Publications

2025

1. Reverse Diffusion Sequential Monte Carlo Samplers

   Luhuan Wu, Han Yi, Christian Naesseth, and John Cunningham

   In Conference on Neural Information Processing Systems, 2025

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   We propose a novel sequential Monte Carlo (SMC) method for sampling from unnormalized target distributions based on a reverse denoising diffusion process. While recent diffusion-based samplers simulate the reverse diffusion using approximate score functions, they can suffer from accumulating errors due to time discretization and imperfect score estimation. In this work, we introduce a principled SMC framework that formalizes diffusion-based samplers as proposals while systematically correcting for their biases. The core idea is to construct informative intermediate target distributions that progressively steer the sampling trajectory toward the final target distribution. Although ideal intermediate targets are intractable, we develop exact approximations using quantities from the score estimation-based proposal, without requiring additional model training or inference overhead. The resulting sampler, termed RDSMC, enables consistent sampling and unbiased estimation of the target’s normalization constant under mild conditions. We demonstrate the effectiveness of our method on a range of synthetic targets and real-world Bayesian inference problems.

   @inproceedings{wu2025reverse,
     title = {Reverse Diffusion Sequential Monte Carlo Samplers},
     author = {Wu, Luhuan and Yi, Han and Naesseth, Christian and Cunningham, John},
     booktitle = {Conference on Neural Information Processing Systems},
     year = {2025},
   }

2. Bayesian Invariance Modeling of Multi-Environment Data

   Luhuan Wu, Mingzhang Yin, Yixin Wang, John Cunningham, and David Blei

   arXiv preprint , 2025

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   Invariant prediction [Peters et al., 2016] analyzes feature/outcome data from multiple environments to identify invariant features - those with a stable predictive relationship to the outcome. Such features support generalization to new environments and help reveal causal mechanisms. Previous methods have primarily tackled this problem through hypothesis testing or regularized optimization. Here we develop Bayesian Invariant Prediction (BIP), a probabilistic model for invariant prediction. BIP encodes the indices of invariant features as a latent variable and recover them by posterior inference. Under the assumptions of Peters et al. [2016], the BIP posterior targets the true invariant features. We prove that the posterior is consistent and that greater environment heterogeneity leads to faster posterior contraction. To handle many features, we design an efficient variational approximation called VI-BIP. In simulations and real data, we find that BIP and VI-BIP are more accurate and scalable than existing methods for invariant prediction.

   @misc{wu2025bayesian,
     title = {Bayesian Invariance Modeling of Multi-Environment Data},
     author = {Wu, Luhuan and Yin, Mingzhang and Wang, Yixin and Cunningham, John and Blei, David},
     eprint = {2506.22675},
     archiveprefix = {arXiv},
     year = {2025},
     primaryclass = {stat.ML},
   }

2024

1. Posterior Uncertainty Quantification in Neural Networks using Data Augmentation

   Luhuan Wu and Sinead A Williamson

   In International Conference on Artificial Intelligence and Statistics, 2024

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   In this paper, we approach the problem of uncertainty quantification in deep learning through a predictive framework, which captures uncertainty in model parameters by specifying our assumptions about the predictive distribution of unseen future data. Under this view, we show that deep ensembling (Lakshminarayanan et al., 2017) is a fundamentally mis-specified model class, since it assumes that future data are supported on existing observations only – a situation rarely encountered in practice. To address this limitation, we propose MixupMP, a method that constructs a more realistic predictive distribution using popular data augmentation techniques. MixupMP operates as a drop-in replacement for deep ensembles, where each ensemble member is trained on a random simulation from this predictive distribution. Grounded in the recently-proposed framework of Martingale posteriors (Fong et al., 2023), MixupMP returns samples from an implicitly defined Bayesian posterior. Our empirical analysis showcases that MixupMP achieves superior predictive performance and uncertainty quantification on various image classification datasets, when compared with existing Bayesian and non-Bayesian approaches.

   @inproceedings{wu2024posterior,
     title = {Posterior Uncertainty Quantification in Neural Networks using Data Augmentation},
     author = {Wu, Luhuan and Williamson, Sinead A},
     booktitle = {International Conference on Artificial Intelligence and Statistics},
     pages = {3376--3384},
     year = {2024},
     organization = {PMLR},
   }

2023

1. Practical and Asymptotically Exact Conditional Sampling in Diffusion Models

   Luhuan Wu Wu, Brian Trippe, Christian Naesseth, David Blei, and John Cunningham

   In Conference on Neural Information Processing Systems, 2023

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   Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or error-prone heuristic approximations. Ideally, a conditional generation method should provide exact samples for a broad range of conditional distributions without requiring task-specific training. To this end, we introduce the Twisted Diffusion Sampler, or TDS. TDS is a sequential Monte Carlo (SMC) algorithm that targets the conditional distributions of diffusion models. The main idea is to use twisting, an SMC technique that enjoys good computational efficiency, to incorporate heuristic approximations without compromising asymptotic exactness. We first find in simulation and on MNIST image inpainting and class-conditional generation tasks that TDS provides a computational statistical trade-off, yielding more accurate approximations with many particles but with empirical improvements over heuristics with as few as two particles. We then turn to motif-scaffolding, a core task in protein design, using a TDS extension to Riemannian diffusion models. On benchmark test cases, TDS allows flexible conditioning criteria and often outperforms the state of the art.

