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Theory · Probabilistic Methods

Zikun Zhang, Zixiang Chen, Quanquan Gu

Diffusion models have achieved great success in generating high-dimensional samples across various applications. While the theoretical guarantees for continuous-state diffusion models have been extensively studied, the convergence analysis of the discrete-state counterparts remains under-explored. In this paper, we study the theoretical aspects of score-based discrete diffusion models under the Continuous Time Markov Chain (CTMC) framework. We introduce a discrete-time sampling algorithm in the general state space $[S]^d$ that utilizes score estimators at predefined time points. We derive convergence bounds for the Kullback-Leibler (KL) divergence and total variation (TV) distance between the generated sample distribution and the data distribution, considering both scenarios with and without early stopping under reasonable assumptions. Notably, our KL divergence bounds are nearly linear in the dimension $d$, aligning with state-of-the-art results for diffusion models. Our convergence analysis employs a Girsanov-based method and establishes key properties of the discrete score function, which are essential for characterizing the discrete-time sampling process.

Kaiwen Zheng, Guande He, Jianfei Chen, Fan Bao, Jun Zhu

Consistency distillation is a prevalent way for accelerating diffusion models adopted in consistency (trajectory) models, in which a student model is trained to traverse backward on the probability flow (PF) ordinary differential equation (ODE) trajectory determined by the teacher model. Preconditioning is a vital technique for stabilizing consistency distillation, by linear combining the input data and the network output with pre-defined coefficients as the consistency function. It imposes the boundary condition of consistency functions without restricting the form and expressiveness of the neural network. However, previous preconditionings are hand-crafted and may be suboptimal choices. In this work, we offer the first theoretical insights into the preconditioning in consistency distillation, by elucidating its design criteria and the connection to the teacher ODE trajectory. Based on these analyses, we further propose a principled way dubbed \textit{Analytic-Precond} to analytically optimize the preconditioning according to the consistency gap (defined as the gap between the teacher denoiser and the optimal student denoiser) on a generalized teacher ODE. We demonstrate that Analytic-Precond can facilitate the learning of trajectory jumpers, enhance the alignment of the student trajectory with the teacher's, and achieve $2\times$ to $3\times$ training acceleration of consistency trajectory models in multi-step generation across various datasets.

Deep Learning · Generative Models and Autoencoders

Kaiwen Zheng, Guande He, Jianfei Chen, Fan Bao, Jun Zhu

Denoising diffusion bridge models (DDBMs) are a powerful variant of diffusion models for interpolating between two arbitrary paired distributions given as endpoints. Despite their promising performance in tasks like image translation, DDBMs require a computationally intensive sampling process that involves the simulation of a (stochastic) differential equation through hundreds of network evaluations. In this work, we take the first step in fast sampling of DDBMs without extra training, motivated by the well-established recipes in diffusion models. We generalize DDBMs via a class of non-Markovian diffusion bridges defined on the discretized timesteps concerning sampling, which share the same marginal distributions and training objectives, give rise to generative processes ranging from stochastic to deterministic, and result in diffusion bridge implicit models (DBIMs). DBIMs are not only up to 25$\times$ faster than the vanilla sampler of DDBMs but also induce a novel, simple, and insightful form of ordinary differential equation (ODE) which inspires high-order numerical solvers. Moreover, DBIMs maintain the generation diversity in a distinguished way, by using a booting noise in the initial sampling step, which enables faithful encoding, reconstruction, and semantic interpolation in image translation tasks. Code is available at \url{https://github.com/thu-ml/DiffusionBridge}.

Deep Learning · Generative Models and Autoencoders

Kaiwen Zheng, Yongxin Chen, Hanzi Mao, Ming-Yu Liu, Jun Zhu, Qinsheng Zhang

Masked diffusion models (MDMs) have emerged as a popular research topic for generative modeling of discrete data, thanks to their superior performance over other discrete diffusion models, and are rivaling the auto-regressive models (ARMs) for language modeling tasks. The recent effort in simplifying the masked diffusion framework further leads to alignment with continuous-space diffusion models and more principled training and sampling recipes. In this paper, however, we reveal that both training and sampling of MDMs are theoretically free from the time variable, arguably the key signature of diffusion models, and are instead equivalent to masked models. The connection on the sampling aspect is drawn by our proposed first-hitting sampler (FHS). Specifically, we show that the FHS is theoretically equivalent to MDMs' original generation process while significantly alleviating the time-consuming categorical sampling and achieving a 20$\times$ speedup. In addition, our investigation raises doubts about whether MDMs can truly beat ARMs in text generation. We identify, for the first time, an underlying numerical issue, even with the commonly used 32-bit floating-point precision, which results in inaccurate categorical sampling. We show that it lowers the effective temperature both theoretically and empirically, and the resulting decrease in token diversity makes previous evaluations, which assess the generation quality solely through the incomplete generative perplexity metric, somewhat unfair.

