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Luhuan Wu

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5 papers

2 author rows

NeurIPS Conference 2025 Conference Paper

Reverse Diffusion Sequential Monte Carlo Samplers

Luhuan Wu
Yi Han
Christian Andersson Naesseth
John Cunningham

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 \emph{exact approximations} using quantities from the score estimation-based proposal, without requiring additional model training or inference overhead. The resulting sampler, termed \textit{\ourmethodfull}, 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.

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NeurIPS Conference 2023 Conference Paper

Practical and Asymptotically Exact Conditional Sampling in Diffusion Models

Luhuan Wu
Brian Trippe
Christian Naesseth
David Blei
John P. Cunningham

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 through simulating a set of weighted particles. 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 in conditional image 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 tasks, TDS allows flexible conditioning criteria and often outperforms the state-of-the-art, conditionally trained model. Code can be found in https: //github. com/blt2114/twisted diffusion sampler

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ICML Conference 2022 Conference Paper

Variational nearest neighbor Gaussian process

Luhuan Wu
Geoff Pleiss
John P. Cunningham

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 $O(K^3)$. 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.

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ICML Conference 2021 Conference Paper

Bias-Free Scalable Gaussian Processes via Randomized Truncations

Andres Potapczynski
Luhuan Wu
Dan Biderman
Geoff Pleiss
John P. Cunningham

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.

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ECAI Conference 2020 Conference Paper

Variational Objectives for Markovian Dynamics with Backward Simulation

Antonio Khalil Moretti
Zizhao Wang
Luhuan Wu
Iddo Drori
Itsik Pe'er

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.

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