Learning Beyond Time: Transformation-Aware Diffusion for Data-Augmented Soft-Sensor Modeling

In industrial soft-sensor modeling, the scarcity and imbalance of process data often lead to overfitting and poor generalization of predictive models. To address these challenges, this article proposes a transformation-aware diffusion model (TA-DM) that integrates transformed-domain supervision for data-augmented soft sensing. We explore transformation-aware designs and introduce a novel structure-breaking loss framework that enhances the denoising objectives of denoising diffusion implicit model and TimeDDIM by encouraging the model to disrupt redundant patterns and capture richer structural variations. In implementation, our proposed approach formulates loss functions across multiple transformation domains—including discrete Fourier transform, wavelet transform, and principal component analysis (PCA)—to explicitly guide the model in learning complementary and diverse structural features beyond the original time domain, significantly advancing the representational quality and diversity of generated time-series data. To further bridge the discrepancy between the data generated by TA-DM and the real data, we propose a just-in-time learning-based sample selection strategy. This strategy leverages the representation space of the diffusion model to adaptively select local samples relevant to the current operating condition through similarity matching. These samples are then fused with limited real data to improve soft-sensor modeling. This targeted augmentation effectively narrows the synthetic-real domain gap and enhances model robustness under complex conditions. Experimental results on a numerical example and real-world industrial datasets demonstrate that TA-DM significantly outperforms existing augmentation baselines under data-scarce and distribution-shifting scenarios.