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Yixuan Zhu, Haolin Wang, Ao Li, Wenliang Zhao, Yansong Tang, Jingxuan Niu, Lei Chen, Jie Zhou, Jiwen Lu

Image enhancement finds wide-ranging applications in real-world scenarios due to complex environments and the inherent limitations of imaging devices. Recent diffusion-based methods yield promising outcomes but necessitate prolonged and computationally intensive iterative sampling. In response, we propose InstaRevive, a straightforward yet powerful image enhancement framework that employs score-based diffusion distillation to harness potent generative capability and minimize the sampling steps. To fully exploit the potential of the pre-trained diffusion model, we devise a practical and effective diffusion distillation pipeline using dynamic noise control to address inaccuracies in updating direction during score matching. Our noise control strategy enables a dynamic diffusing scope, facilitating precise learning of denoising trajectories within the diffusion model and ensuring accurate distribution matching gradients during training. Additionally, to enrich guidance for the generative power, we incorporate textual prompts via image captioning as auxiliary conditions, fostering further exploration of the diffusion model. Extensive experiments substantiate the efficacy of our framework across a diverse array of challenging tasks and datasets, unveiling the compelling efficacy and efficiency of InstaRevive in delivering high-quality and visually appealing results.

Miscellaneous Aspects of Machine Learning · Everything Else

Yuhang Li, Zhuying Li, Yuheng Jia

Complementary label learning (CLL) is a weakly supervised learning paradigm that constructs a multi-class classifier only with complementary labels, specifying classes that the instance does not belong to. We reformulate CLL as an inverse problem that infers the full label information from the output space information. To be specific, we propose to split the inverse problem into two subtasks: positive label guessing (PLG) and negative label enhancement (NLE), collectively called PLNL. Specifically, we use well-designed criteria for evaluating the confidence of the model output, accordingly divide the training instances into three categories: highly-confident, moderately-confident and under-confident. For highly-confident instances, we perform PLG to assign them pseudo labels for supervised training. For moderately-confident and under-confident instances, we perform NLE by enhancing their complementary label set at different levels and train them with the augmented complementary labels iteratively. In addition, we unify PLG and NLE into a consistent framework, in which we can view all the pseudo-labeling-based methods from the perspective of negative label recovery. We prove that the error rates of both PLG and NLE are upper bounded, and based on that we can construct a classifier consistent with that learned by clean full labels. Extensive experiments demonstrate the superiority of PLNL over the state-of-the-art CLL methods, e.g., on STL-10, we increase the classification accuracy from 34.96\% to 55.25\%. The source code is available at https://github.com/yhli-ml/PLNL.

Deep Learning · Robustness

Shuang Liu, Yihan Wang, Yifan Zhu, Yibo Miao, XIAOSHAN GAO

Wasserstein distributionally robust optimization (WDRO) optimizes against worst-case distributional shifts within a specified uncertainty set, leading to enhanced generalization on unseen adversarial examples, compared to standard adversarial training which focuses on pointwise adversarial perturbations. However, WDRO still suffers fundamentally from the robust overfitting problem, as it does not consider statistical error. We address this gap by proposing a novel robust optimization framework under a new uncertainty set for adversarial noise via Wasserstein distance and statistical error via Kullback-Leibler divergence, called the Statistically Robust WDRO. We establish a robust generalization bound for the new optimization framework, implying that out-of-distribution adversarial performance is at least as good as the statistically robust training loss with high probability. Furthermore, we derive conditions under which Stackelberg and Nash equilibria exist between the learner and the adversary, giving an optimal robust model in certain sense.Finally, through extensive experiments, we demonstrate that our method significantly mitigates robust overfitting and enhances robustness within the framework of WDRO.

Deep Learning · Theory

Lijia Yu, Yibo Miao, Yifan Zhu, XIAOSHAN GAO, Lijun Zhang

The primary objective of learning methods is generalization. Classic generalization bounds, based on VC-dimension or Rademacher complexity, are uniformly applicable to all networks in the hypothesis space. On the other hand, algorithm-dependent generalization bounds, like stability bounds, address more practical scenarios and provide generalization conditions for neural networks trained using SGD. However, these bounds often rely on strict assumptions, such as the NTK hypothesis or convexity of the empirical loss, which are typically not met by neural networks. In order to establish generalizability under less stringent assumptions, this paper investigates generalizability of neural networks that minimize the empirical risk. A lower bound for population accuracy is established based on the expressiveness of these networks, which indicates that with adequately large training sample and network sizes, these networks can generalize effectively. Additionally, we provide a lower bound necessary for generalization, demonstrating that, for certain data distributions, the quantity of data required to ensure generalization exceeds the network size needed to represent that distribution. Finally, we provide theoretical insights into several phenomena in deep learning, including robust overfitting, importance of over-parameterization networks, and effects of loss functions.

