ICLR 2025 论文列表

Data valuation plays a crucial role in machine learning. Existing data valuation methods, mainly focused on discriminative models, overlook generative models that have gained attention recently. In generative models, data valuation measures the impact of training data on generated datasets. Very few existing attempts at data valuation methods designed for deep generative models either concentrate on specific models or lack robustness in their outcomes. Moreover, efficiency still reveals vulnerable shortcomings. We formulate the data valuation problem in generative models from a similarity matching perspective to bridge the gaps. Specifically, we introduce Generative Model Valuator (GMValuator), the first training-free and model-agnostic approach to providing data valuation for image generation tasks. It empowers efficient data valuation through our innovative similarity matching module, calibrates biased contributions by incorporating image quality assessment, and attributes credits to all training samples based on their contributions to the generated samples. Additionally, we introduce four evaluation criteria for assessing data valuation methods in generative models. GMValuator is extensively evaluated on benchmark and high-resolution datasets and various mainstream generative architectures to demonstrate its effectiveness. Our code is available at: https://github.com/ubc-tea/GMValuator.

Mechanical meta-materials are solids whose geometric structure results in exotic nonlinear behaviors that are not typically achievable via homogeneous materials. We show how to drastically expand the design space of a class of mechanical meta-materials known as $\textit{cellular solids}$, by generalizing beyond translational symmetry. This is made possible by transforming a reference geometry according to a divergence free flow that is parameterized by a neural network and equivariant under the relevant symmetry group. We show how to construct flows equivariant to the space groups, despite the fact that these groups are not compact. Coupling this flow with a differentiable nonlinear mechanics simulator allows us to represent a much richer set of cellular solids than was previously possible. These materials can be optimized to exhibit desirable mechanical properties such as negative Poisson's ratios or to match target stress-strain curves. We validate these new designs in simulation and by fabricating real-world prototypes. We find that designs with higher-order symmetries can exhibit a wider range of behaviors.

We deal with the task of sampling from an unnormalized Boltzmann density $\rho_D$ by learning a Boltzmann curve given by energies $f_t$ starting in a simple density $\rho_Z$. First, we examine conditions under which Fisher-Rao flows are absolutely continuous in the Wasserstein geometry. Second, we address specific interpolations $f_t$ and the learning of the related density/velocity pairs $(\rho_t,v_t)$. It was numerically observed that the linear interpolation, which requires only a parametrization of the velocity field $v_t$, suffers from a "teleportation-of-mass" issue. Using tools from the Wasserstein geometry, we give an analytical example, where we can precisely measure the explosion of the velocity field. Inspired by Máté and Fleuret, who parametrize both $f_t$ and $v_t$, we propose an interpolation which parametrizes only $f_t$ and fixes an appropriate $v_t$. This corresponds to the Wasserstein gradient flow of the Kullback-Leibler divergence related to Langevin dynamics. We demonstrate by numerical examples that our model provides a well-behaved flow field which successfully solves the above sampling task.

Recent work has shown that diffusion models memorize and reproduce training data examples. At the same time, large copyright lawsuits and legislation such as GDPR have highlighted the need for erasing datapoints from diffusion models. However, retraining from scratch is often too expensive. This motivates the setting of data unlearning, i.e., the study of efficient techniques for unlearning specific datapoints from the training set. Existing concept unlearning techniques require an anchor prompt/class/distribution to guide unlearning, which is not available in the data unlearning setting. General-purpose machine unlearning techniques were found to be either unstable or failed to unlearn data. We therefore propose a family of new loss functions called Subtracted Importance Sampled Scores (SISS) that utilize importance sampling and are the first method to unlearn data with theoretical guarantees. SISS is constructed as a weighted combination between simpler objectives that are responsible for preserving model quality and unlearning the targeted datapoints. When evaluated on CelebA-HQ and MNIST, SISS achieved Pareto optimality along the quality and unlearning strength dimensions. On Stable Diffusion, SISS successfully mitigated memorization on nearly 90% of the prompts we tested. We release our code online.

