Forward-Learned Discrete Diffusion: Learning how to noise to denoise faster

Discrete diffusion models are a powerful class of generative models that demonstrate strong performance across many domains. However, for efficiency, discrete diffusion typically parameterizes the generative (reverse) process with factorized distributions, which makes it difficult for the model to learn a target process in a small number of steps and necessitates a long, computationally expensive sampling procedure. To reduce the gap between the target and model distributions and enable few-step generation, we introduce a learnable noising (forward) process for discrete diffusion. Instead of fixing a Markovian forward chain, we adopt a non-Markovian formulation and introduce learnable marginal and posterior distributions. This allows the generative process to remain factorized while matching the target defined by the noising process. We train all parameters end-to-end under the standard variational objective.