5. Conclusion and thoughts
Our Adversarial Flow line of research explores ways to integrate adversarial modeling and flow modeling, two of the most influential paradigms in generative modeling. Adversarial Flow Models (AFMs) bring adversarial training to discrete-time flow modeling. Now, Continuous Adversarial Flow Models (CAFMs) further extend this idea to continuous time.
I think being able to do adversarial training in continuous time will unlock many more interesting explorations!
Our method is also different from guidance. Both CAFM and FM ensure convergence to the empirical distribution (i.e., the overfitted ground-truth distribution). They differ only in their finite-capacity generalization, while still remaining faithful to the original distribution. In contrast, guidance does not guarantee faithfulness to the original distribution. Guidance can lead to out-of-distribution (OOD) samples, canonical samples, and other distortions. Accurately and faithfully generating the original data distribution remains an important area of research.
We do not claim that CAFMs can always generate high-quality samples without guidance. When training samples are sparse or contain outliers, the manifold learned by the discriminator is not guaranteed to be correct. Guidance can still be applied orthogonally to achieve low-temperature sampling.
Recently, representational latent spaces (RAE) have become a popular research direction. These methods change the data space in which flow matching operates and therefore implicitly affect the model’s generalization. However, they do not directly address the problem of MSE and require operating in latent space. CAFMs directly modify the loss objective to induce different generalization and work effectively even in pixel space. Other representation-alignment approaches (REPA), may also have implicit connections to our work. We hope our work inspires further insights in the research community.