[Bugfix][Multi Modal] Fix incorrect Molmo token processing (#26873)

Signed-off-by: sanghol <sanghol@allenai.org>

vllm/model_executor/models/molmo.py

@@ -1264,13 +1264,16 @@ class MolmoMultiModalProcessor(BaseMultiModalProcessor[MolmoProcessingInfo]):
     ) -> list[int]:
         processor = self.info.get_hf_processor()
 
-        # Apply the chat template to the tokens
+        # The chat template is already applied to the prompt tokens
+        # Use message_format="none" to avoid applying it again
+        # Prepend an empty space if `always_start_with_space` is True
         tokens = processor.processor.get_tokens_input(  # type: ignore
             self.info.get_tokenizer().decode(prompt_tokens),
-            message_format=processor.message_format,
+            message_format="none",
             always_start_with_space=processor.always_start_with_space,
         )
 
+        # Prepend a BOS token id to the tokens
         processed_data = self.info.ctx.call_hf_processor(
             processor,  # type: ignore
             dict(tokens=tokens),