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Learning Energy-Based Models by Cooperative Diffusion Recovery Likelihood
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Proposes CDRL, which jointly trains a sequence of conditional EBMs (on noisy diffusion levels) with Gaussian initializer networks that amortize MCMC sampling, achieving state-of-the-art EBM FID on CIFAR-10 and ImageNet 32x32.
Problem
Training and sampling energy-based models on high-dimensional image data is expensive (many MCMC steps) and EBM sample quality lags behind GANs and diffusion models.
Approach
Learn a sequence of conditional EBMs trained by diffusion recovery likelihood, each paired with a Gaussian initializer that proposes starting points for a few Langevin steps; the initializer absorbs the EBM's MCMC transitions via cooperative training, plus a new log-SNR cosine noise schedule and a fixed-noise pairing for variance reduction.
Key results
- CDRL-large reaches FID 3.68 on unconditional CIFAR-10, versus 9.58 for DRL and 4.31 for CDRL base, the best among EBM methods reported.
- CDRL achieves FID 9.35 on unconditional ImageNet 32x32, against 22.16 for CLEL-base and 26.31 for CF-EBM.
- CDRL uses 15 Langevin steps per noise level (vs 30 in DRL) and reaches FID 4.31 with 90 total MCMC steps; OOD AUROC on CIFAR-100 is 0.78 vs 0.72 for CLEL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace DRL with CDRL cooperative training | EBM generation · CIFAR-10 | FID: 9.58 -> 4.31 | Helped |
| Use CDRL instead of DDPM++(VP, NLL) | Unconditional generation · ImageNet 32×32 | FID: 8.42 -> 9.35 | Hurt |
| Remove cooperative training (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 6.47 | Hurt |
| Remove noise variance reduction (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 5.51 | Hurt |
| Have the initializer predict clean x0 instead of the noised sample (ablation) | CDRL initializer · CIFAR-10 | FID: 4.31 -> 5.17 | Hurt |
| Have the initializer predict total added noise (ablation) | CDRL initializer · CIFAR-10 | FID: 4.31 -> 4.95 | Hurt |
| Replace the proposed noise schedule with DRL-T8 (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 4.94 | Hurt |
| Train the initializer from y_t rather than the EBM-refined sample (ablation) | CDRL initializer · CIFAR-10 | FID: 4.31 -> 5.95 | Hurt |
| Reduce noise levels from 6 to 5 (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 5.08 | Hurt |
| Reduce noise levels from 6 to 4 (ablation) | CDRL · CIFAR-10 | FID | Hurt |
| Reduce Langevin steps from 15 to 10 (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 4.50 | Hurt |
| Increase Langevin steps from 15 to 30 (ablation) | CDRL · CIFAR-10 | FID: 4.31 -> 5.08 | Hurt |
Surprising findings
- Reducing MCMC steps to 3 per noise level degrades FID to 9.67, and increasing Langevin steps to 30 worsens FID to 5.08 relative to 15 steps.
- Training the initializer directly on the data y_t instead of the EBM-refined samples raises FID from 4.31 to 5.95.
Limitations
- A nontrivial number of MCMC steps is still required during generation.
- Only low-resolution (32x32 and 64x64) experiments; high-resolution generation is left to future work.
Experimental setup
Datasets: CIFAR-10 ImageNet 32x32 CelebA CelebA-HQ
Benchmarks: CIFAR-10 ImageNet 32x32 CelebA CIFAR-100 SVHN
Metrics: FID Inception Score AUROC sampling time
Baselines: DRL CLEL CF-EBM EBM-CD VAEBM CoopFlow DDPM++
Builds on: diffusion recovery likelihood CoopNets classifier-free guidance DDPM
Closest papers by meaning
- Improving Adversarial Energy-Based Model via Diffusion Process (ICML 2024 · similarity 0.90)
- Revisiting Diffusion Models: From Generative Pre-training to One-Step Generation (ICML 2025 · similarity 0.89)
- Learning Latent Space Hierarchical EBM Diffusion Models (ICML 2024 · similarity 0.88)
- Energy Matching: Unifying Flow Matching and Energy-Based Models for Generative Modeling (NeurIPS 2025 · similarity 0.88)
- Learning Diffusion Models with Flexible Representation Guidance (NeurIPS 2025 · similarity 0.88)
- Equilibrium Matching: Generative Modeling with Implicit Energy-Based Models (NeurIPS 2026 · similarity 0.88)
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