ICLR 2024 Papers

International Conference on Learning Representations

Decision breakdown

2,260papers

Counted from the official paper list; may differ slightly from the number the conference announced.

  • Oral
    863.8%
  • Spotlight
    36716.2%
  • Poster
    1,80780.0%

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Topic: Diffusion Models · 260 papers · Reset filters

De novo Protein Design Using Geometric Vector Field Networks

Weian Mao, Muzhi Zhu, Zheng Sun, Shuaike Shen, Lin Yuanbo Wu, Hao Chen, Chunhua Shen

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Advances like protein diffusion have marked revolutionary progress in $\textit{de novo}$ protein design, a central topic in life science. These methods typically depend on protein structure encoders to model residue backbone frames, where atoms do not exist. Most prior encoders rely on atom-wise features, such as angles and distances between atoms, which are not available in this context. Only a few basic encoders, like IPA, have been proposed for this scenario, exposing the frame modeling as a bottleneck. In this work, we introduce the Vector Field Network (VFN), that enables network layers to perform learnable vector computations between coordinates of frame-anchored virtual atoms, thus achieving a higher capability for modeling frames. The vector computation operates in a manner similar to a linear layer, with each input channel receiving 3D virtual atom coordinates instead of scalar values. The multiple feature vectors output by the vector computation are then used to update the residue representations and virtual atom coordinates via attention aggregation. Remarkably, VFN also excels in modeling both frames and atoms, as the real atoms can be treated as the virtual atoms for modeling, positioning VFN as a potential $\textit{universal encoder}$. In protein diffusion (frame modeling), VFN exhibits a impressive performance advantage over IPA, excelling in terms of both designability ($\textbf{67.04}$\% vs. 53.58\%) and diversity ($\textbf{66.54}$\% vs. 51.98\%). In inverse folding(frame and atom modeling), VFN outperforms the previous SoTA model, PiFold ($\textbf{54.7}$\% vs. 51.66\%), on sequence recovery rate; we also propose a method of equipping VFN with the ESM model, which significantly surpasses the previous ESM-based SoTA ($\textbf{62.67}$\% vs. 55.65\%), LM-Design, by a substantial margin. Code is available at https://github.com/aim-uofa/VFN

Spotlight
ED-NeRF: Efficient Text-Guided Editing of 3D Scene With Latent Space NeRF

JangHo Park, Gihyun Kwon, Jong Chul Ye

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Recently, there has been a significant advancement in text-to-image diffusion models, leading to groundbreaking performance in 2D image generation. These advancements have been extended to 3D models, enabling the generation of novel 3D objects from textual descriptions. This has evolved into NeRF editing methods, which allow the manipulation of existing 3D objects through textual conditioning. However, existing NeRF editing techniques have faced limitations in their performance due to slow training speeds and the use of loss functions that do not adequately consider editing. To address this, here we present a novel 3D NeRF editing approach dubbed ED-NeRF by successfully embedding real-world scenes into the latent space of the latent diffusion model (LDM) through a unique refinement layer. This approach enables us to obtain a NeRF backbone that is not only faster but also more amenable to editing compared to traditional image space NeRF editing. Furthermore, we propose an improved loss function tailored for editing by migrating the delta denoising score (DDS) distillation loss, originally used in 2D image editing to the three-dimensional domain. This novel loss function surpasses the well-known score distillation sampling (SDS) loss in terms of suitability for editing purposes. Our experimental results demonstrate that ED-NeRF achieves faster editing speed while producing improved output quality compared to state-of-the-art 3D editing models.

Poster
Elucidating the design space of classifier-guided diffusion generation

Jiajun Ma, Tianyang Hu, Wenjia Wang, Jiacheng Sun

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Guidance in conditional diffusion generation is of great importance for sample quality and controllability. However, existing guidance schemes are to be desired. On one hand, mainstream methods such as classifier guidance and classifier-free guidance both require extra training with labeled data, which is time-consuming and unable to adapt to new conditions. On the other hand, training-free methods such as universal guidance, though more flexible, have yet to demonstrate comparable performance. In this work, through a comprehensive investigation into the design space, we show that it is possible to achieve significant performance improvements over existing guidance schemes by leveraging off-the-shelf classifiers in a training-free fashion, enjoying the best of both worlds. Employing calibration as a general guideline, we propose several pre-conditioning techniques to better exploit pretrained off-the-shelf classifiers for guiding diffusion generation. Extensive experiments on ImageNet validate our proposed method, showing that state-of-the-art (SOTA) diffusion models (DDPM, EDM, DiT) can be further improved (up to 20\%) using off-the-shelf classifiers with barely any extra computational cost. With the proliferation of publicly available pretrained classifiers, our proposed approach has great potential and can be readily scaled up to text-to-image generation tasks.

