diff --git a/instaloader/__main__.py b/instaloader/__main__.py
index 9cd2a49..007131d 100644
--- a/instaloader/__main__.py
+++ b/instaloader/__main__.py
@@ -179,6 +179,8 @@ def _main(instaloader: Instaloader, targetlist: List[str],
         if len(profiles) > 1:
             instaloader.context.log("Downloading {} profiles: {}".format(len(profiles),
                                                                          ' '.join([p.username for p in profiles])))
+        if profiles and download_profile_pic and not instaloader.context.is_logged_in:
+            instaloader.context.error("Warning: Use --login to download HD version of profile pictures.")
         instaloader.download_profiles(profiles,
                                       download_profile_pic, download_posts, download_tagged, download_highlights,
                                       download_stories, fast_update, post_filter, storyitem_filter)
diff --git a/instaloader/instaloader.py b/instaloader/instaloader.py
index 2a3e22a..99db1b0 100644
--- a/instaloader/instaloader.py
+++ b/instaloader/instaloader.py
@@ -309,7 +309,9 @@ class Instaloader:
         else:
             filename = '{0}/{1}_{2}_profile_pic.{3}'.format(self.dirname_pattern.format(), profile.username.lower(),
                                                             profile_pic_identifier, profile_pic_extension)
-        if os.path.isfile(filename):
+        content_length = profile_pic_response.headers.get('Content-Length', None)
+        if os.path.isfile(filename) and (not self.context.is_logged_in or
+                                         content_length is not None and os.path.getsize(filename) >= int(content_length)):
             self.context.log(filename + ' already exists')
             return None
         self.context.write_raw(profile_pic_bytes if profile_pic_bytes else profile_pic_response, filename)
diff --git a/instaloader/instaloadercontext.py b/instaloader/instaloadercontext.py
index fb7b42f..0793bc9 100644
--- a/instaloader/instaloadercontext.py
+++ b/instaloader/instaloadercontext.py
@@ -429,6 +429,24 @@ class InstaloaderContext:
             data = _query()
             yield from (edge['node'] for edge in data['edges'])
 
+    def get_iphone_json(self, path: str, params: Dict[str, Any]) -> Dict[str, Any]:
+        """JSON request to ``i.instagram.com``.
+
+        :param path: URL, relative to ``i.instagram.com/``
+        :param params: GET parameters
+        :return: Decoded response dictionary
+        :raises QueryReturnedBadRequestException: When the server responds with a 400.
+        :raises QueryReturnedNotFoundException: When the server responds with a 404.
+        :raises ConnectionException: When query repeatedly failed.
+
+        .. versionadded:: 4.2.1"""
+        tempsession = copy_session(self._session)
+        tempsession.headers['User-Agent'] = 'Instagram 10.3.2 (iPhone7,2; iPhone OS 9_3_3; en_US; en-US; ' \
+                                            'scale=2.00; 750x1334) AppleWebKit/420+'
+        for header in ['Host', 'Origin', 'X-Instagram-AJAX', 'X-Requested-With']:
+            tempsession.headers.pop(header, None)
+        return self.get_json(path, params, 'i.instagram.com', tempsession)
+
     def write_raw(self, resp: Union[bytes, requests.Response], filename: str) -> None:
         """Write raw response data into a file."""
         self.log(filename, end=' ', flush=True)
diff --git a/instaloader/structures.py b/instaloader/structures.py
index 0bb5984..678d350 100644
--- a/instaloader/structures.py
+++ b/instaloader/structures.py
@@ -373,6 +373,10 @@ class Profile:
         self._has_public_story = None
         self._node = node
         self._rhx_gis = None
+        self._iphone_struct_ = None
+        if 'iphone_struct' in node:
+            # if loaded from JSON with load_structure_from_file()
+            self._iphone_struct_ = node['iphone_struct']
 
     @classmethod
     def from_username(cls, context: InstaloaderContext, username: str):
@@ -423,6 +427,8 @@ class Profile:
         json_node.pop('edge_media_collections', None)
         json_node.pop('edge_owner_to_timeline_media', None)
         json_node.pop('edge_saved_media', None)
+        if self._iphone_struct_:
+            json_node['iphone_struct'] = self._iphone_struct_
         return json_node
 
     def _obtain_metadata(self):
@@ -447,6 +453,15 @@ class Profile:
                 d = d[key]
             return d
 
+    @property
+    def _iphone_struct(self) -> Dict[str, Any]:
+        if not self._context.is_logged_in:
+            raise LoginRequiredException("--login required to access iPhone profile info endpoint.")
+        if not self._iphone_struct_:
+            data = self._context.get_iphone_json(path='api/v1/users/{}/info/'.format(self.userid), params={})
+            self._iphone_struct_ = data['user']
+        return self._iphone_struct_
+
     @property
     def userid(self) -> int:
         """User ID"""
@@ -563,10 +578,20 @@ class Profile:
 
     @property
     def profile_pic_url(self) -> str:
-        """Return URL of profile picture
+        """Return URL of profile picture. If logged in, the HD version is returned, otherwise a lower-quality version.
 
-        .. versionadded:: 4.0.3"""
-        return self._metadata("profile_pic_url_hd")
+        .. versionadded:: 4.0.3
+
+        .. versionchanged:: 4.2.1
+           Require being logged in for HD version (as required by Instagram)."""
+        if self._context.is_logged_in:
+            try:
+                return self._iphone_struct['hd_profile_pic_url_info']['url']
+            except (InstaloaderException, KeyError) as err:
+                self._context.error('{} Unable to fetch high quality profile pic.'.format(err))
+                return self._metadata("profile_pic_url_hd")
+        else:
+            return self._metadata("profile_pic_url_hd")
 
     def get_profile_pic_url(self) -> str:
         """.. deprecated:: 4.0.3