diff --git a/.pre-commit-config.yaml b/.pre-commit-config.yaml
index c19d6015..25726931 100644
--- a/.pre-commit-config.yaml
+++ b/.pre-commit-config.yaml
@@ -2,11 +2,11 @@ repos:
   - repo: https://github.com/astral-sh/ruff-pre-commit
     rev: v0.6.4
     hooks:
+      - id: ruff-format # formatter
+        types_or: [python, pyi, jupyter, toml]
       - id: ruff # linter
         types_or: [python, pyi, jupyter, toml]
         args: [--fix]
-      - id: ruff-format # formatter
-        types_or: [python, pyi, jupyter, toml]
   - repo: https://github.com/RobertCraigie/pyright-python
     rev: v1.1.379
     hooks:
diff --git a/equinox/_jit.py b/equinox/_jit.py
index c011b6a9..9be74b85 100644
--- a/equinox/_jit.py
+++ b/equinox/_jit.py
@@ -1,3 +1,4 @@
+import atexit
 import functools as ft
 import inspect
 import logging
@@ -7,8 +8,10 @@
 from typing_extensions import ParamSpec
 
 import jax
+import jax._src.dispatch
 import jax._src.traceback_util as traceback_util
 import jax.core
+import jax.numpy as jnp
 from jaxtyping import PyTree
 
 from ._compile_utils import (
@@ -50,7 +53,8 @@ def fun_wrapped(dynamic_donate, dynamic_nodonate, static):
         assert dummy_arg is None
         out = fun(*args, **kwargs)
         dynamic_out, static_out = partition(out, is_array)
-        return dynamic_out, Static(static_out)
+        marker = jnp.array(0)
+        return marker, dynamic_out, Static(static_out)
 
     fun_name, fun_qualname = fun_names
     fun_wrapped.__name__ = fun_name
@@ -99,7 +103,7 @@ def _preprocess(info, args, kwargs, return_static: bool = False):
 
 
 def _postprocess(out):
-    dynamic_out, static_out = out
+    _, dynamic_out, static_out = out
     return combine(dynamic_out, static_out.value)
 
 
@@ -112,6 +116,22 @@ class XlaRuntimeError(Exception):
         pass
 
 
+try:
+    wait_for_tokens = jax._src.dispatch.wait_for_tokens
+except AttributeError:
+    pass  # forward compatibility
+else:
+    # Fix for https://github.com/patrick-kidger/diffrax/issues/506
+    def wait_for_tokens2():
+        try:
+            wait_for_tokens()
+        except XlaRuntimeError:
+            pass
+
+    atexit.unregister(wait_for_tokens)
+    atexit.register(wait_for_tokens2)
+
+
 # This is the class we use to raise runtime errors from `eqx.error_if`.
 class EquinoxRuntimeError(RuntimeError):
     pass
@@ -178,7 +198,8 @@ def __wrapped__(self):
     def _call(self, is_lower, args, kwargs):
         __tracebackhide__ = True
         # Used by our error messages when figuring out where to stop walking the stack.
-        if not currently_jitting():
+        jitting = currently_jitting()
+        if not jitting:
             __equinox_filter_jit__ = True  # noqa: F841
         info = (
             self._signature,
@@ -207,9 +228,15 @@ def _call(self, is_lower, args, kwargs):
                         warnings.filterwarnings(
                             "ignore", message="Some donated buffers were not usable*"
                         )
-                        out = self._cached(dynamic_donate, dynamic_nodonate, static)
+                        marker, _, _ = out = self._cached(
+                            dynamic_donate, dynamic_nodonate, static
+                        )
                 else:
-                    out = self._cached(dynamic_donate, dynamic_nodonate, static)
+                    marker, _, _ = out = self._cached(
+                        dynamic_donate, dynamic_nodonate, static
+                    )
+                if not jitting:
+                    marker.block_until_ready()
             except XlaRuntimeError as e:
                 # Catch Equinox's runtime errors, and re-raise them with actually useful
                 # information. (By default XlaRuntimeError produces a lot of terrifying