Deep Learning · Other Representation Learning

Ningyuan Li, Haihong E, Tianyu Yao, Tianyi Hu, Yuhan Li, Haoran Luo, Meina Song, Yifan Zhu

Temporal Knowledge Graph(TKG) serves as an efficacious way to store dynamic facts in real-world. Extrapolation reasoning on TKGs, which aims at predicting possible future events, has attracted consistent research interest. Recently, some rule-based methods have been proposed, which are considered more interpretable compared with embedding-based methods. Existing rule-based methods apply rules through path matching or subgraph extraction, which falls short in inference ability and suffers from missing facts in TKGs. Besides, during rule application period, these methods consider the standing of facts as a binary 0 or 1 problem and ignores the validity as well as frequency of historical facts under temporal settings.In this paper, by designing a novel paradigm for rule application, we propose INFER, a neural-symbolic model for TKG extrapolation. With the introduction of Temporal Validity Function, INFER firstly considers the frequency and validity of historical facts and extends the truth value of facts into continuous real number to better adapt for temporal settings. INFER builds Temporal Weight Matrices with a pre-trained static KG embedding model to enhance its inference ability. Moreover, to facilitates potential integration with existing embedding-based methods, INFER adopts a rule projection module which enables it apply rules through conducting matrices operation on GPU. This feature also improves the efficiency of rule application. Experimental results show that INFER achieves state-of-the-art performance on various TKG datasets and significantly outperforms existing rule-based models on our modified, more sparse TKG datasets, which demonstrates the superiority of our model in inference ability.

Applications · Computer Vision

Yunfei Liu, Lei Zhu, Lijian Lin, Ye Zhu, Ailing Zhang, Yu Li

3D facial reconstruction from a single in-the-wild image is a crucial task in human-centered computer vision tasks. While existing methods can recover accurate facial shapes, there remains significant space for improvement in fine-grained expression capture. Current approaches struggle with irregular mouth shapes, exaggerated expressions, and asymmetrical facial movements. We present TEASER (Token EnhAnced Spatial modeling for Expressions Reconstruction), which addresses these challenges and enhances 3D facial geometry performance. TEASER tackles two main limitations of existing methods: insufficient photometric loss for self-reconstruction and inaccurate localization of subtle expressions. We introduce a multi-scale tokenizer to extract facial appearance information. Combined with a neural renderer, these tokens provide precise geometric guidance for expression reconstruction. Furthermore, TEASER incorporates a pose-dependent landmark loss to further improve geometric performance. Our approach not only significantly enhances expression reconstruction quality but also offers interpretable tokens suitable for various downstream applications, such as photorealistic facial video driving, expression transfer, and identity swapping. Quantitative and qualitative experimental results across multiple datasets demonstrate that TEASER achieves state-of-the-art performance in precise expression reconstruction.

Theory · Online Learning and Bandits

Xiaoyi Zhu, Zengfeng Huang

This paper considers the Lipschitz bandit problem, where the set of arms is continuous and the expected reward is a Lipschitz function over the arm space. This problem has been extensively studied. Prior algorithms need to store the reward information of all visited arms, leading to significant memory consumption. We address this issue by introducing an algorithm named Log-space Lipschitz bandits (Log-Li), which achieves an optimal (up to logarithmic factors) regret of $\widetilde{O}\left(T^{\frac{d_z+1}{d_z+2}}\right)$ while only uses $O\left(\log T\right)$ bits of memory. Additionally, we provide a complexity analysis for this problem, demonstrating that $\Omega\left(\log T\right)$ bits of space are necessary for any algorithm to achieve the optimal regret. We also conduct numerical simulations, and the results show that our new algorithm achieves regret comparable to the state-of-the-art while reducing memory usage by orders of magnitude.

