Image Diffusion Preview with Consistency Solver¶

Conference: CVPR 2026
arXiv: 2512.13592
Code: https://github.com/G-U-N/consolver
Area: Diffusion Models / Image Generation
Keywords: Diffusion Model Acceleration, ODE Solver, Reinforcement Learning, Preview-and-Refine, Sampling Efficiency

TL;DR¶

This paper proposes the Diffusion Preview paradigm and ConsistencySolver—a lightweight high-order ODE solver trained via reinforcement learning. It generates high-quality preview images during low-step sampling while ensuring consistency with full-step outputs. It achieves an FID comparable to Multistep DPM-Solver with 47% fewer steps and reduces user interaction time by nearly 50%.

Background & Motivation¶

Background: Diffusion models demonstrate excellence in high-fidelity image generation, but inference requires numerically solving reverse differential equations, which is computationally expensive. Existing acceleration methods fall into two categories: training-free ODE solvers (DDIM, DPM-Solver, UniPC, etc.) and post-training distillation methods (LCM, DMD2, etc.).

Limitations of Prior Work: Training-free solvers rely on theoretical assumptions and produce poor generation quality at low steps. Distillation methods require expensive retraining, destroy the deterministic mapping of the PF-ODE (the correspondence between noise space and data space), and suffer from accumulated distillation errors leading to quality degradation. Crucially, distilled models often lose the flexibility of choosing inference steps.

Key Challenge: In interactive generation (such as design prototyping), users need to quickly preview multiple variants to choose a satisfactory direction before refinement. Existing methods are either "fast but low quality and inconsistent" (training-free solvers) or "high quality but expensive and determinism-breaking" (distillation).

Goal: Design a Preview-and-Refine workflow that satisfies three requirements: (1) high preview fidelity (close to the final output); (2) high preview efficiency (low steps); (3) consistency between preview and final output (the same random seed produces visually consistent results).

Key Insight: Instead of modifying the diffusion model itself, this work optimizes the ODE solver. The integration coefficients of the solver are treated as a learnable strategy, and reinforcement learning is used to search for the optimal integration strategy.

Core Idea: Parameterize the ODE solver coefficients as a lightweight MLP and optimize them using PPO reinforcement learning, enabling low-step sampling to maximize similarity with full-step outputs.

Method¶

Overall Architecture¶

Given a text prompt and noise map, the diffusion model \(\epsilon_\phi\) predicts the denoising direction. The learnable ODE solver \(\Psi_\theta\) generates a preview image \(\mathbf{x}_p\) using a few steps, while a training-free solver \(\Psi\) generates the target image \(\mathbf{x}_{gt}\) using full steps. Similarity rewards \(\mathcal{R}\) are calculated based on depth maps, segmentation masks, DINO features, etc., and \(\theta\) is updated via PPO.

%%{init: {'flowchart': {'rankSpacing': 24, 'nodeSpacing': 28, 'padding': 6, 'wrappingWidth': 400}}}%%
flowchart TD
    DATA["Offline Triplet Dataset<br/>Prompt c + Noise z + Full-step Target x_gt"] --> SOLVER
    DM["Diffusion Model ε_φ (Frozen)"] --> SOLVER["ConsistencySolver Ψθ<br/>MLP outputs timestep-dependent weights for (t_i, t_i+1)"]
    SOLVER --> PREVIEW["K-step Preview Image x_p"]
    DATA --> GT["Full-step Target x_gt (Training-free Solver)"]
    PREVIEW --> REWARD["Multi-dimensional Similarity Reward R<br/>Depth map for training, expanded to 6D for evaluation"]
    GT --> REWARD
    REWARD --> PPO["PPO updates MLP parameters θ<br/>Only a few thousand parameters in the gradient"]
    PPO -->|Policy Iteration| SOLVER

Key Designs¶

1. Learnable Parameterization of ConsistencySolver: Replacing Fixed Theoretical Coefficients with Timestep-dependent Weights

