Transformer-based In-Context Score Operator Learning for Diffusion Models

Wuzhe Xu, Zhaiming Shen, Yulong Lu, Wenjing Liao, Rongjie Lai

Diffusion models typically learn the generative dynamics of a single target distribution or a family of distributions indexed by conditioning variables fixed during training. This limits their ability to adapt to a previously unseen distribution from only a small set of examples. We introduce an in-context solution operator learning framework for diffusion models, in which each target distribution is treated as a task drawn from a meta-distribution and is specified at inference time by an empirical context set. Our method learns an in-context score operator that maps the context samples, a noisy query point, and the diffusion time to the task-dependent score, enabling reverse-diffusion sampling on unseen tasks without retraining or parameter updates. A key observation is that the task-dependent score admits a Gaussian-kernel conditional-mean representation. Its empirical Nadaraya--Watson approximation can be represented exactly by a model in our constructed transformer class, providing a principled foundation for the proposed query-dependent attention architecture. The operator is trained through amortized denoising score matching across task distributions. We establish…