Cheng Yang, Chufan Shi, Yaxin Liu, Bo Shui, JUNJIE WANG, Mohan Jing, Linran XU, Xinyu Zhu, Siheng Li, Yuxiang Zhang 等

We introduce a new benchmark, ChartMimic, aimed at assessing the visually-grounded code generation capabilities of large multimodal models (LMMs). ChartMimic utilizes information-intensive visual charts and textual instructions as inputs, requiring LMMs to generate the corresponding code for chart rendering.ChartMimic includes $4,800$ human-curated (figure, instruction, code) triplets, which represent the authentic chart use cases found in scientific papers across various domains (e.g., Physics, Computer Science, Economics, etc). These charts span $18$ regular types and $4$ advanced types, diversifying into $201$ subcategories.Furthermore, we propose multi-level evaluation metrics to provide an automatic and thorough assessment of the output code and the rendered charts.Unlike existing code generation benchmarks, ChartMimic places emphasis on evaluating LMMs' capacity to harmonize a blend of cognitive capabilities, encompassing visual understanding, code generation, and cross-modal reasoning. The evaluation of $3$ proprietary models and $14$ open-weight models highlights the substantial challenges posed by ChartMimic. Even the advanced GPT-4o, InternVL2-Llama3-76B only achieved an average score across Direct Mimic and Customized Mimic tasks of $82.2$ and $61.6$, respectively, indicating significant room for improvement. We anticipate that ChartMimic will inspire the development of LMMs, advancing the pursuit of artificial general intelligence.

Reinforcement Learning · Batch/Offline

Xianyuan Zhan, Xiangyu Zhu, Peng Cheng, Xiao Hu, Ziteng He, Hanfei Geng, Jichao Leng, Huiwen Zheng, Chenhui Liu, Tianshun Hong 等

The recent advances in information technology and artificial intelligence have fueled a rapid expansion of the data center (DC) industry worldwide, accompanied by an immense appetite for electricity to power the DCs. In a typical DC, around 30-40% of the energy is spent on the cooling system rather than on computer servers, posing a pressing need for developing new energy-saving optimization technologies for DC cooling systems. However, optimizing such real-world industrial systems faces numerous challenges, including but not limited to a lack of reliable simulation environments, limited historical data, and stringent safety and control robustness requirements. In this work, we present a novel physics-informed offline reinforcement learning (RL) framework for energy efficiency optimization of DC cooling systems. The proposed framework models the complex dynamical patterns and physical dependencies inside a server room using a purposely designed graph neural network architecture that is compliant with the fundamental time-reversal symmetry. Because of its well-behaved and generalizable state-action representations, the model enables sample-efficient and robust latent space offline policy learning using limited real-world operational data. Our framework has been successfully deployed and verified in a large-scale production DC for closed-loop control of its air-cooling units (ACUs). We conducted a total of 2000 hours of short and long-term experiments in the production DC environment. The results show that our method achieves 14-21% energy savings in the DC cooling system, without any violation of the safety or operational constraints. We have also conducted a comprehensive evaluation of our approach in a real-world DC testbed environment. Our results have demonstrated the significant potential of offline RL in solving a broad range of data-limited, safety-critical real-world industrial control problems.

Miscellaneous Aspects of Machine Learning · Causality

Xiangru Zhu, Penglei Sun, Yaoxian Song, Yanghua Xiao, Zhixu Li, Chengyu Wang, Jun Huang, Bei Yang, Xiaoxiao Xu

Accurate interpretation and visualization of human instructions are crucial for text-to-image (T2I) synthesis. However, current models struggle to capture semantic variations from word order changes, and existing evaluations, relying on indirect metrics like text-image similarity, fail to reliably assess these challenges. This often obscures poor performance on complex or uncommon linguistic patterns by the focus on frequent word combinations.To address these deficiencies, we propose a novel metric called SemVarEffect and a benchmark named SemVarBench, designed to evaluate the causality between semantic variations in inputs and outputs in T2I synthesis. Semantic variations are achieved through two types of linguistic permutations, while avoiding easily predictable literal variations.Experiments reveal that the CogView-3-Plus and Ideogram 2 performed the best, achieving a score of 0.2/1. Semantic variations in object relations are less understood than attributes, scoring 0.07/1 compared to 0.17-0.19/1. We found that cross-modal alignment in UNet or Transformers plays a crucial role in handling semantic variations, a factor previously overlooked by a focus on textual encoders. Our work establishes an effective evaluation framework that advances the T2I synthesis community's exploration of human instruction understanding. Our benchmark and code are available at https://github.com/zhuxiangru/SemVarBench.

