Classifier-Free Guidance

One-step generators built on MeanFlow synthesize a video in a single function evaluation, yet inherit a rigid treatment of classifier-free guidance (CFG): the guidance scale is frozen during training or, at best, exposed as a single scalar. This conflicts with mounting evidence that the optimal guidance is not a constant but a field that varies with the noise level, with spatial content, and, for video, with frame position. Every existing remedy presupposes a multi-step sampler along which guidance can be re-scheduled--an assumption one-step models violate by construction. We resolve this tension through a single observation: because the MeanFlow target is an integral over a noise interval, an arbitrary guidance field can be absorbed into the target itself and compiled into one evaluation. We formalize this as the interval-integrated CFG identity, prove that the compiled guidance carries no schedule-discretization error and can thus match or exceed any finite multi-step sampler, and instantiate it as AGAVE, which equips the average-velocity field with a learnable temporal schedule, a free motion-saliency spatial modulation, and a frame-position asymmetry. Adding fewer than ten scalars at zero inference cost, AGAVE surpasses all one-step baselines on VBench, UCF-101 and MSR-VTT while matching multi-step guided sampling. Project repository: https://github.com/YMlinfeng/AGAVE.

Classifier-Free Guidance is a widely used inference-time guidance rule for conditional image generation with diffusion models, which exposes a guidance scale that adjusts conditioning strength after training. This flexibility requires conditional and unconditional model evaluations at every sampling step, so an N-step trajectory takes 2N forward passes. Single-pass alternatives reduce such cost, yet most collapse CFG's two components into one opaque guided prediction, losing the separable base flow and guidance direction that support per-step control and diagnostics, even when the scale remains adjustable. This work introduces CtrlFlow, a single-pass guidance method that preserves CFG's separable base-flow and guidance-direction interface. To preserve both components at one-pass cost, CtrlFlow attaches two lightweight LoRA adapters to a frozen backbone, each adding 2.5% parameters, and predicts the base flow and guidance direction from one pass of the shared frozen backbone. Because the guidance scale multiplies the guidance direction only after the forward pass, one evaluation yields the guided velocity at any scale, so a single trained checkpoint remains adjustable at inference without retraining. Preserving two outputs introduces a training mismatch: inference amplifies guidance-direction errors by the chosen scale, while naive component-wise losses weight both outputs equally. To align training with this composed inference-time error, CtrlFlow uses a unified multi-scale distillation loss. Residual guidance errors can still persist at extreme scales, where even small guidance-direction errors are amplified by the guidance scale. To reduce this inference-time error, CtrlFlow applies scale-adaptive modulation to damp velocity-field errors and time-grid warping to concentrate solver evaluations where the trajectory changes most rapidly.

Classifier-free guidance (CFG) is a standard component of conditional diffusion models, and guided generation performance has become the de facto measure of state-of-the-art models. Recent work on latent diffusion models seeks to learn latent spaces that are easier to model with diffusion. However, under CFG, generation additionally depends on how conditions are arranged in the latent space. We study this arrangement under discrete class conditions, termed class geometry, and investigate what class geometry allows a latent space to work well with CFG. Under a Gaussian class model, we show that shifting variance from intra- to inter-class at fixed total variance makes classes more distinguishable under noise, and derive a noisy posterior objective whose per-sample descent direction is proportional to the oracle CFG correction. Based on the analysis, we propose Prototype Regularization (PR), a lightweight surrogate for the intractable noisy posterior objective, which applies a cosine prototype classifier to spatially pooled latents. With a controlled training budget (20 epochs for VAE, 80 epochs for DiT), adding PR to an LDM baseline reduces guided gFID on ImageNet from 3.31 to 2.28, surpassing a DINOv3-aligned VA-VAE (2.44) with negligible overhead. We further demonstrate that PR generalizes to pseudo-labels derived from clustering, continuous text-embedding conditions, and video latents. Together, our findings highlight class geometry as a critical factor in guided generation and take a first step toward CFG-compatible representation learning. Our project page is available at: https://maps-research.github.io/cfg-geometry/.

