# From Samples to Scenarios: A New Paradigm for Probabilistic Forecasting

arXiv: https://arxiv.org/abs/2509.19975 · HTML: https://mlsanity.com/paper/2509.19975/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 38 of its 61 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 30 of 38)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Neural Discrete Representation Learning](https://mlsanity.com/paper/1711.00937/) (2017)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Time Series Forecasting With Deep Learning: A Survey](https://mlsanity.com/paper/2004.13408/) (2020)
- [Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2101.12072/) (2021)
- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Diffusion-based Time Series Imputation and Forecasting with Structured State Space Models](https://mlsanity.com/paper/2208.09399/) (2022)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [GP-VAE: Deep Probabilistic Time Series Imputation](https://mlsanity.com/paper/1907.04155/) (2019)
- [High-Dimensional Multivariate Forecasting with Low-Rank Gaussian Copula Processes](https://mlsanity.com/paper/1910.03002/) (2019)
- [Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows](https://mlsanity.com/paper/2002.06103/) (2020)
- [Learning in an Uncertain World: Representing Ambiguity Through Multiple Hypotheses](https://mlsanity.com/paper/1612.00197/) (2016)
- [Predict, Refine, Synthesize: Self-Guiding Diffusion Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2307.11494/) (2023)
- [Stochastic Multiple Choice Learning for Training Diverse Deep Ensembles](https://mlsanity.com/paper/1606.07839/) (2016)
- [Flow Matching with Gaussian Process Priors for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2410.03024/) (2024)
- [Modeling Temporal Data as Continuous Functions with Stochastic Process Diffusion](https://mlsanity.com/paper/2211.02590/) (2022)
- [TACTiS: Transformer-Attentional Copulas for Time Series](https://mlsanity.com/paper/2202.03528/) (2022)
- [ProbTS: Benchmarking Point and Distributional Forecasting across Diverse Prediction Horizons](https://mlsanity.com/paper/2310.07446/) (2023)
- [Trajectory-wise Multiple Choice Learning for Dynamics Generalization in Reinforcement Learning](https://mlsanity.com/paper/2010.13303/) (2020)
- [Time Series Data Imputation: A Survey on Deep Learning Approaches](https://mlsanity.com/paper/2011.11347/) (2020)
- [DMCL: Distillation Multiple Choice Learning for Multimodal Action Recognition](https://mlsanity.com/paper/1912.10982/) (2019)
- [Non-stationary Diffusion For Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2505.04278/) (2025)
- [TACTiS-2: Better, Faster, Simpler Attentional Copulas for Multivariate Time Series](https://mlsanity.com/paper/2310.01327/) (2023)
- [Deep Generative Quantile-Copula Models for Probabilistic Forecasting](https://mlsanity.com/paper/1907.10697/) (2019)
- [Resilient Multiple Choice Learning: A learned scoring scheme with application to audio scene analysis](https://mlsanity.com/paper/2311.01052/) (2023)

## Built on by (most cited first, 10 of 10)

- [Learning the Context of Errors: Black-Box Online Adaptation of Time Series Foundation Models](https://mlsanity.com/paper/2606.14222/) (2026)
- [Position: Universal Time Series Foundation Models Rest on a Category Error](https://mlsanity.com/paper/2602.05287/) (2026)
- [From Internal Diagnosis to External Auditing: A VLM-Driven Paradigm for Data-Free Online Backdoor Defense](https://mlsanity.com/paper/2601.19448/) (2026)
- [When Agent Automation Becomes Profitable: Quantifying and Insuring Autonomous AI Risk through Trace-Economic Underwriting](https://mlsanity.com/paper/2606.16465/) (2026)
- [LLM Agents Are Latent Context Managers: Eliciting Self-Managed Context via State Proprioception](https://mlsanity.com/paper/2606.30005/) (2026)
- [Signature-Kernel Based Evaluation Metrics for Robust Probabilistic and Tail-Event Forecasting](https://mlsanity.com/paper/2602.10182/) (2026)
- [DiffPTS: Rethinking Diffusion ELBO for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2609.32363/) (2026)
- [STRIDE: State-Transition Representation via Increment Dynamics and Evolution](https://mlsanity.com/paper/2609.32367/) (2026)
- [Pythia: Toward Foundation World Models for Multimodal Time Series](https://mlsanity.com/paper/2610.05240/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)

## Abstract (arXiv)

Most state-of-the-art probabilistic time series forecasting models rely on sampling to represent future uncertainty. However, this paradigm suffers from inherent limitations, such as lacking explicit probabilities, inadequate coverage, and high computational costs. In this work, we introduce Probabilistic Scenarios, an alternative paradigm designed to address the limitations of sampling. It operates by directly producing a finite set of Scenario, Probability pairs, thus avoiding Monte Carlo-like approximation. To validate this paradigm, we propose TimePrism, a simple model composed of only three parallel linear layers. Surprisingly, TimePrism achieves 9 out of 10 state-of-the-art results across five benchmark datasets on two metrics. The effectiveness of our paradigm comes from a fundamental reframing of the learning objective. Instead of modeling an entire continuous probability space, the model learns to represent a set of plausible scenarios and corresponding probabilities. Our work demonstrates the potential of the Probabilistic Scenarios paradigm, opening a promising research direction in forecasting beyond sampling.