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This decoupling leaves the tokenizer unaware of the model that will later generate its tokens. As a result, the learned tokens may preserve image information well but still be difficult for an autoregressive (AR) prior to predict from left to right. We analyze this mismatch using Tripartite Variational Consistency (TVC), which decomposes latent-variable learning into three consistency conditions: conditional-likelihood consistency, prior consistency, and posterior consistency. TVC shows that two-stage training preserves the reconstruction side but leaves prior consistency outside the tokenizer objective: the overall token distribution is fixed before the AR prior participates in training. Motivated by this view, we add a distribution-level prior-matching signal during tokenizer traini","title":"Learning Discrete Autoregressive Priors with Wasserstein Gradient Flow","url":"https://arxiv.org/abs/2605.06148","vendor":"arxiv_cs_ai"},"summary":"arXiv:2605.06148v1 Announce Type: cross \nAbstract: Discrete image tokenizers are commonly trained in two stages: first for reconstruction, and then with a prior model fitted to the frozen token sequences. This decoupling leaves the tokenizer unaware of the model that will later generate its tokens. As a result, the learned tokens may preserve image information well but still be difficult for an autoregressive (AR) prior to predict from left to right. We analyze this mismatch using Tripartite Variational Consistency (TVC), which decomposes latent-variable learning into three consistency conditions: conditional-likelihood consistency, prior consistency, and posterior consistency. TVC shows that two-stage training preserves the reconstruction side but leaves prior consistency outside the tokenizer objective: the overall token distribution is fixed before the AR prior participates in training. 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