Sampling from continuous flow-based generators such as flow matching models requires numerical ODE or SDE integration, making inference cost depend on the number of function evaluations (NFEs).
In practice, the sampling budget is inherited from prior work or selected through expensive FID-versus-NFE sweeps, using FID to assess image-generation quality, requiring sample generation and evaluation at multiple budgets. This makes sampling-budget selection dependent on repeated empirical evaluation.
We therefore ask a complementary question to solver design and timestep allocation: for a fixed pretrained model and solver, what numerical resolution is sufficient?
FLOWBUDGET: A Training-Free Estimator of Solver-Relative Sampling Complexity
We introduce FLOWBUDGET, a training-free estimator of solver-relative sampling complexity. Using simulation-free interpolation probes of the learned dynamics, FLOWBUDGET normalizes the leading one-step discretization error by the motion, estimates its coefficient from interpolation probes, and maps a numerical tolerance to a step budget using the solver order.
We derive estimators for numerical solvers in flow~matching sampling, namely Euler and Heun for ODE sampling and additive-noise Euler--Maruyama for SDE sampling, and connect the ODE coefficients to terminal integration error.
Experiments and Results
Experiments on SiT, FlowDCN and Rectified Flow models, spanning flow-model architectures and formulations, test whether FLOWBUDGET can estimate the NFE budget without generating samples at multiple budgets or performing an FID-versus-NFE sweep.
The code is available at https://github.com/Yasaman-dt/FlowBudget.