Multi-task Neural Diffusion Processes

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 generalization-error bounds that quantify the effects of the context size, the numbers of training tasks and within-task samples, model complexity, and intrinsic and ambient dimensions. Numerically, we evaluate the method on a range of scientific and visual datasets, including Navier-Stokes, ERA5 climate data, QuickDraw sketches, and Food-101. The results show that the proposed method performs well on relatively simple task families, while its performance degrades as task complexity increases, thereby illustrating both the promise and the limitations of in-context learning for diffusion models.

Reinforcement learning has emerged as a powerful tool for improving diffusion-based text-to-image models, but existing methods are largely limited to single-task optimization. Extending RL to multiple tasks is challenging: joint optimization suffers from cross-task interference and imbalance, while cascade RL is cumbersome and prone to catastrophic forgetting. We propose DiffusionOPD, a new multi-task training paradigm for diffusion models based on Online Policy Distillation (OPD). DiffusionOPD first trains task-specific teachers independently, then distills their capabilities into a unified student along the student own rollout trajectories. This decouples single-task exploration from multi-task integration and avoids the optimization burden of solving all tasks jointly from scratch. Theoretically, we lift the OPD framework from discrete tokens to continuous-state Markov processes, deriving a closed-form per-step KL objective that unifies both stochastic SDE and deterministic ODE refinement via mean-matching. We formally and empirically demonstrate that this analytic gradient provides lower variance and better generality compared to conventional PPO-style policy gradients. Extensive experiments show that DiffusionOPD consistently surpasses both multi-reward RL and cascade RL baselines in training efficiency and final performance, while achieving state-of-the-art results on all evaluated benchmarks.

Generative foundation models are attracting interest for their ability to produce desired outputs from demonstrations given at inference time, without updating parameters. However, since a few demonstrations cannot uniquely identify the intended task, the challenge is how to learn and sample from an output distribution that reflects this task uncertainty. In this work, we theoretically analyze how a Diffusion Transformer (DiT), pretrained across diverse tasks, learns and generates predictive distributions for a new query from demonstrations. We first show that the natural target to generate from finite demonstrations is not an output derived from estimating a single task, but rather a predictive distribution that captures the task uncertainty remaining after observing the demonstrations. We then prove that a DiT can learn this predictive distribution through score estimation, using attention to aggregate information from demonstrations and diffusion to generate samples. Owing to this property, with sufficient pretraining resources and diffusion sampling steps, the resulting DiT achieves the minimax optimal rate over a Hölder class of test-time tasks. These results imply that DiT acts as a statistically grounded in-context generator capable of generating distributions adapted to new tasks while retaining the uncertainty inherent in finite demonstrations.