Poster
On gauge freedom, conservativity and intrinsic dimensionality estimation in diffusion models

Christian Horvat, Jean-Pascal Pfister

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Diffusion models are generative models that have recently demonstrated impressive performances in terms of sampling quality and density estimation in high dimensions. They rely on a forward continuous diffusion process and a backward continuous denoising process, which can be described by a time-dependent vector field and is used as a generative model. In the original formulation of the diffusion model, this vector field is assumed to be the score function (i.e. it is the gradient of the log-probability at a given time in the diffusion process). Curiously, on the practical side, most studies on diffusion models implement this vector field as a neural network function and do not constrain it be the gradient of some energy function (that is, most studies do not constrain the vector field to be conservative). Even though some studies investigated empirically whether such a constraint will lead to a performance gain, they lead to contradicting results and failed to provide analytical results. Here, we provide three analytical results regarding the extent of the modeling freedom of this vector field. {Firstly, we propose a novel decomposition of vector fields into a conservative component and an orthogonal component which satisfies a given (gauge) freedom. Secondly, from this orthogonal decomposition, we show that exact density estimation and exact sampling is achieved when the conservative component is exactly equals to the true score and therefore conservativity is neither necessary nor sufficient to obtain exact density estimation and exact sampling. Finally, we show that when it comes to inferring local information of the data manifold, constraining the vector field to be conservative is desirable.

Poster
DiffEnc: Variational Diffusion with a Learned Encoder

Beatrix Miranda Ginn Nielsen, Anders Christensen, Andrea Dittadi, Ole Winther

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Diffusion models may be viewed as hierarchical variational autoencoders (VAEs) with two improvements: parameter sharing for the conditionals in the generative process and efficient computation of the loss as independent terms over the hierarchy. We consider two changes to the diffusion model that retain these advantages while adding flexibility to the model. Firstly, we introduce a data and depth-dependent mean function in the diffusion process, which leads to a modified diffusion loss. Our proposed framework, DiffEnc, achieves a statistically significant improvement in likelihood on CIFAR-10. Secondly, we let the ratio of the noise variance of the reverse encoder process and the generative process be a free weight parameter rather than being fixed to one. This leads to theoretical insights: For a finite depth hierarchy, the evidence lower bound (ELBO) can be used as an objective for a weighted diffusion loss approach and for optimizing the noise schedule specifically for inference. For the infinite-depth hierarchy, on the other hand, the weight parameter has to be one to have a well-defined ELBO.

Poster
R&B: Region and Boundary Aware Zero-shot Grounded Text-to-image Generation

Jiayu Xiao, Henglei Lv, Liang Li, Shuhui Wang, Qingming Huang

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Recent text-to-image (T2I) diffusion models have achieved remarkable progress in generating high-quality images given text-prompts as input. However, these models fail to convey appropriate spatial composition specified by a layout instruction. In this work, we probe into zero-shot grounded T2I generation with diffusion models, that is, generating images corresponding to the input layout information without training auxiliary modules or finetuning diffusion models. We propose a **R**egion and **B**oundary (R&B) aware cross-attention guidance approach that gradually modulates the attention maps of diffusion model during generative process, and assists the model to synthesize images (1) with high fidelity, (2) highly compatible with textual input, and (3) interpreting layout instructions accurately. Specifically, we leverage the discrete sampling to bridge the gap between consecutive attention maps and discrete layout constraints, and design a region-aware loss to refine the generative layout during diffusion process. We further propose a boundary-aware loss to strengthen object discriminability within the corresponding regions. Experimental results show that our method outperforms existing state-of-the-art zero-shot grounded T2I generation methods by a large margin both qualitatively and quantitatively on several benchmarks. Project page: https://sagileo.github.io/Region-and-Boundary.

