Adversarial Flow Models (2511.22475v1)

Abstract: We present adversarial flow models, a class of generative models that unifies adversarial models and flow models. Our method supports native one-step or multi-step generation and is trained using the adversarial objective. Unlike traditional GANs, where the generator learns an arbitrary transport plan between the noise and the data distributions, our generator learns a deterministic noise-to-data mapping, which is the same optimal transport as in flow-matching models. This significantly stabilizes adversarial training. Also, unlike consistency-based methods, our model directly learns one-step or few-step generation without needing to learn the intermediate timesteps of the probability flow for propagation. This saves model capacity, reduces training iterations, and avoids error accumulation. Under the same 1NFE setting on ImageNet-256px, our B/2 model approaches the performance of consistency-based XL/2 models, while our XL/2 model creates a new best FID of 2.38. We additionally show the possibility of end-to-end training of 56-layer and 112-layer models through depth repetition without any intermediate supervision, and achieve FIDs of 2.08 and 1.94 using a single forward pass, surpassing their 2NFE and 4NFE counterparts.

• The paper presents a unified framework that combines adversarial objectives with deterministic flow-based transport to address instability in traditional generative models.
• It incorporates a squared Wasserstein-2 transport constraint and gradient normalization to balance adversarial and transport losses across single-step and multi-step training.
• Empirical results demonstrate state-of-the-art FID scores on ImageNet-256px, highlighting improved stability and efficiency in both guidance-free and guided settings.

Adversarial Flow Models: Unified Framework for Deterministic Transport and Distribution Matching

Introduction and Motivation

The "Adversarial Flow Models" paper (2511.22475) develops a unified generative modeling framework that incorporates adversarial objectives with flow-based transport, addressing fundamental limitations in both classical GANs and flow-matching approaches. Standard GANs enforce marginal distribution matching without constraining the underlying transport plan, resulting in unstable optimization and degenerate generator dynamics. Flow-matching and consistency-based models introduce deterministic transport but rely on iterative prediction of probability flows, leading to high computational overhead, wasted modeling capacity, and error accumulation, especially in few-step or single-step settings.

The proposed adversarial flow models (AFM) leverage a hybridization: they enforce an optimal deterministic transport plan via flow-based objectives while using the adversarial discriminator for perceptual distribution matching. This approach stabilizes adversarial training for transformers, enables native single-step and multi-step generation, and matches or surpasses previous state-of-the-art FIDs on ImageNet-256px under comparable computational budgets and architectures.

Technical Formulation

AFM builds on the standard GAN paradigm, wherein the generator $G$ maps samples $z$ from a prior $\mathcal{Z}$ to data $x$ in $\mathcal{X}$, and the discriminator $D$ differentiates real and generated samples. Unlike traditional GANs, the generator is regularized to learn the deterministic optimal transport identical to linear flow-matching:

$$\mathcal{L}^G_{\mathrm{AF}} = \mathcal{L}^G_{\mathrm{adv}} + \lambda_{\mathrm{ot}} \mathcal{L}^G_{\mathrm{ot}},$$

where $\mathcal{L}^G_{\mathrm{adv}}$ is the relativistic adversarial loss, and $\mathcal{L}^G_{\mathrm{ot}}$ enforces the squared Wasserstein-2 transport constraint. Critically, the prior and data distributions are dimensionally matched ($x, z \in \mathbb{R}^n$), ensuring feasible deterministic mappings.

The multi-step extension proceeds by interpolating between $x$ and $z$ via $x_t = A(t) x + B(t) z$ for $t \in [0, 1]$ (typically linear), and parameterizing $G(x_s, s, t)$ to jump between arbitrary timesteps. This enables both designated few-step and any-step generation, with matching adversarial objectives and optimal transport regularizers at each sampled timestep.

Figure 1: Schematic comparison—GANs learn arbitrary transport, flow matching achieves deterministic transport but suffers discretization error, adversarial flow models yield deterministic optimal transport for any-step training and generation.

