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Inference-Time Scaling for Flow Models via Stochastic Generation and Rollover Budget Forcing
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Enables particle-sampling inference-time scaling for pretrained flow models by converting the deterministic ODE to an SDE, converting the linear interpolant to VP, and adaptively reallocating NFEs via Rollover Budget Forcing.
Problem
Inference-time reward alignment for pretrained flow models is hard because their deterministic ODE sampling yields identical particles, which blocks particle sampling methods that work for diffusion models; uniform NFE allocation across denoising steps is also inefficient.
Approach
Convert the flow ODE to a reverse SDE with a chosen diffusion coefficient to inject stochasticity, convert the linear interpolant to a VP interpolant at inference time to widen the proposal's search space, and use a rollover strategy that adaptively reallocates NFEs across timesteps when a higher-reward particle is found.
Key results
- On compositional T2I, VP-SDE with Rollover Budget Forcing achieves the highest given-reward VQAScore of 0.925 versus 0.788 for Linear-ODE in the ablation table.
- Quantity-aware generation: particle sampling with interpolant conversion reaches a 4-6x accuracy improvement over the base FLUX model, and RBF achieves the highest accuracy among particle methods.
- Linear-SDE already outperforms deterministic Linear-ODE methods (BoN, SoP) across particle sampling methods, showing stochasticity is key to enabling particle sampling in flow models.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| convert deterministic linear ODE generation to Linear-SDE (ablation) | FLUX particle sampling · Compositional text-to-image generation | VQAScore: 0.788 -> 0.900 | Helped |
| add adaptive timestep conversion to Linear-SDE (ablation) | FLUX particle sampling · Compositional text-to-image generation | VQAScore: 0.900 -> 0.908 | Helped |
| add adaptive timestep conversion to Linear-SDE (ablation) | FLUX particle sampling · Compositional text-to-image generation | InstructBLIP: 0.813 -> 0.813 | No clear effect |
| add diffusion coefficient scaling without timestep conversion (ablation) | FLUX particle sampling · Compositional text-to-image generation | VQAScore: 0.900 -> 0.702 | Hurt |
| add diffusion coefficient scaling without timestep conversion (ablation) | FLUX particle sampling · Compositional text-to-image generation | LPIPS-MPD: 0.158 -> 0.429 | Helped |
| combine adaptive timestep conversion and diffusion coefficient scaling as VP-SDE (ablation) | FLUX particle sampling · Compositional text-to-image generation | VQAScore: 0.900 -> 0.925 | Helped |
| combine adaptive timestep conversion and diffusion coefficient scaling as VP-SDE (ablation) | FLUX particle sampling · Compositional text-to-image generation | LPIPS-MPD: 0.158 -> 0.509 | Helped |
| use SDE generation instead of deterministic ODE generation | FLUX particle sampling · Compositional text-to-image generation | given reward | Helped |
| convert Linear-SDE to VP-SDE | FLUX particle sampling · Compositional text-to-image generation | given and held-out rewards | Helped |
| use Rollover Budget Forcing with VP-SDE | FLUX particle sampling · Compositional text-to-image generation | given reward | Helped |
| use SDE and interpolant conversion | FLUX particle sampling · Quantity-aware image generation | object count accuracy: $4\sim6 \times$ | Helped |
| use Rollover Budget Forcing | FLUX particle sampling · Quantity-aware image generation | object count accuracy | Helped |
Surprising findings
- Diffusion coefficient scaling without timestep conversion increases diversity but significantly reduces reward alignment (VQAScore drops to 0.702), showing excessive noise injection harms search.
Limitations
- Introduces additional inference-time overhead that may be a bottleneck when the base model prediction is computationally expensive.
- Pretrained model trained on uncurated data may produce undesirable outputs under malicious use.
- No error bars reported due to computational constraints.
Experimental setup
Datasets: GenAI-Bench T2I-CompBench++ numeracy DDPO animal prompts
Benchmarks: GenAI-Bench T2I-CompBench++
Metrics: VQAScore InstructBLIP score object count accuracy aesthetic score LPIPS-MPD ImageReward HPS PickScore CLIP score
Baselines: Best-of-N Search over Paths SMC (DAS) CoDe SVDD Linear-ODE Linear-SDE
Builds on: SVDD Search over Paths Sequential Monte Carlo CoDe stochastic interpolants
Closest papers by meaning
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