Birth, Death and Diff: Insertion-Based Sequence Generation with Corrections

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Insertion-based masked diffusion models enable flexible-length, parallel generation by interleaving mask insertion with token unmasking. However, because their generation decisions are irreversible, aggressive parallel decoding can introduce errors that subsequent steps cannot correct, necessitating conservative decoding with more forward passes (NFEs). Moreover, they exhibit higher entropy than standard MDMs because they marginalize over multiple alignments during training and therefore require even more conservative decoding in the absence of a correction mechanism. To address this limitation, we introduce $δ$MDM, which makes intermediate generations revisable by equipping an insertion-based model with substitution and deletion operations. During training, we expose the model to errors caused by aggressive unmasking and insertion, teaching it to correct its own mistakes. At inference time, we interleave insertion and unmasking with correction steps that can revise previously unmasked tokens and remove unnecessary masks. This mechanism makes aggressive decoding practical, improving both generation speed and quality. $δ$MDM Pareto-dominates FlexMDM, a vanilla insertion-based MDM, on the speed--quality trade-off. On high-diversity unconditional text generation on OpenWebText, it halves the generative perplexity relative to FlexMDM at the highest inference budget. It also achieves lower generative perplexity at all inference budgets compared to MDM trained from scratch with variable-length padded sequences. On low-diversity conditional text generation on TinyGSM, it matches FlexMDM accuracy with half as many NFEs.