SDFlow: Similarity-Driven Flow Matching for Time Series Generation

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.

Autoregressive (AR) video generation degrades over long horizons due to an overlooked train-inference discrepancy we term KV eviction mismatch: models train on short clips where all context frames reside in the KV cache, but at inference, memory constraints force distant frames to be evicted from the KV cache - removing context the model was conditioned on. Rather than simulating eviction via context truncation - which discards temporal information the model still needs and degrades motion coherence - we keep the context but while progressively reducing the influence of distant frames, making their eventual eviction negligible. To guide this design, we introduce the positional response $R( Δ, \, t_{\text{denoise}})$, a perturbation-based sensitivity measure revealing that context influence decays steeply with temporal distance and varies systematically across denoising steps. Motivated by this analysis, we propose Recency Forcing, which applies a non-positive, timestep-dependent bias, termed Temporal Response Bias (TRB), on pre-softmax attention logits derived directly from $R$, closing the train-inference gap without modifying context length or training objectives. We further introduce Biased Attention Reparameterization (BAR), an exact reformulation that moves the bias outside the softmax, making TRB a standard FlashAttention call at zero overhead. Recency Forcing operates in both training-free mode and training-based mode. Experiments on VBench and VBench-Long demonstrate state-of-the-art long-horizon generation quality at no additional inference cost.

High-fidelity image generation faces a trade-off between speed and quality. Diffusion models produce strong visuals but require costly iterative sampling. Existing efficient methods mainly distill pretrained models into few-step samplers, a challenging process that depends heavily on teacher-model quality. In this paper, we introduce XYZFlow, a framework that rethinks efficient generation through multidimensional scaling of flow matching. Unlike single-step mappings, XYZFlow enhances expressivity by making probability paths more identifiable and learnable through structured multidimensional conditioning. We view autoregressive modeling as implicit flow straightening, where richer context reduces trajectory ambiguity. XYZFlow realizes this idea through two orthogonal dimensions: temporal scaling, which uses non-Markovian conditioning on the full denoising history; and spatial scaling, enabled by Next Shortcut Prediction, which sequentially generates patches using preceding patches' denoising trajectories as priors. Experiments show that XYZFlow achieves state-of-the-art performance, with 7.2-8.5X teacher speedups and competitive FID, while Next Shortcut Prediction delivers superior quality-latency trade-offs over model scaling or step reduction.