Resolving Latent Representation Collapse in Schrödinger Bridges for Multi-Task Inference and Calibrated Forecasting of Panel Time Series: An Application to Astrophysics

Conditional generative modeling via paired Schrödinger Bridges faces severe limitations in sequential forecasting of sparse, irregularly sampled panel time series. In streaming contexts – such as real-time multi-band supernova light curve monitoring – continuous, noisy non-detections during the critical pre-peak phase creates an asymmetric many-to-one mapping deficiency. This sparse conditioning triggers latent representation collapse, leading to miscalibrated uncertainty intervals and severe classification prior saturation toward dominant classes. In this work, we present a framework that maps panel time series into a continuous hidden space, advancing a hidden-layer dynamic variance Image-to-Image Schrödinger Bridge (I2SB) solver to model extension intervals without data-level noise corruption. We solve the uncertainty quantification task by generating parametric prediction intervals derived directly from the hidden-space I2SB trajectories paired with a post-hoc fine-tuned UQNet uncertainty network, cleanly decoupling trajectory synthesis from downstream tasks. Crucially, categorical classification is resolved via a novel pre-softmax logit fusion technique at the terminal boundary. This architecture ensembles an abstract latent-space energy-based model prior with a standalone temporal neural network trained directly on uncompressed temporal flux trajectories using class-explicit inverse-frequency weights. Concurrently, light-curve-driven redshift estimation operates as a completely independent, parallel channel. Evaluated on highly imbalanced astrophysical benchmarks, our joint pipeline significantly improves early-stage calibration – substantially improving empirical coverage in the pre-peak regime – while maximizing macro classification F1-score and reducing prior saturation.