Transition Models (TiM)

• Transition Models (TiM) are generative architectures that model continuous state transitions using a dynamic, interval-conditioned training objective.
• The methodology employs an exact analytic dynamic identity to enable both rapid single-step generation and precise multi-step refinement in image synthesis.
• Empirical results show that TiM achieves superior fidelity and resolution with far fewer parameters compared to larger state-of-the-art models.

Transition Models (TiM) are a class of generative architectures that directly model the transition dynamics between states along the full generative trajectory. The key innovation is a training objective that explicitly matches the continuous-time evolution of state variables over arbitrary finite intervals, enabling both rapid single-step generation and fine-grained multi-step refinement in image synthesis tasks. TiM integrates an exact, analytic dynamic identity for the state evolution, allowing the model to learn and predict transitions between any pair of states, not just infinitesimal steps or direct endpoint mappings. This unified paradigm leads to strong parameter efficiency and scalability, with empirical results demonstrating that a TiM model with 865 million parameters surpasses significantly larger state-of-the-art systems in both fidelity and resolution.

1. Foundational Principles

TiM addresses a persistent dilemma in generative modeling: traditional iterative diffusion models deliver high-fidelity outputs through many incremental denoising steps, incurring substantial computational overhead, while few-step generators are efficient but limited by a premature quality plateau. TiM departs from these approaches by learning the transition between any states along the generative path, parameterized by an arbitrary interval $\Delta t$. This transition objective encompasses both local (infinitesimal) and global (endpoint) mappings, enabling the model to traverse the solution manifold flexibly.

The generative progress is governed by a continuous-time dynamic identity. Rather than repeatedly denoising with PF-ODEs at small steps or fixing a terminal endpoint, TiM operationalizes transitions across variable intervals. This capacity is realized via conditional prediction $f_\theta(\mathbf{x}_t, t, r)$, where the model is trained to map a noisier state $\mathbf{x}_t$ at time $t$ to a cleaner state at time $r<t$ across any $\Delta t$.

2. Mathematical Formalism

The TiM framework rests on analytic identities rooted in probability flow ordinary differential equations (PF-ODEs). Denoting the generative trajectory as $\mathbf{x}_t = \alpha_t + \sigma_t$, the evolution follows:

$$\frac{d\mathbf{x}_t}{dt} = \frac{d\alpha_t}{dt} + \frac{d\sigma_t}{dt}$$

Two auxiliary constructs, $A_{t, r}$ and $B_{t, r}$, define the transformation laws for coefficient interpolation over the interval $[r, t]$. The central invariant is

$$\frac{d}{dt} \Big[ B_{t,r} (\hat{\alpha}_t + \hat{\sigma}_t - f_\theta(\mathbf{x}_t, t, r)) \Big] = 0$$

where $\hat{\alpha}_t$ and $\hat{\sigma}_t$ are the reference coefficients, and $f_\theta$ is the model prediction for transition. The practical training target includes a residual and its exact time derivative:

$$\hat{f} = \hat{\alpha}_t + \hat{\sigma}_t + \frac{B_{t,r}}{\frac{dB_{t,r}}{dt}} \left( \frac{d\hat{\alpha}_t}{dt} + \frac{d\hat{\sigma}_t}{dt} - \frac{d f_\theta(\mathbf{x}_t, t, r)}{dt} \right)$$

The minimization occurs over all possible intervals, forcing the model to match both the value and temporal gradient of the transition across the continuous path. This yields smooth, accurate state-to-state mappings for variable discretizations.

3. Unified Generative Trajectory

TiM is architected to sample along the trajectory with arbitrary step count, adapting to varying computational budgets. Unlike diffusion models, where large timesteps induce discretization error and degrade output quality, TiM's interval-conditioned objective ensures validity for large leaps or iterative refinement. The model is robust to schedule variations, demonstrating monotonic improvement in image quality as the number of steps (NFE) increases. At $1$ NFE, TiM delivers competitive quality, and with greater steps, it continuously refines outputs without saturation, a limitation seen in previous few-step approaches.

In practice, sampling may proceed with a schedule $\{ t_0, t_1, ..., t_N \}$, invoking the same model for each $(t_{i+1}, t_i)$, guaranteeing validity regardless of the number or spacing of steps.

4. Parametric Efficiency and Performance

Empirical benchmarks show that TiM, with $865$M parameters, surpasses much larger models such as SD3.5 (8B) and FLUX.1 (12B) across GenEval scores and other fidelity metrics. For single-step sampling ($1$ NFE), TiM achieves scores around $0.67$, increasing to $0.83$ for $128$ NFE, consistently outstripping larger contemporaries. These results are sustained across FID, Inception Score, and precision/recall measures, and apply under both text-to-image and class-guided tasks.

The model exhibits strong aspect ratio and resolution generalization, maintaining quality up to $4096 \times 4096$ pixels with appropriate preprocessing.

5. Native-Resolution Training Strategy

A central practical advance is TiM's native-resolution strategy. Training is performed on images grouped into resolution buckets, preserving true aspect ratios and pixel dimensions. The time-corruption schedule is adjusted per resolution:

$$t_m = \frac{\sqrt{\frac{m}{n}} t_n}{1 + (\sqrt{\frac{m}{n}} - 1) t_n}$$

where $n$ is a base image resolution and $m$ the pixel count of a given image. This accounts for the higher "forgetting" pressure required at larger resolutions—images are corrupted with stronger noise before restoration, enabling the model to recover fine details and authentic aspect ratios. TiM achieves high-fidelity image synthesis at $4096 \times 4096$, maintaining the native patch structure and minimizing rescaling artifacts.

6. Applications and Implications

TiM is applicable wherever generative models are used and state-to-state consistency is required. Its design supports rapid generation in low-compute settings (single-step or few-step sampling) as well as high-fidelity iterative refinement if resources permit. Demonstrated use cases span text-to-image synthesis and class-conditional image generation.

The theoretically grounded transition objective generalizes naturally to other domains: video synthesis (where inter-frame consistency is critical), audio generation (temporal phase alignment), and any modality with continuous evolution paths. The paradigm challenges conventional trade-offs between fidelity and efficiency, indicating that precise modeling of transition dynamics (rather than endpoint prediction alone) can markedly improve quality and resource usage.

A plausible implication is that future foundation models may adopt similar interval-conditioned training to balance hardware constraints and output precision. By treating the generative path as a continuous manifold, TiM supports broad adaptability without sacrificing quality.

7. Comparative Perspective and Future Directions

TiM synthesizes and supersedes prior approaches—diffusion, consistency, and direct mapping—through its continuous-time, interval-adaptive objective. Its monotonic improvement and parametric economy position it as a candidate for scalable deployment. Potential future directions include extending the analytic transition framework to multimodal tasks, investigating expressiveness for stochastic (non-deterministic) transitions, and formalizing convergence properties for related ODE-based generative models.

Open research avenues encompass learning transition models for non-image domains, devising efficient training schedules for extremely high-resolution data, and applying product-derivative constraints to alternative architectures.

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Transition Models (TiM) establish a unified, mathematically rigorous learning objective for generative paths, enabling high-quality, resolution-robust synthesis with strong parametric efficiency. The TiM framework not only addresses longstanding limitations in computational cost vs. output quality but also introduces a principled strategy for interval-adaptive generative modeling across diverse applications.