We consider the problem of extracting a reward function by comparing a decision-making diffusion model that models low-reward behavior and one that models high-reward behavior; a setting related to inverse reinforcement learning. We first define the notion of a relative reward function of two diffusion models and show conditions under which it exists and is unique.

We can expand the loss (4), i.e., Table 5 shows more results of our method with different configurations and hyperparameter settings.

Currently, there are two approaches to collapse prevention.

Geometric data and purpose-built generative models on them have become ubiquitous in high-impact deep learning application domains, ranging from protein backbone generation and computational chemistry to geospatial data. Current geometric generative models remain computationally expensive at inference -- requiring many steps of complex numerical simulation -- as they are derived from dynamical measure transport frameworks such as diffusion and flow-matching on Riemannian manifolds. In this paper, we propose Generalised Flow Maps (GFM), a new class of few-step generative models that generalises the Flow Map framework in Euclidean spaces to arbitrary Riemannian manifolds. We instantiate GFMs with three self-distillation-based training methods: Generalised Lagrangian Flow Maps, Generalised Eulerian Flow Maps, and Generalised Progressive Flow Maps. We theoretically show that GFMs, under specific design decisions, unify and elevate existing Euclidean few-step generative models, such as consistency models, shortcut models, and meanflows, to the Riemannian setting. We benchmark GFMs against other geometric generative models on a suite of geometric datasets, including geospatial data, RNA torsion angles, and hyperbolic manifolds, and achieve state-of-the-art sample quality for single- and few-step evaluations, and superior or competitive log-likelihoods using the implicit probability flow.

We can expand the loss (4), i.e., Table 5 shows more results of our method with different configurations and hyperparameter settings.

Currently, there are two approaches to collapse prevention.

Stochastic optimal control (SOC) aims to direct the behavior of noisy systems and has widespread applications in science, engineering, and artificial intelligence. In particular, reward fine-tuning of diffusion and flow matching models and sampling from unnormalized methods can be recast as SOC problems. A recent work has introduced Adjoint Matching (Domingo-Enrich et al., 2024), a loss function for SOC problems that vastly outperforms existing loss functions in the reward fine-tuning setup. The goal of this work is to clarify the connections between all the existing (and some new) SOC loss functions. Namely, we show that SOC loss functions can be grouped into classes that share the same gradient in expectation, which means that their optimization landscape is the same; they only differ in their gradient variance. We perform simple SOC experiments to understand the strengths and weaknesses of different loss functions.

Diffusion models have achieved remarkable results in image generation, and have similarly been used to learn high-performing policies in sequential decision-making tasks. Decision-making diffusion models can be trained on lower-quality data, and then be steered with a reward function to generate near-optimal trajectories. We consider the problem of extracting a reward function by comparing a decision-making diffusion model that models low-reward behavior and one that models high-reward behavior; a setting related to inverse reinforcement learning. We first define the notion of a relative reward function of two diffusion models and show conditions under which it exists and is unique. We then devise a practical learning algorithm for extracting it by aligning the gradients of a reward function -- parametrized by a neural network -- to the difference in outputs of both diffusion models. Our method finds correct reward functions in navigation environments, and we demonstrate that steering the base model with the learned reward functions results in significantly increased performance in standard locomotion benchmarks. Finally, we demonstrate that our approach generalizes beyond sequential decision-making by learning a reward-like function from two large-scale image generation diffusion models. The extracted reward function successfully assigns lower rewards to harmful images.