Discrete Diffusion in Large Language Models: How Continuous-Time Markov Chains, Absorbing States, and Score Entropy Challenge Autoregressive Generation
The dominance of autoregressive architectures in large language models rests on a fundamental mathematical formulation: the chain rule of probability. By factoring the joint distribution of a sequence into a product of conditional probabilities, $p(x) = \prod_{i=1}^N p(x_i \mid x_{<i})$, autoregressive models reduce text generation to sequential next-token prediction. While this left-to-right causal factorization has scaled effectively across compute regimes, it imposes rigid operational constr
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