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Refining Generative Process with Discriminator Guidance in Score-based Diffusion Models

Dongjun Kim, Yeongmin Kim, Se Jung Kwon, Wanmo Kang, Il-Chul Moon

arXiv:2211.17091v4cs.CVcs.AIcs.LG

TL;DR

Improving sample quality with pre-trained diffusion score models has received limited research attention. This paper keeps the score model fixed and adds discriminator-based guidance during sampling; it reports new state-of-the-art FIDs across its evaluated datasets. The approach is limited at very low sampling NFEs, where discretization error dominates sampling error.

  • Problem

    Few research efforts focus on improving sample quality with pre-trained score models, even as reuse grows because training a new score model from scratch can be expensive.

    Source: §1 · p. 1

  • Method

    Discriminator Guidance keeps the pre-trained score fixed and adds a discriminator-derived correction during sample generation to steer denoising toward realistic regions.

    Source: §1 · pp. 1–2

  • Results

    The paper reports new state-of-the-art FIDs on all evaluated datasets and says discriminator-guided samples are closer to real-world data than non-guided samples.

    Source: §1 · p. 2, §7 · p. 9

  • Takeaways & Limitations

    At the optimal discriminator, the correction adjusts the model score toward the data score, providing complementary score estimation.

    Source: §1 · p. 2

    At lower CIFAR-10 sampling NFEs, discretization error dominates sampling error and makes Discriminator Guidance's gain suboptimal.

    Source: §5.2 · p. 8

Abstract

from arXiv · show

The proposed method, Discriminator Guidance, aims to improve sample generation of pre-trained diffusion models. The approach introduces a discriminator that gives explicit supervision to a denoising sample path whether it is realistic or not. Unlike GANs, our approach does not require joint training of score and discriminator networks. Instead, we train the discriminator after score training, making discriminator training stable and fast to converge. In sample generation, we add an auxiliary term to the pre-trained score to deceive the discriminator. This term corrects the model score to the data score at the optimal discriminator, which implies that the discriminator helps better score estimation in a complementary way. Using our algorithm, we achive state-of-the-art results on ImageNet 256x256 with FID 1.83 and recall 0.64, similar to the validation data's FID (1.68) and recall (0.66). We release the code at https://github.com/alsdudrla10/DG.

1. Introduction

Although pre-trained score models are increasingly reused because training from scratch is expensive, few efforts target improving their sample quality. Discriminator Guidance keeps the score model fixed, uses a discriminator to correct denoising, and reports improved generation results.

1. Introduction

  • Diffusion models have achieved human-level generation in several domains, but the authors say their behavior remains insufficiently understood.The cited domains include image, video, and text-to-image generation.Source: §1 · p. 1
  • Discriminator Guidance adjusts a pre-trained score model with an auxiliary discriminator that supplies feedback about whether denoising sample paths are realistic.The discriminator provides supervision during sample generation rather than requiring further score training.Source: §1 · pp. 1–2
  • The method achieves new state-of-the-art performance on CIFAR-10, CelebA/FFHQ 64x64, and ImageNet 256x256.Discriminator training is described as stable and fast to converge, enabling the reported gains with a cheap budget.Source: §1 · p. 2
  • The authors report that discriminator-guided samples are closer to real-world data than non-guided samples, theoretically and empirically.The figure caption says combining Classifier Guidance with Discriminator Guidance improves sample quality and intra-class diversity over Classifier Guidance alone.Source: §1 · p. 2, Figure 2 · p. 2

2. Preliminary

The preliminary section presents diffusion as a latent-variable generative process and describes its continuous-time score-based formulation. It also situates the paper's fixed-score refinement against prior approaches to improving score accuracy.

2. Preliminary

  • Diffusion models construct latent variables by progressively adding Gaussian noise to data, while the generative process reverses that sequence.The Markov-chain formulation makes the surrogate KL objective tractable.Source: §2 · p. 2
  • In the continuous-time formulation, the score network targets the data distribution's diffused score, and the reverse-time process uses that score.The text says the continuous-time framework is used mainly for notational simplicity and that the model applies to discrete- and continuous-time settings.Source: §2 · p. 3
  • Score training uses denoising score matching, which under a specified temporal weighting coincides with a joint KL-divergence objective.The text also describes equivalent noise-matching and data-reconstruction interpretations under different weighting functions.Source: §2 · p. 3
  • Prior work improves score precision through score updates or regularization, whereas this paper refines a fixed model score using noise contrastive estimation.Source: §2 · p. 3

3. Refining Generative Process with Discriminator Guidance

Discriminator Guidance corrects a fixed, converged score model during sampling using a discriminator trained on real and generated data across noise levels. The analysis relates this correction to score error and describes a quality–diversity trade-off.

