Plain Flow Maps with Analytic Heads

Flow maps learn direct jumps between arbitrary points along diffusion ODE trajectories via differential objectives. This requires differentiating the entire model with respect to time, incurring severe overheads. We show that this is unnecessary. We introduce plain flow maps, which retain a standard diffusion backbone and expose the differentiated time only to a lightweight analytic head. We show that this head can be as simple as a single layer featuring time-adaptive spatial and channel mixing, yet remains highly effective. We introduce two parameterizations, secant and velocity, allowing terminal-time differentiation to be resolved solely within the head via closed-form derivatives and integrals, respectively. This design completely bypasses explicit differentiation tools and their associated drawbacks. Extensive experiments demonstrate remarkable performance on from-scratch ImageNet and text-to-image training.