Social Aspects · Fairness, Equity, Justice and Safety

Qingjie Zhang, Han Qiu, Di Wang, Yiming Li, Tianwei Zhang, Wenyu Zhu, Haiqin Weng, Liu Yan, Chao Zhang

Large language models (LLMs) can output sensitive information, which has emerged as a novel safety concern. Previous works focus on structured sensitive information (e.g. personal identifiable information). However, we notice that sensitive information can also be at semantic level, i.e. semantic sensitive information (SemSI). Particularly, *simple natural questions* can let state-of-the-art (SOTA) LLMs output SemSI. %which is hard to be detected compared with structured ones. Compared to previous work of structured sensitive information in LLM's outputs, SemSI are hard to define and are rarely studied. Therefore, we propose a novel and large-scale investigation on the existence of SemSI in SOTA LLMs induced by simple natural questions. First, we construct a comprehensive and labeled dataset of semantic sensitive information, SemSI-Set, by including three typical categories of SemSI. Then, we propose a large-scale benchmark, SemSI-Bench, to systematically evaluate semantic sensitive information in 25 SOTA LLMs. Our finding reveals that SemSI widely exists in SOTA LLMs' outputs by querying with simple natural questions.We open-source our project at https://semsi-project.github.io/.

Yushi Bai, Jiajie Zhang, Xin Lv, Linzhi Zheng, Siqi Zhu, Lei Hou, Yuxiao Dong, Jie Tang, Juanzi Li

Current long context large language models (LLMs) can process inputs up to 100,000 tokens, yet struggle to generate outputs exceeding even a modest length of 2,000 words. Through controlled experiments, we find that the model's effective generation length is inherently bounded by the sample it has seen during supervised fine-tuning (SFT). In other words, their output limitation is due to the scarcity of long-output examples in existing SFT datasets. To address this, we introduce AgentWrite, an agent-based pipeline that decomposes ultra-long generation tasks into subtasks, enabling off-the-shelf LLMs to generate coherent outputs exceeding 20,000 words. Leveraging AgentWrite, we construct LongWriter-6k, a dataset containing 6,000 SFT data with output lengths ranging from 2k to 32k words. By incorporating this dataset into model training, we successfully scale the output length of existing models to over 10,000 words while maintaining output quality. We also develop LongBench-Write, a comprehensive benchmark for evaluating ultra-long generation capabilities. Our 9B parameter model, further improved through DPO, achieves state-of-the-art performance on this benchmark, surpassing even much larger proprietary models. In general, our work demonstrates that existing long context LLM already possesses the potential for a larger output window--all you need is data with extended output during model alignment to unlock this capability.

Optimization · Everything Else

Shulan Zhu, Chenglong Bao, Defeng Sun, Yancheng Yuan

The \textbf{i}nexact \textbf{s}tochastic \textbf{p}roximal \textbf{p}oint \textbf{a}lgorithm (isPPA) is popular for solving stochastic composite optimization problems with many applications in machine learning. While the convergence theory of the (inexact) PPA has been well established, the known convergence guarantees of isPPA require restrictive assumptions. In this paper, we establish the stability and almost sure convergence of isPPA under mild assumptions, where smoothness and (restrictive) strong convexity of the objective function are not required. Imposing a local Lipschitz condition on component functions and a quadratic growth condition on the objective function, we establish last-iterate iteration complexity bounds of isPPA regarding the distance to the solution set and the Karush–Kuhn–Tucker (KKT) residual. Moreover, we show that the established iteration complexity bounds are tight up to a constant by explicitly analyzing the bounds for the regularized Fr\'echet mean problem. We further validate the established convergence guarantees of isPPA by numerical experiments.

