diff --git a/outlines/processors/base_logits_processor.py b/outlines/processors/base_logits_processor.py
index feedf5253..9a52abecd 100644
--- a/outlines/processors/base_logits_processor.py
+++ b/outlines/processors/base_logits_processor.py
@@ -75,10 +75,10 @@ def __call__(
 
         # Guarantee passed as 2D Tensors, then covert back to original (1D or 2D) shape
         if len(torch_logits.shape) == 2:
-            processed_logits = self.process_logits(input_ids.tolist(), torch_logits)
+            processed_logits = self.process_logits(input_ids, torch_logits)
         elif len(torch_logits.shape) == 1:
             processed_logits = self.process_logits(
-                [input_ids.tolist()], torch_logits.unsqueeze(0)
+                input_ids.unsqueeze(0), torch_logits.unsqueeze(0)
             ).squeeze(0)
 
         # return logits as passed array type
diff --git a/outlines/processors/structured.py b/outlines/processors/structured.py
index d9a912c89..e3b9e60d3 100644
--- a/outlines/processors/structured.py
+++ b/outlines/processors/structured.py
@@ -70,7 +70,7 @@ def __init__(self, tokenizer: "Tokenizer", guide: Guide):
         self._seq_start_idx = None
 
     def process_logits(
-        self, input_ids: List[List[int]], logits: torch.Tensor
+        self, input_ids: torch.LongTensor, logits: torch.FloatTensor
     ) -> torch.Tensor:
         """Use the Guide to bias the logits before sampling the next token.
 
@@ -93,19 +93,32 @@ def process_logits(
 
         for seq_ids in input_ids:
             gen_ids = seq_ids[self._seq_start_idx :]
-            curr_state_key = hash(tuple(gen_ids))
+            curr_state_key = hash(tuple(gen_ids.tolist()))
 
             if curr_state_key not in self._guide_states:
-                prev_state = self._guide_states[hash(tuple(gen_ids[:-1]))]
-                curr_state = self.guide.get_next_state(prev_state, gen_ids[-1])
+                prev_state = self._guide_states[hash(tuple(gen_ids[:-1].tolist()))]
+                curr_state = self.guide.get_next_state(prev_state, gen_ids[-1].item())
                 self._guide_states[curr_state_key] = curr_state
 
             sequence_states.append(self._guide_states[curr_state_key])
 
         mask = torch.ones_like(logits, dtype=torch.bool)
+
+        allowed_tokens_batch = []
+        batch_indices = []
         for i, guide_state in enumerate(sequence_states):
-            allowed_tokens = self.guide.get_next_instruction(guide_state).tokens
-            mask[i, allowed_tokens] = False
+            allowed_tokens = self.guide.get_next_instruction(guide_state).tokens.to(
+                mask.device, non_blocking=True
+            )
+            allowed_tokens_batch.append(allowed_tokens)
+            batch_indices.append(
+                torch.full_like(allowed_tokens, i)
+            )  # Store batch index for each allowed token
+
+        allowed_tokens_concat = torch.cat(allowed_tokens_batch)
+        batch_indices_concat = torch.cat(batch_indices)
+
+        mask[batch_indices_concat, allowed_tokens_concat] = False
         logits.masked_fill_(mask, float("-inf"))
 
         return logits
@@ -202,7 +215,7 @@ def __init__(self, cfg_str: str, tokenizer: "Tokenizer"):
         super().__init__(tokenizer=tokenizer, guide=cfg_guide)
 
     def process_logits(
-        self, input_ids: List[List[int]], logits: torch.Tensor
+        self, input_ids: torch.LongTensor, logits: torch.Tensor
     ) -> torch.Tensor:
         """Same behavior as GuideLogitsProcessor, but uses rejection sampling"""
         if self._seq_start_idx is None:
@@ -212,11 +225,11 @@ def process_logits(
 
         for seq_ids in input_ids:
             gen_ids = seq_ids[self._seq_start_idx :]
-            curr_state_key = hash(tuple(gen_ids))
+            curr_state_key = hash(tuple(gen_ids.tolist()))
 
             if curr_state_key not in self._guide_states:
-                prev_state = self._guide_states[hash(tuple(gen_ids[:-1]))]
-                curr_state = self.guide.get_next_state(prev_state, gen_ids[-1])
+                prev_state = self._guide_states[hash(tuple(gen_ids[:-1].tolist()))]
+                curr_state = self.guide.get_next_state(prev_state, gen_ids[-1].item())
                 self._guide_states[curr_state_key] = curr_state
 
             sequence_states.append(self._guide_states[curr_state_key])