This paper addresses the challenge of posterior inference in diffusion models, which are widely used in vision, language, and reinforcement learning. The authors propose a novel training objective called *relative trajectory balance (RTB)* to sample from the posterior distribution given a diffusion prior and an arbitrary constraint function. RTB is derived from the perspective of diffusion models as continuous generative flow networks, allowing for the use of deep reinforcement learning techniques to improve mode coverage. The method is shown to be effective in various experiments, including classifier-guided image generation, text-to-image generation, and continuous control tasks. The paper also discusses the theoretical foundations of RTB and its generalization to other hierarchical generative processes. Overall, RTB provides a flexible and efficient approach to posterior inference in diffusion models, achieving state-of-the-art results in multiple domains.This paper addresses the challenge of posterior inference in diffusion models, which are widely used in vision, language, and reinforcement learning. The authors propose a novel training objective called *relative trajectory balance (RTB)* to sample from the posterior distribution given a diffusion prior and an arbitrary constraint function. RTB is derived from the perspective of diffusion models as continuous generative flow networks, allowing for the use of deep reinforcement learning techniques to improve mode coverage. The method is shown to be effective in various experiments, including classifier-guided image generation, text-to-image generation, and continuous control tasks. The paper also discusses the theoretical foundations of RTB and its generalization to other hierarchical generative processes. Overall, RTB provides a flexible and efficient approach to posterior inference in diffusion models, achieving state-of-the-art results in multiple domains.