We study Text-and-Image-to-Image (TI2I) flow matching methods for controllable image editing. In a broader generative modeling context, Classifier-Free Guidance (CFG) is established as a key component responsible for high quality outputs. However, we argue that its role in TI2I modeling is poorly understood. Specifically, we make the surprising observation that the CFG mechanism is implicitly harmful for editing in the noisy phase of flow modeling, hindering instruction following and controllability. We propose a simple correction in the early flow steps, enabling a richer alignment-preservation tradeoff at no extra cost. The effectiveness of our approach is demonstrated on both pixel-space and latent TI2I flows.

Classifier-Free Guidance (CFG) with guidance scale $γ$ is commonly motivated by the $ω$-powered conditional distribution obtained by setting $ω=γ$, but CFG does not, in general, sample from this distribution exactly. We study whether the powered target can instead be learned explicitly. We introduce Importance-Weighted Conditional Flow Matching (IW-CFM), which reweights conditional flow-matching examples using density ratios obtained from frozen conditional and unconditional flow models. With exact normalized weights, the resulting objective has the same gradient as flow matching on the powered target; in practice, we use self-normalized estimation and a regularized empirical approximation for high-dimensional data. On synthetic distributions, IW-CFM recovers analytical powered targets for which numerically matched CFG, $γ=ω$, exhibits a visible mismatch. On ImageNet, an amortized lightweight corrector achieves better alignment than fixed- and matched-guidance CFG with the corresponding weighted and filtered reference distributions. We additionally present an exploratory CLIP analysis of powered-density rankings on real ImageNet data. Aggregate shifts across selected prompt-specific contrasts coexist with heterogeneous classwise responses, including nonmonotonic trajectories. These results provide a practical route for studying and approximating model-defined powered conditional distributions.

DiffusionNFT (NFT) fine-tunes diffusion models toward task-specific rewards, but optimizing these rewards does not guarantee fidelity to the full prompt. Although classifier-free guidance (CFG) strengthens prompt alignment, NFT is formulated as a CFG-free method, and applying CFG to the fine-tuned velocity field can reduce the optimized reward. This motivates optimizing rewards over the guided output distribution while seeking to retain its prompt alignment. However, applying standard NFT directly to guided samples can cause reward degradation or training collapse. We trace this failure to a mismatch between the reference velocity used in the NFT loss and the score of the guided sample distribution, which biases the improvement direction. We propose GuidanceNFT, which estimates the matching reference velocity through online flow matching on guided samples and uses it to correct both regression terms. With an exact reference, the corrected objective recovers NFT's intended update. In our experiments, the learned correction sustains reward improvement under both explicit and built-in guidance. On SD3.5-M, GuidanceNFT achieves higher optimized rewards than NFT with and without CFG across GenEval, text-rendering, and multi-reward objectives, together with better overall prompt alignment as measured by off-domain evaluation metrics. Experiments on models with built-in guidance, including Model Guidance and ELF, further demonstrate improved ImageNet generation, a better perplexity-entropy tradeoff on OpenWebText, and higher accuracy on GSM8K.

Unified vision-language models (VLMs) perform both text-to-image (T2I) and image-to-text (I2T) generation with one shared Transformer backbone, yet how the backbone processes the condition in either direction remains poorly understood. We study this question from the perspective of conditional guidance: we probe every attention head to show the activation difference between two branches of classifier-free guidance (CFG) with different conditional guidance. On two unified VLMs of autoregressive and masked-diffusion paradigms, the probing reveals a subset of heads that are more sensitive to the change of condition while others are agnostic to it. This characteristic pattern holds in both T2I and I2T generation and is largely stable across data samples, demonstrating the internal mechanism of unified VLMs. Motivated by this, we propose a new inference-time intervention approach for unified multimodal generation, named HeadTuned-CFG, which uses the probed condition-change awareness to select and tune the conditional guidance at the attention-head level. Experiments show consistent benefits in both multimodal generation directions of unified VLMs without additional training, and in particular substantial improvements over strong baselines in T2I generation. These results further support the key finding of our probing analysis: the observed pattern of functional specialization is an intrinsic property of unified VLMs.

