diff --git a/rest_framework/schemas/inspectors.py b/rest_framework/schemas/inspectors.py
index c3ff8b74c0b..5c9659a57d7 100644
--- a/rest_framework/schemas/inspectors.py
+++ b/rest_framework/schemas/inspectors.py
@@ -7,6 +7,7 @@
 import re
 import warnings
 from collections import OrderedDict
+from weakref import WeakKeyDictionary
 
 from django.db import models
 from django.utils.encoding import force_text, smart_text
@@ -129,6 +130,35 @@ class ViewInspector(object):
     Provide subclass for per-view schema generation
     """
 
+    def __init__(self):
+        self.instance_schemas = WeakKeyDictionary()
+
+    def __get__(self, instance, owner):
+        """
+        Enables `ViewInspector` as a Python _Descriptor_.
+
+        This is how `view.schema` knows about `view`.
+
+        `__get__` is called when the descriptor is accessed on the owner.
+        (That will be when view.schema is called in our case.)
+
+        `owner` is always the owner class. (An APIView, or subclass for us.)
+        `instance` is the view instance or `None` if accessed from the class,
+        rather than an instance.
+
+        See: https://docs.python.org/3/howto/descriptor.html for info on
+        descriptor usage.
+        """
+        if instance in self.instance_schemas:
+            return self.instance_schemas[instance]
+
+        self.view = instance
+        return self
+
+    def __set__(self, instance, other):
+        self.instance_schemas[instance] = other
+        other.view = instance
+
     @property
     def view(self):
         """View property."""
@@ -171,6 +201,7 @@ def __init__(self, manual_fields=None):
         * `manual_fields`: list of `coreapi.Field` instances that
             will be added to auto-generated fields, overwriting on `Field.name`
         """
+        super(AutoSchema, self).__init__()
         if manual_fields is None:
             manual_fields = []
         self._manual_fields = manual_fields
@@ -437,6 +468,7 @@ def __init__(self, fields, description='', encoding=None):
         * `fields`: list of `coreapi.Field` instances.
         * `descripton`: String description for view. Optional.
         """
+        super(ManualSchema, self).__init__()
         assert all(isinstance(f, coreapi.Field) for f in fields), "`fields` must be a list of coreapi.Field instances"
         self._fields = fields
         self._description = description
@@ -456,9 +488,15 @@ def get_link(self, path, method, base_url):
         )
 
 
-class DefaultSchema(object):
+class DefaultSchema(ViewInspector):
     """Allows overriding AutoSchema using DEFAULT_SCHEMA_CLASS setting"""
     def __get__(self, instance, owner):
+        result = super(DefaultSchema, self).__get__(instance, owner)
+        if not isinstance(result, DefaultSchema):
+            return result
+
         inspector_class = api_settings.DEFAULT_SCHEMA_CLASS
         assert issubclass(inspector_class, ViewInspector), "DEFAULT_SCHEMA_CLASS must be set to a ViewInspector (usually an AutoSchema) subclass"
-        return inspector_class()
+        inspector = inspector_class()
+        inspector.view = instance
+        return inspector
diff --git a/rest_framework/views.py b/rest_framework/views.py
index e25f2882934..1f51517db32 100644
--- a/rest_framework/views.py
+++ b/rest_framework/views.py
@@ -3,8 +3,6 @@
 """
 from __future__ import unicode_literals
 
-from copy import deepcopy
-
 from django.conf import settings
 from django.core.exceptions import PermissionDenied
 from django.db import connection, models, transaction
@@ -110,14 +108,6 @@ class APIView(View):
 
     schema = DefaultSchema()
 
-    def __init__(self, **kwargs):
-        super(APIView, self).__init__(**kwargs)
-        if self.schema is not None:
-            # copy class-level schema to prevent instances using the same object
-            if 'schema' not in self.__dict__:
-                self.schema = deepcopy(self.schema)
-            self.schema.view = self
-
     @classmethod
     def as_view(cls, **initkwargs):
         """