Image Diffusion Preview with Consistency Solver

1. Introduction

• Diffusion Preview uses low-step sampling for rapid prompt or seed iteration, then applies full-step sampling with the same parameters once users approve a preview.The refinement stage produces a high-fidelity output using the model’s full capabilities.Source: §1 · pp. 1–2
• The framework targets fidelity, efficiency, and consistency; deterministic PF-ODE full-step sampling with fixed prompts and initial noise defines the refined output that previews should approximate.The three criteria require previews to resemble final outputs, minimize iteration cost, and maintain a predictable mapping from initial parameters to refined results.Source: §1 · p. 2
• Training-free ODE solvers can produce poor previews, while ODE and score distillation are costly and can disrupt PF-ODE correspondence; ODE distillation also accumulates errors.Score distillation can alter learned trajectories, and distilled models typically lose flexible inference-step selection and score estimation.Source: §1 · p. 2
• ConsistencySolver is a trainable high-order solver that uses RL to adapt pretrained-model sampling dynamics, improving low-step previews while preserving deterministic PF-ODE mapping and model flexibility.It learns a sampling strategy from data without modifying the base model.Source: §1 · p. 2
• The authors report experiments demonstrating that ConsistencySolver balances preview fidelity, efficiency, and consistency for Diffusion Preview workflows.The introduction also presents its RL-based sampling optimization as an alternative to existing acceleration techniques.Source: §1 · p. 2

• Despite diffusion models’ generative quality [15] [39], their sampling latency remains a bottleneck relative to GANs and VAEs [18].Source: §2 · p. 2

Training-free ODE solvers

• Training-free PF-ODE solvers reduced NFE from 1000 to under 50 and pushed it toward 10 using analytic, Taylor, extrapolation, multistep, and predictor-corrector methods [29, 38, 3, 24, 51, 25, 16, 23, 52].Examples include DPM-Solver’s Taylor expansion, DEIS’s polynomial extrapolation, and UniPC’s unified predictor-corrector.Source: §2 · p. 2

Distilling ODE sampling dynamics

• Distillation methods emulate multistep trajectories with single-step predictions through KID-trained DDPMs, Taylor-gradient prediction, timestep regression, or residual coefficients [46] [8] [54] [17].These methods differ in formulation but share trajectory matching as their training approach.Source: §2 · p. 2
• The proposed generalized functional form uses reinforcement learning to target efficiency, efficacy, and final-sample consistency despite limitations of segment-wise trajectory matching.Segment-wise matching can yield locally consistent but globally suboptimal alignment.Source: §2 · p. 3

3.1. PF-ODE

• The PF-ODE is the deterministic reversal of the diffusion noise-adding SDE, and can be reformulated using the noise-prediction function ε(x_t, t).Diffusion models define intermediate distributions before describing the SDE and its deterministic reversal.Source: §3.1 · p. 3

3.2. Diffusion ODE solvers

• DDIM uses a constant-noise approximation, while DPM-Solver-2 evaluates the noise prediction at a midpoint to approximate the PF-ODE integral.The section first expresses the PF-ODE solution as an integral, then describes these two approximations.Source: §3.2 · p. 3

3.3. Linear multistep method

• Linear multistep methods use multiple prior states in an ODE update to improve accuracy and convergence; explicit variants favor efficiency, while implicit variants improve stiff-ODE stability.An m-step method combines stored state vectors with derivative evaluations using method-specific coefficients.Source: §3.3 · p. 3

4.1. Adaptive ODE solvers for faithful previews

• ConsistencySolver learns timestep-conditioned multistep integration weights to maximize perceptual similarity between few-step previews and full-step outputs, optimizing its policy with PPO.Training uses a fixed, reusable offline dataset of prompt–noise–reference triples, with full-step generations serving as targets.Source: §4.1 · pp. 3–4

4.2. Theoretical grounding

• ConsistencySolver adapts classical LMMs to PF-ODE sampling with explicit updates, a current-state anchor, and timestep-conditioned learnable coefficients.The design sets w0 = 0 because PF-ODE trajectories are described as smooth and nonstiff, and retains only the latest state as the integration base.Source: §4.2 · pp. 4–5

4.3. RL vs. distillation

• Compared with distillation baselines AMED [54] and Ours-Distill, RL supports nondifferentiable rewards, generalizes better, improves reported fidelity and consistency, and reduces training memory.The method avoids backpropagation through the diffusion trajectory and stores no intermediate gradients; the passage reports higher average consistency across CLIP, DINO, Depth, and additional metrics.Source: §4.3 · p. 5

