Projected Gradient Ascent for Efficient Reward-Guided Updates with One-Step Generative Models

We propose a constrained latent optimization method for reward-guided generation that preserves white Gaussian noise characteristics with negligible overhead. Test-time latent optimization can unlock substantially better reward-guided generations from pretrained generative models, but it is prone to reward hacking that degrades quality and also too slow for practical use. In this work, we make test-time optimization both efficient and reliable by replacing soft regularization with hard white Gaussian noise constraints enforced via projected gradient ascent. Our method applies a closed-form projection after each update to keep the latent vector explicitly noise-like throughout optimization, preventing the drift that leads to unrealistic artifacts. This enforcement adds minimal cost: the projection matches the $O(N \log N)$ complexity of standard algorithms such as sorting or FFT and does not practically increase wall-clock time. In experiments, our approach reaches a comparable Aesthetic Score using only 30% of the wall-clock time required by the SOTA regularization-based method, while preventing reward hacking.

PairFlow: Closed-Form Source-Target Coupling for Few-Step Generation in Discrete Flow Models

We introduce $\texttt{PairFlow}$, a lightweight preprocessing step for training Discrete Flow Models (DFMs) to achieve few-step sampling without requiring a pretrained teacher. DFMs have recently emerged as a new class of generative models for discrete data, offering strong performance. However, they suffer from slow sampling due to their iterative nature. Existing acceleration methods largely depend on finetuning, which introduces substantial additional training overhead. $\texttt{PairFlow}$ addresses this issue with a lightweight preprocessing step. Inspired by ReFlow and its extension to DFMs, we train DFMs from coupled samples of source and target distributions, without requiring any pretrained teacher. At the core of our approach is a closed-form inversion for DFMs, which allows efficient construction of paired source-target samples. Despite its extremely low cost, taking only up to 1.7% of the compute needed for full model training, $\texttt{PairFlow}$ matches or even surpasses the performance of two-stage training involving finetuning. Furthermore, models trained with our framework provide stronger base models for subsequent distillation, yielding further acceleration after finetuning. Experiments on molecular data as well as binary and RGB images demonstrate the broad applicability and effectiveness of our approach.

Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing

We propose an inference-time scaling approach for pretrained flow models. Recently, inference-time scaling has gained significant attention in LLMs and diffusion models, improving sample quality or better aligning outputs with user preferences by leveraging additional computation. For diffusion models, particle sampling has allowed more efficient scaling due to the stochasticity at intermediate denoising steps. On the contrary, while flow models have gained popularity as an alternative to diffusion models--offering faster generation and high-quality outputs in state-of-the-art image and video generative models--efficient inference-time scaling methods used for diffusion models cannot be directly applied due to their deterministic generative process. To enable efficient inference-time scaling for flow models, we propose three key ideas: 1) SDE-based generation, enabling particle sampling in flow models, 2) Interpolant conversion, broadening the search space and enhancing sample diversity, and 3) Rollover Budget Forcing (RBF), an adaptive allocation of computational resources across timesteps to maximize budget utilization. Our experiments show that SDE-based generation, particularly variance-preserving (VP) interpolant-based generation, improves the performance of particle sampling methods for inference-time scaling in flow models. Additionally, we demonstrate that RBF with VP-SDE achieves the best performance, outperforming all previous inference-time scaling approaches.