Deep Learning · Generative Models and Autoencoders

Xin Gu, Ming Li, Libo Zhang, Fan Chen, Longyin Wen, Tiejian Luo, Sijie Zhu

High-quality training triplets (instruction, original image, edited image) are essential for instruction-based image editing. Predominant training datasets (e.g., InsPix2Pix) are created using text-to-image generative models (e.g., Stable Diffusion, DALL-E) which are not trained for image editing. Accordingly, these datasets suffer from inaccurate instruction following, poor detail preserving, and generation artifacts. In this paper, we propose to address the training data quality issue with multi-perspective reward data instead of refining the ground-truth image quality. 1) we first design a quantitative metric system based on best-in-class LVLM (Large Vision Language Model), i.e., GPT-4o in our case, to evaluate the generation quality from 3 perspectives, namely, instruction following, detail preserving, and generation quality. For each perspective, we collected quantitative score in $0\sim 5$ and text descriptive feedback on the specific failure points in ground-truth edited images, resulting in a high-quality editing reward dataset, i.e., RewardEdit20K. 2) We further proposed a novel training framework to seamlessly integrate the metric output, regarded as multi-reward, into editing models to learn from the imperfect training triplets. During training, the reward scores and text descriptions are encoded as embeddings and fed into both the latent space and the U-Net of the editing models as auxiliary conditions. During inference, we set these additional conditions to the highest score with no text description for failure points, to aim at the best generation outcome. 3) We also build a challenging evaluation benchmark with real-world images/photos and diverse editing instructions, named as Real-Edit. Experiments indicate that our multi-reward conditioned model outperforms its no-reward counterpart on two popular editing pipelines, i.e., InsPix2Pix and SmartEdit. Code is released at https://github.com/bytedance/Multi-Reward-Editing.

Theory · Optimization

Zhen Qin, Zhuqing Liu, Songtao Lu, Yingbin Liang, Jia (Kevin) Liu

Decentralized bilevel optimization (DBO) provides a powerful framework for multi-agent systems to solve local bilevel tasks in a decentralized fashion without the need for a central server. However, most existing DBO methods rely on lower-level strong convexity (LLSC) to guarantee unique solutions and a well-defined hypergradient for stationarity measure, hindering their applicability in many practical scenarios not satisfying LLSC. To overcome this limitation, we introduce a new single-loop DBO algorithm called diminishing quadratically-regularized bilevel decentralized optimization (DUET), which eliminates the need for LLSC by introducing a diminishing quadratic regularization to the lower-level (LL) objective. We show that DUET achieves an iteration complexity of $O(1/T^{1-5p-\frac{11}{4}\tau})$ for approximate KKT-stationary point convergence under relaxed assumptions, where $p$ and $\tau $ are control parameters for LL learning rate and averaging, respectively.In addition, our DUET algorithm incorporates gradient tracking to address data heterogeneity, a key challenge in DBO settings. To the best of our knowledge, this is the first work to tackle DBO without LLSC under decentralized settings with data heterogeneity.Numerical experiments validate the theoretical findings and demonstrate the practical effectiveness of our proposed algorithms.

Deep Learning · Large Language Models

Huajian Xin, Z.Z. Ren, Junxiao Song, Zhihong Shao, Wanjia Zhao, Haocheng Wang, Bo Liu, Liyue Zhang, Xuan Lu, Qiushi Du 等

Lean is an advanced proof assistant designed to facilitate formal theorem proving by providing a variety of interactive feedback. In this paper, we explore methodologies to leverage proof assistant feedback to augment the capabilities of large language models in constructing formal proofs. First, we deploy online reinforcement learning using Lean verification outcomes as the reward signal to improve the proof completion policy. This straightforward approach shows great promise in enhancing the model's alignment with the formal verification system. In addition, we propose RMaxTS, a variant of Monte-Carlo tree search that employs an intrinsic-reward-driven exploration strategy to generate diverse proof paths. The tree structure is organized to represent the transitions of intermediate tactic states, extracted from the compilation messages given by Lean's tactic mode. The intrinsic reward is constructed to incentivize the discovery of novel tactic states, which helps to to mitigate the sparse-reward problem inherent in proof search. These techniques lead to a more efficient planning scheme for formal proof generation, achieving new state-of-the-art results on both miniF2F and ProofNet benchmarks.

