:
-    fh.seek(0)
+    if fh.seekable():
+        fh.seek(0)
 
     filename = guess_filename(fh)
     content_type, _ = mimetypes.guess_type(filename)
diff --git a/python/cog/types.py b/python/cog/types.py
index e781ca9c2a..f4110e68ca 100644
--- a/python/cog/types.py
+++ b/python/cog/types.py
@@ -104,6 +104,7 @@ def __get_pydantic_json_schema__(
                 }
             )
             return json_schema
+
     else:
 
         @classmethod
@@ -223,6 +224,7 @@ def __get_pydantic_json_schema__(
             json_schema = handler(core_schema)
             json_schema.update(type="string", format="uri")
             return json_schema
+
     else:
 
         @classmethod
@@ -286,6 +288,15 @@ class URLFile(io.IOBase):
     __slots__ = ("__target__", "__url__")
 
     def __init__(self, url: str) -> None:
+        parsed = urllib.parse.urlparse(url)
+        if parsed.scheme not in {
+            "http",
+            "https",
+        }:
+            raise ValueError(
+                "URLFile requires URL to conform to HTTP or HTTPS protocol"
+            )
+        object.__setattr__(self, "name", os.path.basename(parsed.path))
         object.__setattr__(self, "__url__", url)
 
     # We provide __getstate__ and __setstate__ explicitly to ensure that the
@@ -413,6 +424,7 @@ def __get_pydantic_json_schema__(
                 }
             )
             return json_schema
+
     else:
 
         @classmethod
diff --git a/python/tests/test_json.py b/python/tests/test_json.py
index 95243fbbf3..e79f1a1049 100644
--- a/python/tests/test_json.py
+++ b/python/tests/test_json.py
@@ -3,11 +3,12 @@
 
 import numpy as np
 import pydantic
+import responses
 
 import cog
 from cog.files import upload_file
 from cog.json import make_encodeable, upload_files
-from cog.types import PYDANTIC_V2
+from cog.types import PYDANTIC_V2, URLFile
 
 
 def test_make_encodeable_recursively_encodes_tuples():
@@ -57,6 +58,20 @@ def test_upload_files():
     }
 
 
+@responses.activate
+def test_upload_files_with_url():
+    responses.get(
+        "https://example.com/some/url.txt",
+        body="file content",
+        status=200,
+    )
+
+    obj = {"path": URLFile("https://example.com/some/url.txt")}
+    assert upload_files(obj, upload_file) == {
+        "path": "data:text/plain;base64,ZmlsZSBjb250ZW50"
+    }
+
+
 def test_numpy():
     class Model(pydantic.BaseModel):
         ndarray: np.ndarray
diff --git a/python/tests/test_types.py b/python/tests/test_types.py
index 6ed027db05..95f7b237f8 100644
--- a/python/tests/test_types.py
+++ b/python/tests/test_types.py
@@ -7,6 +7,14 @@
 from cog.types import Secret, URLFile, get_filename
 
 
+def test_urlfile_protocol_validation():
+    with pytest.raises(ValueError):
+        URLFile("file:///etc/shadow")
+
+    with pytest.raises(ValueError):
+        URLFile("data:text/plain,hello")
+
+
 @responses.activate
 def test_urlfile_acts_like_response():
     responses.get(