Diffusion LLMs have emerged as a promising alternative to conventional autoregressive LLMs, offering substantial potential for improving runtime efficiency. However, existing diffusion models fail to provably enforce user-specified formal constraints, such as regular expressions, which makes them unreliable for tasks that require structured outputs, such as fixed-schema JSON generation. Unlike autoregressive models, which generate tokens sequentially, diffusion LLMs predict a block of tokens in parallel. This parallelism makes traditional constrained decoding algorithms, designed to enforce constraints with sequential token prediction, ineffective at preserving the true output distribution. To address this limitation, we propose DINGO, a dynamic programming-based constrained decoding strategy that is both efficient and provably distribution-preserving. DINGO enables sampling of output strings with the highest probability under the model's predicted distribution while strictly adhering to any user-specified regular expression. On standard symbolic math and JSON generation benchmarks, DINGO achieves up to a 68%points of improvement over unconstrained inference. The code is available at DINGO.

We introduce a new graph diffusion model for small drug molecule generation which simultaneously offers a 10-fold reduction in the number of diffusion steps when compared to existing methods, preservation of small molecule graph motifs via motif compression, and an average 3% improvement in SMILES validity over the DiGress model across all real-world molecule benchmarking datasets. Furthermore, our approach outperforms the state-of-the-art DeFoG method with respect to motif-conservation by roughly 4%, as evidenced by high ChEMBLlikeness, QED and newly introduced shingles distance scores. The key ideas behind the approach are to use a combination of deterministic and random subgraph perturbations, so that the node and edge noise schedules are codependent; to modify the loss function of the training process in order to exploit the deterministic component of the schedule; and, to "compress" a collection of highly relevant carbon ring and other motif structures into supernodes in a way that allows for simple subsequent integration into the molecular scaffold1.

Diffusion models (DMs) have emerged as powerful tools for modeling complex data distributions and generating realistic new samples. Over the years, advanced architectures and sampling methods have been developed to make these models practically usable. However, certain synthesis process decisions still rely on heuristics without a solid theoretical foundation. In our work, we offer a novel analysis of the DM's inference process, introducing a comprehensive frequency response perspective. Specifically, by relying on Gaussianity assumption, we present the inference process as a closed-form spectral transfer function, capturing how the generated signal evolves in response to the initial noise. We demonstrate how the proposed analysis can be leveraged to design a noise schedule that aligns effectively with the characteristics of the data. The spectral perspective also provides insights into the underlying dynamics and sheds light on the relationship between spectral properties and noise schedule structure. Our results lead to scheduling curves that are dependent on the spectral content of the data, offering a theoretical justification for some of the heuristics taken by practitioners.

Diffusion models have demonstrated strong performance in time series modeling due to their ability to progressively capture complex data distributions through iterative denoising. However, existing approaches struggle with frequency-sensitive denoising, high-frequency reconstruction and balancing global trends with local dynamics. To address these limitations, we propose \textbf{HyFAD}, a \textbf{Hy}brid time-frequency \textbf{D}iffusion model with \textbf{F}requency-\textbf{A}ware embedding for time series imputation. Built upon the DDPM paradigm, HyFAD adopts a coupled time-frequency diffusion framework, in which the reverse denoising proceeds sequentially from the time domain to the frequency domain, enabling coarse-to-fine generation. Specifically, the time-domain diffusion process captures low-frequency global trends, while the frequency-domain diffusion process refines high-frequency spectral components. We further introduce a frequency-aware step embedding that exploits the relationship between diffusion steps and spectral components, providing step-dependent spectral guidance and facilitates more accurate band-wise reconstruction. Extensive experiments on multiple benchmark datasets demonstrate that HyFAD achieves state-of-the-art performance. Our source code is available at https://github.com/hongfangao/HyFAD.

Diffusion models have achieved state-of-the-art performance in generative modeling tasks across various domains. Prior works on time series diffusion models have primarily focused on developing conditional models tailored to specific forecasting or imputation tasks. In this work, we explore the potential of taskagnostic, unconditional diffusion models for several time series applications. We propose TSDiff, an unconditionally-trained diffusion model for time series. Our proposed self-guidance mechanism enables conditioning TSDiff for downstream tasks during inference, without requiring auxiliary networks or altering the training procedure. We demonstrate the effectiveness of our method on three different time series tasks: forecasting, refinement, and synthetic data generation. First, we show that TSDiff is competitive with several task-specific conditional forecasting methods (predict). Second, we leverage the learned implicit probability density of TSDiff to iteratively refine the predictions of base forecasters with reduced computational overhead over reverse diffusion (refine). Notably, the generative performance of the model remains intact -- downstream forecasters trained on synthetic samples from TSDiff outperform forecasters that are trained on samples from other state-of-the-art generative time series models, occasionally even outperforming models trained on real data (synthesize).