Classifier-free guidance (CFG) typically applies a shared scale to all latent tokens, although their velocity predictions evolve differently during sampling. We introduce Trajectory-Adaptive Classifier-Free Guidance (TrajCFG), a training-free method for flow-matching models that adapts token-wise guidance using historical changes in guided velocity direction. TrajCFG maps this feedback to bounded scales, assigning stronger guidance to larger directional changes and weaker guidance to more consistent directions. It combines adjacent-step and interval-normalized longer-span feedback, reusing standard CFG predictions without additional model evaluations. Controlled diagnostics and ablations examine the roles of directional feedback, token-wise allocation, and history-span fusion. Experiments on text-to-video, image-to-video, text-to-audio-video, text-to-image, and image-to-3D generation show improvements over base samplers across multiple backbones. For text-to-video generation, TrajCFG improves VBench Total scores by 0.30-0.75 points over the strongest evaluated baseline on each of three backbones. These results support historical directional feedback as a broadly applicable signal for fine-grained guidance allocation. The project page is available at https://jyliu-98.github.io/trajcfg-project-page/.

Classifier-free guidance (CFG) is a standard technique for improving conditional generation in diffusion models, yet its activation schedule is usually selected heuristically. In practice, most existing CFG-based methods rely on a pre-defined activation policy throughout inference, while recent dynamic variants often depend on hand-designed schedules without a principled theoretical explanation of when conditional information is most useful. In order to understand how the informational relevance between conditioning inputs and the score function evolves over the course of generation, we explore when guidance should be activated from an information-theoretic perspective. In this work, we formulate the diffusion trajectory as a time-dependent information bottleneck and show that the effectiveness of conditional information is not uniform throughout sampling, but becomes significantly stronger after a critical stage characterized by a Fisher-information balance condition. Motivated by this insight, we propose a training-free dynamic CFG strategy for inference. Rather than prescribing a fixed schedule in advance, our method constructs a stochastic process from conditional and unconditional score statistics and activates guidance when the estimated guidance gain crosses a prescribed threshold. This yields an adaptive activation rule that aligns condition injection with the underlying generation dynamics, while also recovering interval-based guidance as a limiting special case. Extensive experiments across diverse architectures and tasks, demonstrate that our method is effective, robust, and broadly applicable. Beyond empirical improvements, our framework provides an interpretation of dynamic guidance methods and a principled foundation for inference-time control in conditional diffusion models.

Regression-based RL for flow models mandates sampling without classifier-free guidance (CFG) to align the rectification target with the reference marginal velocity. Extending Advantage-Weighted Rectification (AWR), which dynamically scales this regression target based on reward, to video generation encounters a cold-start pathology: unguided rollouts collapse into low-fidelity regions where intra-group reward gaps remain wide but no longer track perceptual quality, rendering the optimization target arbitrary. Conversely, utilizing guided rollouts to restore fidelity, while keeping the regression target tied to the guided sampling distribution, provably triggers a geometric guidance blow-up under exponential-moving-average (EMA) updates. We propose VideoAWR, which resolves this tension by untying sampling from the optimization anchor. An EMA reference policy generates guided rollouts to restore reward separability, while the trainable policy is rectified against the unguided conditional anchor. We prove this decoupled objective is mathematically exact: the centered advantage cancels the anchor in expectation, filtering out the reward-neutral guidance offset and retaining only the reward-correlated covariance increment. Consequently, inference runs single-branch and CFG-free, yet inference-time CFG preserves its original semantics. Furthermore, we introduce Decoupled Timestep Rectification, supervising each rollout at an independently sampled timestep without bias to improve sample efficiency. Experiments on Wan2.1-1.3B and 14B demonstrate stable optimization and superior visual and motion quality in both CFG-free and CFG-enabled regimes. Code is available at \pdfstartlink attr{/Border [0 0 0]} user{/Subtype /Link /A << /S /URI /URI (https://github.com/Fuzm7/FlowAWR) >>}% \textcolor{pearDark}{VideoAWR}\pdfendlink.