We propose a gradient flow procedure for generative modeling by transporting particles from an initial source distribution to a target distribution, where the gradient field on the particles is given by a noise-adaptive Wasserstein Gradient of the Maximum Mean Discrepancy (MMD). The noise adaptive MMD is trained on data distributions corrupted by increasing levels of noise, obtained via a forward diffusion process, as commonly used in denoising diffusion probabilistic models. The result is a generalization of MMD Gradient Flow, which we call Diffusion-MMD-Gradient Flow or DMMD. The divergence training procedure is related to discriminator training in Generative Adversarial Networks (GAN), but does not require adversarial training. We obtain competitive empirical performance in unconditional image generation on CIFAR10, MNIST, CELEB-A (64 x64) and LSUN Church (64 x 64). Furthermore, we demonstrate the validity of the approach when MMD is replaced by a lower bound on the KL divergence.

Generative models have shown impressive capabilities in synthesizing high-quality outputs across various domains. However, a persistent challenge is the occurrence of "hallucinations," where the model produces outputs that are not grounded in the underlying facts. While empirical strategies have been explored to mitigate this issue, a rigorous theoretical understanding remains elusive. In this paper, we develop a theoretical framework to analyze the *learnability* of non-hallucinating generative models from a learning-theoretic perspective. Our results reveal that non-hallucinating learning is statistically *impossible* when relying solely on the training dataset, even for a hypothesis class of size two and when the entire training set is truthful. To overcome these limitations, we show that incorporating *inductive biases* aligned with the actual facts into the learning process is essential. We provide a systematic approach to achieve this by restricting the fact set to a concept class of finite VC-dimension and demonstrate its effectiveness under various learning paradigms. Although our findings are primarily conceptual, they represent a first step towards a principled approach to addressing hallucinations in learning generative models.

Discrete diffusion has achieved state-of-the-art performance, outperforming or approaching autoregressive models on standard benchmarks. In this work, we introduce *Discrete Diffusion with Planned Denoising* (DDPD), a novel framework that separates the generation process into two models: a planner and a denoiser. At inference time, the planner selects which positions to denoise next by identifying the most corrupted positions in need of denoising, including both initially corrupted and those requiring additional refinement. This plan-and-denoise approach enables more efficient reconstruction during generation by iteratively identifying and denoising corruptions in the optimal order. DDPD outperforms traditional denoiser-only mask diffusion methods, achieving superior results on language modeling benchmarks such as *text8*, *OpenWebText*, and token-based generation on *ImageNet 256 × 256*. Notably, in language modeling, DDPD significantly reduces the performance gap between diffusion-based and autoregressive methods in terms of generative perplexity. Code is available at [github.com/liusulin/DDPD](https://github.com/liusulin/DDPD).

Normalizing Flows (NFs) are powerful and efficient models for density estimation. When modeling densities on manifolds, NFs can be generalized to injective flows but the Jacobian determinant becomes computationally prohibitive. Current approaches either consider bounds on the log-likelihood or rely on some approximations of the Jacobian determinant. In contrast, we propose injective flows for star-like manifolds and show that for such manifolds we can compute the Jacobian determinant exactly and efficiently. This aspect is particularly relevant for variational inference settings, where no samples are available and only some unnormalized target is known. Among many, we showcase the relevance of modeling densities on star-like manifolds in two settings. Firstly, we introduce a novel Objective Bayesian approach for penalized likelihood models by interpreting level-sets of the penalty as star-like manifolds. Secondly, we consider probabilistic mixing models and introduce a general method for variational inference by defining the posterior of mixture weights on the probability simplex.

Vector Quantized Variational AutoEncoders (VQ-VAEs) are designed to compress a continuous input to a discrete latent space and reconstruct it with minimal distortion. They operate by maintaining a set of vectors---often referred to as the codebook---and quantizing each encoder output to the nearest vector in the codebook. However, as vector quantization is non-differentiable, the gradient to the encoder flows _around_ the vector quantization layer rather than _through_ it in a straight-through approximation. This approximation may be undesirable as all information from the vector quantization operation is lost. In this work, we propose a way to propagate gradients through the vector quantization layer of VQ-VAEs. We smoothly transform each encoder output into its corresponding codebook vector via a rotation and rescaling linear transformation that is treated as a constant during backpropagation. As a result, the relative magnitude and angle between encoder output and codebook vector becomes encoded into the gradient as it propagates through the vector quantization layer and back to the encoder. Across 11 different VQ-VAE training paradigms, we find this restructuring improves reconstruction metrics, codebook utilization, and quantization error.

