Generative Models Can Now Be Trained End-to-End? The Key Is a For Loop

Generative models struggle with end-to-end training because reconstruction loss averages over multiple valid targets, leading to 'mode blurring'—the optimal solution is precisely the least realistic answer. The paper points out that direct end-to-end regression predicts a single point in the middle of three clusters, blurs dog photos into a mess, and degenerates a sentence into repeated 'the'.

Existing models avoid mode blurring by decomposing the generation process (autoregressive predicts one element at a time, diffusion denoises a bit at a time), but this also makes training and inference sampling inconsistent, leading to exposure bias: each step's error feeds into the next, and inputs drift from the training distribution.

XM's core is to decompose the training loop: each training step generates K candidates, trains only the one closest to real data, and backpropagates, implemented as a 3-5 line for loop. The authors use a dart metaphor: when allowed to guess K times and only the closest counts, the optimal strategy is to cover different landing spots, capturing multiple modes.

The paper proposes two exploration directions: Forward fixes the real target and searches for the closest in generation, favoring recall; Reverse fixes generation and searches for the closest in real data, favoring precision with almost no extra compute, but may collapse. They can be combined.

The authors add exploration to diffusion/flow models, Jumpy models, and masked diffusion language models, consistently seeing monotonic performance improvements across image, video, and language modalities. Key numbers: gains rise from 7% to 36% as data grows, from 13% to 23% as model grows, and efficiency gain more than doubles when compute triples.

In efficiency, exploration improves FLOP efficiency by 4.1x, sample efficiency by 6.2x, and parameter efficiency by 47%. In image generation, it pushes RAE recipe to ImageNet unguided FID 1.43. A Large model exploring 5 modes outperforms an XLarge model with 47% more parameters but no exploration.

The authors explain that at small scale, parameters and data are bottlenecks; as scale increases, generative expressiveness becomes the bottleneck, and exploration directly amplifies it. Given that real foundation model training compute is about four orders of magnitude higher than the paper's largest experiments, these numbers may be a lower bound on gains at larger scales.

Applying XM as a standalone end-to-end model for robot control: in behavior cloning, Explorative Policy matches or exceeds Diffusion Policy with 100 forward passes in a single forward pass; in goal-oriented world modeling, Explorative World Model achieves better average performance with 16 to 256 times less inference compute than Diffuser.

The gap stems from diffusion models using hundreds of steps at inference for expressiveness, while XM shifts the cost to training-time exploration, requiring only one forward pass at inference. The authors choose to explore once during training rather than slowly decompose at inference.

First author Alexi Gladstone previously led Energy-Based Transformers (EBT), which claimed to beat standard feedforward Transformer scaling curves on multiple dimensions for the first time. XM builds on the Mode Forcing theory by the authors and collaborators (Yilun Du and Heng Ji), and the paper admits that most results were predicted by theory before being verified by experiments.

The authors acknowledge that best-of-K is not new; it has been done before. The real contribution is clarifying that this simple loop directly amplifies generative expressiveness without decomposing the generation process. Limitations include: autoregressive language models remain the hardest, and pure end-to-end Forward XM is too expensive on extremely multi-modal distributions (like image generation).