Optimal-transport couplings have been shown to reduce training variance in unconditional flow models, but their role in conditional generation remains unclear. A natural approach constructs separate couplings for each condition, but this is impractical for large or continuous conditioning spaces found in modern image foundation models. We introduce Global Transport (GT), a global class-agnostic optimal-transport coupling, computed without class labels. GT can associate different conditions with different regions of the source noise, and consequently worsens performance without guidance. However, when combined with classifier-free guidance (CFG), GT consistently improves generation across domains, model scales, and sampling budgets. This reversal suggests that couplings for conditional flows should be evaluated both empirically and theoretically under the guided flow used at inference, rather than on unguided generation. We evaluate GT over both discrete class and continuous text conditioned image generation across model scales, and investigate how coupling choice alters guided trajectories. These results identify coupling design in the guided flow setting as a simple training time axis to improve performance without modifying existing architectures, samplers, or guidance mechanisms.

Diffusion models generate samples by learning to reverse a fixed corruption process, and classifier-free guidance (CFG) is the standard mechanism for conditioning this process on a desired class or prompt. CFG can be applied at varying guidance strengths, and while higher strengths improve image quality and conditional alignment, too high a guidance strength can degrade image quality and diversity. Furthermore, CFG violates principled diffusion sampling dynamics, and existing explanations for why it works despite the violation disagree on the underlying theory or do not extend to deterministic samplers used in practice. We address both these issues. We first frame CFG sampling as a continuous-time optimal control problem, treating the sampling trajectory as a sequence of controls chosen to maximise the probability of the desired condition. Solving the resulting Hamilton--Jacobi--Bellman equation shows that CFG is recovered under specific path costs when using an unconstrained control set. We argue this lack of constraint is responsible for CFG's failure at high guidance strengths, since it permits the sampling path to move arbitrarily far from the current image estimate. To fix this, we propose curvature-aware CFG (CACFG), which constrains the control set to a hypersphere informed by the Gaussian regularisation used when training variational autoencoders. We show that the control inputs produced by CFG sampling routinely violate this bound, and that across diffusion models, datasets, and guidance schedules, CACFG achieves superior generative quality at mid-to-high guidance strengths with a less severe quality-diversity tradeoff than regular CFG.

The practical success of conditional image generation hinges on fine-grained differences in condition alignment and visual fidelity. Classifier-free guidance (CFG) is central to this success, but its lack of an explicit criterion makes it difficult to assess whether the guided trajectory is progressing as intended. To address this gap, we show that spectral alignment provides a principled criterion for understanding guidance behavior and improving guided diffusion sampling through adaptive correction. Our analysis identifies the spectra of intermediate states as an indicator of consistency with the expected spectral evolution of the forward process. Based on this observation, we introduce Spectral Correction Guidance, a method that corrects deviations from an analytic reference spectrum during sampling. The proposed method is training-free and applicable across diffusion backbones and conditional generation tasks without modifying the underlying model. Experiments demonstrate consistent gains in preference-based metrics over baseline guidance methods in text-to-image generation and improved generation quality over CFG on ImageNet. These improvements persist across a range of guidance scales and with fewer denoising steps. Our analyses and ablations provide insight into guidance behavior and how the proposed method affects generation quality.

Post-training quantization for diffusion models increasingly exploits timestep, feature, and layer structure. While recent work has begun incorporating CFG structure into diffusion quantization, activation quantization still operates independently across conditional and unconditional coordinates, leaving cross-activation structure unexploited. We show that matched CFG activations form a strongly correlated two-dimensional source and that, under a fixed bit budget, the choice of branch coding basis materially affects quantization fidelity. Motivated by this observation, we introduce branch-space transform coding, which rotates matched CFG branches via an offline derived 2x2 orthogonal matrix, requiring minimal modifications to model parameters or the quantization pipeline. We further derive the Guidance-Correlation Branch Transform (GCBT), which jointly incorporates the CFG guidance direction and cross-branch second moments. Under an equal-rate quantization-noise surrogate, GCBT admits a closed-form per-layer solution without gradient optimization or angle search. Applied on top of existing diffusion PTQ methods, GCBT yields statistically significant fidelity gains in most evaluated comparisons with no statistically significant degradation, while leaving the underlying host quantization pipeline unchanged.

