DDNO: Discrete Diffusion Noise Optimization

Test-time reward alignment of discrete diffusion models currently relies on either step-wise guidance, which uses myopic approximations that can distort the generative process, or on search with stochastic generation. We introduce Discrete Diffusion Noise Optimization (DDNO), a training-free method for uniform discrete diffusion models that enables gradient-based reward optimization at test-time despite the non-differentiable categorical sampling that blocks gradient flow through the reverse process. DDNO relaxes the discrete initial noise to continuous logits and propagates terminal reward gradients end-to-end through straight-through estimation and soft mixing. By fixing all intermediate randomness, generation becomes controllable through variation of the initial noise. On text-to-image generation and steering text generation, DDNO outperforms existing test-time methods, achieving 0.94 GenEval overall accuracy, with gains measured under held-out evaluators distinct from the optimization reward. Under matched compute, search-based methods are preferable at smaller budgets but plateau, while DDNO scales consistently with optimization budget across both modalities, establishing gradient-based noise optimization as a new axis for test-time scaling in discrete generative models.