Deep Learning · Generative Models and Autoencoders

Bing Cao, Quanhao Lu, Jiekang Feng, Qilong Wang, Pengfei Zhu, Qinghua Hu

The dynamic imbalance of the fore-background is a major challenge in video object counting, which is usually caused by the sparsity of target objects. This remains understudied in existing works and often leads to severe under-/over-prediction errors. To tackle this issue in video object counting, we propose a density-embedded Efficient Masked Autoencoder Counting (E-MAC) framework in this paper. To empower the model’s representation ability on density regression, we develop a new Density-Embedded Masked mOdeling (DEMO) method, which first takes the density map as an auxiliary modality to perform multimodal self-representation learning for image and density map. Although DEMO contributes to effective cross-modal regression guidance, it also brings in redundant background information, making it difficult to focus on the foreground regions. To handle this dilemma, we propose an efficient spatial adaptive masking derived from density maps to boost efficiency. Meanwhile, we employ an optical flow-based temporal collaborative fusion strategy to effectively capture the dynamic variations across frames, aligning features to derive multi-frame density residuals. The countingaccuracy of the current frame is boosted by harnessing the information from adjacent frames. In addition, considering that most existing datasets are limited to human-centric scenarios, we propose a large video bird counting dataset, DroneBird, in natural scenarios for migratory bird protection. Extensive experiments on three crowd datasets and our DroneBird validate our superiority againstthe counterparts. The code and dataset are available.

Deep Learning · Algorithms

Junjie Wu, Qilong Wang, Jiangtao Xie, Pengfei Zhu, Qinghua Hu

As a core component of Transformer-like deep architectures, a feed-forward network (FFN) for channel mixing is responsible for learning features of each token. Recent works show channel mixing can be enhanced by increasing computational burden or can be slimmed at the sacrifice of performance. Although some efforts have been made, existing works are still struggling to solve the paradox of performance and complexity trade-offs. In this paper, we propose an Asymmetric Factorized Bilinear Operation (AFBO) to replace FFN of vision transformer (ViT), which attempts to efficiently explore rich statistics of token features for achieving better performance and complexity trade-off. Specifically, our AFBO computes second-order statistics via a spatial-channel factorized bilinear operation for feature learning, which replaces a simple linear projection in FFN and enhances the feature learning ability of ViT by modeling second-order correlation among token features. Furthermore, our AFBO presents two structured-sparsity channel mapping strategies, namely Grouped Cross Channel Mapping (GCCM) and Overlapped Cycle Channel Mapping (OCCM). They decompose bilinear operation into grouped channel features by considering information interaction between groups, significantly reducing computational complexity while guaranteeing model performance. Finally, our AFBO is built with GCCM and OCCM in an asymmetric way, aiming to achieve a better trade-off. Note that our AFBO is model-agnostic, which can be flexibly integrated with existing ViTs. Experiments are conducted with twenty ViTs on various tasks, and the results show our AFBO is superior to its counterparts while improving existing ViTs in terms of generalization and robustness.

Applications · Computer Vision

Jeremy Irvin, Emily Liu, Joyce Chen, Ines Dormoy, Jinyoung Kim, Samar Khanna, Zhuo Zheng, Stefano Ermon

Large vision and language assistants have enabled new capabilities for interpreting natural images. These approaches have recently been adapted to earth observation data, but they are only able to handle single image inputs, limiting their use for many real-world tasks. In this work, we develop a new vision and language assistant called TEOChat that can engage in conversations about temporal sequences of earth observation data. To train TEOChat, we curate an instruction-following dataset composed of many single image and temporal tasks including building change and damage assessment, semantic change detection, and temporal scene classification. We show that TEOChat can perform a wide variety of spatial and temporal reasoning tasks, substantially outperforming previous vision and language assistants, and even achieving comparable or better performance than several specialist models trained to perform specific tasks. Furthermore, TEOChat achieves impressive zero-shot performance on a change detection and change question answering dataset, outperforms GPT-4o and Gemini 1.5 Pro on multiple temporal tasks, and exhibits stronger single image capabilities than a comparable single image instruction-following model on scene classification, visual question answering, and captioning. We publicly release our data, models, and code at https://github.com/ermongroup/TEOChat .

Deep Learning · Sequential Models, Time series

Barbora Barancikova, Zhuoyue Huang, Cristopher Salvi

Score-based diffusion models have recently emerged as state-of-the-art generativemodels for a variety of data modalities. Nonetheless, it remains unclear how toadapt these models to generate long multivariate time series. Viewing a timeseries as the discretisation of an underlying continuous process, we introduceSigDiffusion, a novel diffusion model operating on log-signature embeddingsof the data. The forward and backward processes gradually perturb and denoiselog-signatures while preserving their algebraic structure. To recover a signal fromits log-signature, we provide new closed-form inversion formulae expressing thecoefficients obtained by expanding the signal in a given basis (e.g. Fourier ororthogonal polynomials) as explicit polynomial functions of the log-signature.Finally, we show that combining SigDiffusions with these inversion formulaeresults in high-quality long time series generation, competitive with the currentstate-of-the-art on various datasets of synthetic and real-world examples.