On-policy distillation (OPD) has demonstrated two important capabilities in language models: compressing large teachers into smaller students and merging expert models into a single model. Existing diffusion OPD, however, mostly focus on the latter, with teachers and students sharing the same backbone and scale. We investigate large-to-small diffusion opd from large teachers to a small student and find that the standard recipe fails. To find the underlying cause, we propose Fixed-State KL, an effective and fair way to measure the distribution gap between student and teacher during OPD training for diffusion models. We are the first to clarify why large-to-small OPD is challenging for diffusion models: a smaller student struggles to perfectly match the distribution of a larger teacher, while classifier-free guidance can accumulate and amplify the distributional discrepancies between the student's conditional and unconditional branches and those of the teacher. To solve this problem, we propose GFD-OPD, a simple yet effective method that reduces the student-teacher gap while avoiding the error amplification of the CFG composition. Across numerous experiments, GFD outperforms previous baselines in both training efficiency and final performance, achieving state-of-the-art results on all benchmarks.

Text-to-image diffusion models are personalized to a subject by DreamBooth fine-tuning on a handful of its images. Increasingly, these images come from a diffusion model rather than a camera. We show that fine-tuning on such synthetic images degrades subject fidelity, producing oversaturated color and excess high-frequency detail. To isolate the cause, we fine-tune two models from the same base model with the same DreamBooth recipe, one on real photos of a subject and one on synthetic images of that subject generated by the first. We trace the degradation to classifier-free guidance (CFG). For the model personalized on synthetic images, the angle between the conditional and unconditional noise predictions, and with it the norm of their difference, is much larger than for the model personalized on real photos. This inflation grows toward high frequencies and also appears at other prompts semantically close to the subject, such as its class noun, but not at unrelated ones. We propose ReGain, a training-free correction applied at sampling time that measures how much each frequency band of the guidance is inflated relative to the base model and scales that band down accordingly. ReGain needs no real photos. On Stable Diffusion v1.5, ReGain closes 51-64% of the subject-fidelity gap to the model personalized on real photos, as measured by DINO, DINOv2 and CLIP-I. It also improves subject fidelity on SDXL and SD 3.5 and preserves text alignment on all three backbones.

Diffusion models enable high-quality visual generation, but iterative denoising remains computationally expensive, especially under classifier-free guidance (CFG), which requires both conditional and unconditional evaluations. Training-free caching reduces this cost by reuse of previously computed features or predictions. However, existing branch-local reuse criteria do not explicitly account for how cache errors combine under CFG or how local perturbations affect the final output. We identify two misalignments in cache control: a branch-guided mismatch, where guided error depends on both the magnitudes and alignment of branch errors, and a local-final mismatch, where the downstream impact of a local error varies across timesteps. We propose RA-CFGCache, a Risk-Aligned Caching framework under CFG that incorporates both factors while keeping the sampling schedule and guidance rule fixed. CFG-aware Guided-Risk Composition combines existing branch-wise proxies using CFG coefficients and offline-calibrated cross-branch alignment. Propagation-Aware Rescaling further weights the resulting guided-risk estimate with a timestep-dependent propagation prior calibrated from isolated reuse perturbations. An online threshold controller then determines when to jointly refresh or reuse both branches. Experiments on FLUX.1-dev, Wan2.1-T2V-1.3B, and CogVideoX-2B demonstrate improved efficiency--fidelity trade-offs over evaluated training-free caching baselines. Moreover, RA-CFGCache is compatible with diverse base proxy families, including TeaCache-, DiCache-, and MagCache-style estimators, and consistently improves fidelity at nearly unchanged latency. Code is available at https://github.com/yiming-l21/RA-CFGCache.git.

Instruction-guided image editing should change what the instruction names and leave the rest of the image untouched. In dual classifier-free guidance (CFG), an editor combines two directions at every denoising step, one that pushes toward the instructed edit and one that pulls back toward the source image, using global weights. We introduce Attention-Scoped Guidance (ASG), a sampler wrapper that makes these weights spatial. It reads a soft support map from the instruction attention that the editor already computes, then weakens text guidance where support is low and strengthens image anchoring where support is high. The wrapper requires no training, no external mask, and no additional network evaluation. On the full MagicBrush and PIE-Bench++ splits, ASG improves preservation-oriented metrics, leading three of four MagicBrush metrics and PIE-Bench++ background PSNR. A dose-matched control that removes the spatial placement loses up to 0.73 CLIP on PIE-Bench++, confirming that the spatial allocation itself carries the gain.