3.1. Correction of Pre-trained Model Score

  • At the optimal discriminator, the adjusted score matches the correction needed for the reverse-time generative process to coincide with the data process, under Theorem 1’s assumptions.The correction is nonzero when the converged score model’s local optimum differs from the global optimum.Source: §3.1 · p. 3

3.2. Discriminator Guidance

  • A discriminator trained on real and generated samples at each noise level estimates the correction term, which is added to the fixed model score during sampling.The paper reports that discriminator guidance improves sample quality with quick convergence on CIFAR-10.Source: §3.2 · p. 4

3.3. Theoretical Analysis

  • The gain is approximately zero for an untrained, blind discriminator and is maximized at the optimal discriminator, though Theorem 2 does not guarantee strictly positive gain.The gain is the difference between the original and discriminator-adjusted score errors.Source: §3.3 · pp. 4–5

3.4. Optimality Analysis

  • ImageNet experiments show a sweet spot in DG weight that trades off sample quality (FID) and diversity (recall).At the optimal discriminator, the resulting sample distribution balances the data distribution and the non-guided distribution.Source: §3.4 · p. 5, Figure 5 · p. 5

3.5. Connection with Classifier Guidance

  • Unlike classifier guidance, which may cause mode collapse by maximizing class probability, Discriminator Guidance supervises realism and offers enhanced mode coverage.The paper suggests combining the two guidance methods because sampling from the joint distribution requires accurate score estimation.Source: §3.5 · p. 5

4. Related Works

Prior work combines diffusion and GAN models in several ways, but the paper distinguishes Discriminator Guidance by having its discriminator intervene directly during generation and training it without a generator. It also contrasts DG with rejection and MCMC sampling approaches.

Related work

  • Unlike prior diffusion–GAN approaches, DG’s discriminator intervenes directly in generation and is trained without a generator.The paper describes discriminator training as stable in this setup.Source: §4 · p. 6
  • Prior rejection-sampling and MCMC approaches use likelihood-ratio methods to reweight or sample from model distributions, whereas DG applies discriminator guidance during diffusion generation.The cited approaches include rejection sampling for implicit generator distributions and MCMC sampling.Source: §4 · p. 6
  • DG does not require sample rejection and is described as scalable to high dimensions.The paper interprets DG as maximizing and reweighting the model distribution.Source: §4 · p. 6

5. Experiments

Experiments test Discriminator Guidance on a toy score mismatch, image generation, and image-to-image translation. The method improves reported sample quality and diversity, while its gains become suboptimal at low sampling NFEs.

5.1. A Toy 2-dimensional Case

  • In the toy case, adding discriminator guidance steers an incorrect score toward the data score, unlike unguided sampling from the wrong distribution.The guided score is described as successfully guiding s to ∇log p_t^r.Source: §5.1 · p. 6

5.2. Image Generation

  • Discriminator Guidance achieves new state-of-the-art FIDs across CIFAR-10, CelebA, FFHQ, and ImageNet; on ImageNet 256x256, DiT-XL/2-G++ has the strongest FID and recall.The ImageNet comparison is presented in Table 5; the supplied passages do not give its metric values.Source: §5.2 · p. 7, Table 5 · p. 7
  • On CIFAR-10, guidance improves both data-diffusion EDM and latent-diffusion LSGM results, with other hyperparameters held fixed.The paper attributes the performance gain to the discriminator component; it also reports notable gains on human-face datasets.Source: §5.2 · p. 7
  • On FFHQ, discriminator-adjusted scores yield more accurate score estimates by the average-reconstruction diagnostic, while the adjusted density-ratio curve closely approximates the data forward-SDE curve.The reconstruction comparison uses a small σ(t) = 1; Figure 7 reports regeneration FID 1.25 without DG and 1.09 with DG after standard-Gaussian perturbation.Source: Figure 7 · p. 7, §5.2 · p. 8, Figure 8 · p. 8
  • As sampling NFEs decrease, discretization error dominates sampling error and DG’s gain becomes suboptimal; fitting DG to extremely low-NFE samplers is left for future work.Figure 9 illustrates the effect of DG with respect to sampling NFEs on CIFAR-10.Source: §5.2 · p. 8, Figure 9 · p. 8
  • Discriminator training mitigates Classifier Guidance’s precision-recall trade-off, whose initial samples have higher precision and lower recall than validation data.Figure 10 tracks precision and recall across discriminator training.Source: §5.2 · p. 8, Figure 10 · p. 8
  • The discriminator captures score-estimation error particularly at large diffusion times, which determine sample diversity.The comparison uses the same weighting function for discriminator and score losses.Source: §5.2 · p. 8, Figure 11 · p. 8

5.3. Image-2-Image Translation

  • For image-to-image translation, DG partially mitigates the realism-faithfulness trade-off, and weighted DG improves realism without hurting faithfulness.At the same translation starting time t_mid = 0.5, guided SDEdit samples are reported as more realistic than non-guided samples.Source: §5.3 · p. 8, Figure 12 · p. 9

6. Discussion

The discussion considers divergence formulations of Discriminator Guidance and possible simultaneous score-discriminator training. It presents the former as a route to a new divergence family and notes a constraint on the latter.