Deep Learning · Robustness

Alexander Li, Ananya Kumar, Deepak Pathak

Discriminative approaches to classification often learn shortcuts that hold in-distribution but fail even under minor distribution shift. This failure mode stems from an overreliance on features that are spuriously correlated with the label. We show that generative classifiers, which use class-conditional generative models, can avoid this issue by modeling all features, both core and spurious, instead of mainly spurious ones. These generative classifiers are simple to train, avoiding the need for specialized augmentations, strong regularization, extra hyperparameters, or knowledge of the specific spurious correlations to avoid. We find that diffusion-based and autoregressive generative classifiers achieve state-of-the-art performance on five standard image and text distribution shift benchmarks and reduce the impact of spurious correlations in realistic applications, such as medical or satellite datasets. Finally, we carefully analyze a Gaussian toy setting to understand the inductive biases of generative classifiers, as well as the data properties that determine when generative classifiers outperform discriminative ones.

Zekun Wang, Mingyang Yi, Shuchen Xue, Zhenguo Li, Ming Liu, Bing Qin, Zhi-Ming Ma

Diffusion Probabilistic Models (DPMs) have achieved significant success in generative tasks. However, their training and sampling processes suffer from the issue of distribution mismatch. During the denoising process, the input data distributions differ between the training and inference stages, potentially leading to inaccurate data generation. To obviate this, we analyze the training objective of DPMs and theoretically demonstrate that this mismatch can be alleviated through Distributionally Robust Optimization (DRO), which is equivalent to performing robustness-driven Adversarial Training (AT) on DPMs. Furthermore, for the recently proposed Consistency Model (CM), which distills the inference process of the DPM, we prove that its training objective also encounters the mismatch issue. Fortunately, this issue can be mitigated by AT as well. Based on these insights, we propose to conduct efficient AT on both DPM and CM. Finally, extensive empirical studies validate the effectiveness of AT in diffusion-based models. The code is available at https://github.com/kugwzk/AT_Diff.

Applications · Language, Speech and Dialog

Keon Lee, Dong Won Kim, Jaehyeon Kim, Seungjun Chung, Jaewoong Cho

Large-scale latent diffusion models (LDMs) excel in content generation across various modalities, but their reliance on phonemes and durations in text-to-speech (TTS) limits scalability and access from other fields. While recent studies show potential in removing these domain-specific factors, performance remains suboptimal. In this work, we introduce DiTTo-TTS, a Diffusion Transformer (DiT)-based TTS model, to investigate whether LDM-based TTS can achieve state-of-the-art performance without domain-specific factors. Through rigorous analysis and empirical exploration, we find that (1) DiT with minimal modifications outperforms U-Net, (2) variable-length modeling with a speech length predictor significantly improves results over fixed-length approaches, and (3) conditions like semantic alignment in speech latent representations are key to further enhancement. By scaling our training data to 82K hours and the model size to 790M parameters, we achieve superior or comparable zero-shot performance to state-of-the-art TTS models in naturalness, intelligibility, and speaker similarity, all without relying on domain-specific factors. Speech samples are available at https://ditto-tts.github.io.

Zhengyang Geng, Ashwini Pokle, Weijian Luo, Justin Lin, Zico Kolter

Consistency models (CMs) offer faster sampling than traditional diffusion models, but their training is resource-intensive. For example, as of 2024, training a state-of-the-art CM on CIFAR-10 takes one week on 8 GPUs. In this work, we propose an effective scheme for training CMs that largely improves the efficiency of building such models. Specifically, by expressing CM trajectories via a particular differential equation, we argue that diffusion models can be viewed as a special case of CMs. We can thus fine-tune a consistency model starting from a pretrained diffusion model and progressively approximate the full consistency condition to stronger degrees over the training process. Our resulting method, which we term Easy Consistency Tuning (ECT), achieves vastly reduced training times while improving upon the quality of previous methods: for example, ECT achieves a 2-step FID of 2.73 on CIFAR10 within 1 hour on a single A100 GPU, matching Consistency Distillation trained for hundreds of GPU hours. Owing to this computational efficiency, we investigate the scaling laws of CMs under ECT, showing that they obey the classic power law scaling, hinting at their ability to improve efficiency and performance at larger scales. Our [code](https://github.com/locuslab/ect) is available.

