CoBiST: A Coupled Bidirectional Survival Transport Operator for Probabilistic Time-Series Generative Forecaster

Probabilistic time-series forecasting targets the joint distribution of a segmentation of the future path. Modern generators approximate this distribution through sampling full trajectories. Most existing generative forecasters delegate the interaction between forecast positions to a generic backbone and typically lack a unified, normalized accounting of information routing across forecast positions. To capture such internal interaction during generation, we propose Coupled Bidirectional Survival Transport (CoBiST), a generator-agnostic cross-horizon transport operator with explicit probabilistic semantics for directional propagation, locality, and memory mechanisms. CoBiST can be plugged into multiple types of generator without changing the outer objective or sampler, where a shared gate produces directional preferences and one-step survival probabilities to jointly determine the budget assigned to causal and anti-causal recurrent scans and to a direct-local branch. The resulting transport operator is theoretically verified to admit an exact augmented row-stochastic kernel, a linear-time semiseparable realization, frozen-gate non-expansiveness, and a finite-horizon sensitivity bound for state-dependent gates. We instantiate the same operator in GAN, flow-matching, and diffusion forecasters, achieving average Projected CRPS reductions relative to capacity-matched dense controls of 6.72%, 21.48%, and 20.78% across eight datasets, respectively. CoBiST-Flow and CoBiST-Diffusion also achieve the best two average Projected CRPS, Marginal CRPS and Energy Score ranks among all evaluated forecasters.