6. Discussion

  • The discriminator BCE loss can be generalized to h-Bregman divergence, and BCE is the unique divergence belonging to both the h-Bregman and f-divergence families.The paper presents this as suggesting a new divergence family for score estimation.Source: §6 · p. 9
  • Simultaneous score-discriminator training is a possible min-min alternative to GAN’s min-max setup, but independent losses restrict joint interplay and only marginally enhance score accuracy.Figure 13 presents the simultaneous-training experiment on CIFAR-10.Source: §6 · p. 9, Figure 13 · p. 9
  • An alternative is to modify score loss to an f-divergence, which can connect discriminator and score losses when a neural ratio approximates the true likelihood ratio.The passage says f-divergence may weight score matching more in high-density-ratio spatial regions than KL training; this is left for future work.Source: §6 · p. 9

7. Conclusion

The conclusion presents Discriminator Guidance as a way to refine denoising through adjusted score estimation, with empirical gains across datasets and a potential misuse risk.

7. Conclusion

  • Discriminator Guidance refines denoising through adjusted score estimation and achieves new state-of-the-art FIDs on all evaluated datasets.The conclusion also identifies deepfake images as a potential risk of negative use.Source: §7 · p. 9

A.1. Proof of Theorem 1

The appendix proves the score-adjustment result under stated assumptions and examines whether an assumption holds in practice. It also explains why the discriminator uses forward-time marginals.

A.1. Proof of Theorem 1

  • Under Theorem 1’s conditions, the discriminator correction is the log density ratio between the data and model marginals, and the adjusted process coincides with a diffusion process using that corrected score.The result assumes the model score matches the prior score at T and the log-likelihood equals its evidence lower bound.Source: §A.1 · p. 13
  • The proof uses the condition that the log-likelihood equals the evidence lower bound if and only if the score belongs to S_sol, alongside a twice-continuously-differentiable score assumption.The stated theorem proof also assumes the conditions from Appendix A of Song et al. (2021).Source: §A.1 · p. 13

A.2. Proof of Theorem 2

  • Theorem 2’s proof applies Girsanov’s theorem and the data-processing inequality to relate the generative and data SDEs.The supplied passages state the theorem and proof step but do not provide its full conclusion.Source: §A.2 · pp. 13–14

A.3. Validity of Assumption in Theorem 1

  • In practice, NLL and NELBO are approximately equal across a wide time horizon, supporting the theorem assumption’s validity in that examined setting.The comparison uses an EDM checkpoint and truncated NLL and NELBO estimates.Source: §A.3 · p. 14, Figure 14 · p. 14
  • Using forward-time marginals saves memory by avoiding storage of full sample trajectories and permits arbitrary diffusion noise during discriminator training, providing data augmentation that can prevent overfitting at large times.With generative marginals, the discriminator would need more sample data to prevent overfitting.Source: §A.3 · pp. 15–16

B. More on Bregman Divergences

This section frames discriminator training as density-ratio estimation with time-dependent Bregman divergences and compares several losses. BCE gives the strongest sample-quality results, while UKL is the most robust to its guidance weight.

Time-dependent Bregman divergence

  • The framework estimates a density ratio with a discriminator trained using a time-dependent Bregman divergence, including LSIF, BCE/BKL, and UKL examples.Bregman divergence measures discrepancy between density ratios; BCE is also called Binary Kullback-Leibler, and UKL is also known as KLIEP.Source: B. More on Bregman Divergences · p. 16

Bregman-divergence comparison

  • BCE concentrates most of its cumulative loss at large diffusion scales, unlike LSIF, which resembles the noise-matching loss concentrated at small scales.The authors suggest this difference may explain BCE’s performance advantage.Source: B. More on Bregman Divergences · p. 19
  • BCE performs best on CIFAR-10, while UKL is the most robust to the choice of guidance weight.The toy cases also find that BCE estimates the score-correction term most robustly.Source: B. More on Bregman Divergences · pp. 16, 19

C. Details on Image-to-Image Translation

For image-to-image translation, discriminator guidance is applied during denoising from a source image toward a target domain. It guides away from the source distribution near the intermediate time and supports realistic translations with a smaller starting noise level than SDEdit.