Stabilizing Adversarial Training

A major challenge in transformer-based GAN training is generator drifting and divergence, driven by the lack of uniquely defined transport targets. Incorporating the optimal transport loss into adversarial flow models breaks the generative symmetry and enforces a single global minimum, yielding robust convergence and stable training even for large architectures. Gradient normalization is introduced to stabilize scale between adversarial and transport loss components, enabling hyperparameter transferability across model scales.

Varying the scale $\lambda_{\mathrm{ot}}$ empirically demonstrates its necessity: too small fails regularization, too large enforces the identity map, which damages distribution matching.

Figure 2: Influence of $\lambda_{\mathrm{ot}}$—small values insufficiently regularize, large values force identity; careful annealing is required for optimal performance.

Distribution Matching, Guidance Integration, and Deep Architectures

Flow-based models trained with Euclidean objectives exhibit semantic mixing, limited perceptual realism, and susceptibility to out-of-distribution sampling in high-dimensional spaces. By contrast, adversarial flow leverages the learnable discriminator as a semantic metric, optimizing for perceptual quality and distributional fidelity. In guidance-free settings, adversarial flow models outperform flow matching, producing more natural samples—substantiated by lower FID scores and visually richer outputs.

Classifier guidance (CG) and classifier-free guidance (CFG) are elegantly incorporated: AFM permits flow-based guidance via time-conditioned classifiers, with guidance gradients progressively accumulated along the probability flow. This decouples conditional alignment and sampling temperature, paralleling techniques in diffusion models.

Figure 3: Qualitative ImageNet samples (B/2, FID=3.05, IS=269.18), demonstrating high-fidelity single-step generation with CG+DA.

Deep model architectures are enabled via transformer block repetition—extra-deep single-step models (56 and 112 layers) are trained with pure single-step objectives and no intermediate supervision, delivering new best FIDs (2.08/1.94) and affirming the importance of depth scaling for generative capacity.

Figure 4: XL/2 56-layer 1NFE (FID=2.08, IS=298.33), revealing superior sample quality through deep end-to-end transport.

Quantitative Evaluation and Empirical Insights

Extensive ablation, comparative, and qualitative analyses are provided. Key empirical findings include:

• Single-step adversarial flow models approach or surpass the best consistency-based models at matched batch size and architecture, demonstrating superlinear scaling with model size.
• Guidance-free adversarial flow models outperform flow-matching baselines with dramatically fewer NFE—XL/2 1NFE (FID=3.98) vs. DiT-XL/2 250NFE (FID=9.62).
• Guidance integration is effective but less critical for AFM: unguided models are already perceptually superior compared to their consistency counterparts.
• Depth scaling is transformative: extra-deep single-pass models outperform multi-step versions, highlighting architectural over objective limitations.

Figure 5: XL/2 2NFE No-Guidance (FID=2.36), underscoring the perceptual realism of unguided adversarial flow generation.

Practical and Theoretical Implications

Adversarial flow models reconcile the deterministic transport of flow-matching with the semantic perceptual reach of adversarial training, crucially enhancing stability and quality for transformer-based architectures. Their capacity for native single-step generation (without intermediate time propagation or teacher-forcing), efficient few-step training, and end-to-end depth scaling makes them highly attractive for large-scale image synthesis, and potentially extensible to video, multimodal, or non-Euclidean generative domains.

Theoretically, AFM demonstrates that a learnable $R^n \rightarrow R^1$ distance metric (the discriminator) is a principled solution for perceptual distribution matching in high-dimensional data, a limitation inherited by traditional flow and diffusion frameworks. The separation and disentanglement of transport and distribution objectives in AFM may further inspire hybrid training approaches for other generative models.

Future Directions

Research directions include: principled alternatives for discriminator augmentation, efficient regularizations and computation sharing for adversarial objectives, representational latent space integration, further scaling studies, and extensions to autoregressive and multimodal generative modeling. The framework promises deeper insights into the geometry, optimization, and interpretability of modern generative models.

Conclusion

Adversarial flow models establish a unifying paradigm for generative modeling, combining deterministic transport with robust distribution matching. By resolving long-standing instability in adversarial training for transformers and unlocking highly efficient and realistic generation, this framework sets a new benchmark in single-step and few-step image synthesis. It suggests profound practical and theoretical prospects for the next generation of generative models.