The poor quality of training-free solvers at low steps stems from their use of hard-coded integration coefficients. These coefficients are derived under theoretical assumptions of "sufficient steps and negligible discretization error," which collapse when steps are compressed to 5–8. Starting from the general Linear Multi-step Method (LMM), this work formulates each update as \(\mathbf{y}_{t_{i+1}} = \mathbf{y}_{t_i} + (n_{t_{i+1}} - n_{t_i}) \cdot \big[\sum_{j=1}^{m} w_j(t_i, t_{i+1}) \cdot \epsilon_{i+1-j}\big]\) (where \(\mathbf{y}_t = \mathbf{x}_t / \alpha_t\) is the state normalized by noise scale). The key modification is that the multi-step weights \(w_j\) are no longer constants but are dynamically generated by a lightweight MLP \(\mathbf{f}_\theta(t_i, t_{i+1})\) based on "current timestep and target timestep."

The advantage of this form is its backward compatibility with the entire family of classical solvers: DDIM is a special case of first-order fixed weights, and DPM-Solver-2 is a special case of midpoint approximation—both simply represent specific fixed weight values within this framework. By making the weights learnable, the solver can fit the actual sampling dynamics of the model rather than adhering to theoretical values, which is why it outperforms fixed-coefficient solvers in the 5–8 step range.

2. Searching for Coefficients via PPO Instead of Distilling Them

How is the weight MLP trained? The ultimate consistency goal is that "low-step previews should closely match full-step outputs," but consistency metrics (like depth map similarity) are often non-differentiable, preventing direct backpropagation through diffusion trajectories. This work treats the solving process as a sequential decision problem and uses PPO to search: first, an offline dataset of fixed triplets \(\{(c^{(k)}, z^{(k)}, x_{gt}^{(k)})\}\) (prompt, noise, full-step target) is generated for reuse; in each episode, a batch of triplets is sampled, and the MLP-driven solver executes a \(K\)-step preview trajectory. After the trajectory, a similarity reward \(\mathcal{R} = \text{Sim}(x_{gt}, x_p)\) is computed, and the policy is updated using the standard PPO clipped surrogate objective, with advantages self-normalized by batch mean/standard deviation.

Choosing RL over distillation is not for novelty's sake: distillation requires either differentiable rewards or backpropagation through the entire diffusion trajectory, which is expensive and prone to error accumulation. RL is compatible with non-differentiable rewards, does not touch the gradients of the diffusion trajectory, and only involves a few thousand parameters of the MLP in gradient calculations, resulting in extremely low training overhead and better generalization (FID 20.39 vs. 22.91 for the distilled version in ablations).

3. Multi-dimensional Similarity Reward: Consistency Beyond a Single Metric

The "consistency between preview and final output" is multifaceted—involving semantic correctness, structural stability, and geometric accuracy. During training, depth map similarity is used as the default RL reward (geometric structure is most sensitive to low-step sampling and provides the most stable signal). During evaluation, this is expanded to six dimensions for cross-validation: CLIP semantic alignment, DINO structural consistency, Inception perceptual similarity, SegFormer segmentation accuracy, pixel-level PSNR, and depth consistency. This ensures the training signal is concentrated while confirming that previews are faithful across semantic, structural, and geometric levels during evaluation.

Loss & Training¶

A PPO clipped surrogate objective is used with a clipping parameter \(\epsilon \in (0,1)\). Advantages are normalized with batch mean and standard deviation. Only the lightweight MLP parameters (a few thousand) are updated during training; the diffusion model is fully frozen. Once trained on Stable Diffusion, the solver can be directly migrated to different architectures and scales like SD1.4, DreamShaper, and even SDXL.