5.1. Experimental setup

• Evaluation covers Stable Diffusion text-to-image prompts from COCO 2017 and FLUX.1-Kontext editing tasks from KontextBench, using FID or editing scores, inference time, and consistency metrics.For each model, the evaluation samples 2,000 caption-noise-sample pairs; text-to-image fidelity uses FID, while editing fidelity and instruction alignment use Edit Reward and Edit Score.Source: §5.1 · p. 5

5.2. Quantitative comparison

• At 5 steps, ConsistencySolver achieves FID 20.39 versus multistep DPM-Solver’s 25.87; at up to 12 steps, it reaches FID 18.53, CLIP 97.9, and Inception 95.1.It outperforms training-free ODE solvers at equivalent steps and is competitive with or better than distillation methods at 4–8 steps.Source: §5.2 · pp. 5–6, Table 2 · p. 6
• At 5 steps on FLUX.1-Kontext, ConsistencySolver achieves the best results across all metrics, including Edit Reward 0.86 and Depth consistency 25.18.At 4 steps, its Edit Reward is 0.73 versus 0.61 and its Edit Score is 5.67 versus 5.45 for FLUX.1-Kontext.Source: Table 3 · p. 6, §5.2 · p. 6

5.3. Qualitative comparison

• Visual comparisons show sharper details and better alignment to refined outputs than training-free ODE solvers and distillation methods across text-to-image and editing examples.Editing examples include character reference, text editing, style reference, global editing, and local editing.Source: §5.3 · p. 6, Figure 3 · p. 7, Figure 4 · p. 8

5.2. Quantitative comparison

• Without retraining, the solver trained on SD1.5 achieves FID 23.32 on SDXL at 10 steps versus 26.32 for multistep DPM-Solver, and FID 20.22 on SD1.4 at 5 steps versus 25.22.It consistently outperforms training-free ODE solvers on the unseen models evaluated.Source: §5.2 · p. 6, Table 4 · p. 7

5.4. Studies on Diffusion Preview

• On LAION, Diffusion Preview reduces average inference time by up to 55% while increasing average attempts only from 6.00 to 6.35.Preview mode uses an 8-step ConsistencySolver and triggers one 40-step refinement only after the preview is judged satisfactory; prompts are capped at 10 attempts.Source: §5.4 · p. 7, Table 5 · p. 8
• On GenEval prompts, ConsistencySolver satisfies 94.2% of prompts within 10 attempts, compared with 57.0% for DMD2 with GAN and 47.1% without GAN.The study uses Claude Sonnet 4 as a proxy evaluator; the authors argue that distillation’s consistency loss is not captured by FID alone.Source: Table 6 · p. 8, §5.4 · p. 8

5.5. Ablation study

• Order 4 gives the best overall performance and Depth reward the most balanced trade-off across step counts, so both are adopted as defaults.Order 5 provides only marginal gains, while lower orders reduce structural fidelity; six reward choices were compared.Source: §5.5 · p. 8

6. Conclusion

• ConsistencySolver provides reliable few-step previews and outperforms training-free and distillation-based approaches in consistency.Source: §6 · p. 8

A. Common diffusion ODE solvers via Taylor expansion

• The integral is approximated by a Taylor expansion around n_t, yielding terms in h and successive derivatives of the noise prediction.Source: A. Common diffusion ODE solvers via… · p. 11

A.1. First-order: DDIM / Euler (na¨ıve)

• DDIM / Euler retains only the zeroth-order Taylor term, giving the approximation Δy ≈ hϵ_t.Source: §A.1 · p. 11

A.2. Second-order: DPM-Solver-2 / midpoint

• DPM-Solver-2 uses an intermediate evaluation, and its hϵr update matches the second-order Taylor integral when the derivative is estimated by a midpoint difference.It typically selects the geometric midpoint in noise-scale space.Source: §A.2 · p. 11

B. Common diffusion ODE solvers interpreted using ConsistencySolver

• DDIM maps to a one-step method with w1 = 1, while DPM-Solver-2 alternates between one-step and two-step computations.Source: B. Common diffusion ODE solvers… · pp. 11–12
• PNDM’s explicit four-step Adams–Bashforth update corresponds to a ConsistencySolver method with m = 4 and its listed four coefficients.Source: B. Common diffusion ODE solvers… · p. 11

C. Visualization of ConsistencySolver

• The Order-4 solver uses a network to generate adaptive coefficients for a multi-step noise estimate before updating the sample.At each sampling step, the diffusion model predicts noise conditioned on the prompt and timestep; the solver then updates the sample from one timestep to the next.Source: Figure S1 · p. 12, C. Visualization of ConsistencySolver · p. 12

D.1. ConsistencySolver training

• Training uses 2,000 LAION prompts paired with images generated by a 40-step multistep DPM-Solver.Source: §D.1 · p. 12