Diffusion Transformers with Mixture-of-Experts (MoE) routing are a leading recipe for scaling generative models. Classifier-Free Guidance (CFG) is essential for generation quality, yet excessively high guidance scales trigger collapse. We identify a previously unreported failure mode in their combination: the two CFG branches route independently, so their realized activations occupy different subspaces. The unconditional write then leaves the conditional subspace, and CFG amplifies that residual linearly in the guidance scale. We propose SAGE, a training-time regularizer that aligns unconditional MoE activations to the conditional subspace without restricting routing diversity, at zero inference cost. Toy experiments show that SAGE dramatically suppresses extreme drift by 9.2x. When scaled to a 1B-parameter text-to-image model, SAGE significantly improves generation quality, delivering a 9.3% boost in peak DPG-Bench performance. Extensive experiments demonstrate that SAGE consistently outperforms the baseline.

Flow-based image editing (FlowEdit) enables inversion-free semantic changes through the difference between source and target velocities. In this paper, we observe that FlowEdit's default classifier-free guidance (CFG) configuration, with asymmetric source and target scales, causes substantial background leakage. Matching these guidance scales, for example by removing CFG, improves edit-relevant localization but severely degrades editability. To get the best of both worlds, we propose DecFlowEdit, which decouples the optimal guidance scales for localization and for editing in flow-based generative models. In particular, DecFlowEdit first extracts an edit-relevant prior by temporally aggregating velocity differences evaluated without CFG, and then uses this prior to reweight the original updates under default CFG. Our method remains training-free and inversion-free, requiring neither external spatial masks nor attention manipulation. Experiments on PIE-Bench across FLUX, SD3, and SD3.5 show that DecFlowEdit improves background preservation, reducing structure distance by approximately 61 to 73 percent and background LPIPS by 68 to 80 percent relative to FlowEdit at comparable editing fidelity.

Target-speaker automatic speech recognition (TS-ASR) must identify and transcribe a desired speaker under varying overlap and noise conditions. These changes alter the acoustic evidence for the target speaker in the speech mixture, motivating inference-time calibration of speaker conditioning. We introduce asymmetric classifier-free guidance (CFG) for TS-ASR using Whisper: the speaker-conditioned branch predicts the target transcript, while the speaker-unconditioned branch predicts serialized multi-speaker transcripts. CFG adjusts the contribution of speaker conditioning during decoding through a single guidance scale. We select a global guidance scale on target-domain development data and train a lightweight encoder-based predictor to adjust it for each utterance, keeping the recognition model fixed. Under domain shifts, our full system achieves relative word error rate (WER) reductions of up to 21.8% over the condition-only baseline, and 5.6% over standard conditional decoding of the same CFG-trained model. Oracle analysis shows that substantially larger WER reductions are possible through utterance-level scale selection and identifies how beneficial adjustments vary with domain shifts.

Classifier-free Guidance (CFG) is widely adopted in text-to-speech (TTS) systems to enhance generation quality and conditioning fidelity by interpolating between conditioned and unconditioned predictions. A common unconditional technique is to use an empty representation, in the form of a fixed null vector. In this work, we propose replacing this representation with a learnable unconditional embedding, optimized to represent a meaningful unconditional state. Objective and subjective evaluations demonstrate that learnable null embeddings consistently outperform fixed null embeddings across speaker similarity, speech stability, and expressiveness, while exhibiting greater robustness to larger guidance scales. We further show that learning a distinct unconditional embedding for each of the TTS conditioning modalities allows fine-grained control over speaker and text guidance, showcasing the trade-off between similarity and quality, and stability and expressiveness in the generated speech.

