# Triangular Resampling for Long-Horizon Motion Generation

arXiv: https://arxiv.org/abs/2609.34697 · HTML: https://mlsanity.com/paper/2609.34697/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Diffusion foundations and sampling, one of 14 directions in Diffusion models.
- Builds on 16 of its 17 references that are in the map.
- First posted on arXiv 28 Sep 2026.

## Placed in

- Diffusion models / [Diffusion foundations and sampling](https://mlsanity.com/diffusion/diffusion-foundations-and-sampling/)

## Builds on (most cited first, 16 of 16)

- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [One-step Diffusion with Distribution Matching Distillation](https://mlsanity.com/paper/2311.18828/) (2023)
- [Self Forcing: Bridging the Train-Test Gap in Autoregressive Video Diffusion](https://mlsanity.com/paper/2506.08009/) (2025)
- [Human Motion Diffusion as a Generative Prior](https://mlsanity.com/paper/2303.01418/) (2023)
- [BABEL: Bodies, Action and Behavior with English Labels](https://mlsanity.com/paper/2106.09696/) (2021)
- [Rolling Forcing: Autoregressive Long Video Diffusion in Real Time](https://mlsanity.com/paper/2509.25161/) (2025)
- [Causal Forcing: Autoregressive Diffusion Distillation Done Right for High-Quality Real-Time Interactive Video Generation](https://mlsanity.com/paper/2602.02214/) (2026)
- [TEACH: Temporal Action Composition for 3D Humans](https://mlsanity.com/paper/2209.04066/) (2022)
- [MotionStreamer: Streaming Motion Generation via Diffusion-based Autoregressive Model in Causal Latent Space](https://mlsanity.com/paper/2503.15451/) (2025)
- [DartControl: A Diffusion-Based Autoregressive Motion Model for Real-Time Text-Driven Motion Control](https://mlsanity.com/paper/2410.05260/) (2024)
- [Seamless Human Motion Composition with Blended Positional Encodings](https://mlsanity.com/paper/2402.15509/) (2024)
- [End-to-End Training for Autoregressive Video Diffusion via Self-Resampling](https://mlsanity.com/paper/2512.15702/) (2025)
- [Self Gradient Forcing: Native Long Video Extrapolation](https://mlsanity.com/paper/2607.20368/) (2026)
- [FloodDiffusion: Tailored Diffusion Forcing for Streaming Motion Generation](https://mlsanity.com/paper/2512.03520/) (2025)
- [T2LM: Long-Term 3D Human Motion Generation from Multiple Sentences](https://mlsanity.com/paper/2406.00636/) (2024)
- [PRISM: Streaming Human Motion Generation with Per-Joint Latent Decomposition](https://mlsanity.com/paper/2603.08590/) (2026)

## Abstract (arXiv)

We introduce Triangular Resampling (TR), a post-training method for mitigating long-horizon error accumulation in motion diffusion models. Built on FloodDiffusion's triangular denoising schedule, TR addresses the mismatch between ground-truth-derived training windows and model-generated inference states. Replacing only completed motion history leaves this mismatch unresolved in partially denoised states within the active window. TR therefore extends rollout-based training to these states, using ground-truth clamping to limit excessive drift. For each replayed sample, TR draws one denoising threshold, shared across latent positions and replay updates, and replays multi-step triangular denoising without gradient tracking. After each update, states below the threshold are replaced with noise-matched ground truth, while those at or above it retain model predictions. The resulting latent window enters the standard training update. This rollout construction supports both supervised training (TR) and distribution matching (TR-DMD). On 120-second motion generation from HumanML3D test prompts, TR and TR-DMD achieve state-of-the-art FID AUC within their respective non-DMD and DMD comparison groups. Supervised TR reduces FID AUC by 40.9% and FID degradation slope by 55.3% relative to matched post-training without replay.