Because a diffusion model shares parameters for all diffusion steps, the noise schedule (parametrized by 1:T) is an important hyperparameter that determines how much weight we assign to each denoising problem. We find that standard noise schedules for continuous diffusions are not robust for text data. We hypothesize that the discrete nature of text and the rounding step make the model insensitive to noise near t =0 . Concretely, adding small amount of Gaussian noise to a word embedding is unlikely to change its nearest neighbor in the embedding space, making denoising an easy task near t =0 . To address this, we introduce a new sqrt noise schedule that is better suited for text, shown in Figure 5 defined by t =1 p t/T +s, where s is a small constant that corresponds to the starting noise level11. Compared to standard linear and cosine schedules, our sqrt schedule starts with a higher noise level and increase noise rapidly for the first 50 steps. Then sqrt slows down injecting noise to avoid spending much steps in the high-noise problems, which may be too difficult to solve well. The hyperparameters that are specific to Diffusion-LM include the number of diffusion steps, the architecture of the Diffusion-LM, the embedding dimension, and the noise schedule, . We set the diffusion steps to be 2000, the architecture to be BERT-base [7], and the sequence length to be 64. For the embedding dimensions, we select from d 2{ 16,64,128,256} and select d = 16for the E2E dataset and d = 128for ROCStories. For the noise schedule, we design the sqrt schedule (Appendix A) that is more robust to different parametrizations and embedding dimensions as shown in Appendix M. However, once we picked the x0-parametrization ( 4.2) the advantage of sqrt schedule is not salient. We train Diffusion-LMs using AdamW optimizer and a linearly decay learning rate starting at 1e-4, dropout of 0.1, batch size of 64, and the total number of training iteration is 200K for E2E dataset, and 800K for ROCStories dataset. Our Diffusion-LMs are trained on a single GPU: NVIDIARTXA5000, NVIDIAGeForce RTX 3090, or NVIDIAA100.

Neural network-based Combinatorial Optimization (CO) methods have shown promising results in solving various NP-complete (NPC) problems without relying on hand-crafted domain knowledge. This paper broadens the current scope of neural solvers for NPC problems by introducing a new graph-based diffusion framework, namely DIFUSCO. Our framework casts NPC problems as discrete {0,1}-vector optimization problems and leverages graph-based denoising diffusion models to generate high-quality solutions. We investigate two types of diffusion models with Gaussian and Bernoulli noise, respectively, and devise an effective inference schedule to enhance the solution quality. We evaluate our methods on two well-studied NPC combinatorial optimization problems: Traveling Salesman Problem (TSP) and Maximal Independent Set (MIS). Experimental results show that DIFUSCO strongly outperforms the previous state-of-the-art neural solvers, improving the performance gap between ground-truth and neural solvers from 1.76% to 0.46% on TSP-500, from 2.46% to 1.17% on TSP-1000, and from 3.19% to 2.58% on TSP-10000. For the MIS problem, DIFUSCO outperforms the previous state-of-the-art neural solver on the challenging SATLIB benchmark.

While diffusion models have demonstrated exceptional image generation capabilities, the iterative noise estimation process required for these models is computeintensive and their practical implementation is limited by slow sampling speeds. In this paper, we propose a novel approach to speed up the noise estimation network by leveraging the robustness of early-stage diffusion models. Our findings indicate that inaccurate computation during the early-stage of the reverse diffusion process has minimal impact on the quality of generated images, as this stage primarily outlines the image while later stages handle the finer details that require more sensitive information. To improve computational efficiency, we combine our findings with post-training quantization (PTQ) and introduce a method that utilizes low-bit activations for the early reverse diffusion process while maintaining high-bit activations for the later stages. Experimental results show that the proposed method can accelerate the early-stage computation without sacrificing the quality of the generated images.

The pre-trained text-to-image diffusion models have been increasingly employed to tackle the real-world image super-resolution (Real-ISR) problem due to their powerful generative image priors. Most of the existing methods start from random noise to reconstruct the high-quality (HQ) image under the guidance of the given low-quality (LQ) image. While promising results have been achieved, such Real-ISR methods require multiple diffusion steps to reproduce the HQ image, increasing the computational cost. Meanwhile, the random noise introduces uncertainty in the output, which is unfriendly to image restoration tasks. To address these issues, we propose a one-step effective diffusion network, namely OSEDiff, for the Real-ISR problem.