Flow matching

中文導讀

Flow matching 是一類 continuous-time generative 方法:學一個 time-dependent velocity field,把 source distribution 沿 ODE 連續搬到 target distribution,訓練上比 diffusion 更直接 (regress 一個 conditional velocity)。在 RNA velocity 脈絡裡,FlowVelo 用 conditional flow matching 來描述 cell-state dynamics,目標是把 physical-time-grounding 的 temporal 軸補起來。跟 optimal-transport 關係密切——OT path 常被當 flow matching 的 target coupling。

Definition

A continuous-time generative-modeling paradigm that learns a time-dependent velocity field v_θ(x, t) transporting a source distribution to a target along an ODE, trained by regressing a tractable conditional velocity (conditional flow matching) rather than simulating the full path. Closely tied to optimal-transport: OT-induced couplings give straight, low-cost transport paths used as flow-matching targets.

Relevance to RNA velocity

FlowVelo adopts conditional flow matching to model single-cell dynamics, aiming to carry a physically interpretable time on the physical-time-grounding axis — in contrast to GRN-coupled but temporally ungrounded methods like RegVelo.

NOTE: open question — does a flow-matching field carry metric time, or only a reparameterized ordinal flow, absent an absolute-time anchor? See metabolic-labeling and physical-time-grounding.

Related

FlowVelo · optimal-transport · transport-operators · physical-time-grounding · RNA velocity