C. Details on Image-to-Image Translation

D.1. Training and Sampling Details

The appendix details sampling configurations and ablations for discriminator guidance across diffusion models and datasets. It reports CIFAR-10 and FFHQ gains, and studies how discriminator data, training choices, and solver settings affect performance.

D.1. Training and Sampling Details

  • For unconditional CIFAR-10 with the Heun solver, the best reported weights are (wDG_t,1st, wDG_t,2nd) = (1.67, 0), so DG need not be applied at the second-order correction stage.Omitting that correction reduces the computation needed at each denoising step.Source: §D.1 · p. 23, Figure 22 · p. 23
  • Conditional CIFAR-10 obtains an FID gain of 1.66 with (wDG_t,2nd) = (1, 0); adaptive weighting improves FID to 1.64.The adaptive strategy changes wDG_t,1st for samples with negative density-ratio on odd steps and sets Schurn = 4.Source: §D.1 · p. 23, Figure 23 · p. 23
  • On FFHQ, EDM-G++ improves from FID 2.04 with (wDG_t,2nd) = (2, 0) to FID 1.98 with adaptive DG weighting.The adaptive strategy is identical to the conditional CIFAR-10 case.Source: §D.1 · p. 24
  • Adaptive DG improves FFHQ FID from 2.04 to 1.98 using the same adaptive strategy tested on conditional CIFAR-10.The appendix also reports FID 1.64 for adaptive weighting on conditional CIFAR-10.Source: §D.1 · pp. 23–24

D.3.1. DISCRIMINATOR TRAINING

  • Reducing generated training data makes the discriminator overfit; reducing both real and generated data makes overfitting arise faster and performance worsen faster.The experiments compare full real data with partial generated data against reductions in both data sets.Source: §D.3.1 · p. 25, Figure 26 · p. 26
  • Batch size is not a crucial factor for final performance, and the tested temporal-weight choices show no significant FID difference.The discriminator training also found EMA to have nearly no effect.Source: §D.3.1 · pp. 26–27, Figure 27 · p. 26
  • Figure 25 concerns further score training of a pre-trained score model.Source: Figure 25 · p. 26
  • LVPSDE discriminator training performs better than WVE-SDE, and fine-tuning a pretrained classifier with a shallow U-Net performs strictly better than training all parameters from scratch.The authors use LVPSDE and fine-tuning as their defaults.Source: §D.3.1 · p. 26, Figure 28 · p. 27

D.3.2. AFTER DISCRIMINATOR TRAINING

These appendices examine discriminator-training saturation, guidance scales, sampling steps, and uncurated outputs. They report that guidance adjusts global generation structure and improves fidelity, while some settings impose training or scale boundaries.

D.3.2. AFTER DISCRIMINATOR TRAINING

  • LSGM’s discriminator-training performance saturates after nearly 300 epochs, with a U-Net encoder trained from scratch and no pretrained latent extractor.The authors note there is no pretrained classifier for a generic diffusion strategy or latent diffusion space.Source: §D.3.2 · p. 27, Figure 29 · p. 27
  • The optimal minimum scale for applying DG is near σ*mid = 0.0025, a strictly positive value that the authors associate partly with score-adjustment inaccuracy or discretization error.They also identify the density-chasm problem as one possible reason for the positive optimum.Source: §D.3.2 · pp. 27–28
  • Applying DG over a larger maximum diffusion scale improves performance, suggesting its effect lies in constructing global generation context rather than capturing fine details.The authors characterize DG as adjusting context-generation ability rather than cleansing fine dust in images.Source: §D.3.2 · p. 28
  • On FFHQ, discriminator guidance continues to enhance FID across the tested NFE settings.Figure 31 reports the NFE ablation after discriminator training.Source: §D.3.2 · p. 28, Figure 31 · p. 28

D.4. Uncurated Samples

  • ADM-G++ (cfg=0.10) reports FID 4.45 and recall 0.60, compared with ADM at FID 10.94 and recall 0.63.The accompanying uncurated sample figures compare the two methods across ImageNet classes.Source: §D.4 · p. 28, Figure 32 · p. 29, Figure 33 · p. 30
  • With ADM-G++ (cfg=0.75), the uncurated figures compare against ADM-G (cfg=1.50) and are presented as evidence of DG’s effectiveness on high-dimensional data.The captions report ADM-G++ FID 3.18 and recall 0.53, versus ADM-G FID 4.59 and recall 0.52.Source: §D.4 · p. 28, Figure 39 · p. 36, Figure 40 · p. 37
  • The uncurated sample figures also show outputs from LSGM-G++, EDM-G++, Soft Truncation-G++, and image-to-image translation.The sample sets cover unconditional and conditional CIFAR-10, CelebA, and FFHQ.Source: §D.4 · p. 28, Figure 46 · p. 43, Figure 47 · p. 44

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