Since WGANs were first introduced, there has been considerable debate whether their success in generating realistic images can be attributed to minimizing the Wasserstein distance between the distribution of generated images and the training distribution. In this paper we present theoretical and experimental results that show that successful WGANs {\em do} minimize the Wasserstein distance but the form of the distance that is minimized depends highly on the discriminator architecture and its inductive biases. Specifically, we show that when the discriminator is convolutional, WGANs minimize the Wasserstein distance between {\em patches} in the generated images and the training images, not the Wasserstein distance between images. Our results are obtained by considering {\em discrete} generators for which the Wasserstein distance between the generator distribution and the training distribution can be computed exactly and the minimum can be characterized analytically. We present experimental results with discrete GANs that generate realistic fake images (comparable in quality to their continuous counterparts) and present evidence that they are minimizing the Wasserstein distance between real and fake patches and not the distance between real and fake images.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Learning generative models of 3D point clouds is one of the fundamental problems in 3D generative learning. One of the key properties of point clouds is their permutation invariance, i.e., changing the order of points in a point cloud does not change the shape they represent. In this paper, we analyze the recently proposed equivariant OT flows that learn permutation invariant generative models for point-based molecular data and we show that these models scale poorly on large point clouds. Also, we observe learning (equivariant) OT flows is generally challenging since straightening flow trajectories makes the learned flow model complex at the beginning of the trajectory. To remedy these, we propose not-so-optimal transport flow models that obtain an approximate OT by an offline OT precomputation, enabling an efficient construction of OT pairs for training. During training, we can additionally construct a hybrid coupling by combining our approximate OT and independent coupling to make the target flow models easier to learn. In an extensive empirical study, we show that our proposed model outperforms prior diffusion- and flow -based approaches on a wide range of unconditional generation and shape completion on the ShapeNet benchmark.

Generative Flow Networks (GFlowNets) are a novel class of generative models designed to sample from unnormalized distributions and have found applications in various important tasks, attracting great research interest in their training algorithms. In general, GFlowNets are trained by fitting the forward flow to the backward flow on sampled training objects. Prior work focused on the choice of training objects, parameterizations, sampling and resampling strategies, and backward policies, aiming to enhance credit assignment, exploration, or exploitation of the training process. However, the choice of regression loss, which can highly influence the exploration and exploitation behavior of the under-training policy, has been overlooked. Due to the lack of theoretical understanding for choosing an appropriate regression loss, most existing algorithms train the flow network by minimizing the squared error of the forward and backward flows in log-space, i.e., using the quadratic regression loss. In this work, we rigorously prove that distinct regression losses correspond to specific divergence measures, enabling us to design and analyze regression losses according to the desired properties of the corresponding divergence measures. Specifically, we examine two key properties: zero-forcing and zero-avoiding, where the former promotes exploitation and higher rewards, and the latter encourages exploration and enhances diversity. Based on our theoretical framework, we propose three novel regression losses, namely, Shifted-Cosh, Linex(1/2), and Linex(1). We evaluate them across three benchmarks: hyper-grid, bit-sequence generation, and molecule generation. Our proposed losses are compatible with most existing training algorithms, and significantly improve the performances of the algorithms concerning convergence speed, sample diversity, and robustness.

Flow matching (FM) has gained significant attention as a simulation-free generative model. Unlike diffusion models, which are based on stochastic differential equations, FM employs a simpler approach by solving an ordinary differential equation with an initial condition from a normal distribution, thus streamlining the sample generation process. This paper discusses the convergence properties of FM in terms of the $p$-Wasserstein distance, a measure of distributional discrepancy. We establish that FM can achieve an almost minimax optimal convergence rate for $1 \leq p \leq 2$, presenting the first theoretical evidence that FM can reach convergence rates comparable to those of diffusion models. Our analysis extends existing frameworks by examining a broader class of mean and variance functions for the vector fields and identifies specific conditions necessary to attain these optimal rates.