Building upon large language models (LLMs), recent large multimodal models (LMMs) unify cross-model understanding and generation into a single framework. However, LMMs still struggle to achieve accurate vision-language alignment, prone to generating text responses contradicting the visual input or failing to follow the text-to-image prompts. Current solutions require external supervision (e.g., human feedback or reward models) and only address unidirectional tasks-either understanding or generation. In this work, based on the observation that understanding and generation are naturally inverse dual tasks, we propose \textbf{SUDER} (\textbf{S}elf-improving \textbf{U}nified LMMs with \textbf{D}ual s\textbf{E}lf-\textbf{R}ewards), a framework reinforcing the understanding and generation capabilities of LMMs with a self-supervised dual reward mechanism. SUDER leverages the inherent duality between understanding and generation tasks to provide self-supervised optimization signals for each other. Specifically, we sample multiple outputs for a given input in one task domain, then reverse the input-output pairs to compute the dual likelihood within the model as self-rewards for optimization. Extensive experimental results on visual understanding and generation benchmarks demonstrate that our method can effectively enhance the performance of the model without any external supervision, especially achieving remarkable improvements in text-to-image tasks.