Poster
Local Graph Clustering with Noisy Labels

Artur Back de Luca, Kimon Fountoulakis, Shenghao Yang

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The growing interest in machine learning problems over graphs with additional node information such as texts, images, or labels has popularized methods that require the costly operation of processing the entire graph. Yet, little effort has been made to the development of fast local methods (i.e. without accessing the entire graph) that extract useful information from such data. To that end, we propose a study of local graph clustering using noisy node labels as a proxy for additional node information. In this setting, nodes receive initial binary labels based on cluster affiliation: 1 if they belong to the target cluster and 0 otherwise. Subsequently, a fraction of these labels is flipped. We investigate the benefits of incorporating noisy labels for local graph clustering. By constructing a weighted graph with such labels, we study the performance of graph diffusion-based local clustering method on both the original and the weighted graphs. From a theoretical perspective, we consider recovering an unknown target cluster with a single seed node in a random graph with independent noisy node labels. We provide sufficient conditions on the label noise under which, with high probability, using diffusion in the weighted graph yields a more accurate recovery of the target cluster. This approach proves more effective than using the given labels alone or using diffusion in the label-free original graph. Empirically, we show that reliable node labels can be obtained with just a few samples from an attributed graph. Moreover, utilizing these labels via diffusion in the weighted graph leads to significantly better local clustering performance across several real-world datasets, improving F1 scores by up to 13\%.

Poster
Detecting, Explaining, and Mitigating Memorization in Diffusion Models

Yuxin Wen, Yuchen Liu, Chen Chen, Lingjuan Lyu

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Recent breakthroughs in diffusion models have exhibited exceptional image-generation capabilities. However, studies show that some outputs are merely replications of training data. Such replications present potential legal challenges for model owners, especially when the generated content contains proprietary information. In this work, we introduce a straightforward yet effective method for detecting memorized prompts by inspecting the magnitude of text-conditional predictions. Our proposed method seamlessly integrates without disrupting sampling algorithms, and delivers high accuracy even at the first generation step, with a single generation per prompt. Building on our detection strategy, we unveil an explainable approach that shows the contribution of individual words or tokens to memorization. This offers an interactive medium for users to adjust their prompts. Moreover, we propose two strategies i.e., to mitigate memorization by leveraging the magnitude of text-conditional predictions, either through minimization during inference or filtering during training. These proposed strategies effectively counteract memorization while maintaining high-generation quality. Code is available at https://github.com/YuxinWenRick/diffusion_memorization.

Oral
Continuous-Multiple Image Outpainting in One-Step via Positional Query and A Diffusion-based Approach

Shaofeng Zhang, Jinfa Huang, Qiang Zhou, Zhibin Wang, Fan Wang, Jiebo Luo, Junchi Yan

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Image outpainting aims to generate the content of an input sub-image beyond its original boundaries. It is an important task in content generation yet remains an open problem for generative models. This paper pushes the technical frontier of image outpainting in two directions that have not been resolved in literature: 1) outpainting with arbitrary and continuous multiples (without restriction), and 2) outpainting in a single step (even for large expansion multiples). Moreover, we develop a method that does not depend on a pre-trained backbone network, which is in contrast commonly required by the previous SOTA outpainting methods. The arbitrary multiple outpainting is achieved by utilizing randomly cropped views from the same image during training to capture arbitrary relative positional information. Specifically, by feeding one view and positional embeddings as queries, we can reconstruct another view. At inference, we generate images with arbitrary expansion multiples by inputting an anchor image and its corresponding positional embeddings. The one-step outpainting ability here is particularly noteworthy in contrast to previous methods that need to be performed for $N$ times to obtain a final multiple which is $N$ times of its basic and fixed multiple. We evaluate the proposed approach (called PQDiff as we adopt a diffusion-based generator as our embodiment, under our proposed \textbf{P}ositional \textbf{Q}uery scheme) on public benchmarks, demonstrating its superior performance over state-of-the-art approaches. Specifically, PQDiff achieves state-of-the-art FID scores on the Scenery (\textbf{21.512}), Building Facades (\textbf{25.310}), and WikiArts (\textbf{36.212}) datasets. Furthermore, under the 2.25x, 5x and 11.7x outpainting settings, PQDiff only takes \textbf{40.6\%}, \textbf{20.3\%} and \textbf{10.2\%} of the time of the benchmark state-of-the-art (SOTA) method.

