A financial diffusion sampler gets a new time grid: TAPES posts the lowest paired error in all 24 rows, cutting audit error about 10%
Synopsis
Financial scenario pipelines often run diffusion samplers at very few function evaluations, where time-grid discretization error can quietly distort terminal reports such as covariances, tails and drawdown proxies. TAPES treats grid construction as a goal-oriented numerical problem: Richardson comparisons estimate each step's signed local defect, a terminal-report adjoint transports those defects through the remaining discrete flow, and the squared norm of their sum is minimized before a capped direct refinement. Across six budgets on Regime-SV and Mag7, TAPES gives the lowest design- and audit-report errors in all 24 dataset–budget–report rows within the reported five-pipeline panel, with cross-budget mean relative audit-error reductions of about 10–11% and about 1%.
Interpretation
A frozen financial diffusion sampler is deployed with only 4 to 32 Euler calls, and what downstream consumes is not the raw path but a small set of terminal reports: covariances, volatility persistence, tail quantiles and drawdown proxies. TAPES changes only this offline time grid, leaving the score network, conditioning, solver, report normalization and deployment call count fixed, so the few steps land where the terminal report is most sensitive. Earlier timestep schedules allocate steps by local error or sample-quality objectives; ART, for instance, minimizes a rescaled Euclidean Richardson defect over the same positive-clock family with no adjoint, no cross-time term and no report refinement, treating each step's error as additive. Within the reported five-pipeline panel, TAPES has the lowest sample mean in all 24 rows spanning two data sources, six budgets and the design and audit report families; all 24 paired pointwise 95% intervals against AYS lie below zero, and 23 of 24 against ART do, the exception being the Mag7 design row.
Grid construction runs in two stages: a candidate clock comes from the transported signed-defect sum, then a small capped direct refinement of paired report error on development items refines it, and one positive grid per budget is frozen for evaluation. The signed defect is estimated by Richardson comparison, the difference between one full step and two half steps over an interval; it is then back-propagated through vector–Jacobian products of the frozen Euler maps and weighted by the terminal-report adjoint, and the objective squares the sum of transported defects, keeping cross-step reinforcement and cancellation. Construction uses development items only: 64 development paths and at most 8 L-BFGS-B iterations for Regime-SV, at most 4 for Mag7; evaluation uses 376 independent noise paths and 120 chronologically held-out Mag7 contexts, with every method sharing the same initial noise and high-NFE reference path.
Perspective
The demonstrated scope is two data sources (simulated Regime-SV and Mag7 equity returns), three frozen checkpoints, the Euler solver plus a small Heun probe, and one exploratory 21-day extension; the high-NFE reference comes from the same generator and is a numerical target, not the market law. The intended reader is an engineer building scenario generation or risk computation that reuses a frozen diffusion sampler at a fixed deployment call count.
Intervals condition on frozen checkpoints and selected grids, some methods use audit-family data during development, and offline compute is not equalized across methods; broader comparison across alternative solver and schedule stacks, a causal marginal adjoint effect, and replication across training runs remain open. The allocation configuration was selected on the same return period, so its metrics are exploratory, and other assets, periods, targets, costs and constraints remain untested.