Maximum Entropy Inverse Reinforcement Learning of Diffusion Models with Energy-Based Models

We present a maximum entropy inverse reinforcement learning (IRL) approach for improving the sample quality of diffusion generative models, especially when the number of generation time steps is small. Similar to how IRL trains a policy based on the reward function learned from expert demonstrations, we train (or fine-tune) a diffusion model using the log probability density estimated from training data. Since we employ an energy-based model (EBM) to represent the log density, our approach boils down to the joint training of a diffusion model and an EBM. Our IRL formulation, named Diffusion by Maximum Entropy IRL (DxMI), is a minimax problem that reaches equilibrium when both models converge to the data distribution. The entropy maximization plays a key role in DxMI, facilitating the exploration of the diffusion model and ensuring the convergence of the EBM. We also propose Diffusion by Dynamic Programming (DxDP), a novel reinforcement learning algorithm for diffusion models, as a subroutine in DxMI. DxDP makes the diffusion model update in DxMI efficient by transforming the original problem into an optimal control formulation where value functions replace back-propagation in time. Our empirical studies show that diffusion models fine-tuned using DxMI can generate high-quality samples in as few as 4 and 10 steps. Additionally, DxMI enables the training of an EBM without MCMC, stabilizing EBM training dynamics and enhancing anomaly detection performance.

Generalized Contrastive Divergence: Joint Training of Energy-Based Model and Diffusion Model through Inverse Reinforcement Learning

We present Generalized Contrastive Divergence (GCD), a novel objective function for training an energy-based model (EBM) and a sampler simultaneously. GCD generalizes Contrastive Divergence (Hinton, 2002), a celebrated algorithm for training EBM, by replacing Markov Chain Monte Carlo (MCMC) distribution with a trainable sampler, such as a diffusion model. In GCD, the joint training of EBM and a diffusion model is formulated as a minimax problem, which reaches an equilibrium when both models converge to the data distribution. The minimax learning with GCD bears interesting equivalence to inverse reinforcement learning, where the energy corresponds to a negative reward, the diffusion model is a policy, and the real data is expert demonstrations. We present preliminary yet promising results showing that joint training is beneficial for both EBM and a diffusion model. GCD enables EBM training without MCMC while improving the sample quality of a diffusion model.

Variational Weighting for Kernel Density Ratios

Kernel density estimation (KDE) is integral to a range of generative and discriminative tasks in machine learning. Drawing upon tools from the multidimensional calculus of variations, we derive an optimal weight function that reduces bias in standard kernel density estimates for density ratios, leading to improved estimates of prediction posteriors and information-theoretic measures. In the process, we shed light on some fundamental aspects of density estimation, particularly from the perspective of algorithms that employ KDEs as their main building blocks.

Energy-Based Models for Anomaly Detection: A Manifold Diffusion Recovery Approach

We present a new method of training energy-based models (EBMs) for anomaly detection that leverages low-dimensional structures within data. The proposed algorithm, Manifold Projection-Diffusion Recovery (MPDR), first perturbs a data point along a low-dimensional manifold that approximates the training dataset. Then, EBM is trained to maximize the probability of recovering the original data. The training involves the generation of negative samples via MCMC, as in conventional EBM training, but from a different distribution concentrated near the manifold. The resulting near-manifold negative samples are highly informative, reflecting relevant modes of variation in data. An energy function of MPDR effectively learns accurate boundaries of the training data distribution and excels at detecting out-of-distribution samples. Experimental results show that MPDR exhibits strong performance across various anomaly detection tasks involving diverse data types, such as images, vectors, and acoustic signals.

Evaluating Out-of-Distribution Detectors Through Adversarial Generation of Outliers

A reliable evaluation method is essential for building a robust out-of-distribution (OOD) detector. Current robustness evaluation protocols for OOD detectors rely on injecting perturbations to outlier data. However, the perturbations are unlikely to occur naturally or not relevant to the content of data, providing a limited assessment of robustness. In this paper, we propose Evaluation-via-Generation for OOD detectors (EvG), a new protocol for investigating the robustness of OOD detectors under more realistic modes of variation in outliers. EvG utilizes a generative model to synthesize plausible outliers, and employs MCMC sampling to find outliers misclassified as in-distribution with the highest confidence by a detector. We perform a comprehensive benchmark comparison of the performance of state-of-the-art OOD detectors using EvG, uncovering previously overlooked weaknesses.

Autoencoding Under Normalization Constraints

Likelihood is a standard estimate for outlier detection. The specific role of the normalization constraint is to ensure that the out-of-distribution (OOD) regime has a small likelihood when samples are learned using maximum likelihood. Because autoencoders do not possess such a process of normalization, they often fail to recognize outliers even when they are obviously OOD. We propose the Normalized Autoencoder (NAE), a normalized probabilistic model constructed from an autoencoder. The probability density of NAE is defined using the reconstruction error of an autoencoder, which is differently defined in the conventional energy-based model. In our model, normalization is enforced by suppressing the reconstruction of negative samples, significantly improving the outlier detection performance. Our experimental results confirm the efficacy of NAE, both in detecting outliers and in generating in-distribution samples.

Image-to-Image Retrieval by Learning Similarity between Scene Graphs

As a scene graph compactly summarizes the high-level content of an image in a structured and symbolic manner, the similarity between scene graphs of two images reflects the relevance of their contents. Based on this idea, we propose a novel approach for image-to-image retrieval using scene graph similarity measured by graph neural networks. In our approach, graph neural networks are trained to predict the proxy image relevance measure, computed from human-annotated captions using a pre-trained sentence similarity model. We collect and publish the dataset for image relevance measured by human annotators to evaluate retrieval algorithms. The collected dataset shows that our method agrees well with the human perception of image similarity than other competitive baselines.