Test-Time Alignment of Discrete Diffusion Models with Sequential Monte Carlo

Discrete diffusion models have become highly effective across various domains. However, real-world applications often require the generative process to adhere to certain constraints but without task-specific fine-tuning. To this end, we propose a training-free method based on Sequential Monte Carlo (SMC) to sample from the reward-aligned target distribution at the test time. Our approach leverages twisted SMC with an approximate locally optimal proposal, obtained via a first-order Taylor expansion of the reward function. To address the challenge of ill-defined gradients in discrete spaces, we incorporate a Gumbel-Softmax relaxation, enabling efficient gradient-based approximation within the discrete generative framework. Empirical results on both synthetic datasets and image modelling validate the effectiveness of our approach.

Discrete Neural Flow Samplers with Locally Equivariant Transformer

Sampling from unnormalised discrete distributions is a fundamental problem across various domains. While Markov chain Monte Carlo offers a principled approach, it often suffers from slow mixing and poor convergence. In this paper, we propose Discrete Neural Flow Samplers (DNFS), a trainable and efficient framework for discrete sampling. DNFS learns the rate matrix of a continuous-time Markov chain such that the resulting dynamics satisfy the Kolmogorov equation. As this objective involves the intractable partition function, we then employ control variates to reduce the variance of its Monte Carlo estimation, leading to a coordinate descent learning algorithm. To further facilitate computational efficiency, we propose locally equivaraint Transformer, a novel parameterisation of the rate matrix that significantly improves training efficiency while preserving powerful network expressiveness. Empirically, we demonstrate the efficacy of DNFS in a wide range of applications, including sampling from unnormalised distributions, training discrete energy-based models, and solving combinatorial optimisation problems.

Target Concrete Score Matching: A Holistic Framework for Discrete Diffusion

Discrete diffusion is a promising framework for modeling and generating discrete data. In this work, we present Target Concrete Score Matching (TCSM), a novel and versatile objective for training and fine-tuning discrete diffusion models. TCSM provides a general framework with broad applicability. It supports pre-training discrete diffusion models directly from data samples, and many existing discrete diffusion approaches naturally emerge as special cases of our more general TCSM framework. Furthermore, the same TCSM objective extends to post-training of discrete diffusion models, including fine-tuning using reward functions or preference data, and distillation of knowledge from pre-trained autoregressive models. These new capabilities stem from the core idea of TCSM, estimating the concrete score of the target distribution, which resides in the original (clean) data space. This allows seamless integration with reward functions and pre-trained models, which inherently only operate in the clean data space rather than the noisy intermediate spaces of diffusion processes. Our experiments on language modeling tasks demonstrate that TCSM matches or surpasses current methods. Additionally, TCSM is versatile, applicable to both pre-training and post-training scenarios, offering greater flexibility and sample efficiency.

TabRep: a Simple and Effective Continuous Representation for Training Tabular Diffusion Models

Diffusion models have been the predominant generative model for tabular data generation. However, they face the conundrum of modeling under a separate versus a unified data representation. The former encounters the challenge of jointly modeling all multi-modal distributions of tabular data in one model. While the latter alleviates this by learning a single representation for all features, it currently leverages sparse suboptimal encoding heuristics and necessitates additional computation costs. In this work, we address the latter by presenting TabRep, a tabular diffusion architecture trained with a unified continuous representation. To motivate the design of our representation, we provide geometric insights into how the data manifold affects diffusion models. The key attributes of our representation are composed of its density, flexibility to provide ample separability for nominal features, and ability to preserve intrinsic relationships. Ultimately, TabRep provides a simple yet effective approach for training tabular diffusion models under a continuous data manifold. Our results showcase that TabRep achieves superior performance across a broad suite of evaluations. It is the first to synthesize tabular data that exceeds the downstream quality of the original datasets while preserving privacy and remaining computationally efficient.

Neural Flow Samplers with Shortcut Models

Sampling from unnormalized densities is a fundamental task across various domains. Flow-based samplers generate samples by learning a velocity field that satisfies the continuity equation, but this requires estimating the intractable time derivative of the partition function. While importance sampling provides an approximation, it suffers from high variance. To mitigate this, we introduce a velocity-driven Sequential Monte Carlo method combined with control variates to reduce variance. Additionally, we incorporate a shortcut model to improve efficiency by minimizing the number of sampling steps. Empirical results on both synthetic datasets and $n$-body system targets validate the effectiveness of our approach.