   @inproceedings{wu2023tds,
     title = {Practical and Asymptotically Exact Conditional Sampling in Diffusion Models},
     author = {Wu, Luhuan Wu and Trippe, Brian and Naesseth, Christian and Blei, David and Cunningham, John},
     booktitle = {Conference on Neural Information Processing Systems},
     year = {2023},
   }

2022

1. Variational Nearest Neighbor Gaussian Process

   Luhuan Wu, Geoff Pleiss, and John Cunningham

   In International Conference on Machine Learning, 2022

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   Variational approximations to Gaussian processes (GPs) typically use a small set of inducing points to form a low-rank approximation to the covariance matrix. In this work, we instead exploit a sparse approximation of the precision matrix. We propose variational nearest neighbor Gaussian process (VNNGP), which introduces a prior that only retains correlations within 𝐾 nearest-neighboring observations, thereby inducing sparse precision structure. Using the variational framework, VNNGP’s objective can be factorized over both observations and inducing points, enabling stochastic optimization with a time complexity of 𝑂(𝐾3). Hence, we can arbitrarily scale the inducing point size, even to the point of putting inducing points at every observed location. We compare VNNGP to other scalable GPs through various experiments, and demonstrate that VNNGP (1) can dramatically outperform low-rank methods, and (2) is less prone to overfitting than other nearest neighbor methods.

   @inproceedings{wu2022variational,
     title = {Variational Nearest Neighbor Gaussian Process},
     author = {Wu, Luhuan and Pleiss, Geoff and Cunningham, John},
     booktitle = {International Conference on Machine Learning},
     pages = {24114-24130},
     year = {2022},
     organization = {PMLR},
     talk = {https://slideslive.com/38983939/vnngp-variational-nearest-neighbor-gaussian-process},
   }

2021

1. Bias-free Scalable Gaussian Processes via Randomized Truncations

   Andres Potapczynski, Luhuan Wu, Dan Biderman, Geoff Pleiss, and John P Cunningham

   In International Conference on Machine Learning, 2021

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   Scalable Gaussian Process methods are computationally attractive, yet introduce modeling biases that require rigorous study. This paper analyzes two common techniques: early truncated conjugate gradients (CG) and random Fourier features (RFF). We find that both methods introduce a systematic bias on the learned hyperparameters: CG tends to underfit while RFF tends to overfit. We address these issues using randomized truncation estimators that eliminate bias in exchange for increased variance. In the case of RFF, we show that the bias-to-variance conversion is indeed a trade-off: the additional variance proves detrimental to optimization. However, in the case of CG, our unbiased learning procedure meaningfully outperforms its biased counterpart with minimal additional computation. Our code is available at https://github.com/ cunningham-lab/RTGPS.

   @inproceedings{potapczynski2021bias,
     title = {Bias-free Scalable Gaussian Processes via Randomized Truncations},
     author = {Potapczynski, Andres and Wu, Luhuan and Biderman, Dan and Pleiss, Geoff and Cunningham, John P},
     booktitle = {International Conference on Machine Learning},
     pages = {8609--8619},
     year = {2021},
     organization = {PMLR},
     talk = {https://icml.cc/virtual/2021/poster/10577},
   }

2. Hierarchical Inducing Point Gaussian Process for Inter-domian Observations

   Luhuan Wu, Andrew Miller, Lauren Anderson, Geoff Pleiss, David Blei, and 1 more author

   In International Conference on Artificial Intelligence and Statistics, 2021

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   We examine the general problem of inter-domain Gaussian Processes (GPs): problems where the GP realization and the noisy observations of that realization lie on different domains. When the mapping between those domains is linear, such as integration or differentiation, inference is still closed form. However, many of the scaling and approximation techniques that our community has developed do not apply to this setting. In this work, we introduce the hierarchical inducing point GP (HIP-GP), a scalable inter-domain GP inference method that enables us to improve the approximation accuracy by increasing the number of inducing points to the millions. HIP-GP, which relies on inducing points with grid structure and a stationary kernel assumption, is suitable for low-dimensional problems. In developing HIP-GP, we introduce (1) a fast whitening strategy, and (2) a novel preconditioner for conjugate gradients which can be helpful in general GP settings.

