Amortised Inference through One-Step Implicit Sampling
Abstract
Efficient sampling from Bayesian posterior distributions in high dimensions remains a hard problem, despite advances in theory and algorithms. Multiple steps are usually required to draw unbiased samples, for example, iterations of an MCMC algorithm or integration steps in a diffusion-based amortised sampler. However, scalable one-step amortised inference remains a challenging open problem. In this work, we build upon recent progress in data-driven generative modelling to offer a possible solution for one-step amortised sampling. Our one-step implicit sampler (OSIS) uses short-time MCMC dynamics to define a local target for the evolution of an implicitly modelled distribution. In the asymptotic limit, the modelled distribution is a fixed point of the MCMC kernel and thus samples from the target. We analyse the convergence properties of OSIS and show connections with other generative modelling and sampling algorithms. We study various design choices and show that OSIS performs well compared to multi-step amortised samplers and non-amortised MCMC baselines while being far more efficient at sampling time.
Related
- Amortised adaptive importance sampling
- Order elevation of directly self-starting sub-step implicit integrators for transient dynamics
- An energy-constrained implicit step-and-truncate algorithm and its robust error estimates
- Power-posterior implicit sampling for efficient Bayesian experimental design: Application to contaminant source identification in groundwater flow
- Denoising Implicit Variational Inference
BibTeX
@misc{pauline2026amortised,
title = {{Amortised Inference through One-Step Implicit Sampling}},
author = {Vincent Pauline and Kirill Tamogashev and Arran Carter and Sanghyeok Choi and Stefan Bauer and Esmeralda S. Whitammer},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.12679},
eprint = {2610.12679},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.12679},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Amortised Inference through One-Step Implicit Sampling
AU - Vincent Pauline
AU - Kirill Tamogashev
AU - Arran Carter
AU - Sanghyeok Choi
AU - Stefan Bauer
AU - Esmeralda S. Whitammer
PY - 2026
DA - 2026/10/08
PB - arXiv
DO - 10.48550/arxiv.2610.12679
UR - https://arxiv.org/abs/2610.12679
AB - Efficient sampling from Bayesian posterior distributions in high dimensions remains a hard problem, despite advances in theory and algorithms. Multiple steps are usually required to draw unbiased samples, for example, iterations of an MCMC algorithm or integration steps in a diffusion-based amortised sampler. However, scalable one-step amortised inference remains a challenging open problem. In this work, we build upon recent progress in data-driven generative modelling to offer a possible solution for one-step amortised sampling. Our one-step implicit sampler (OSIS) uses short-time MCMC dynamics to define a local target for the evolution of an implicitly modelled distribution. In the asymptotic limit, the modelled distribution is a fixed point of the MCMC kernel and thus samples from the target. We analyse the convergence properties of OSIS and show connections with other generative modelling and sampling algorithms. We study various design choices and show that OSIS performs well compared to multi-step amortised samplers and non-amortised MCMC baselines while being far more efficient at sampling time.
ER -