Classifier-free guidance (CFG) improves conditional generation in Flow Matching, but strong guidance can distort the generated distribution and reduce diversity. We provide a geometric account of this behavior by viewing Flow Matching as a time-varying gradient flow and characterizing how CFG reshapes its underlying potential. This view explains how stronger alignment can be accompanied by mean displacement and trajectory concentration, and motivates controlling guidance through the model-implied terminal posterior mean. We therefore propose Posterior-Mean-Capped CFG (PMC-CFG), a training-free, per-sample method that adaptively retains the strongest feasible guidance without additional network evaluations. Experiments on synthetic and large-scale image-generation benchmarks show that PMC-CFG limits guidance-induced distortion and concentration while improving the alignment--diversity trade-off, with particularly strong benefits when nominal guidance is large.

Gradient-guided diffusion samplers provide flexible priors for inverse problems and conditional generation, but strong guidance can move the sampling trajectory into regions where the learned score is poorly supported. Existing tangent-projection strategies limit first-order departure from an iso-density surface, yet discard potentially useful normal motion and overlook the second-order departure induced by tangent motion on a curved surface. We introduce curvature-adaptive tubular correction (CAT), a training-free plugin that regulates both effects within a shared, noise-dependent geometric budget. CAT decomposes the guidance gradient into normal and tangent components, charges normal displacement at first order and tangent displacement according to directional curvature, and obtains their jointly optimal magnitudes from a one-dimensional dual equation. Armijo backtracking calibrates the resulting finite step against the actual guidance objective, while matrix-free directional derivatives avoid constructing the full score Jacobian. We establish local guarantees for the tubular approximation, uniqueness of the correction, and sufficient objective decrease. Across seven inverse problems on FFHQ and ImageNet, CAT improves the evaluated pixel- and latent-space host samplers, with particularly consistent gains in perceptual metrics. It also improves black hole reconstruction on InverseBench and yields the lowest FID among the compared methods at every tested classifier-free guidance scale, while maintaining stable saturation and contrast. These results support curvature-aware tubular control as a reusable mechanism for stabilizing diffusion guidance.

Fairness auditing of text-to-image diffusion models often requires generating large numbers of images across sampling configurations, making comprehensive evaluation computationally expensive. We propose a causal-abstraction-based audit instrument for efficiently evaluating fairness under interventions on the classifier-free guidance scale. Given a fixed prompt and a target feature function, we represent the diffusion process as a low-level structural causal model and construct a corresponding high-level model over abstract denoising states. We characterize the projected causal structure, establish identifiability of the fairness-relevant interventional query, and provide sufficient conditions under which the high-level model preserves this query. A probabilistic transformer implements the high-level model as an amortized predictor of target-feature distributions across guidance scales. Experiments evaluate distributional fidelity, fairness-query accuracy, and computational efficiency. We present two auditing demonstrations: one using standard Stable Diffusion 1.5 and another using StayFair, a fairness-enhanced Stable Diffusion model, to examine their behavior across guidance scales.

Flow matching, together with classifier-free guidance (CFG), is widely used in generative modeling, yet much of the theoretical understanding remains distribution-wise. Since practical sampling follows individual trajectories, distribution-level guarantees alone do not fully capture how trajectories interact with the data geometry or how guidance reshapes it. To overcome this limitation, we establish a unified stagewise geometric theory of attraction and absorption for both continuous dynamics and explicit Euler discretization. Specifically, with $t\in[0,1]$ running from noise to data, we show that unconditional flow trajectories are successively attracted toward a neighborhood of the global mean, the data convex hull, and a neighborhood of a possibly nonconvex local cluster. Across these stages, the corresponding distance satisfies a common contraction estimate, yielding an ${O}(1-t)$ decay of the distance in the final stage. For CFG, the same structure persists with an extrapolated mean, an inflated conditional convex hull, and, near the target cluster, the restored local geometry of conditional flow matching. We further show that a general time schedule $a(t)$ replaces the $O(1-t)$ decay by $O(1-a(t))$. Together, these results provide a unified particle-level geometric account of flow matching and CFG across continuous and discrete sampling.

