Reward-guided image editing at test time seeks to improve a specified reward while preserving source content and visual plausibility. Many existing approaches optimize candidates through pretrained generation processes, making repeated adjustment depend on costly large-model execution and, in some cases, backbone backpropagation. We develop a theoretical framework that jointly accounts for reward, source preservation, and pretrained-prior preferences, allowing the desired output distribution to be specified separately from the dynamics used to realize it. Based on this framework, we introduce FASTER, which trains a small network for each source and objective to perform inexpensive editing, while pretrained and reward models provide feedback on candidate outputs. By reusing each candidate and its feedback across multiple small-network updates, FASTER reduces repeated sampling and supervision queries without placing the pretrained generative backbone inside the inner optimization loop. On SD3, FASTER leads all four target metrics and several validation metrics among the evaluated methods. Compared with the evaluated baseline that optimizes controls along pretrained generation trajectories, FASTER achieves editing-time speedups of up to \({6.91\times}\) on Stable Diffusion 3 and \({24.14\times}\) on Stable Diffusion 1.5.

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