diff --git a/test/test_dynamic_shapes.py b/test/test_dynamic_shapes.py
index d3f9e415ff944..50fb3952cc080 100644
--- a/test/test_dynamic_shapes.py
+++ b/test/test_dynamic_shapes.py
@@ -4465,6 +4465,54 @@ def f(x, start, end):
         res = f(x, start, 0)
         self.assertEqual(res.shape, torch.Size([0]))
 
+    @skipIfTorchDynamo()
+    @torch.fx.experimental._config.patch("backed_size_oblivious", True)
+    def test_backed_size_oblivious_broadcast(self):
+        cnt = CompileCounterWithBackend("inductor")
+        torch._dynamo.reset()
+
+        def func(a, b):
+            torch.broadcast_shapes(a.size(), b.size())
+            return a + b
+
+        compiled = torch.compile(func, fullgraph=True, backend=cnt, dynamic=True)
+
+        def run(a, b):
+            self.assertEqual(compiled(a, b), func(a, b))
+
+        # No 0/1 specializations, no broadcasts.
+        # but a[0] == b[0] and a[1] == b[1] are asserted.
+        run(torch.rand(1, 10), torch.rand(1, 10))
+        run(torch.rand(1, 1), torch.rand(1, 1))
+        run(torch.rand(10, 10), torch.rand(10, 10))
+
+        self.assertEqual(cnt.frame_count, 1)
+        run(torch.rand(10, 10), torch.rand(1, 10))
+        self.assertEqual(cnt.frame_count, 2)
+
+        cnt.clear()
+        torch._dynamo.reset()
+
+        # specialize a[0] == 1. b[0] not specialized.
+        run(torch.rand(1, 10), torch.rand(9, 10))
+        run(torch.rand(1, 10), torch.rand(1, 10))
+        self.assertEqual(cnt.frame_count, 1)
+        # if we change a[0] we get recompilation.
+        run(torch.rand(10, 10), torch.rand(10, 10))
+        self.assertEqual(cnt.frame_count, 2)
+
+        cnt.clear()
+        torch._dynamo.reset()
+
+        # TODO duck sizing shall be disabled when backed_size_oblivious
+        # is on probably.
+        # specialize b[0] == 1. a[0] not specialized.
+        run(torch.rand(10, 11), torch.rand(1, 11))
+        run(torch.rand(1, 10), torch.rand(1, 10))
+        self.assertEqual(cnt.frame_count, 1)
+        run(torch.rand(2, 10), torch.rand(2, 10))
+        self.assertEqual(cnt.frame_count, 2)
+
 
 instantiate_parametrized_tests(TestUnbacked)
 
diff --git a/torch/_refs/__init__.py b/torch/_refs/__init__.py
index 9224643fe55ab..5137a65545b11 100644
--- a/torch/_refs/__init__.py
+++ b/torch/_refs/__init__.py
@@ -385,7 +385,13 @@ def handle_noncontiguous_outputs(input_tlist, output):
 
 
 def _broadcast_shapes(*_shapes):
-    from torch.fx.experimental.symbolic_shapes import guard_or_false, is_nested_int
+    from torch.fx.experimental.symbolic_shapes import (
+        guard_or_false,
+        is_nested_int,
+        size_hint,
+    )
+
+    backed_so = torch.fx.experimental._config.backed_size_oblivious
 
     shapes = tuple(
         (x,) if isinstance(x, IntLike) else x
@@ -418,6 +424,22 @@ def _broadcast_shapes(*_shapes):
                 ):
                     continue
             else:
+                # When backed size oblivious is used, we specialize for broadcasting
+                # if its the only way to compile the example input.
+                # i.e: s0:1, s1:1 ==>
+                #           assert s0==s1, no specialization on ==1 or !=1.
+                #            The non-broadcast path is picked
+                #      s0:1, s1:4 ==>
+                #           specialize(s0) to be 1.
+                #      s0:4, s1:1 ==>
+                #           specialize(s1) to be 1.
+                if backed_so:
+                    a = size_hint(shape[idx], allow_none=True)
+                    b = size_hint(common_shape[idx], allow_none=True)
+                    if a == 1 and b != 1:
+                        torch._check(shape[idx] == 1)
+                    if b == 1 and a != 1:
+                        torch._check(common_shape[idx] == 1)
                 if guard_or_false(shape[idx] == common_shape[idx]):
                     continue
 
diff --git a/torch/fx/experimental/symbolic_shapes.py b/torch/fx/experimental/symbolic_shapes.py
index 693d25aea6130..c3b64f2d85a53 100644
--- a/torch/fx/experimental/symbolic_shapes.py
+++ b/torch/fx/experimental/symbolic_shapes.py
@@ -131,6 +131,7 @@ class PendingUnbackedSymbolNotFound(RuntimeError):
 aten = torch._ops.ops.aten  # type: ignore[has-type]
 
 __all__ = [
+    "size_hint",
     "guard_or_false",
     "guard_or_true",
     "has_symbolic_sizes_strides",
@@ -255,6 +256,17 @@ def _nested_int_aware_sort(
     )
 
 
+def size_hint(x: int | torch.SymInt, *, allow_none: bool = False) -> int | None:
+    """Gets a size hint for a given expression from the underlying shapes we had.
+    Does not introduce a guard, so only use this when you can guarantee that
+    your code is still valid for arbitrary shapes (such as optimization decisions)
+    """
+    if isinstance(x, int):
+        return x
+    assert isinstance(x, torch.SymInt)
+    return x.node.shape_env.size_hint(x.node.expr, allow_none=allow_none)
+
+
 # Wrapper on lru_cache that reports statistics at process end
 def lru_cache(
     maxsize: Optional[int],