Meta Flow Maps enable scalable reward alignment

Controlling generative models is computationally expensive. This is because optimal alignment with a reward function--whether via inference-time steering or fine-tuning--requires estimating the value function.

This task demands access to the conditional posterior $p_{1|t}(x_1|x_t)$, the distribution of clean data $x_1$ consistent with an intermediate state $x_t$, a requirement that typically compels methods to resort to costly trajectory simulations. To address this bottleneck, we introduce Meta Flow Maps (MFMs), a framework extending consistency models and flow maps into the stochastic regime.

MFMs are trained to perform stochastic one-step posterior sampling, generating arbitrarily many i.i.d. draws of clean data $x_1$ from any intermediate state.

Crucially, these samples provide a differentiable reparametrization that unlocks efficient value function estimation. We leverage this capability to solve bottlenecks in both paradigms: enabling inference-time steering without inner rollouts, and facilitating unbiased, off-policy fine-tuning to general rewards.

Empirically, our single-particle steered-MFM sampler outperforms a Best-of-1000 baseline on ImageNet across multiple rewards at a fraction of the compute.