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We introduce a novel alignment method for diffusion models from distribution optimization perspectives while providing rigorous convergence guarantees. We first formulate the problem as a generic regularized loss minimization over…

Machine Learning · Computer Science 2025-03-07 Ryotaro Kawata , Kazusato Oko , Atsushi Nitanda , Taiji Suzuki

Adaptation methods have been a workhorse for unlocking the transformative power of pre-trained diffusion models in diverse applications. Existing approaches often abstract adaptation objectives as a reward function and steer diffusion…

Machine Learning · Computer Science 2026-02-19 Qijie Zhu , Zeqi Ye , Han Liu , Zhaoran Wang , Minshuo Chen

This tutorial provides an in-depth guide on inference-time guidance and alignment methods for optimizing downstream reward functions in diffusion models. While diffusion models are renowned for their generative modeling capabilities,…

Artificial Intelligence · Computer Science 2025-01-22 Masatoshi Uehara , Yulai Zhao , Chenyu Wang , Xiner Li , Aviv Regev , Sergey Levine , Tommaso Biancalani

This paper introduces a rigorous framework for defining generative diffusion models in infinite dimensions via Doob's h-transform. Rather than relying on time reversal of a noising process, a reference diffusion is forced towards the target…

Machine Learning · Statistics 2026-02-09 Thorben Pieper-Sethmacher , Daniel Paulin

Inference-time controllable generation is essential for real-world applications of unconditional diffusion models. However, most existing techniques focus on individual samples, struggling in applications that require the sample population…

Machine Learning · Computer Science 2026-05-11 Hao Luan , See-Kiong Ng , Chun Kai Ling

Diffusion models are an important tool for generative modelling, serving as effective priors in applications such as imaging and protein design. A key challenge in applying diffusion models for downstream tasks is efficiently sampling from…

Machine Learning · Computer Science 2026-02-12 Alexander Denker , Shreyas Padhy , Francisco Vargas , Johannes Hertrich

Diffusion models have shown promising generative capabilities across diverse domains, yet aligning their outputs with desired reward functions remains a challenge, particularly in cases where reward functions are non-differentiable. Some…

Machine Learning · Computer Science 2025-06-04 Xiner Li , Masatoshi Uehara , Xingyu Su , Gabriele Scalia , Tommaso Biancalani , Aviv Regev , Sergey Levine , Shuiwang Ji

In this work, we focus on the alignment problem of diffusion models with a continuous reward function, which represents specific objectives for downstream tasks, such as increasing darkness or improving the aesthetics of images. The central…

Machine Learning · Computer Science 2024-10-03 Zhiwei Tang , Jiangweizhi Peng , Jiasheng Tang , Mingyi Hong , Fan Wang , Tsung-Hui Chang

Diffusion models are state-of-the-art generative models, yet their samples often fail to satisfy application objectives such as safety constraints or domain-specific validity. Existing techniques for alignment require gradients, internal…

Score-based diffusion models have recently been extended to infinite-dimensional function spaces, with uses such as inverse problems arising from partial differential equations. In the Bayesian formulation of inverse problems, the aim is to…

Machine Learning · Computer Science 2026-05-12 Elizabeth L. Baker , Alexander Denker , Jes Frellsen

We consider the problem of simulating diffusion bridges, which are diffusion processes that are conditioned to initialize and terminate at two given states. The simulation of diffusion bridges has applications in diverse scientific fields…

Computation · Statistics 2025-06-19 Jeremy Heng , Valentin De Bortoli , Arnaud Doucet , James Thornton

We introduce a new class of generative diffusion models that, unlike conventional denoising diffusion models, achieve a time-homogeneous structure for both the noising and denoising processes, allowing the number of steps to adaptively…

Machine Learning · Statistics 2026-01-23 Sören Christensen , Jan Kallsen , Claudia Strauch , Lukas Trottner

We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event…

Artificial Intelligence · Computer Science 2026-03-10 Zhengyi Guo , Wenpin Tang , Renyuan Xu

Diffusion models have demonstrated empirical successes in various applications and can be adapted to task-specific needs via guidance. This paper studies a form of gradient guidance for adapting a pre-trained diffusion model towards…

Machine Learning · Statistics 2024-10-17 Yingqing Guo , Hui Yuan , Yukang Yang , Minshuo Chen , Mengdi Wang

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…

Machine Learning · Computer Science 2026-05-22 Kushagra Pandey , Farrin Marouf Sofian , Jan Niklas Groeneveld , Felix Draxler , Stephan Mandt

Adapting a pretrained diffusion model to new objectives at inference time remains an open problem in generative modeling. Existing steering methods suffer from inaccurate value estimation, especially at high noise levels, which biases…

Machine Learning · Computer Science 2025-06-27 Vineet Jain , Kusha Sareen , Mohammad Pedramfar , Siamak Ravanbakhsh

Inference-time alignment provides an efficient alternative for aligning LLMs with humans. However, these approaches still face challenges, such as limited scalability due to policy-specific value functions and latency during the inference…

Computation and Language · Computer Science 2025-05-27 Ruizhe Chen , Wenhao Chai , Zhifei Yang , Xiaotian Zhang , Joey Tianyi Zhou , Tony Quek , Soujanya Poria , Zuozhu Liu

While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…

Machine Learning · Computer Science 2023-10-12 Salva Rühling Cachay , Bo Zhao , Hailey Joren , Rose Yu

Test-time adaptation harnesses test inputs to improve the accuracy of a model trained on source data when tested on shifted target data. Existing methods update the source model by (re-)training on each target domain. While effective,…

Machine Learning · Computer Science 2023-06-22 Jin Gao , Jialing Zhang , Xihui Liu , Trevor Darrell , Evan Shelhamer , Dequan Wang

Diffusion approximation provides weak approximation for stochastic gradient descent algorithms in a finite time horizon. In this paper, we introduce new tools motivated by the backward error analysis of numerical stochastic differential…

Machine Learning · Computer Science 2019-09-05 Yuanyuan Feng , Tingran Gao , Lei Li , Jian-Guo Liu , Yulong Lu
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