Poster
Parameter-Efficient Orthogonal Finetuning via Butterfly Factorization

Weiyang Liu, Zeju Qiu, Yao Feng, Yuliang Xiu, Yuxuan Xue, Longhui Yu, Haiwen Feng, Zhen Liu, Juyeon Heo, Songyou Peng, Yandong Wen, Michael J. Black, Adrian Weller, Bernhard Schölkopf

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Large foundation models are becoming ubiquitous, but training them from scratch is prohibitively expensive. Thus, efficiently adapting these powerful models to downstream tasks is increasingly important. In this paper, we study a principled finetuning paradigm -- Orthogonal Finetuning (OFT) -- for downstream task adaptation. Despite demonstrating good generalizability, OFT still uses a fairly large number of trainable parameters due to the high dimensionality of orthogonal matrices. To address this, we start by examining OFT from an information transmission perspective, and then identify a few key desiderata that enable better parameter-efficiency. Inspired by how the Cooley-Tukey fast Fourier transform algorithm enables efficient information transmission, we propose an efficient orthogonal parameterization using butterfly structures. We apply this parameterization to OFT, creating a novel parameter-efficient finetuning method, called Orthogonal Butterfly (BOFT). By subsuming OFT as a special case, BOFT introduces a generalized orthogonal finetuning framework. Finally, we conduct an extensive empirical study of adapting large vision transformers, large language models, and text-to-image diffusion models to various downstream tasks in computer vision and natural language. The results validate the effectiveness of BOFT as a generic finetuning method.

Poster
SLiMe: Segment Like Me

Aliasghar Khani, Saeid Asgari, Aditya Sanghi, Ali Mahdavi-Amiri, Ghassan Hamarneh

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Significant strides have been made using large vision-language models, like Stable Diffusion (SD), for a variety of downstream tasks, including image generation, image editing, and 3D shape generation. Inspired by these advancements, we explore leveraging these vision-language models for segmenting images at any desired granularity using as few as one annotated sample. We propose SLiMe, which frames this problem as an optimization task. Specifically, given a single image and its segmentation mask, we first extract our novel “weighted accumulated self-attention map” along with cross-attention map from the SD prior. Then, using these extracted maps, the text embeddings of SD are optimized to highlight the segmented region in these attention maps, which in turn can be used to derive new segmentation results. Moreover, leveraging additional training data when available, i.e. few-shot, improves the performance of SLiMe. We performed comprehensive experiments examining various design factors and showed that SLiMe outperforms other existing one-shot and few-shot segmentation methods.

Poster
NoiseDiffusion: Correcting Noise for Image Interpolation with Diffusion Models beyond Spherical Linear Interpolation

PengFei Zheng, Yonggang Zhang, Zhen Fang, Tongliang Liu, Defu Lian, Bo Han

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Image interpolation based on diffusion models is promising in creating fresh and interesting images. Advanced interpolation methods mainly focus on spherical linear interpolation, where images are encoded into the noise space and then interpolated for denoising to images. However, existing methods face challenges in effectively interpolating natural images (not generated by diffusion models), thereby restricting their practical applicability. Our experimental investigations reveal that these challenges stem from the invalidity of the encoding noise, which may no longer obey the expected noise distribution, e.g., a normal distribution. To address these challenges, we propose a novel approach to correct noise for image interpolation, NoiseDiffusion. Specifically, NoiseDiffusion approaches the invalid noise to the expected distribution by introducing subtle Gaussian noise and introduces a constraint to suppress noise with extreme values. In this context, promoting noise validity contributes to mitigating image artifacts, but the constraint and introduced exogenous noise typically lead to a reduction in signal-to-noise ratio, i.e., loss of original image information. Hence, NoiseDiffusion performs interpolation within the noisy image space and injects raw images into these noisy counterparts to address the challenge of information loss. Consequently, NoiseDiffusion enables us to interpolate natural images without causing artifacts or information loss, thus achieving the best interpolation results.

Spotlight
DreamClean: Restoring Clean Image Using Deep Diffusion Prior

Jie Xiao, Ruili Feng, Han Zhang, Zhiheng Liu, Zhantao Yang, Yurui Zhu, Xueyang Fu, Kai Zhu, Yu Liu, Zheng-Jun Zha

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Image restoration poses a garners substantial interest due to the exponential surge in demands for recovering high-quality images from diverse mobile camera devices, adverse lighting conditions, suboptimal shooting environments, and frequent image compression for efficient transmission purposes. Yet this problem gathers significant challenges as people are blind to the type of restoration the images suffer, which, is usually the case in real-day scenarios and is most urgent to solve for this field. Current research, however, heavily relies on prior knowledge of the restoration type, either explicitly through rules or implicitly through the availability of degraded-clean image pairs to define the restoration process, and consumes considerable effort to collect image pairs of vast degradation types. This paper introduces DreamClean, a training-free method that needs no degradation prior knowledge but yields high-fidelity and generality towards various types of image degradation. DreamClean embeds the degraded image back to the latent of pre-trained diffusion models and re-sample it through a carefully designed diffusion process that mimics those generating clean images. Thanks to the rich image prior in diffusion models and our novel Variance Preservation Sampling (VPS) technique, DreamClean manages to handle various different degradation types at one time and reaches far more satisfied final quality than previous competitors. DreamClean relies on elegant theoretical supports to assure its convergence to clean image when VPS has appropriate parameters, and also enjoys superior experimental performance over various challenging tasks that could be overwhelming for previous methods when degradation prior is unavailable.

