Abstract: We introduce LLaVA-MoD, a novel framework designed to enable the efficient training of small-scale Multimodal Language Models ($s$-MLLM) distilling knowledge from large-scale MLLM ($l$-MLLM). Our approach tackles two fundamental challenges in MLLM distillation. First, we optimize the network structure of $s$-MLLM by integrating a sparse Mixture of Experts (MoE) architecture into the language model, striking a balance between computational efficiency and model expressiveness. Second, we propose a progressive knowledge transfer strategy for comprehensive knowledge transfer. This strategy begins with mimic distillation, where we minimize the Kullback-Leibler (KL) divergence between output distributions to enable $s$-MLLM to emulate $s$-MLLM's understanding. Following this, we introduce preference distillation via Preference Optimization (PO), where the key lies in treating $l$-MLLM as the reference model. During this phase, the $s$-MLLM's ability to discriminate between superior and inferior examples is significantly enhanced beyond $l$-MLLM, leading to a better $s$-MLLM that surpasses $l$-MLLM, particularly in hallucination benchmarks.Extensive experiments demonstrate that LLaVA-MoD surpasses existing works across various benchmarks while maintaining a minimal activated parameters and low computational costs. Remarkably, LLaVA-MoD-2B surpasses Qwen-VL-Chat-7B with an average gain of 8.8\%, using merely $0.3\%$ of the training data and 23\% trainable parameters. The results underscore LLaVA-MoD's ability to effectively distill comprehensive knowledge from its teacher model, paving the way for developing efficient MLLMs.