Flow-matching diffusion models have recently emerged as a strong paradigm for high-fidelity visual generation. However, their prohibitively high fine-tuning cost limits scalability to downstream tasks. While Low-Rank Adaptation (LoRA) combined with spectral initialization has demonstrated accelerated convergence and improved performance in autoregressive language models by better aligning gradient directions, we find that it fails to deliver similar gains in diffusion fine-tuning, often yielding marginal or even negative improvements over vanilla LoRA.We attribute this discrepancy to a fundamental mismatch between LoRA's low-rank parameterization and the intrinsically high-rank gradients induced by the flow-matching objective. In particular, stochastic timestep sampling introduces directionally heterogeneous gradient signals across training steps, leading to misaligned updates under low-rank constraints.To address this issue, we propose Prism-LoRA,a Principal-timestep Restricted Init via Sparse Matrix-decomposition framework that improves gradient alignment during fine-tuning. Our method consists of two key components: (i) principal timestep selection, which restricts initialization gradients to a subset of dominant timesteps to suppress effective gradient rank, and (ii) principal channel filtering, which removes task-irrelevant channels, enabling the one-step spectral initialization gradient to better align with the long-horizon optimization trajectory. Extensive experiments demonstrate that our method consistently improves both convergence speed and final performance across multiple diffusion fine-tuning benchmarks, including subject-driven generation, controllable generation, and deblurring, achieving not only performance improvement but also earlier stages of convergence over baseline LoRA and other spectral-init methods.
We propose SpectralDiT, a lightweight modification to flow-matching Diffusion Transformers that adds timestep-conditioned spectral correction to the MLP residual branch. The module decomposes each residual update into low- and high-frequency components on the patch-token grid, then learns a zero-initialized additive gate so the model initially matches the baseline DiT. On CIFAR-10 pixel-space generation, SpectralDiT improves FID from 20.78 to 19.71 at patch size 1 and reduces the radial Fourier spectrum gap. Furthermore, we scale our method to latent diffusion on ImageNet-100. With 0.6% additional theoretical FLOPs and 1.36% additional parameters, SpectralDiT improves latent flow-matching, achieving an 8.7% relative FID reduction under classifier-free guidance (CFG 2.0). All reported results are averaged over five seeds. Ablations and gate visualizations on CIFAR-10 reveal stable block-specific spectral correction patterns.
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 ℓ2 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.
Selecting LoRA rank for diffusion fine-tuning requires balancing quality and compute cost. We present a controlled study on CIFAR-10 using a DDPM U-Net with ranks {2,4,8,16,32}, fixed optimization settings, and a reproducible local-folder pytorch-fid protocol. We report FID, trainable parameters, runtime, and GPU memory, then validate trends with extended-budget DDPM runs (20 epochs; ranks 4/8/16) and a Tiny DiT backbone (10 epochs; ranks 4/8/16). Results show moderate ranks are most efficient: rank 4 achieves the best DDPM FID (124.1380), rank 8 is close (124.2136), and higher ranks provide limited gains despite larger adaptation cost. These findings support small-to-moderate ranks as practical defaults under fixed training budgets.