Deep Learning · Generative Models and Autoencoders

Silas Alberti, Kenan Hasanaliyev, Manav Shah, Stefano Ermon

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.

Applications · Computer Vision

Kyeongmin Yeo, Jaihoon Kim, Minhyuk Sung

We propose a zero-shot method for generating images in arbitrary spaces (e.g., a sphere for 360◦ panoramas and a mesh surface for texture) using a pretrained image diffusion model. The zero-shot generation of various visual content using a pretrained image diffusion model has been explored mainly in two directions. First, Diffusion Synchronization–performing reverse diffusion processes jointly across different projected spaces while synchronizing them in the target space–generates high-quality outputs when enough conditioning is provided, but it struggles in its absence. Second, Score Distillation Sampling–gradually updating the target space data through gradient descent–results in better coherence but often lacks detail. In this paper, we reveal for the first time the interconnection between these two methods while highlighting their differences. To this end, we propose StochSync, a novel approach that combines the strengths of both, enabling effective performance with weak conditioning. Our experiments demonstrate that StochSync provides the best performance in 360◦ panorama generation (where image conditioning is not given), outperforming previous finetuning-based methods, and also delivers comparable results in 3D mesh texturing (where depth conditioning is provided) with previous methods.

Shansan Gong, Shivam Agarwal, Yizhe Zhang, Jiacheng Ye, Lin Zheng, Mukai Li, Chenxin An, Peilin Zhao, Wei BI, Jiawei Han 等

Diffusion Language Models (DLMs) have emerged as a promising new paradigm for text generative modeling, potentially addressing limitations of autoregressive (AR) models. However, current DLMs have been studied at a smaller scale compared to their AR counterparts and lack fair comparison on language modeling benchmarks. Additionally, training diffusion models from scratch at scale remains challenging. Given the prevalence of open-source AR language models, we propose adapting these models to build text diffusion models. We demonstrate connections between AR and diffusion modeling objectives and introduce a simple continual pre-training approach for training diffusion models. Through systematic evaluation on language modeling, reasoning, and commonsense benchmarks, we show that we can convert AR models ranging from 127M to 7B parameters (GPT2 and LLaMA) into diffusion models DiffuGPT and DiffuLLaMA, using less than 200B tokens for training. Our experimental results reveal that these models outperform earlier DLMs and are competitive with their AR counterparts. We release a suite of DLMs (127M-355M-7B) capable of generating fluent text, performing in-context learning, filling in the middle without prompt re-ordering, and following instructions.

Deep Learning · Generative Models and Autoencoders

Xiaofeng Lin, Chenheng Xu, Matthew Yang, Guang Cheng

Generative Foundation Models (GFMs) have achieved remarkable success in producing high-quality synthetic data for images and text. However, their application to tabular data presents significant challenges due to the heterogeneous nature of table features. Current cross-table learning frameworks struggle because they lack a generative model backbone and an effective mechanism to decode heterogeneous feature values. To address these challenges, we propose the Cross-Table Synthesizer (CTSyn), a diffusion-based generative foundation model for tabular data generation. CTSyn comprises two key components. The first is an autoencoder network that consolidates diverse tables into a unified latent space. It dynamically reconstructs table values using a table schema embedding, allowing adaptation to heterogeneous datasets. The second is a conditional latent diffusion model that generates samples from the learned latent space, conditioned on the table schema. Through large-scale pre-training, CTSyn outperforms existing table synthesizers on standard benchmarks in both utility and diversity. These results position CTSyn as a promising framework for synthetic table generation and lay the groundwork for developing large-scale tabular foundation models.

Deep Learning · Graph Neural Networks

Simon Heilig, Alessio Gravina, Alessandro Trenta, Claudio Gallicchio, Davide Bacciu

The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and regulate the degree of propagation and dissipation of information throughout the neural flow. Motivated by this, we introduce port-Hamiltonian Deep Graph Networks, a novel framework that models neural information flow in graphs by building on the laws of conservation of Hamiltonian dynamical systems. We reconcile under a single theoretical and practical framework both non-dissipative long-range propagation and non-conservative behaviors, introducing tools from mechanical systems to gauge the equilibrium between the two components. Our approach can be applied to general message-passing architectures, and it provides theoretical guarantees on information conservation in time. Empirical results prove the effectiveness of our port-Hamiltonian scheme in pushing simple graph convolutional architectures to state-of-the-art performance in long-range benchmarks.

