Title: White Gaussian Noise Constraints for Reward-Guided Generation
Primary area: generative models
Keywords: Gaussianity, Generative Models, Guided Generation

Abstract: We propose a constrained optimization framework that preserves Gaussianity during latent optimization for reward-guided generation. At its core is a novel constraint formulation that allows efficient projection while tightly characterizing Gaussian properties. In deep generative models, supplying white Gaussian noise as input is essential for stable and realistic generation, but preserving its characteristics during optimization remains challenging. This challenge is amplified in reward-guided generation, where gradient-based updates can exploit the reward and produce unrealistic or low-quality outputs. Prior methods address this by introducing regularization terms that encourage certain Gaussian properties, particularly in the spectral domain. However, regularization offers only soft penalties and cannot guarantee that the latent vector retains its Gaussian properties throughout optimization. To overcome this, we propose a constrained optimization approach that directly projects the latent onto a feasible set. Our constraints, based on a novel observation that maps a Gaussian in the spatial domain to another Gaussian in a compact spectral domain, tightly characterize Gaussianity and allow a closed-form projection, enabling efficient updates through projected gradient ascent. In experiments on reward-guided text-to-image generation, our approach outperforms regularization-based baselines across four reward functions in terms of reward, sample quality, and maximization speed.

TL;DR: We propose a constrained optimization framework that preserves Gaussianity during latent optimization for reward-guided generation.