Organizations: College of Information Science and Engineering, Ritsumeikan University, Osaka, Japan
Abstract
Single-cell RNA sequencing (scRNA-seq) has become an essential tool in modern cellular biology, and generating accurate synthetic scRNA-seq data is becoming increasingly important. Although diffusion models have achieved promising results in conditional scRNA-seq generation, existing guidance strategies, including classifier guidance and classifier-free guidance (CFG), rely on an unconditional branch trained to approximate the true marginal distribution, which may retain substantial gene-specific structure and limit guidance effectiveness. Inspired by recent work showing that diffusion models can be effectively guided using intentionally degraded references, we propose a sparsity-biased classifier-free guidance (SB-CFG) strategy for scRNA-seq generation. Rather than approximating the assumed "neutral" marginal distribution, SB-CFG introduces a deliberately under-informative sparse reference for the unconditional branch, removing gene identity while preserving only coarse sparsity statistics. This "bad" reference amplifies the contrast between conditional and unconditional predictions, leading to stronger and more effective guidance during sampling. We evaluated SB-CFG as a training-free sampling modification on five publicly available scRNA-seq datasets. Experimental results demonstrate consistent improvements over standard CFG-based sampling in terms of marker gene expression fidelity, cell-type consistency, and sparsity preservation, indicating that SB-CFG better captures biologically meaningful gene expression patterns.
Classifier-free guidance (CFG) is the default mechanism for conditional generation in diffusion models, but the distribution sampled by its deterministic guided dynamics is not captured by the usual product-distribution heuristic p0ωq01−ω. We analyze CFG through the probability flow ODE and derive exact analytic path-integral representations of the induced distributions for both constant and time-dependent guidance. The resulting formulas show that CFG modifies pt0 by an exponential path-integral correction, and that a time-dependent schedule enters this correction through the weight ω(t)−1. This characterization explains how score discrepancies accumulate along sampling trajectories and motivates Distribution-Guided CFG (DG-CFG), a schedule that balances timestep contributions while accounting for signal strength and low-noise score-error amplification. A toy model with analytic scores closely verifies the predicted distributions. Across Stable Diffusion1.5, Stable Diffusion2.1, and Stable DiffusionXL, DG-CFG yields a stronger diversity--fidelity trade-off and robustly mitigates the saturation and quality degradation caused by strong constant or heuristic guidance. Complete NFE experiments on Stable Diffusion1.5 and Stable Diffusion~2.1 confirm that these gains persist across sampling budgets, while fixed-quality experiments on both backbones show that DG-CFG reaches target metrics with fewer sampling steps.
Classifier-free guidance (CFG) is the standard way to strengthen class-conditioning in diffusion and flow-matching samplers, yet at large guidance it oversaturates and destabilizes, symptoms practitioners suppress with more steps or limited-interval schedules. We analyze CFG through an asymptotic-preserving, numerical-analysis lens. Building on a recent result that the deterministic DDIM step is the unique fitted operator for the unguided terminal layer, exact on the final small-sigma stretch of sampling, we show that guidance re-stiffens exactly the discriminative subspace to an anomalous exponent 1+w. DDIM is therefore no longer fitted there, and on coarse meshes its guided residual diverges as sigma_min goes to zero. We prove a guided clock barrier with three ordered step-size thresholds, and read one-step oversaturation as its endpoint: a solver artifact on the calibration model rather than the continuous guided law. The same analysis yields a one-coefficient, zero-extra-NFE repair: replace CFG's w(r-1) by r^(1+w)-r on the guidance direction. On the calibration model's discriminative crossover, this removes CFG's sigma_min-divergent blow-up and is first-order accurate against the exact guided flow as sigma_min goes to zero. On learned CIFAR-10 checkpoints, and as a cross-domain smoke test on Stable Diffusion 1.5 DDIM, it acts as a high-guidance stabilizer at no extra cost rather than a universal quality knob: it cuts residual amplification and saturation, gives 9/9 point-FID wins over CFG on the tested grid, and preserves classifier-proxy target accuracy in the hard-cell blocks. We report the limits alongside: it is not a universal image-quality win, and against a dense vanilla-CFG reference it is not a uniformly better integrator of that field.
Diffusion models have emerged as state-of-the-art generative models for high-fidelity image synthesis, particularly in their classifier-free guided and classifier-guided forms. However, standard classifier guidance concentrates probability mass around high-density class mean, leading to poor coverage of rare samples in the tails of the class-conditional distributions. Recent work on diffusion-based tail sampling mitigates this by training an additional low-density-seeking classifier with a synthetic-vs-real discriminator, at the cost of additional networks and training. In parallel, a number of samplers and distillation techniques accelerate or refine diffusion sampling, but do not explicitly address long-tail coverage. We propose a purely sampling-time, density-aware extension of classifier-guided conditional diffusion model that targets low-density regions without any additional training. We have applied guidance at noisy images not on predicted noise like most diffusion models. Starting from a pretrained conditional diffusion model and classifier on ImageNet, we modify the guided reverse dynamics by steering trajectories toward low-confidence regions via the modified classifier gradient, and at each time step, we also guide the sampling process toward the predicted real image. 1st guidance helps explore low-probability samples, and 2nd guidance helps to generate samples to be close to the real data manifold. The proposed sampler consistently improves ADM model recall at 64x64 resolution while maintaining a comparable FID, and with a 256x256 ADM model, we showed the results visually with different combinations of both guidance. We also showed that standard ADM classifier guidance, combined with predicted real image guidance, helps generate high perceptual quality samples with a 256x256 ADM model on ImageNet.