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Greed is Good: A Unifying Perspective on Guided Generation
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Shows that posterior guidance (Tweedie-style target-prediction gradient) is a greedy special case of end-to-end guidance (DTO/OTD), and interpolates between them with higher-order solvers to trade compute for gradient accuracy.
Problem
Training-free gradient-based guidance of flow/diffusion models has two families, posterior guidance (cheap, gradient through predicted clean sample) and end-to-end guidance (backprop through the full ODE solve, expensive), with no unified theory connecting them.
Approach
Views posterior guidance as a greedy one-step (Euler) approximation of end-to-end guidance, proves it is an explicit Euler DTO scheme and first iterate of implicit Euler OTD, bounds the gradient error by O(h^2), and proposes using multi-step or higher-order Runge-Kutta solvers to interpolate between the two families.
Key results
- On HDR reconstruction, Greedy (5-step Euler) reaches PSNR 28.27 and FID 35.35, beating DAPS (27.12 PSNR, FID 42.97) and DPS (22.73 PSNR).
- On QM9 polarizability guidance, DTO (50-step) achieves MAE 1.404 vs. greedy (Euler) 11.282, while greedy (5-step Euler) reaches 4.177.
- Greedy (Euler) on random inpainting gives PSNR 30.87 vs. DAPS 31.12 and DPS 25.46 on 100 FFHQ images.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use midpoint instead of Euler guidance (ablation) | Greedy guidance · FFHQ Inpaint (random) | PSNR: 30.87 -> 31.03 | No clear effect |
| Use 2-step Euler instead of Euler guidance (ablation) | Greedy guidance · FFHQ Inpaint (random) | PSNR: 30.87 -> 30.80 | No clear effect |
| Use midpoint instead of Euler guidance (ablation) | Greedy guidance · FFHQ Gaussian deblurring | PSNR: 28.01 -> 28.36 | No clear effect |
| Use more Euler guidance steps (ablation) | Greedy guidance · HDR reconstruction | PSNR: 25.07_{\pm 4.25} -> \textbf{28.27} _{\pm 4.01} | Helped |
| Use 2-step Euler instead of Euler guidance (ablation) | Greedy guidance · QM9 polarizability α | MAE: 11.282 -> 5.667 | Helped |
| Use midpoint instead of Euler guidance (ablation) | Greedy guidance · QM9 polarizability α | MAE: 11.282 -> 5.313 | Helped |
| Use 5-step Euler guidance instead of Euler guidance (ablation) | Greedy guidance · QM9 polarizability α | MAE: 11.282 -> 4.177 | Helped |
| Use greedy Euler guidance instead of unguided generation | EquiFM · QM9 polarizability α | MAE: 9.525 -> 11.282 | Hurt |
| Increase DTO gradient discretization steps (ablation) | DTO guidance · HDR reconstruction | PSNR: 13.16 _{\pm 1.15} -> 16.37 _{\pm 1.38} | Helped |
| Use Greedy (5-step Euler) instead of DAPS | Greedy guidance · HDR reconstruction | PSNR: ${2 7 . 1 2}_{ \pm 3.53}$ -> \textbf{28.27} _{\pm 4.01} | Helped |
Surprising findings
- Greedy posterior guidance with multi-step Euler outperforms full end-to-end DTO at similar compute budgets on HDR reconstruction.
- Single-step greedy (Euler) guidance is highly unstable on QM9 molecule property guidance, performing worse than the unguided EquiFM model on polarizability.
Limitations
- No statistical error bars reported for most experiments, as stated in the checklist.
- Higher-order Runge-Kutta solvers (Ralston, RK4) were unstable with large step sizes on molecular generation.
- Theory assumes affine probability paths and a flow model trained to zero loss.
Experimental setup
Datasets: FFHQ 256x256 QM9
Benchmarks: FFHQ inverse problems (inpainting, deblurring, HDR) QM9 property-guided generation
Metrics: PSNR SSIM LPIPS FID MAE atom stability molecule stability
Baselines: DPS DAPS RED-diff DTO (D-Flow) EquiFM
Builds on: DPS (diffusion posterior sampling) D-Flow DAPS adjoint method for neural ODEs EquiFM
Closest papers by meaning
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