diff --git a/detectron2/modeling/postprocessing.py b/detectron2/modeling/postprocessing.py
index 84512606a4..910ce02072 100644
--- a/detectron2/modeling/postprocessing.py
+++ b/detectron2/modeling/postprocessing.py
@@ -2,6 +2,7 @@
 import torch
 from torch.nn import functional as F
 
+from detectron2.layers.wrappers import check_if_dynamo_compiling
 from detectron2.structures import Instances, ROIMasks
 
 
@@ -55,7 +56,9 @@ def detector_postprocess(
     output_boxes.scale(scale_x, scale_y)
     output_boxes.clip(results.image_size)
 
-    results = results[output_boxes.nonempty()]
+    if not check_if_dynamo_compiling():
+        # If we're tracing with Dynamo, we can't guard on a data-dependent condition
+        results = results[output_boxes.nonempty()]
 
     if results.has("pred_masks"):
         if isinstance(results.pred_masks, ROIMasks):
diff --git a/detectron2/structures/boxes.py b/detectron2/structures/boxes.py
index fd396f6864..eea80fcf8c 100644
--- a/detectron2/structures/boxes.py
+++ b/detectron2/structures/boxes.py
@@ -6,6 +6,8 @@
 import torch
 from torch import device
 
+from detectron2.layers.wrappers import check_if_dynamo_compiling
+
 _RawBoxType = Union[List[float], Tuple[float, ...], torch.Tensor, np.ndarray]
 
 
@@ -147,7 +149,13 @@ def __init__(self, tensor: torch.Tensor):
         if not isinstance(tensor, torch.Tensor):
             tensor = torch.as_tensor(tensor, dtype=torch.float32, device=torch.device("cpu"))
         else:
-            tensor = tensor.to(torch.float32)
+            if tensor.dtype != torch.float32:
+                # If we're tracing with Dynamo, this will prevent `tensor` to be mutated.
+                # This if-statement works at least for the case where needless recasting is done.
+                tensor = tensor.to(torch.float32)
+                # If some use case still fails with 'cannot mutate tensors with frozen storage'
+                # we can add `tensor = tensor.clone()` here.
+                # Reference: https://github.com/pytorch/pytorch/issues/127571
         if tensor.numel() == 0:
             # Use reshape, so we don't end up creating a new tensor that does not depend on
             # the inputs (and consequently confuses jit)
@@ -188,7 +196,9 @@ def clip(self, box_size: Tuple[int, int]) -> None:
         Args:
             box_size (height, width): The clipping box's size.
         """
-        assert torch.isfinite(self.tensor).all(), "Box tensor contains infinite or NaN!"
+        if not check_if_dynamo_compiling():
+            # If we're tracing with Dynamo we can't guard on a data-dependent expression
+            assert torch.isfinite(self.tensor).all(), "Box tensor contains infinite or NaN!"
         h, w = box_size
         x1 = self.tensor[:, 0].clamp(min=0, max=w)
         y1 = self.tensor[:, 1].clamp(min=0, max=h)