# Time Series Forecasting via Direct Per-Step Probability Distribution Modeling

arXiv: https://arxiv.org/abs/2511.23260 · HTML: https://mlsanity.com/paper/2511.23260/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 35 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 15 of 15)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Diffusion-TS: Interpretable Diffusion for General Time Series Generation](https://mlsanity.com/paper/2403.01742/) (2024)
- [Large Language Models for Time Series: A Survey](https://mlsanity.com/paper/2402.01801/) (2024)
- [Koopa: Learning Non-stationary Time Series Dynamics with Koopman Predictors](https://mlsanity.com/paper/2305.18803/) (2023)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [VisionTS: Visual Masked Autoencoders Are Free-Lunch Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2408.17253/) (2024)
- [FreDF: Learning to Forecast in the Frequency Domain](https://mlsanity.com/paper/2402.02399/) (2024)
- [Rethinking Channel Dependence for Multivariate Time Series Forecasting: Learning from Leading Indicators](https://mlsanity.com/paper/2401.17548/) (2024)
- [Linear Transformers as VAR Models: Aligning Autoregressive Attention Mechanisms with Autoregressive Forecasting](https://mlsanity.com/paper/2502.07244/) (2025)

## Built on by (most cited first, 2 of 2)

- [SPDM: Geometry-Modulated State Space Modeling with Manifold Constraints for Time Series Forecasting](https://mlsanity.com/paper/2606.09917/) (2026)
- [Structured Latent Space Modeling over Multi-Scale Temporal Patches for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2607.19404/) (2026)

## Abstract (arXiv)

Deep neural network-based time series prediction models have recently demonstrated superior capabilities in capturing complex temporal dependencies. However, it is challenging for these models to account for uncertainty associated with their predictions, because they directly output scalar values at each time step. To address such a challenge, we propose a novel model named interleaved dual-branch Probability Distribution Network (interPDN), which directly constructs discrete probability distributions per step instead of a scalar. The regression output at each time step is derived by computing the expectation of the predictive distribution on a predefined support set. To mitigate prediction anomalies, a dual-branch architecture is introduced with interleaved support sets, augmented by coarse temporal-scale branches for long-term trend forecasting. Outputs from another branch are treated as auxiliary signals to impose self-supervised consistency constraints on the current branch's prediction. Extensive experiments on multiple real-world datasets demonstrate the superior performance of interPDN.