Optimal Weighted Convolution for Classification and Denosing

We introduce a novel weighted convolution operator that enhances traditional convolutional neural networks (CNNs) by integrating a spatial density function into the convolution operator. This extension enables the network to differentially weight neighbouring pixels based on their relative position to the reference pixel, improving spatial characterisation and feature extraction. The proposed operator maintains the same number of trainable parameters and is fully compatible with existing CNN architectures. Although developed for 2D image data, the framework is generalisable to signals on regular grids of arbitrary dimensions, such as 3D volumetric data or 1D time series. We propose an efficient implementation of the weighted convolution by pre-computing the density function and achieving execution times comparable to standard convolution layers. We evaluate our method on two deep learning tasks: image classification using the CIFAR-100 dataset [KH+09] and image denoising using the DIV2K dataset [AT17]. Experimental results with state-of-the-art classification (e.g., VGG [SZ15], ResNet [HZRS16]) and denoising (e.g., DnCNN [ZZC+17], NAFNet [CCZS22]) methods show that the weighted convolution improves performance with respect to standard convolution across different quantitative metrics. For example, VGG achieves an accuracy of 66.94% with weighted convolution versus 56.89% with standard convolution on the classification problem, while DnCNN improves the PSNR value from 20.17 to 22.63 on the denoising problem. All models were trained on the CINECA Leonardo cluster to reduce the execution time and improve the tuning of the density function values. The PyTorch implementation of the weighted convolution is publicly available at: https://github.com/cammarasana123/weightedConvolution2.0.

Time Series Similarity Score Functions to Monitor and Interact with the Training and Denoising Process of a Time Series Diffusion Model applied to a Human Activity Recognition Dataset based on IMUs

Denoising diffusion probabilistic models are able to generate synthetic sensor signals. The training process of such a model is controlled by a loss function which measures the difference between the noise that was added in the forward process and the noise that was predicted by the diffusion model. This enables the generation of realistic data. However, the randomness within the process and the loss function itself makes it difficult to estimate the quality of the data. Therefore, we examine multiple similarity metrics and adapt an existing metric to overcome this issue by monitoring the training and synthetisation process using those metrics. The adapted metric can even be fine-tuned on the input data to comply with the requirements of an underlying classification task. We were able to significantly reduce the amount of training epochs without a performance reduction in the classification task. An optimized training process not only saves resources, but also reduces the time for training generative models.

Effective Probabilistic Time Series Forecasting with Fourier Adaptive Noise-Separated Diffusion

We propose the Fourier Adaptive Lite Diffusion Architecture (FALDA), a novel probabilistic framework for time series forecasting. First, we introduce the Diffusion Model for Residual Regression (DMRR) framework, which unifies diffusion-based probabilistic regression methods. Within this framework, FALDA leverages Fourier-based decomposition to incorporate a component-specific architecture, enabling tailored modeling of individual temporal components. A conditional diffusion model is utilized to estimate the future noise term, while our proposed lightweight denoiser, DEMA (Decomposition MLP with AdaLN), conditions on the historical noise term to enhance denoising performance. Through mathematical analysis and empirical validation, we demonstrate that FALDA effectively reduces epistemic uncertainty, allowing probabilistic learning to primarily focus on aleatoric uncertainty. Experiments on six real-world benchmarks demonstrate that FALDA consistently outperforms existing probabilistic forecasting approaches across most datasets for long-term time series forecasting while achieving enhanced computational efficiency without compromising accuracy. Notably, FALDA also achieves superior overall performance compared to state-of-the-art (SOTA) point forecasting approaches, with improvements of up to 9%.

Non-stationary Diffusion For Probabilistic Time Series Forecasting

Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.

T2S: High-resolution Time Series Generation with Text-to-Series Diffusion Models

Text-to-Time Series generation holds significant potential to address challenges such as data sparsity, imbalance, and limited availability of multimodal time series datasets across domains. While diffusion models have achieved remarkable success in Text-to-X (e.g., vision and audio data) generation, their use in time series generation remains in its nascent stages. Existing approaches face two critical limitations: (1) the lack of systematic exploration of general-proposed time series captions, which are often domain-specific and struggle with generalization; and (2) the inability to generate time series of arbitrary lengths, limiting their applicability to real-world scenarios. In this work, we first categorize time series captions into three levels: point-level, fragment-level, and instance-level. Additionally, we introduce a new fragment-level dataset containing over 600,000 high-resolution time series-text pairs. Second, we propose Text-to-Series (T2S), a diffusion-based framework that bridges the gap between natural language and time series in a domain-agnostic manner. T2S employs a length-adaptive variational autoencoder to encode time series of varying lengths into consistent latent embeddings. On top of that, T2S effectively aligns textual representations with latent embeddings by utilizing Flow Matching and employing Diffusion Transformer as the denoiser. We train T2S in an interleaved paradigm across multiple lengths, allowing it to generate sequences of any desired length. Extensive evaluations demonstrate that T2S achieves state-of-the-art performance across 13 datasets spanning 12 domains.