Poster
Scale-Adaptive Diffusion Model for Complex Sketch Synthesis

Jijin Hu, Ke Li, Yonggang Qi, Yi-Zhe Song

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While diffusion models have revolutionized generative AI, their application to human sketch generation, especially in the creation of complex yet concise and recognizable sketches, remains largely unexplored. Existing efforts have primarily focused on vector-based sketches, limiting their ability to handle intricate sketch data. This paper introduces an innovative extension of diffusion models to pixellevel sketch generation, addressing the challenge of dynamically optimizing the guidance scale for classifier-guided diffusion. Our approach achieves a delicate balance between recognizability and complexity in generated sketches through scale-adaptive classifier-guided diffusion models, a scaling indicator, and the concept of a residual sketch. We also propose a three-phase sampling strategy to enhance sketch diversity and quality. Experiments on the QuickDraw dataset showcase the potential of diffusion models to push the boundaries of sketch generation, particularly in complex scenarios unattainable by vector-based methods.

Poster
ControlVideo: Training-free Controllable Text-to-video Generation

Yabo Zhang, Yuxiang Wei, Dongsheng Jiang, Xiaopeng Zhang, Wangmeng Zuo, Qi Tian

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Text-driven diffusion models have unlocked unprecedented abilities in image generation, whereas their video counterpart lags behind due to the excessive training cost. To avert the training burden, we propose a training-free ControlVideo to produce high-quality videos based on the provided text prompts and motion sequences. Specifically, ControlVideo adapts a pre-trained text-to-image model (i.e., ControlNet) for controllable text-to-video generation. To generate continuous videos without flicker effect, we propose an interleaved-frame smoother to smooth the intermediate frames. In particular, interleaved-frame smoother splits the whole videos with successive three-frame clips, and stabilizes each clip by updating the middle frame with the interpolation among other two frames in latent space. Furthermore, a fully cross-frame interaction mechanism have been exploited to further enhance the frame consistency, while a hierarchical sampler is employed to produce long videos efficiently. Extensive experiments demonstrate that our ControlVideo outperforms the state-of-the-arts both quantitatively and qualitatively. It is worthy noting that, thanks to the efficient designs, ControlVideo could generate both short and long videos within several minutes using one NVIDIA 2080Ti. Code and videos are available at [this link](https://github.com/YBYBZhang/ControlVideo).

Poster
Diffusion-TS: Interpretable Diffusion for General Time Series Generation

Xinyu Yuan, Yan Qiao

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Denoising diffusion probabilistic models (DDPMs) are becoming the leading paradigm for generative models. It has recently shown breakthroughs in audio synthesis, time series imputation and forecasting. In this paper, we propose Diffusion-TS, a novel diffusion-based framework that generates multivariate time series samples of high quality by using an encoder-decoder transformer with disentangled temporal representations, in which the decomposition technique guides Diffusion-TS to capture the semantic meaning of time series while transformers mine detailed sequential information from the noisy model input. Different from existing diffusion-based approaches, we train the model to directly reconstruct the sample instead of the noise in each diffusion step, combining a Fourier-based loss term. Diffusion-TS is expected to generate time series satisfying both interpretablity and realness. In addition, it is shown that the proposed Diffusion-TS can be easily extended to conditional generation tasks, such as forecasting and imputation, without any model changes. This also motivates us to further explore the performance of Diffusion-TS under irregular settings. Finally, through qualitative and quantitative experiments, results show that Diffusion-TS achieves the state-of-the-art results on various realistic analyses of time series.

