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RefineBridge: Generative Bridge Models Improve Financial Forecasting by Foundation Models

Anthony Bolton, Wuyang Zhou, Zehua Chen, Giorgos Iacovides, Danilo Mandic

TL;DR

RefineBridge introduces a Schrödinger Bridge–based refinement module that post-processes forecasts from time-series foundation models (TSFMs) to better capture financial signal under non-stationarity and heavy tails. By treating TSFM predictions as a prior and learning context-conditioned stochastic transport maps, it provides a complementary objective distinct from LoRA fine-tuning, and refines predictions through time-conditioned denoising in either ODE or SDE form. Empirical results across three financial assets and multiple horizons show RefineBridge consistently improves TSFM performance, with larger gains at longer horizons, and robustness to low-quality priors. This approach offers a practical, parameter-efficient enhancement for financial forecasting without modifying the underlying TSFM weights, with strong implications for deployment in trading and risk management pipelines.

Abstract

Financial time series forecasting is particularly challenging for transformer-based time series foundation models (TSFMs) due to non-stationarity, heavy-tailed distributions, and high-frequency noise present in data. Low-rank adaptation (LoRA) has become a popular parameter-efficient method for adapting pre-trained TSFMs to downstream data domains. However, it still underperforms in financial data, as it preserves the network architecture and training objective of TSFMs rather than complementing the foundation model. To further enhance TSFMs, we propose a novel refinement module, RefineBridge, built upon a tractable Schrödinger Bridge (SB) generative framework. Given the forecasts of TSFM as generative prior and the observed ground truths as targets, RefineBridge learns context-conditioned stochastic transport maps to improve TSFM predictions, iteratively approaching the ground-truth target from even a low-quality prior. Simulations on multiple financial benchmarks demonstrate that RefineBridge consistently improves the performance of state-of-the-art TSFMs across different prediction horizons.

RefineBridge: Generative Bridge Models Improve Financial Forecasting by Foundation Models

TL;DR

RefineBridge introduces a Schrödinger Bridge–based refinement module that post-processes forecasts from time-series foundation models (TSFMs) to better capture financial signal under non-stationarity and heavy tails. By treating TSFM predictions as a prior and learning context-conditioned stochastic transport maps, it provides a complementary objective distinct from LoRA fine-tuning, and refines predictions through time-conditioned denoising in either ODE or SDE form. Empirical results across three financial assets and multiple horizons show RefineBridge consistently improves TSFM performance, with larger gains at longer horizons, and robustness to low-quality priors. This approach offers a practical, parameter-efficient enhancement for financial forecasting without modifying the underlying TSFM weights, with strong implications for deployment in trading and risk management pipelines.

Abstract

Financial time series forecasting is particularly challenging for transformer-based time series foundation models (TSFMs) due to non-stationarity, heavy-tailed distributions, and high-frequency noise present in data. Low-rank adaptation (LoRA) has become a popular parameter-efficient method for adapting pre-trained TSFMs to downstream data domains. However, it still underperforms in financial data, as it preserves the network architecture and training objective of TSFMs rather than complementing the foundation model. To further enhance TSFMs, we propose a novel refinement module, RefineBridge, built upon a tractable Schrödinger Bridge (SB) generative framework. Given the forecasts of TSFM as generative prior and the observed ground truths as targets, RefineBridge learns context-conditioned stochastic transport maps to improve TSFM predictions, iteratively approaching the ground-truth target from even a low-quality prior. Simulations on multiple financial benchmarks demonstrate that RefineBridge consistently improves the performance of state-of-the-art TSFMs across different prediction horizons.
Paper Structure (12 sections, 8 equations, 2 figures, 1 table)

This paper contains 12 sections, 8 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Related Work
  3. RefineBridge
  4. Bridging TSFM Predictions and Ground Truth
  5. Complementary Training Objective
  6. Prior-to-Target: Iterative Refinement for TSFM
  7. Network Architecture
  8. EXPERIMENTS
  9. Datasets
  10. Experimental Settings
  11. Results
  12. CONCLUSION

Figures (2)

  • Figure 1: RefineBridge learns an optimal transport map from TSFM predictions to the ground truth via Schrödinger Bridge. At inference time, RefineBridge progressively refines the TSFM forecasts along sampling steps.
  • Figure 2: The proposed RefineBridge model learns how to refine the predictions of TSFMs towards ground truth conditioned on the context window during training. During inference, the trained model is frozen and uses SDE or ODE sampling to iteratively refine the predictions of TSFMs conditioned on the context window. The bottom right corner shows an example of a comparison between the original TSFM prediction and the refined prediction through RefineBridge.