Yi Shi 0008, Jingbo Wang 0003, Xuekun Jiang, Bingkun Lin, Bo Dai 0002, Xue Bin Peng

Real-time character control is an essential component for interactive experiences, with a broad range of applications, including physics simulations, video games, and virtual reality. The success of diffusion models for image synthesis has led to the use of these models for motion synthesis. However, the majority of these motion diffusion models are primarily designed for offline applications, where space-time models are used to synthesize an entire sequence of frames simultaneously with a pre-specified length. To enable real-time motion synthesis with diffusion model that allows time-varying controls, we propose A-MDM (Auto-regressive Motion Diffusion Model). Our conditional diffusion model takes an initial pose as input, and auto-regressively generates successive motion frames conditioned on the previous frame. Despite its streamlined network architecture, which uses simple MLPs, our framework is capable of generating diverse, long-horizon, and high-fidelity motion sequences. Furthermore, we introduce a suite of techniques for incorporating interactive controls into A-MDM, such as task-oriented sampling, in-painting, and hierarchical reinforcement learning (See Figure 1). These techniques enable a pre-trained A-MDM to be efficiently adapted for a variety of new downstream tasks. We conduct a comprehensive suite of experiments to demonstrate the effectiveness of A-MDM, and compare its performance against state-of-the-art auto-regressive methods.

Zheng Gu 0001, Shiyuan Yang, Jing Liao 0001, Jing Huo, Yang Gao 0001

Visual In-Context Learning (ICL) has emerged as a promising research area due to its capability to accomplish various tasks with limited example pairs through analogical reasoning. However, training-based visual ICL has limitations in its ability to generalize to unseen tasks and requires the collection of a diverse task dataset. On the other hand, existing methods in the inference-based visual ICL category solely rely on textual prompts, which fail to capture fine-grained contextual information from given examples and can be time-consuming when converting from images to text prompts. To address these challenges, we propose Analogist, a novel inference-based visual ICL approach that exploits both visual and textual prompting techniques using a text-to-image diffusion model pretrained for image inpainting. For visual prompting, we propose a self-attention cloning (SAC) method to guide the fine-grained structural-level analogy between image examples. For textual prompting, we leverage GPT-4V's visual reasoning capability to efficiently generate text prompts and introduce a cross-attention masking (CAM) operation to enhance the accuracy of semantic-level analogy guided by text prompts. Our method is out-of-the-box and does not require fine-tuning or optimization. It is also generic and flexible, enabling a wide range of visual tasks to be performed in an in-context manner. Extensive experiments demonstrate the superiority of our method over existing approaches, both qualitatively and quantitatively. Our project webpage is available at https://analogist2d.github.io.

Longwen Zhang, Ziyu Wang, Qixuan Zhang, Qiwei Qiu, Anqi Pang, Haoran Jiang, Wei Yang 0034, Lan Xu 0003, Jingyi Yu 0001

In the realm of digital creativity, our potential to craft intricate 3D worlds from imagination is often hampered by the limitations of existing digital tools, which demand extensive expertise and efforts. To narrow this disparity, we introduce CLAY, a 3D geometry and material generator designed to effortlessly transform human imagination into intricate 3D digital structures. CLAY supports classic text or image inputs as well as 3D-aware controls from diverse primitives (multi-view images, voxels, bounding boxes, point clouds, implicit representations, etc). At its core is a large-scale generative model composed of a multi-resolution Variational Autoencoder (VAE) and a minimalistic latent Diffusion Transformer (DiT), to extract rich 3D priors directly from a diverse range of 3D geometries. Specifically, it adopts neural fields to represent continuous and complete surfaces and uses a geometry generative module with pure transformer blocks in latent space. We present a progressive training scheme to train CLAY on an ultra large 3D model dataset obtained through a carefully designed processing pipeline, resulting in a 3D native geometry generator with 1.5 billion parameters. For appearance generation, CLAY sets out to produce physically-based rendering (PBR) textures by employing a multi-view material diffusion model that can generate 2K resolution textures with diffuse, roughness, and metallic modalities. We demonstrate using CLAY for a range of controllable 3D asset creations, from sketchy conceptual designs to production ready assets with intricate details. Even first time users can easily use CLAY to bring their vivid 3D imaginations to life, unleashing unlimited creativity.

