We introduce “Generative Fusion Decoding” (GFD), a novel shallow fusion framework, utilized to integrate large language models(LLMs) into cross-modal text recognition systems inlculding automatic speech recognition (ASR) and optical character recognition (OCR). We derive the formulas necessary to enable GFD to operate across mismatched token spaces of different models by calculating likelihood at the byte level, thereby enabling seamless fusion and synchronous progression during the decoding process. GFD is plug-and-play bydesign, making it readily compatible with various auto-regressive models without the need for any re-training. GFD proves effective for general ASR and OCR tasks through intermediate and frequent interactions with LLMs, surpassing cascaded methods in English and Mandarin benchmarks. In addition, GFD transfers in-context learning abilities of LLMs and allows for adaptive ASR in instruction-aware andlong-context settings, yielding significant WER reductions of up to 17.7%.