diff --git a/jax/_src/lax/control_flow/loops.py b/jax/_src/lax/control_flow/loops.py
index 4991aea909f1..cde578a5849d 100644
--- a/jax/_src/lax/control_flow/loops.py
+++ b/jax/_src/lax/control_flow/loops.py
@@ -1855,18 +1855,26 @@ def _while_typecheck(_, *in_atoms, cond_jaxpr, body_jaxpr, cond_nconsts,
         f'Effects not supported in `while`: {disallowed_effects}')
   return body_jaxpr.out_avals, joined_effects
 
-def _while_discharge_rule(in_avals, out_avals, *args, cond_jaxpr, body_jaxpr,
+def _while_partial_discharge_rule(should_discharge, in_avals, out_avals, *args, cond_jaxpr, body_jaxpr,
                           cond_nconsts, body_nconsts):
   # TODO(sharadmv): enable supporting state effects in the cond
   if any(isinstance(eff, state.RefEffect) for eff in cond_jaxpr.effects):
     raise NotImplementedError
+  cond_consts_discharge, body_consts_discharge, carry_discharge = split_list(
+      should_discharge, [cond_nconsts, body_nconsts])
+
+  if any(cond_consts_discharge):
+    raise NotImplementedError
   cond_consts, body_consts, carry = split_list(args, [cond_nconsts, body_nconsts])
   cond_consts_avals, body_consts_avals, carry_avals = split_list(in_avals,
                                                                  [cond_nconsts,
                                                                   body_nconsts])
   # There shouldn't be any `Ref`s in the `cond` (because of our check above).
   assert not any(isinstance(aval, state.AbstractRef) for aval in cond_consts_avals)
-  is_ref = [isinstance(aval, state.AbstractRef) for aval in body_consts_avals]
+  is_ref = [
+      isinstance(aval, state.AbstractRef) and should
+      for aval, should in zip(body_consts_avals, body_consts_discharge)
+  ]
   remaining_body_consts, refs = partition_list(is_ref, body_consts)
   remaining_body_const_avals, ref_avals = partition_list(is_ref,
                                                          body_consts_avals)
@@ -1886,7 +1894,7 @@ def _while_discharge_rule(in_avals, out_avals, *args, cond_jaxpr, body_jaxpr,
   # Therefore we need to rewrite the jaxpr to shuffle around the `Ref`s so that
   # they are part of the carry.
   discharged_body_jaxpr, discharged_consts = state_discharge.discharge_state(
-      body_jaxpr, ())
+      body_jaxpr, (), should_discharge=[*body_consts_discharge, *carry_discharge])
   if discharged_consts: raise NotImplementedError
 
   def new_body(*consts_refs_carry):
@@ -1943,7 +1951,7 @@ def new_cond(*consts_refs_carry):
 pe.partial_eval_jaxpr_custom_rules[while_p] = _while_partial_eval_custom
 mlir.register_lowering(while_p, _while_lowering)
 core.custom_typechecks[while_p] = _while_typecheck
-state_discharge.register_discharge_rule(while_p)(_while_discharge_rule)
+state_discharge.register_partial_discharge_rule(while_p)(_while_partial_discharge_rule)
 
 
 def _pred_bcast_select_hlo(ctx,
diff --git a/jax/_src/pallas/mosaic_gpu/lowering.py b/jax/_src/pallas/mosaic_gpu/lowering.py
index 037d104eea76..3a22086ad1ae 100644
--- a/jax/_src/pallas/mosaic_gpu/lowering.py
+++ b/jax/_src/pallas/mosaic_gpu/lowering.py
@@ -1430,15 +1430,6 @@ def _run_scoped_lowering_rule(
         ctx.module_ctx, ctx.launch_ctx, jaxpr, input_refs, consts
     )
 
-  for o in outs:
-    # This is definitely one of the accumulators we produced. Each
-    # run_scoped call is responsible for dereferencing its own
-    # accumulators.
-    if isinstance(o, mgpu.WGMMAAccumulator) or (
-        isinstance(o, ir.Value) and ir.MemRefType.isinstance(o.type)
-    ):
-      raise ValueError(f"No references are allowed to escape a scope. (got {o})")
-
   assert len(outs) == len(jaxpr.outvars), (jaxpr, outs)
   return outs
 
diff --git a/jax/_src/pallas/primitives.py b/jax/_src/pallas/primitives.py
index 9c07bcb49b65..ed22fdebe8fd 100644
--- a/jax/_src/pallas/primitives.py
+++ b/jax/_src/pallas/primitives.py
@@ -896,22 +896,25 @@ def _run_scoped_discharge_rule(
     **_):
   del out_avals
   num_consts = len(args_flat)
+  # discharge_state only discharges invars, not consts, so in order to
+  # discharge the requested refs we need to move them to the invar set.
   jaxpr_noconst = pe.convert_constvars_jaxpr(jaxpr)
   num_return_values = len(jaxpr_noconst.outvars)
-  should_discharge = should_discharge + [
-      isinstance(var.aval, state.AbstractRef) for var in jaxpr.invars
-  ]
   discharged_body, new_consts = state_discharge.discharge_state(
-      jaxpr_noconst, [], should_discharge=should_discharge)
+      jaxpr_noconst,
+      [],
+      should_discharge=should_discharge + [False] * len(jaxpr.invars),
+  )
   if new_consts:
     raise NotImplementedError(
         "Cannot handle new consts created by state discharge.")
-  # Create inputs filled with uninitialized values to the body.
-  body_avals = [v.aval for v in discharged_body.invars[num_consts:]]
-  init_vals = [uninitialized_value(
-      aval.shape, aval.dtype) for aval in body_avals]
-  init_vals_with_consts = args_flat + tuple(init_vals)
-  out = jax_core.eval_jaxpr(discharged_body, [], *init_vals_with_consts)
+
+  # Lowering expects that the jaxpr.consts to be the eqn.invals.
+  discharged_body = pe.convert_invars_to_constvars(discharged_body, num_consts)
+
+  # Run_scoped discharged the external variables but the scoped ones
+  # are not discharged.
+  out = run_scoped_p.bind(*args_flat, jaxpr=discharged_body)
   # Order of outputs:
   # (1) return values, (2) closed refs, (3) scoped refs.
   return_values = out[:num_return_values]
@@ -919,8 +922,8 @@ def _run_scoped_discharge_rule(
   # We update all ref values with their updated values from the discharged
   # body. For other values we leave them in place.
   updates = [
-      ref_outputs.pop(0) if isinstance(aval, pallas_core.AbstractMemoryRef)
-      else None for aval in in_avals]
+      ref_outputs.pop(0) if should and isinstance(aval, pallas_core.AbstractMemoryRef)
+      else None for should, aval in zip(should_discharge, in_avals)]
   assert len(updates) == len(in_avals), f'{len(updates)} != {len(in_avals)}'
   return updates, return_values