diff --git a/mypy/subtypes.py b/mypy/subtypes.py
index df040dcb1311..c76b3569fdd4 100644
--- a/mypy/subtypes.py
+++ b/mypy/subtypes.py
@@ -2024,6 +2024,16 @@ def infer_variance(info: TypeInfo, i: int) -> bool:
 
             typ = find_member(member, self_type, self_type)
             if typ:
+                # It's okay for a method in a generic class with a contravariant type
+                # variable to return a generic instance of the class, if it doesn't involve
+                # variance (i.e. values of type variables are propagated). Our normal rules
+                # would disallow this. Replace such return types with 'Any' to allow this.
+                #
+                # This could probably be more lenient (e.g. allow self type be nested, don't
+                # require all type arguments to be identical to self_type), but this will
+                # hopefully cover the vast majority of such cases, including Self.
+                typ = erase_return_self_types(typ, self_type)
+
                 typ2 = expand_type(typ, {tvar.id: object_type})
                 if not is_subtype(typ, typ2):
                     co = False
@@ -2066,3 +2076,20 @@ def infer_class_variances(info: TypeInfo) -> bool:
             if not infer_variance(info, i):
                 success = False
     return success
+
+
+def erase_return_self_types(typ: Type, self_type: Instance) -> Type:
+    """If a typ is function-like and returns self_type, replace return type with Any."""
+    proper_type = get_proper_type(typ)
+    if isinstance(proper_type, CallableType):
+        ret = get_proper_type(proper_type.ret_type)
+        if isinstance(ret, Instance) and ret == self_type:
+            return proper_type.copy_modified(ret_type=AnyType(TypeOfAny.implementation_artifact))
+    elif isinstance(proper_type, Overloaded):
+        return Overloaded(
+            [
+                cast(CallableType, erase_return_self_types(it, self_type))
+                for it in proper_type.items
+            ]
+        )
+    return typ
diff --git a/test-data/unit/check-python312.test b/test-data/unit/check-python312.test
index 2f0b912c439e..085cc052705d 100644
--- a/test-data/unit/check-python312.test
+++ b/test-data/unit/check-python312.test
@@ -213,7 +213,7 @@ b: Invariant[int]
 if int():
     a = b  # E: Incompatible types in assignment (expression has type "Invariant[int]", variable has type "Invariant[object]")
 if int():
-    b = a  # E: Incompatible types in assignment (expression has type "Invariant[object]", variable has type "Invariant[int]")
+    b = a
 
 c: Covariant[object]
 d: Covariant[int]
@@ -393,6 +393,62 @@ inv3_1: Invariant3[float] = Invariant3[int](1)  # E: Incompatible types in assig
 inv3_2: Invariant3[int] = Invariant3[float](1)  # E: Incompatible types in assignment (expression has type "Invariant3[float]", variable has type "Invariant3[int]")
 [builtins fixtures/property.pyi]
 
+[case testPEP695InferVarianceWithInheritedSelf]
+from typing import overload, Self, TypeVar, Generic
+
+T = TypeVar("T")
+S = TypeVar("S")
+
+class C(Generic[T]):
+    def f(self, x: T) -> Self: ...
+    def g(self) -> T: ...
+
+class D[T1, T2](C[T1]):
+    def m(self, x: T2) -> None: ...
+
+a1: D[int, int] = D[int, object]()
+a2: D[int, object] = D[int, int]()  # E: Incompatible types in assignment (expression has type "D[int, int]", variable has type "D[int, object]")
+a3: D[int, int] = D[object, object]()  # E: Incompatible types in assignment (expression has type "D[object, object]", variable has type "D[int, int]")
+a4: D[object, int] = D[int, object]()  # E: Incompatible types in assignment (expression has type "D[int, object]", variable has type "D[object, int]")
+
+[case testPEP695InferVarianceWithReturnSelf]
+from typing import Self, overload
+
+class Cov[T]:
+    def f(self) -> Self: ...
+
+a1: Cov[int] = Cov[float]()  # E: Incompatible types in assignment (expression has type "Cov[float]", variable has type "Cov[int]")
+a2: Cov[float] = Cov[int]()
+
+class Contra[T]:
+    def f(self) -> Self: ...
+    def g(self, x: T) -> None: ...
+
+b1: Contra[int] = Contra[float]()
+b2: Contra[float] = Contra[int]()  # E: Incompatible types in assignment (expression has type "Contra[int]", variable has type "Contra[float]")
+
+class Cov2[T]:
+    @overload
+    def f(self, x): ...
+    @overload
+    def f(self) -> Self: ...
+    def f(self, x=None): ...
+
+c1: Cov2[int] = Cov2[float]()  # E: Incompatible types in assignment (expression has type "Cov2[float]", variable has type "Cov2[int]")
+c2: Cov2[float] = Cov2[int]()
+
+class Contra2[T]:
+    @overload
+    def f(self, x): ...
+    @overload
+    def f(self) -> Self: ...
+    def f(self, x=None): ...
+
+    def g(self, x: T) -> None: ...
+
+d1: Contra2[int] = Contra2[float]()
+d2: Contra2[float] = Contra2[int]()  # E: Incompatible types in assignment (expression has type "Contra2[int]", variable has type "Contra2[float]")
+
 [case testPEP695InheritInvariant]
 class Invariant[T]:
     x: T
diff --git a/test-data/unit/pythoneval.test b/test-data/unit/pythoneval.test
index 26fc419030bf..89f01bff963e 100644
--- a/test-data/unit/pythoneval.test
+++ b/test-data/unit/pythoneval.test
@@ -2196,3 +2196,23 @@ type K4 = None | B[int]
 
 type L1 = Never
 type L2 = list[Never]
+
+[case testPEP695VarianceInferenceSpecialCaseWithTypeshed]
+# flags: --python-version=3.12
+class C1[T1, T2](list[T1]):
+    def m(self, a: T2) -> None: ...
+
+def func1(p: C1[int, object]):
+    x: C1[int, int] = p
+
+class C2[T1, T2, T3](dict[T2, T3]):
+    def m(self, a: T1) -> None: ...
+
+def func2(p: C2[object, int, int]):
+    x: C2[int, int, int] = p
+
+class C3[T1, T2](tuple[T1, ...]):
+    def m(self, a: T2) -> None: ...
+
+def func3(p: C3[int, object]):
+    x: C3[int, int] = p