D.2. Distillation baseline training

• Final-state distillation backpropagates negative final-state reward through the full sampling chain, increasing compute by requiring diffusion-model gradients and causing severe MLP training instability.The underlying diffusion model typically contains billions of parameters, and the MLP fails to converge effectively in practice.Source: §D.2 · p. 12
• Trajectory distillation matches few-step ConsistencySolver states to corresponding states in a stored 40-step multistep DPM-Solver trajectory, outperforming final-state distillation but trailing RL training.For 5-step sampling, each ConsistencySolver step aligns with 8 reference-solver steps; the loss is negative state similarity. The comparison is reported in Tab. 2.Source: §D.2 · p. 12
• The distillation comparison uses the same 2,000 training samples as ConsistencySolver training to ensure fairness.Source: §D.2 · p. 12

• The study uses 553 GenEval prompts [11], 5,000 COCO 2017 validation prompts [22], and 5,000 randomly sampled LAION prompts [35].Source: §D.3 · p. 13
• Claude Sonnet 4 serves as an automated judge simulating a discerning user, instructed to approve an AI-generated image only when it perfectly matches prompt composition, quality, details, and realism.The prompt requires only “SATIS-FIED” for a perfect image or “NOT SATISFIED: [brief reason]” otherwise, with the reason under 50 words.Source: §D.3 · p. 13
• Twenty volunteers each evaluate 100 prompts, sequentially reviewing up to 10 pre-generated images per prompt and stopping at the first satisfactory image.Trials with no satisfactory image are discarded; generation times for the images are recorded.Source: §D.3 · p. 13

D.4. Ablation study on model structures

• The structural ablation varies hidden dimension and tests a deep 12-layer MLP with residual LayerNorm at 8 and 10 steps.Source: §D.4 · p. 13

D.5. Ablation study on solver orders

• Order 4 achieves the best overall performance across 5, 8, and 10 steps, balancing structural and perceptual metrics, semantic alignment, efficiency, and complexity.The cited table is identified as the solver-order ablation at 5, 8, and 10 steps; the prose reports the comparative findings.Source: Table S2 · p. 13, §D.5 · p. 13

D.4. Ablation study on model structures

• The 256-dimensional model consistently outperforms other tested dimensions in image similarity, semantic alignment, and overall consistency.The passage attributes this comparison to Tab. S1, which is not among the supplied passages.Source: §D.4 · p. 13
• Larger dimensions such as 1024 slightly improve depth estimation but compromise balance and efficiency.Source: §D.4 · p. 13
• The deep MLP variant shows no meaningful advantage over the standard 256-dimensional architecture, indicating moderate capacity is sufficient for this task.Source: §D.4 · p. 13

D.5. Ablation study on solver orders

• The solver-order ablation evaluates preview consistency at 5, 8, and 10 steps by varying order m in Eq. (5).The accompanying table covers solver orders at those three step counts.Source: §D.5 · p. 13, Table S2 · p. 13
• Orders 2 and 3 reduce layout and depth consistency, while Order 5 brings only marginal gains in minor dimensions, likely because its RL search space is more complex.Source: §D.5 · p. 13

D.6. Ablation study on reward models

• Depth reward consistently provides strong structural fidelity across all steps and the best balance of structural consistency and robustness, so it is adopted by default.The ablation compares reward models at 5, 8, and 10 steps.Source: §D.6 · p. 13, Table S3 · p. 14
• Img. reward performs well in pixel-level fidelity, particularly at higher steps.Source: §D.6 · p. 13
• CLIP and DINO show competitive results in semantic alignment.Source: §D.6 · p. 13

E. Latency analysis across hardware configurations

• Up to 2.04× speedup remains on resource-constrained hardware after accounting for user interaction time.The comparison incorporates an assumed user reaction time of approximately 0.3 seconds per sample.Source: E. Latency analysis across hardware… · p. 14
• On H100 GPUs, accounting for user interaction reduces overall speedup, while on M4 chips and Platinum 8480 CPUs the evaluation overhead is negligible relative to sampling.Sampling time per trial is substantially longer on the M4 chips and CPUs.Source: E. Latency analysis across hardware… · p. 14
• The latency comparison reports end-to-end preview-and-refine inference time across three datasets and different hardware configurations.It assumes approximately 0.3 seconds of user reaction time per sample, following prior studies on human visual perception.Source: E. Latency analysis across hardware… · p. 14

F. Cross-model generalization

• ConsistencySolver trained on SD1.5 produces visually superior results to training-free ODE solvers on SD1.4 and DreamShaper.The qualitative comparisons support transfer across model families.Source: F. Cross-model generalization · p. 14, Figure S2 · p. 14
• ConsistencySolver trained on SD1.5 also produces visually superior results to training-free ODE solvers on SDXL.The paper presents these qualitative comparisons as evidence of transferability across model families.Source: F. Cross-model generalization · p. 14, Figure S2 · p. 14