  This tutorial provides a comprehensive survey of methods for fine-tuning
diffusion models to optimize downstream reward functions. While diffusion
models are widely known to provide excellent generative modeling capability,
practical applications in domains such as biology require generating samples
that maximize some desired metric (e.g., translation efficiency in RNA, docking
score in molecules, stability in protein). In these cases, the diffusion model
can be optimized not only to generate realistic samples but also to explicitly
maximize the measure of interest. Such methods are based on concepts from
reinforcement learning (RL). We explain the application of various RL
algorithms, including PPO, differentiable optimization, reward-weighted MLE,
value-weighted sampling, and path consistency learning, tailored specifically
for fine-tuning diffusion models. We aim to explore fundamental aspects such as
the strengths and limitations of different RL-based fine-tuning algorithms
across various scenarios, the benefits of RL-based fine-tuning compared to
non-RL-based approaches, and the formal objectives of RL-based fine-tuning
(target distributions). Additionally, we aim to examine their connections with
related topics such as classifier guidance, Gflownets, flow-based diffusion
models, path integral control theory, and sampling from unnormalized
distributions such as MCMC. The code of this tutorial is available at
https://github.com/masa-ue/RLfinetuning_Diffusion_Bioseq
