Wavelet Flow Matching for Time Series

Vector quantization (VQ) with autoregressive (AR) token modeling is a widely adopted and highly competitive paradigm for time-series generation. However, such models are fundamentally limited by exposure bias: during inference, errors can accumulate across sequential predictions, leading to pronounced quality degradation in long-horizon generation. To address this, we propose SDFlow ($\textbf{S}$imilarity-$\textbf{D}$riven $\textbf{Flow}$ Matching), a non-autoregressive framework that operates entirely in the frozen VQ latent space and enables parallel sequence generation via flow matching. We tackle three key challenges in making this transition: (1) eliminating exposure bias by replacing step-wise token prediction with a global transport map; (2) mitigating the high-dimensionality of VQ token spaces via a low-rank manifold decomposition with a learned anchor prior over the latent manifold; and (3) incorporating discrete supervision into continuous transport dynamics by introducing a categorical posterior over codebook indices within a variational flow-matching formulation. Extensive experiments show that SDFlow achieves state-of-the-art performance, improving Discriminative Score and substantially reducing Context-FID, particularly for challenging long-sequence generation. Moreover, SDFlow provides significant inference speedups over autoregressive baselines, offering both high fidelity and computational efficiency. Code is available at https://anonymous.4open.science/r/SDFlow-D6F3/

Generating high-quality time-series data is challenging because real-world signals often exhibit multimodal patterns and multiscale dynamics, including oscillations and high-frequency variations. Flow Matching (FM) offers an efficient alternative to diffusion models, but practical implementations typically rely on a single finite-capacity global vector-field estimator. In such heterogeneous temporal distributions, distinct regimes may pass through nearby flow states while requiring incompatible conditional velocities. A monolithic estimator trained with the standard $\ell_2$ velocity-matching objective may therefore learn an overly smoothed approximation of the local transport field. This estimator-level smoothing can attenuate branch-specific dynamics, leading to spectral distortion and poor mode coverage. To address this, we propose PrismFlow, a new FM method with Koopman-inspired dynamical experts. Each expert learns residual corrections in a latent space where local nonlinear temporal evolution can be approximated by linear transitions. We further propose a confidence-aware Winner-Take-All (WTA) objective that updates only the expert best aligned with each sample while masking gradients to the others, encouraging mode-specific specialization. During sampling, the selected expert adds a residual dynamical correction to the global transport field, preserving FM stability while recovering fine-grained and high-frequency temporal structures. Across various benchmarks, PrismFlow effectively mitigates the spectral contraction in standard FM and achieves state-of-the-art performance, with a 15.6% gain in Context-FID and a 38.6% improvement in Discriminative Score, while remaining robust in low-data settings and effective for forecasting and imputation.

As image generation models scale to ever higher resolutions, global coherence, local detail, and texture fidelity become critical axes for generation quality. However, standard flow matching treats all spatial frequencies uniformly, ignoring the natural frequency hierarchy where high-frequency bands become indistinguishable from pure noise far earlier than coarse structures. We introduce WaiT, a Wavelet-aware image Transformer that decomposes generation into coarse and fine bands via lossless wavelets. True to its name, the high-frequency bands wait for the signal: staying pure noise until coarse structure has emerged, then joining the flow for joint refinement. Since standard FID discards fine-grained detail through aggressive downsampling, we introduce a more stringent three-axis evaluation protocol to assess quality at native resolution. On ImageNet 512x512, WaiT achieves a pixel-space FID of 1.43 and is Pareto-optimal across all three axes, reducing sampling compute by up to 50%. With our largest 2B model, we set a new state-of-the-art FID of 1.3 for pixel-space models on ImageNet 512 resolution. Our formulation outperforms even the strongest latent-space models on texture fidelity, and scales seamlessly to high-resolution OpenImages and to video generation, achieving a state-of-the-art FVD of 0.84 on Kinetics-600 with no algorithmic modifications.