Key Experimental Results¶

Main Results¶

Stable Diffusion Text-to-Image Generation (COCO 2017):

Method	Steps	FID↓	CLIP↑	DINO↑	Depth↑
DDIM	5	52.59	87.8	73.2	14.2
Multistep DPM	5	25.87	93.1	85.5	19.1
UniPC	5	23.15	93.2	85.5	18.7
ConsistencySolver	5	20.39	94.2	86.5	19.3
Multistep DPM	10	19.29	97.0	93.0	24.1
ConsistencySolver	8	18.82	96.4	91.2	22.2
LCM (Distill)	4	22.00	90.0	75.1	14.3
DMD2 (Distill)	1	19.88	89.3	73.8	12.6

Cross-model Generalization (Trained on SD1.5 → Direct Migration):

Target Model	Steps	Multistep DPM FID	ConsistencySolver FID
SDXL	10	26.32	23.32
SD1.4	5	25.22	20.22

Ablation Study¶

Comparison Dimension	Configuration	FID↓	DINO↑
Training Method	RL (PPO)	20.39	86.5
	Distillation (Ours-Distill)	22.91	85.1
	AMED (Distill)	31.09	80.8
Efficiency Comparison	ConsistencySolver 8 steps	18.82	91.2
	DPM-Solver 10 steps (Similar quality)	19.29	93.0

Key Findings¶

The FID of ConsistencySolver-5 steps (20.39) is already superior to Multistep DPM-Solver-5 steps (25.87), a reduction of approximately 21%.
8-step ConsistencySolver (FID 18.82) can match or even exceed 10-step Multistep DPM-Solver (FID 19.29), achieving a 47% step reduction (8 vs. ~15 steps to reach equivalent quality).
RL training is significantly better than distillation training (FID 20.39 vs. 22.91) and exhibits better generalization.
Solvers trained on SD1.5 can be directly migrated to SDXL, suggesting that different diffusion models share similar optimal sampling dynamics.
User studies indicate a nearly 50% reduction in overall interaction time.

Highlights & Insights¶

Paradigm of "Optimizing the Solver, Not the Model": Without touching the diffusion model weights, only a lightweight MLP with a few thousand parameters is trained, yielding significant results with minimal investment. This approach can be extended to any generative model requiring accelerated sampling.
Discovery of Cross-model Generalization: The effectiveness of a solver trained on SD1.5 when applied to SDXL suggests that optimal sampling strategies for different diffusion models share commonalities—a valuable theoretical insight.
Practical Value of the Preview-and-Refine Workflow: Dividing diffusion model usage into "rapid exploration" and "refinement" stages aligns perfectly with the actual needs of designers.

Limitations & Future Work¶

Currently only validated on image generation and image editing; not yet extended to video generation acceleration.
The choice of reward function (defaulting to depth maps) may not be optimal for all tasks.
The MLP only accepts two scalar inputs \((t_i, t_{i+1})\), without considering the state of the current image, which may limit adaptive capabilities.
Future work could explore combining ConsistencySolver with distillation methods.

vs. DPM-Solver / UniPC (Training-free Solvers): These methods use fixed theoretical coefficients, whereas ConsistencySolver uses learned adaptive coefficients, showing a clear advantage at low steps.
vs. LCM / DMD2 (Distillation Methods): Distillation methods modify model weights, destroy PF-ODE mapping, and require expensive training. ConsistencySolver leaves the model untouched, maintains complete deterministic mapping, and has extremely low training costs.
vs. AMED (Distillation Solver): Also trains solver coefficients, but AMED uses trajectory distillation, while ConsistencySolver uses RL, resulting in better generalization for the latter.

Rating¶

Novelty: ⭐⭐⭐⭐ Training an ODE solver via RL is a novel angle, and the Preview-and-Refine paradigm is highly practical.
Experimental Thoroughness: ⭐⭐⭐⭐⭐ Validation across two models, cross-model generalization, multiple baseline comparisons, user research, and detailed ablations.
Writing Quality: ⭐⭐⭐⭐⭐ Clear theoretical derivation and well-articulated relationship with classical solvers.
Value: ⭐⭐⭐⭐ High practical value, extremely low training cost, and plug-and-play capability.