Lan Feng, Wuyang Li, Eloi Zablocki, Matthieu Cord, Alexandre Alahi
5 min
Abstract
We elucidate the design space of Representation Distribution Matching (RDM), our name for the paradigm that trains a one-step image generator by matching generated and reference feature distributions under frozen pretrained encoders. We identify two design axes, how the distributions are compared and the representations they are compared in, and controlled studies along them yield three findings. First, the classical MMD, which could not train convincing generators a decade ago, becomes a strong and scalable objective once estimated right. Second, the generated batch is then the operative variable, with an optimum above 2048, far beyond customary batch sizes. Third, any single representation can be gamed, driven below the real score while images stay visibly fake, so we match against a balanced battery of encoders and evaluate with SW_r14, a Sliced-Wasserstein distance over 14 encoders that is independent of the training loss and resists gaming. Combining the preferred choices yields improved RDM (iRDM): it sets the one-step state of the art on ImageNet at SW_r14 1.30, corroborated by PickScore, a human-preference proxy our objective never optimizes, which prefers it over the prior best one-step generator on 71.2% of matched samples. The same recipe post-trains the four-step FLUX.2 [klein] into a one-step generator, surpassing the four-step version on GenEval, 0.826 to 0.794, and on PickScore, 22.76 to 22.58, in 90 H200 GPU-hours. Project page: https://alan-lanfeng.github.io/rdm/.
Alex: Right. So what's their fix?
Sam: They use a technique called Nyström approximation. Instead of a tiny, random sample every time, they pre-calculate a set of "landmarks" that represent the entire dataset. These landmarks act like a fixed, reliable anchor. The generated images are constantly pulled toward this anchor, while a second force—repulsion—pushes the generated images away from each other. Without that repulsion, the model would collapse and produce the same identical, boring output every single time.
Alex: So it's a constant push and pull. Attraction toward the real data, repulsion to keep variety high.
Sam: Exactly. And to verify this actually works, the authors ran a controlled experiment using a simple spiral shape hidden in a complex, high-dimensional space. While other distance-measuring methods struggled when the batch size changed, the Nyström approach stayed accurate across every test.
Alex: That raises a question, though. If you use this panel of judges to train the model, how do you know the evaluation itself isn't being gamed?
Sam: That's a critical point. The authors address it by using a completely separate metric for the final score—one called Sliced-Wasserstein distance. Think of it as a separate exam board that uses entirely different rules than the study guide. Because this metric shares no machinery with the training process, the model has no way to cheat by optimizing for it. It gives an honest picture of how well the generator captures the full variety of real-world images.
Alex: So it's an independent check. Putting all of this together—the panel of judges, the stable anchor, the repulsion force—what does the final system actually look like?
Sam: The authors call it iRDM. By combining a stable, Nyström-based measurement with a diverse, dynamically balanced panel of encoders, they've created a one-step generator that sets a meaningful new standard for image quality—without needing the complex, multi-step processes that other models rely on. That said, the authors are careful to note that iRDM hasn't perfectly captured the full complexity of real-world data distributions yet. It's a significant step forward, but not the final word.
Alex: So the honest answer is: it's a clear improvement, but there's still work to do.
Sam: That's a fair summary. The contribution is in identifying two specific, fixable problems—how you measure the gap, and how many judges you use—and showing that fixing both together produces noticeably better results. That's a meaningful advance, even if the broader challenge of one-step generation remains open.
Alex: Thanks for walking us through that, Sam. And thanks to everyone listening to ResearchPod.