Xiang Xu 0008, Joseph G. Lambourne, Pradeep Kumar Jayaraman, Zhengqing Wang, Karl D. D. Willis, Yasutaka Furukawa

This paper presents BrepGen, a diffusion-based generative approach that directly outputs a Boundary representation (B-rep) Computer-Aided Design (CAD) model. BrepGen represents a B-rep model as a novel structured latent geometry in a hierarchical tree. With the root node representing a whole CAD solid, each element of a B-rep model (i.e., a face, an edge, or a vertex) progressively turns into a child-node from top to bottom. B-rep geometry information goes into the nodes as the global bounding box of each primitive along with a latent code describing the local geometric shape. The B-rep topology information is implicitly represented by node duplication. When two faces share an edge, the edge curve will appear twice in the tree, and a T-junction vertex with three incident edges appears six times in the tree with identical node features. Starting from the root and progressing to the leaf, BrepGen employs Transformer-based diffusion models to sequentially denoise node features while duplicated nodes are detected and merged, recovering the B-Rep topology information. Extensive experiments show that BrepGen advances the task of CAD B-rep generation, surpassing existing methods on various benchmarks. Results on our newly collected furniture dataset further showcase its exceptional capability in generating complicated geometry. While previous methods were limited to generating simple prismatic shapes, BrepGen incorporates free-form and doubly-curved surfaces for the first time. Additional applications of BrepGen include CAD autocomplete and design interpolation. The code, pretrained models, and dataset are available at https://github.com/samxuxiang/BrepGen.

Arman Maesumi, Dylan Hu, Krishi Saripalli, Vladimir G. Kim, Matthew Fisher, Sören Pirk, Daniel Ritchie

Procedural noise is a fundamental component of computer graphics pipelines, offering a flexible way to generate textures that exhibit "natural" random variation. Many different types of noise exist, each produced by a separate algorithm. In this paper, we present a single generative model which can learn to generate multiple types of noise as well as blend between them. In addition, it is capable of producing spatially-varying noise blends despite not having access to such data for training. These features are enabled by training a denoising diffusion model using a novel combination of data augmentation and network conditioning techniques. Like procedural noise generators, the model's behavior is controllable via interpretable parameters plus a source of randomness. We use our model to produce a variety of visually compelling noise textures. We also present an application of our model to improving inverse procedural material design; using our model in place of fixed-type noise nodes in a procedural material graph results in higher-fidelity material reconstructions without needing to know the type of noise in advance. Open-sourced materials can be found at https://armanmaesumi.github.io/onenoise/

Daoyi Gao, Dávid Rozenberszki, Stefan Leutenegger, Angela Dai

Perceiving 3D structures from RGB images based on CAD model primitives can enable an effective, efficient 3D object-based representation of scenes. However, current approaches rely on supervision from expensive yet imperfect annotations of CAD models associated with real images, and encounter challenges due to the inherent ambiguities in the task - both in depth-scale ambiguity in monocular perception, as well as inexact matches of CAD database models to real observations. We thus propose DiffCAD, the first weakly-supervised probabilistic approach to CAD retrieval and alignment from an RGB image. We learn a probabilistic model through diffusion, modeling likely distributions of shape, pose, and scale of CAD objects in an image. This enables multi-hypothesis generation of different plausible CAD reconstructions, requiring only a few hypotheses to characterize ambiguities in depth/scale and inexact shape matches. Our approach is trained only on synthetic data, leveraging monocular depth and mask estimates to enable robust zero-shot adaptation to various real target domains. Despite being trained solely on synthetic data, our multi-hypothesis approach can even surpass the supervised state-of-the-art on the Scan2CAD dataset by 5.9% with 8 hypotheses.

Lvmin Zhang, Maneesh Agrawala

We present an approach enabling large-scale pretrained latent diffusion models to generate transparent images. The method allows generation of single transparent images or of multiple transparent layers. The method learns a "latent transparency" that encodes alpha channel transparency into the latent manifold of a pretrained latent diffusion model. It preserves the production-ready quality of the large diffusion model by regulating the added transparency as a latent offset with minimal changes to the original latent distribution of the pretrained model. In this way, any latent diffusion model can be converted into a transparent image generator by finetuning it with the adjusted latent space. We train the model with 1M transparent image layer pairs collected using a human-in-the-loop collection scheme. We show that latent transparency can be applied to different open source image generators, or be adapted to various conditional control systems to achieve applications like foreground/background-conditioned layer generation, joint layer generation, structural control of layer contents, etc. A user study finds that in most cases (97%) users prefer our natively generated transparent content over previous ad-hoc solutions such as generating and then matting. Users also report the quality of our generated transparent images is comparable to real commercial transparent assets like Adobe Stock.