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.

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.

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.

Training Discrete Energy-Based Models with Energy Discrepancy

Training energy-based models (EBMs) on discrete spaces is challenging because sampling over such spaces can be difficult. We propose to train discrete EBMs with energy discrepancy (ED), a novel type of contrastive loss functional which only requires the evaluation of the energy function at data points and their perturbed counter parts, thus not relying on sampling strategies like Markov chain Monte Carlo (MCMC). Energy discrepancy offers theoretical guarantees for a broad class of perturbation processes of which we investigate three types: perturbations based on Bernoulli noise, based on deterministic transforms, and based on neighbourhood structures. We demonstrate their relative performance on lattice Ising models, binary synthetic data, and discrete image data sets.

Energy Discrepancies: A Score-Independent Loss for Energy-Based Models

Energy-based models are a simple yet powerful class of probabilistic models, but their widespread adoption has been limited by the computational burden of training them. We propose a novel loss function called Energy Discrepancy (ED) which does not rely on the computation of scores or expensive Markov chain Monte Carlo. We show that ED approaches the explicit score matching and negative log-likelihood loss under different limits, effectively interpolating between both. Consequently, minimum ED estimation overcomes the problem of nearsightedness encountered in score-based estimation methods, while also enjoying theoretical guarantees. Through numerical experiments, we demonstrate that ED learns low-dimensional data distributions faster and more accurately than explicit score matching or contrastive divergence. For high-dimensional image data, we describe how the manifold hypothesis puts limitations on our approach and demonstrate the effectiveness of energy discrepancy by training the energy-based model as a prior of a variational decoder model.

Modeling Semantic Composition with Syntactic Hypergraph for Video Question Answering

A key challenge in video question answering is how to realize the cross-modal semantic alignment between textual concepts and corresponding visual objects. Existing methods mostly seek to align the word representations with the video regions. However, word representations are often not able to convey a complete description of textual concepts, which are in general described by the compositions of certain words. To address this issue, we propose to first build a syntactic dependency tree for each question with an off-the-shelf tool and use it to guide the extraction of meaningful word compositions. Based on the extracted compositions, a hypergraph is further built by viewing the words as nodes and the compositions as hyperedges. Hypergraph convolutional networks (HCN) are then employed to learn the initial representations of word compositions. Afterwards, an optimal transport based method is proposed to perform cross-modal semantic alignment for the textual and visual semantic space. To reflect the cross-modal influences, the cross-modal information is incorporated into the initial representations, leading to a model named cross-modality-aware syntactic HCN. Experimental results on three benchmarks show that our method outperforms all strong baselines. Further analyses demonstrate the effectiveness of each component, and show that our model is good at modeling different levels of semantic compositions and filtering out irrelevant information.

Learning Set Functions Under the Optimal Subset Oracle via Equivariant Variational Inference

Learning set functions becomes increasingly more important in many applications like product recommendation and compound selection in AI-aided drug discovery. The majority of existing works study methodologies of set function learning under the function value oracle, which, however, requires expensive supervision signals. This renders it impractical for applications with only weak supervisions under the Optimal Subset (OS) oracle, the study of which is surprisingly overlooked. In this work, we present a principled yet practical maximum likelihood learning framework, termed as EquiVSet, that simultaneously meets the following desiderata of learning set functions under the OS oracle: i) permutation invariance of the set mass function being modeled; ii) permission of varying ground set; iii) fully differentiability; iv) minimum prior; and v) scalability. The main components of our framework involve: an energy-based treatment of the set mass function, DeepSet-style architectures to handle permutation invariance, mean-field variational inference, and its amortized variants. Although the framework is embarrassingly simple, empirical studies on three real-world applications (including Amazon product recommendation, set anomaly detection and compound selection for virtual screening) demonstrate that EquiVSet outperforms the baselines by a large margin.