Discrete diffusion models for categorical generation are defined by a corruption kernel, which determines the intermediate state space and the associated reverse prediction problem. We study uniform discrete diffusion and ask whether its training objective and reverse transitions can be enriched without changing the underlying categorical corruption process. We introduce Simplax, an exact Dirichlet--categorical augmentation that couples each corrupted categorical state with an auxiliary simplex-valued variable while preserving the original uniform diffusion process as its categorical marginal. This augmentation yields a tractable Rao--Blackwellized reverse-bridge objective and a corresponding stochastic reverse sampler, while retaining the corrupted categorical state as the denoiser input. Empirically, Simplax improves the generative perplexity--entropy tradeoff on unconditional OpenWebText generation. On Sudoku, a model trained exclusively on $30$-clue puzzles achieves the highest accuracy among the compared methods across all evaluated clue densities, including the minimum uniquely solvable $17$-clue regime, and also achieves the highest validity in unconditional generation.
Jinya Sakurai, Patrick Pynadath, Satoshi Hayakawa et al.· 1 citation
Ensuring safety and policy compliance in text-to-image diffusion models remains a critical challenge, as benign or adversarial prompts can often elicit prohibited content, e.g. nudity and protected intellectual property. While training-based unlearning methods are effective, they are computationally expensive and prone to catastrophic interference with general capabilities. Conversely, existing test-time defenses are primarily prompt-centric, relying on modifying textual descriptions only, and overlook the visual signals for detection. In this paper, we propose to leverage the intermediate clean image estimated during the generation process and employ a sparse margin objective to detect prohibited concepts. When a violation is detected, we immediately intervene by optimizing a structured low-rank residual in the text-conditioning space via truncated backpropagation. This design allows weight-preserving detection, keeps non-violating inference latency nearly unchanged as the maximum budget increases, and offers flexibility in safety performance via test-time scaling. Extensive experiments on Stable Diffusion v1.4 and v3.5 across nudity removal, IP protection, and style erasure demonstrate superior performance across suppression, fidelity and preservation compared to prior weight-preserving baselines, providing a scalable and flexible solution for safe generative deployment.