A Time-Series Data Augmentation Model through Diffusion and Transformer Integration

With the development of Artificial Intelligence, numerous real-world tasks have been accomplished using technology integrated with deep learning. To achieve optimal performance, deep neural networks typically require large volumes of data for training. Although advances in data augmentation have facilitated the acquisition of vast datasets, most of this data is concentrated in domains like images and speech. However, there has been relatively less focus on augmenting time-series data. To address this gap and generate a substantial amount of time-series data, we propose a simple and effective method that combines the Diffusion and Transformer models. By utilizing an adjusted diffusion denoising model to generate a large volume of initial time-step action data, followed by employing a Transformer model to predict subsequent actions, and incorporating a weighted loss function to achieve convergence, the method demonstrates its effectiveness. Using the performance improvement of the model after applying augmented data as a benchmark, and comparing the results with those obtained without data augmentation or using traditional data augmentation methods, this approach shows its capability to produce high-quality augmented data.

H3AE: High Compression, High Speed, and High Quality AutoEncoder for Video Diffusion Models

Autoencoder (AE) is the key to the success of latent diffusion models for image and video generation, reducing the denoising resolution and improving efficiency. However, the power of AE has long been underexplored in terms of network design, compression ratio, and training strategy. In this work, we systematically examine the architecture design choices and optimize the computation distribution to obtain a series of efficient and high-compression video AEs that can decode in real time on mobile devices. We also unify the design of plain Autoencoder and image-conditioned I2V VAE, achieving multifunctionality in a single network. In addition, we find that the widely adopted discriminative losses, i.e., GAN, LPIPS, and DWT losses, provide no significant improvements when training AEs at scale. We propose a novel latent consistency loss that does not require complicated discriminator design or hyperparameter tuning, but provides stable improvements in reconstruction quality. Our AE achieves an ultra-high compression ratio and real-time decoding speed on mobile while outperforming prior art in terms of reconstruction metrics by a large margin. We finally validate our AE by training a DiT on its latent space and demonstrate fast, high-quality text-to-video generation capability.

Integrating Fourier Neural Operators with Diffusion Models to improve Spectral Representation of Synthetic Earthquake Ground Motion Response

Nuclear reactor buildings must be designed to withstand the dynamic load induced by strong ground motion earthquakes. For this reason, their structural behavior must be assessed in multiple realistic ground shaking scenarios (e.g., the Maximum Credible Earthquake). However, earthquake catalogs and recorded seismograms may not always be available in the region of interest. Therefore, synthetic earthquake ground motion is progressively being employed, although with some due precautions: earthquake physics is sometimes not well enough understood to be accurately reproduced with numerical tools, and the underlying epistemic uncertainties lead to prohibitive computational costs related to model calibration. In this study, we propose an AI physics-based approach to generate synthetic ground motion, based on the combination of a neural operator that approximates the elastodynamics Green's operator in arbitrary source-geology setups, enhanced by a denoising diffusion probabilistic model. The diffusion model is trained to correct the ground motion time series generated by the neural operator. Our results show that such an approach promisingly enhances the realism of the generated synthetic seismograms, with frequency biases and Goodness-Of-Fit (GOF) scores being improved by the diffusion model. This indicates that the latter is capable to mitigate the mid-frequency spectral falloff observed in the time series generated by the neural operator. Our method showcases fast and cheap inference in different site and source conditions.

Frequency-Aware Attention-LSTM for PM$_{2.5}$ Time Series Forecasting

To enhance the accuracy and robustness of PM$_{2.5}$ concentration forecasting, this paper introduces FALNet, a Frequency-Aware LSTM Network that integrates frequency-domain decomposition, temporal modeling, and attention-based refinement. The model first applies STL and FFT to extract trend, seasonal, and denoised residual components, effectively filtering out high-frequency noise. The filtered residuals are then fed into a stacked LSTM to capture long-term dependencies, followed by a multi-head attention mechanism that dynamically focuses on key time steps. Experiments conducted on real-world urban air quality datasets demonstrate that FALNet consistently outperforms conventional models across standard metrics such as MAE, RMSE, and $R^2$. The model shows strong adaptability in capturing sharp fluctuations during pollution peaks and non-stationary conditions. These results validate the effectiveness and generalizability of FALNet for real-time air pollution prediction, environmental risk assessment, and decision-making support.

Enhanced Diffusion Sampling via Extrapolation with Multiple ODE Solutions

Diffusion probabilistic models (DPMs), while effective in generating high-quality samples, often suffer from high computational costs due to their iterative sampling process. To address this, we propose an enhanced ODE-based sampling method for DPMs inspired by Richardson extrapolation, which reduces numerical error and improves convergence rates. Our method, RX-DPM, leverages multiple ODE solutions at intermediate time steps to extrapolate the denoised prediction in DPMs. This significantly enhances the accuracy of estimations for the final sample while maintaining the number of function evaluations (NFEs). Unlike standard Richardson extrapolation, which assumes uniform discretization of the time grid, we develop a more general formulation tailored to arbitrary time step scheduling, guided by local truncation error derived from a baseline sampling method. The simplicity of our approach facilitates accurate estimation of numerical solutions without significant computational overhead, and allows for seamless and convenient integration into various DPMs and solvers. Additionally, RX-DPM provides explicit error estimates, effectively demonstrating the faster convergence as the leading error term's order increases. Through a series of experiments, we show that the proposed method improves the quality of generated samples without requiring additional sampling iterations.