While modern generative models excel at modeling complex data, precise inference-time control in conditional generation remains a critical challenge. Classifier-free guidance (CFG) is a primary mechanism for such control, yet it is typically treated as a static tuning parameter. In flow-based models, however, the guidance scale fundamentally dictates the velocity field and the resulting probability path, making guidance selection a dynamic path-optimization problem. We introduce PathGuide, a framework that reformulates scalar CFG selection as an on-policy transport problem. Leveraging the weak form of the continuity equation, we derive a selection criterion with a direct path-correctness interpretation: we prove that if the guided field is weakly equivalent to the exact conditional field along the generated rollout, the sampler's path coincides with the target conditional law. For scalar CFG, this criterion yields a strictly quadratic local objective with an efficient, closed-form selector for each solver interval. PathGuide enables optimal guidance scales to be computed and used online during generation or fitted offline as a reusable piecewise-constant schedule. We validate our method on low-resolution image manifolds and controlled settings across various continuous-time flow constructions, demonstrating that this transport-based selector improves path alignment and sample fidelity over both fixed and state-of-the-art adaptive guidance baselines.

Multimodal protein language models (pLMs) learn joint protein sequence-structure distributions, and their generation performance should also depend critically on inference-time sampling strategies. Yet prior work has focused more on model training than on how inference-time strategies behave. In this paper, we establish a three-stage investigation framework to empirically study the inference design space of multimodal pLMs across three representative pLMs and four fundamental tasks. We evaluate vanilla sampling, task-specific classifier-free guidance, and reward-guided beam search on multimodal pLMs, corresponding to controls over sampling distributions, per-step logits, and parallel trajectories. Throughout the complementary advancements centered on exploration-exploitation trade-off, we (1) reveal the suboptimality of default inference protocols and identify task-oriented sampling preferences; (2) observe substantial quantitative gains across tasks, consistently boosting the upper bound performance of multimodal pLMs without updating model parameters; (3) derive conclusions about base models that differ from prior consensus.

Correcting flawed reasoning traces remains a significant challenge for Large Language Models (LLMs), whose autoregressive generation can propagate early mistakes into subsequent reasoning. We introduce DCGC, a Masked Diffusion Model (MDM) framework for global correction that uses an imperfect solution draft from an upstream solver as auxiliary context. DCGC combines task-specific Supervised Fine-Tuning (SFT) with a novel inference-time mechanism called Dynamic Dual-CFG. This mechanism separates problem-only and joint problem-draft branches and scales the draft-conditioned residual using a relative confidence gap. Across math, code, and knowledge reasoning benchmarks, DCGC outperforms standard sampling and simpler CFG variants, with additional results suggesting transfer to different diffusion backbones. In test-time setting where ground-truth failure labels are unavailable, DCGC improves full test set accuracy by correcting low-consensus upstream outputs, highlighting its utility as a verifier-free global correction module for difficult reasoning instances.

Diffusion Transformers (DiTs) incur high memory traffic and energy costs because sampling repeatedly evaluates large denoisers dominated by linear operations. Analog compute-in-memory (CIM) can alleviate these costs by executing linear operations within weight-storing memory arrays. However, CIM nonidealities perturb effective weights, with errors accumulating along the state-dependent denoising trajectory; their interaction with classifier-free guidance (CFG) remains underexplored. In this paper, we characterize the impact of analog CIM nonidealities on DiT sampling. Although conditional and unconditional predictions can each remain close to their clean counterparts, their difference (the CFG residual) is disproportionately attenuated and rotated. Identifying this residual as a controllable failure channel, we propose a retraining-free, sampler-side recalibration that adjusts only the CFG scale for a given CIM condition. Trajectory-level analysis shows that moderate recalibration strengthens the target-oriented component preserved in the distorted residual, enabling earlier commitment to a prompt-consistent semantic region. In contrast, excessive guidance amplifies the full noisy residual and degrades quality, resulting in a finite, noise-dependent optimum. Extensive experiments on PixArt-Sigma, PixArt-alpha, and DiT-XL/2 show that the optimal guidance scale increases with CIM noise. Using 30,000 samples per condition, guidance recalibration consistently restores generation quality across simulated CIM mappings, closing at least 87% of the CIM-induced FID gap at a CIM noise level of 0.20. It reduces FID from 59.22 to 20.49 on PixArt-Sigma, 72.37 to 21.12 on PixArt-alpha, and 20.89 to 6.62 on DiT-XL/2.