Diffusion Controller: Framework, Algorithms and Parameterization

Controllable generation with diffusion models is often treated as a collection of heuristics rather than a unified optimization problem. We propose a principled control formulation by viewing the diffusion reverse process as an instance of a (generalized) linearly-solvable Markov decision process (LS-MDP). This perspective turns controllable generation into regularized optimal control around a pretrained diffusion policy, yielding tractable objectives and algorithmic updates.
Under this framework, we study two practical finetuning regimes. When paired target data are available, we obtain a supervised finetuning (SFT) objective. When only a terminal reward model is available, we derive reinforcement-learning finetuning (RLFT) methods from the LS-MDP solution structure, including (i) a reward-weighted regression loss and (ii) a policy-gradient approach (with standard extensions such as PPO).
Crucially, the LS-MDP optimality conditions imply an explicit relationship between the optimal and pretrained score functions. We leverage this to derive a new score-function parameterization that isolates the control signal and enables “gray-box” finetuning with substantially fewer trainable parameters. Experiments across SFT and RLFT show this parameterization improves over existing finetuning baselines while achieving stronger sample/parameter efficiency.