# Diversified Scaling Inference in Time Series Foundation Models

arXiv: https://arxiv.org/abs/2601.17376 · HTML: https://mlsanity.com/paper/2601.17376/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Placed in Diffusion reasoning and test-time scaling, one of 17 directions in LLM reasoning.
- Builds on 40 of its 47 references that are in the map.
- First posted on arXiv 24 Jan 2026.

## Placed in

- LLM reasoning / [Diffusion reasoning and test-time scaling](https://mlsanity.com/lr/diffusion-reasoning-and-test-time-scaling/)

## Builds on (most cited first, 30 of 40)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [On the Opportunities and Risks of Foundation Models](https://mlsanity.com/paper/2108.07258/) (2021)
- [Lost in the Middle: How Language Models Use Long Contexts](https://mlsanity.com/paper/2307.03172/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [The Curious Case of Neural Text Degeneration](https://mlsanity.com/paper/1904.09751/) (2019)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Beyond Accuracy: Behavioral Testing of NLP models with CheckList](https://mlsanity.com/paper/2005.04118/) (2020)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [EDA: Easy Data Augmentation Techniques for Boosting Performance on Text Classification Tasks](https://mlsanity.com/paper/1901.11196/) (2019)
- [Chronos: Learning the Language of Time Series](https://mlsanity.com/paper/2403.07815/) (2024)
- [Universal Adversarial Triggers for Attacking and Analyzing NLP](https://mlsanity.com/paper/1908.07125/) (2019)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [Unified Training of Universal Time Series Forecasting Transformers](https://mlsanity.com/paper/2402.02592/) (2024)
- [Adversarial Examples for Evaluating Reading Comprehension Systems](https://mlsanity.com/paper/1707.07328/) (2017)
- [MOMENT: A Family of Open Time-series Foundation Models](https://mlsanity.com/paper/2402.03885/) (2024)
- [True Few-Shot Learning with Language Models](https://mlsanity.com/paper/2105.11447/) (2021)
- [Diverse Beam Search: Decoding Diverse Solutions from Neural Sequence Models](https://mlsanity.com/paper/1610.02424/) (2016)
- [Inference Scaling Laws: An Empirical Analysis of Compute-Optimal Inference for Problem-Solving with Language Models](https://mlsanity.com/paper/2408.00724/) (2024)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [AlphaMath Almost Zero: Process Supervision without Process](https://mlsanity.com/paper/2405.03553/) (2024)

## Built on by (most cited first, 3 of 3)

- [TimeRadar: A Domain-Rotatable Foundation Model for Time Series Anomaly Detection](https://mlsanity.com/paper/2602.19068/) (2026)
- [GITCO: Gated Inference-Time Context Optimization in TSFMs](https://mlsanity.com/paper/2606.05332/) (2026)
- [A Unified Scaling Law for Time Series Foundation Models](https://mlsanity.com/paper/2610.05269/) (2026)

## Abstract (arXiv)

The advancement of Time Series Foundation Models (TSFMs) has been driven primarily by large-scale pre-training, but inference-time compute potential remains largely untapped. This work systematically investigates two questions: how do TSFMs behave under standard sampling-based inference scaling, and can controlled sampling diversity enhance performance? We first examine the properties of TSFMs under standard sampling often fail to adhere to scaling laws due to insufficient exploration of the solution space. Building on this, we then delve into diversified inference scaling via tailored time series perturbations to expand the generative distribution's support. We theoretically analyze the diversity-fidelity trade-off and derive a critical sample threshold for diversified sampling to outperform standard sampling. Extensive experiments across various TSFMs and datasets show proper diversified inference scaling yields substantial performance gains without parameter updates, establishing inference design as a critical, compute-efficient dimension of TSFM optimization. As an application, we propose RobustMSE, a rigorous metric to quantify the headroom performance of TSFM under a fixed budget. Overall, our findings clarify these factor interactions, enabling reliable performance via diverse large-scale inference time series in parallel environments without re-training TSFMs.