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Adaptive Inference-Time Scaling via Cyclic Diffusion Search
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Proposes Adaptive Bi-directional Cyclic Diffusion (ABCD), a search-based inference framework that cycles denoising and re-noising across a temperature pool and stops adaptively, evaluated on toy MoG, OGBench PointMaze, Sudoku, pixel maze, QM9 molecules and text-to-image.
Problem
Fixed denoising schedules in diffusion inference-time scaling cannot allocate computation adaptively according to instance difficulty, so compute is either wasted or insufficient.
Approach
Iteratively cycle bi-directionally through the diffusion timeline: denoise a coarse DDIM trajectory, select top-K particles, replicate them and re-noise to multiple go-back levels from a temperature pool, and stop when top-K particles all originate from the lowest temperature for kappa consecutive cycles.
Key results
- On Sudoku harder set, ABCD reaches 0.996 accuracy at kappa=20, versus 0.955 for the best SoP setting, and 100% accuracy on the OGBench PointMaze Giant at max_iter=35 (vs 96% for best SoP).
- On QM9 molecule generation, ABCD reaches peak molecule stability of about 0.99 versus 0.94 for SoP.
- On the toy MoG Dataset 2, ABCD attains 100% success with mean 7.02 cycles, while every fixed single go-back level fails on at least one dataset.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use multiple go-back temperatures instead of a fixed go-back timestep | Diffusion inference on MoG · MoG Dataset 2, fixed 25 cycles | success rate (%): 26 -> 100 | Helped |
| Use multiple go-back temperatures instead of a fixed go-back timestep | Diffusion inference on MoG · MoG Dataset 1, fixed 25 cycles | success rate (%): 95 -> 100 | Helped |
| Use multiple go-back temperatures instead of a fixed go-back timestep | Diffusion inference on MoG · MoG Dataset 2, early stopping | success rate (%): 79 -> 100 | Helped |
| Increase ABCD max_iter from 1 to 35 (ablation) | ABCD · OGBench PointMaze Giant | success rate (%): 82±11 -> 100±0 | Helped |
| Increase ABCD max_iter beyond 35 (ablation) | ABCD · OGBench PointMaze Giant | success rate (%): 100±0 -> 100±0 | No clear effect |
| Increase persistence parameter κ from 1 to 20 (with percentage = 1.0) (ablation) | ABCD · Sudoku harder test set (17–28 given entities) | accuracy: 0.95 ± 0.06 -> 0.996 ± 0.01 | Helped |
| Use an adaptive terminal criterion rather than a fixed cycle length (ablation) | ABCD · Pixel Maze size 15 | success rate | Helped |
| Increase the percentage threshold from 0.6 to 1.0 (with κ = 1) (ablation) | ABCD · Sudoku harder test set (17–28 given entities) | accuracy: 0.82 ± 0.14 -> 0.95 ± 0.06 | Helped |
Surprising findings
- Fixed small go-back steps succeed on one-region MoG but fail to escape poor initializations on two-region MoG, whereas large go-back steps overshoot and degrade on the single-region case.
Limitations
- Scalability to high-dimensional outputs such as high-resolution image or video generation is unexplored.
- Theoretical properties of the search are largely unexamined.
- Search requires online compute at inference; the authors suggest amortizing the search as future work.
Experimental setup
Datasets: Mixture of Gaussians (toy) OGBench PointMaze SAT-Net Sudoku RRN Sudoku maze-dataset pixel mazes QM9 Stable Diffusion pretraining data
Benchmarks: OGBench PointMaze (Large, Giant) Sudoku harder set (17-28 givens) Pixel Maze (sizes 11-15) QM9 molecule stability Text-to-image compressibility, aesthetic, HPSv2
Metrics: success rate accuracy molecule stability reward score wall-clock time NFE
Baselines: Base Diffusion Best-of-N Diffusion Beam Search Sequential Monte Carlo Diffusion Search over Paths
Builds on: DDIM Search-over-Paths Sequential Monte Carlo diffusion Diffusion beam search Diffuser
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