Towards Training One-Step Diffusion Models Without Distillation

Recent advances in one-step generative models typically follow a two-stage process: first training a teacher diffusion model and then distilling it into a one-step student model. This distillation process traditionally relies on both the teacher model's score function to compute the distillation loss and its weights for student initialization. In this paper, we explore whether one-step generative models can be trained directly without this distillation process. First, we show that the teacher's score function is not essential and propose a family of distillation methods that achieve competitive results without relying on score estimation. Next, we demonstrate that initialization from teacher weights is indispensable in successful training. Surprisingly, we find that this benefit is not due to improved ``input-output" mapping but rather the learned feature representations, which dominate distillation quality. Our findings provide a better understanding of the role of initialization in one-step model training and its impact on distillation quality.

Energy-Based Modelling for Discrete and Mixed Data via Heat Equations on Structured Spaces

Energy-based models (EBMs) offer a flexible framework for probabilistic modelling across various data domains. However, training EBMs on data in discrete or mixed state spaces poses significant challenges due to the lack of robust and fast sampling methods. In this work, we propose to train discrete EBMs with Energy Discrepancy, a loss function which only requires the evaluation of the energy function at data points and their perturbed counterparts, thus eliminating the need for Markov chain Monte Carlo. We introduce perturbations of the data distribution by simulating a diffusion process on the discrete state space endowed with a graph structure. This allows us to inform the choice of perturbation from the structure of the modelled discrete variable, while the continuous time parameter enables fine-grained control of the perturbation. Empirically, we demonstrate the efficacy of the proposed approaches in a wide range of applications, including the estimation of discrete densities with non-binary vocabulary and binary image modelling. Finally, we train EBMs on tabular data sets with applications in synthetic data generation and calibrated classification.

Mutual Information Multinomial Estimation

Estimating mutual information (MI) is a fundamental yet challenging task in data science and machine learning. This work proposes a new estimator for mutual information. Our main discovery is that a preliminary estimate of the data distribution can dramatically help estimate. This preliminary estimate serves as a bridge between the joint and the marginal distribution, and by comparing with this bridge distribution we can easily obtain the true difference between the joint distributions and the marginal distributions. Experiments on diverse tasks including non-Gaussian synthetic problems with known ground-truth and real-world applications demonstrate the advantages of our method.

Entropy-Based Decoding for Retrieval-Augmented Large Language Models

Augmenting Large Language Models (LLMs) with retrieved external knowledge has proven effective for improving the factual accuracy of generated responses. Despite their success, retrieval-augmented LLMs still face the distractibility issue, where the generated responses are negatively influenced by noise from both external and internal knowledge sources. In this paper, we introduce a novel, training-free decoding method guided by entropy considerations to mitigate this issue. Our approach utilizes entropy-based document-parallel ensemble decoding to prioritize low-entropy distributions from retrieved documents, thereby enhancing the extraction of relevant information of context. Additionally, it incorporates a contrastive decoding mechanism that contrasts the obtained low-entropy ensemble distribution with the high-entropy distribution derived from the model's internal knowledge across layers, which ensures a greater emphasis on reliable external information. Extensive experiments on open-domain question answering datasets demonstrate the superiority of our method.

Diffusion Model With Optimal Covariance Matching

The probabilistic diffusion model has become highly effective across various domains. Typically, sampling from a diffusion model involves using a denoising distribution characterized by a Gaussian with a learned mean and either fixed or learned covariances. In this paper, we leverage the recently proposed full covariance moment matching technique and introduce a novel method for learning covariances. Unlike traditional data-driven covariance approximation approaches, our method involves directly regressing the optimal analytic covariance using a new, unbiased objective named Optimal Covariance Matching (OCM). This approach can significantly reduce the approximation error in covariance prediction. We demonstrate how our method can substantially enhance the sampling efficiency of both Markovian (DDPM) and non-Markovian (DDIM) diffusion model families.