Diffusion and flow models achieve State-Of-The-Art (SOTA) generative performance, yet many practically important behaviors such as fine-grained prompt fidelity, compositional correctness, and text rendering are weakly specified by score or flow matching pretraining objectives. Reinforcement Learning (RL) fine-tuning with external, black-box rewards is a natural remedy, but diffusion RL is often brittle. Trajectory-based methods incur high memory cost and high-variance gradient estimates; forward-process approaches converge faster but can suffer from distribution drift, and hence reward hacking. In this work, we present \textbf{Centered Reward Distillation (CRD)}, a diffusion RL framework derived from KL-regularized reward maximization built on forward-process-based fine-tuning. The key insight is that the intractable normalizing constant cancels under \emph{within-prompt centering}, yielding a well-posed reward-matching objective. To enable reliable text-to-image fine-tuning, we introduce techniques that explicitly control distribution drift: (\textit{i}) decoupling the sampler from the moving reference to prevent ratio-signal collapse, (\textit{ii}) KL anchoring to a CFG-guided pretrained model to control long-run drift and align with the inference-time semantics of the pre-trained model, and (\textit{iii}) reward-adaptive KL strength to accelerate early learning under large KL regularization while reducing late-stage exploitation of reward-model loopholes. Experiments on text-to-image post-training with \texttt{GenEval} and \texttt{OCR} rewards show that CRD achieves competitive SOTA reward optimization results with fast convergence and reduced reward hacking, as validated on unseen preference metrics.