   @inproceedings{wu2021hierarchical,
     title = {Hierarchical Inducing Point Gaussian Process for Inter-domian Observations},
     author = {Wu, Luhuan and Miller, Andrew and Anderson, Lauren and Pleiss, Geoff and Blei, David and Cunningham, John},
     booktitle = {International Conference on Artificial Intelligence and Statistics},
     pages = {2926--2934},
     year = {2021},
     organization = {PMLR},
     talk = {https://slideslive.com/38953216/hipgp-hierarchical-inducing-point-gaussian-process-for-interdomian-observations?ref=speaker-31741},
   }

2020

1. Variational Objectives for Markovian Dynamics with Backward Simulation

   Antonio Khalil Moretti, Zizhao Wang, Luhuan Wu, Iddo Drori, and Itsik Pe’er

   In European Conference on Artificial Intelligence, 2020

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   Sequential Monte Carlo (SMC) and Variational Inference (VI) are two families of approximate inference algorithms for Bayesian latent variable models. A body of recent work has focused on constructing a variational family of filtered distributions using SMC. Inspired by this work, we introduce Particle Smoothing Variational Objectives (SVO), a novel backward simulation technique and variational objective constructed from a smoothed approximate posterior. Our method sub-samples auxiliary random variables to enhance the support of the proposal distribution and increase particle diversity. We demonstrate our approach on three benchmark latent nonlinear dynamical systems tasks. SVO consistently outperforms filtered objectives when given fewer Monte Carlo samples.

   @inproceedings{khalil2020variational,
     title = {Variational Objectives for Markovian Dynamics with Backward Simulation},
     author = {Khalil Moretti, Antonio and Wang, Zizhao and Wu, Luhuan and Drori, Iddo and Pe’er, Itsik},
     booktitle = {European Conference on Artificial Intelligence},
     pages = {1371--1378},
     year = {2020},
     publisher = {IOS Press},
   }

2. Inverse Articulated-body Dynamics from Video via Variational Sequential Monte Carlo

   Dan Biderman, Christian A Naesseth, Luhuan Wu, Taiga Abe, Alice C Mosberger, and 4 more authors

   In NeurIPS Workshop on Differentiable Vision, Graphics, and Physics in Machine Learning, 2020

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   Convolutional neural networks for pose estimation are continuously improving in identifying joints of moving agents from video. However, state-of-the-art algorithms offer no insight into the underlying mechanics of articulated limbs. "Seeing" the mechanics of movement is of major importance for fields like neuroscience, studying how the brain controls movement, and engineering, e.g., using vision to correct for errors in the action of a robotic manipulator. In the pipeline proposed here, we use a convolutional network to track joint positions, and embed these as the joints of a linked robotic manipulator. We develop a probabilistic physical model whose states specify second-order rigid-body dynamics and the torques applied to each actuator. Observations are generated by mapping the joint angles through the forward kinematics function to Cartesian coordinates. For nonlinear state estimation and parameter learning, we build on variational Sequential Monte Carlo (SMC), a differentiable variant of the classical SMC method leveraging variational inference. We extend with a distributed nested SMC algorithm, which, at inference time, wraps multiple independent SMC samplers within an outer-level importance sampler. We extract mechanical quantities from simulated data and newly acquired videos of mice and humans, offering a novel tool for studying e.g. biological motor control.

2019

1. Smoothing Nonlinear Variational Objectives with Sequential Monte Carlo

   Antonio Moretti, Zizhao Wang, Luhuan Wu, and Itsik Pe’er

   In ICLR Workshop on Deep Generative Models for Highly Structured Data, 2019

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   The task of recovering nonlinear dynamics and latent structure from a population recording is a challenging problem in statistical neuroscience motivating the development of novel techniques in time series analysis. Recent work has focused on connections between Variational Inference and Sequential Monte Carlo for performing inference and parameter estimation on sequential data. Inspired by this work, we present a framework to develop Smoothed Variational Objectives (SVOs) that condition proposal distributions on the full time-ordered sequence of observations. SVO maintains both expressiveness and tractability by sharing parameters of the transition function between the proposal and target. We apply the method to several dimensionality reduction/expansion tasks and examine the dynamics learned with a quantitative metric. SVO performs favorably against the state of the art.

   @inproceedings{moretti2019smoothing,
     title = {Smoothing Nonlinear Variational Objectives with Sequential Monte Carlo},
     author = {Moretti, Antonio and Wang, Zizhao and Wu, Luhuan and Pe'er, Itsik},
     year = {2019},
     booktitle = {ICLR Workshop on Deep Generative Models for Highly Structured Data},
   }