Poster
Towards Non-Asymptotic Convergence for Diffusion-Based Generative Models

Gen Li, Yuting Wei, Yuxin Chen, Yuejie Chi

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Diffusion models, which convert noise into new data instances by learning to reverse a Markov diffusion process, have become a cornerstone in contemporary generative modeling. While their practical power has now been widely recognized, the theoretical underpinnings remain far from mature. In this work, we develop a suite of non-asymptotic theory towards understanding the data generation process of diffusion models in discrete time, assuming access to $\ell_2$-accurate estimates of the (Stein) score functions. For a popular deterministic sampler (based on the probability flow ODE), we establish a convergence rate proportional to $1/T$ (with $T$ the total number of steps), improving upon past results; for another mainstream stochastic sampler (i.e., a type of the denoising diffusion probabilistic model), we derive a convergence rate proportional to $1/\sqrt{T}$, matching the state-of-the-art theory. Imposing only minimal assumptions on the target data distribution (e.g., no smoothness assumption is imposed), our results characterize how $\ell_2$ score estimation errors affect the quality of the data generation process. In contrast to prior works, our theory is developed based on an elementary yet versatile non-asymptotic approach without resorting to toolboxes for SDEs and ODEs.

Poster
Mixed-Type Tabular Data Synthesis with Score-based Diffusion in Latent Space

Hengrui Zhang, Jiani Zhang, Zhengyuan Shen, Balasubramaniam Srinivasan, Xiao Qin, Christos Faloutsos, Huzefa Rangwala, George Karypis

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Recent advances in tabular data generation have greatly enhanced synthetic data quality. However, extending diffusion models to tabular data is challenging due to the intricately varied distributions and a blend of data types of tabular data. This paper introduces TabSyn, a methodology that synthesizes tabular data by leveraging a diffusion model within a variational autoencoder (VAE) crafted latent space. The key advantages of the proposed Tabsyn include (1) Generality: the ability to handle a broad spectrum of data types by converting them into a single unified space and explicitly capturing inter-column relations; (2) Quality: optimizing the distribution of latent embeddings to enhance the subsequent training of diffusion models, which helps generate high-quality synthetic data; (3) Speed: much fewer number of reverse steps and faster synthesis speed than existing diffusion-based methods. Extensive experiments on six datasets with five metrics demonstrate that Tabsyn outperforms existing methods. Specifically, it reduces the error rates by 86% and 67% for column-wise distribution and pair-wise column correlation estimations compared with the most competitive baselines. The code has been made available at https://github.com/amazon-science/tabsyn.

Oral
DORSal: Diffusion for Object-centric Representations of Scenes $\textit{et al.}$

Allan Jabri, Sjoerd van Steenkiste, Emiel Hoogeboom, Mehdi S. M. Sajjadi, Thomas Kipf

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Recent progress in 3D scene understanding enables scalable learning of representations across large datasets of diverse scenes. As a consequence, generalization to unseen scenes and objects, rendering novel views from just a single or a handful of input images, and controllable scene generation that supports editing, is now possible. However, training jointly on a large number of scenes typically compromises rendering quality when compared to single-scene optimized models such as NeRFs. In this paper, we leverage recent progress in diffusion models to equip 3D scene representation learning models with the ability to render high-fidelity novel views, while retaining benefits such as object-level scene editing to a large degree. In particular, we propose DORSal, which adapts a video diffusion architecture for 3D scene generation conditioned on frozen object-centric slot-based representations of scenes. On both complex synthetic multi-object scenes and on the real-world large-scale Street View dataset, we show that DORSal enables scalable neural rendering of 3D scenes with object-level editing and improves upon existing approaches.

Poster
Generative Learning for Solving Non-Convex Problem with Multi-Valued Input-Solution Mapping

Enming Liang, Minghua Chen

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By employing neural networks (NN) to learn input-solution mappings and passing a new input through the learned mapping to obtain a solution instantly, recent studies have shown remarkable speed improvements over iterative algorithms for solving optimization problems. Meanwhile, they also highlight methodological challenges to be addressed. In particular, general non-convex problems often present multiple optimal solutions for identical inputs, signifying a complex, multi-valued input-solution mapping. Conventional learning techniques, primarily tailored to learn single-valued mappings, struggle to train NNs to accurately decipher multi-valued ones, leading to inferior solutions. We address this fundamental issue by developing a generative learning approach using a rectified flow (RectFlow) model built upon ordinary differential equations. In contrast to learning input-solution mapping, we learn the mapping from input to solution distribution, exploiting the universal approximation capability of the RectFlow model. Upon receiving a new input, we employ the trained RectFlow model to sample high-quality solutions from the input-dependent distribution it has learned. Our approach outperforms conceivable GAN and Diffusion models in terms of training stability and run-time complexity. We provide a detailed characterization of the optimality loss and runtime complexity associated with our generative approach. Simulation results for solving non-convex problems show that our method achieves significantly better solution optimality than recent NN schemes, with comparable feasibility and speedup performance.

Poster