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Transition Models: Rethinking the Generative Learning Objective

Zidong Wang, Yiyuan Zhang, Xiaoyu Yue, Xiangyu Yue, Yangguang Li, Wanli Ouyang, Lei Bai

arXiv:2509.04394v1cs.LGcs.CV

TL;DR

Diffusion models require many function evaluations, while few-step objectives can plateau or lose refinement dynamics. TiM learns arbitrary-interval state transitions and reports strong GenEval results with quality improving from one step to many.

  • Problem

    Diffusion incurs high inference cost from many NFEs, while few-step objectives can plateau and lack the trajectory consistency needed for refinement.

    Source: §1 · pp. 1–2

  • Method

    TiM learns state-to-state transitions along the PF-ODE trajectory for arbitrary time intervals.

    Source: §1 · p. 2

  • Results

    TiM scores 0.67 on GenEval at 1-NFE and 0.83 at 128-NFE, outperforming SD3.5-Large (8B) and FLUX.1-Dev (12B).

    Source: §1 · p. 2

  • Takeaways & Limitations

    The paper concludes that a unified model can improve in quality from one step to many while scaling to ultra-high resolutions.

    Source: §5 · p. 8

    Content safety and controllability remain open; fidelity can degrade on text and hands, and occasional 3072 × 4096 artifacts may reflect autoencoder bias.

    Source: §5 · p. 8

Abstract

from arXiv · show

A fundamental dilemma in generative modeling persists: iterative diffusion models achieve outstanding fidelity, but at a significant computational cost, while efficient few-step alternatives are constrained by a hard quality ceiling. This conflict between generation steps and output quality arises from restrictive training objectives that focus exclusively on either infinitesimal dynamics (PF-ODEs) or direct endpoint prediction. We address this challenge by introducing an exact, continuous-time dynamics equation that analytically defines state transitions across any finite time interval. This leads to a novel generative paradigm, Transition Models (TiM), which adapt to arbitrary-step transitions, seamlessly traversing the generative trajectory from single leaps to fine-grained refinement with more steps. Despite having only 865M parameters, TiM achieves state-of-the-art performance, surpassing leading models such as SD3.5 (8B parameters) and FLUX.1 (12B parameters) across all evaluated step counts. Importantly, unlike previous few-step generators, TiM demonstrates monotonic quality improvement as the sampling budget increases. Additionally, when employing our native-resolution strategy, TiM delivers exceptional fidelity at resolutions up to 4096x4096.

1. Introduction

Diffusion and few-step generators face a fidelity–compute trade-off rooted in objectives restricted to local dynamics or fixed endpoints. TiM instead learns arbitrary-interval state transitions along the PF-ODE trajectory.

1. Introduction

  • TiM scores 0.67 on GenEval at 1-NFE and 0.83 at 128-NFE, outperforming SD3.5-Large (8B) and FLUX.1-Dev (12B).Figure 1 also shows TiM outperforming Flux.1 models across NFEs, resolutions, and aspect ratios.Source: Figure 1 · p. 1, §1 · p. 2
  • Diffusion’s iterative denoising raises inference latency and compute cost, while few-step methods plateau and remain below high-NFE diffusion quality.The paper frames this as a trade-off between fidelity and computational efficiency rooted in the granularity of training supervision.Source: §1 · pp. 1–2
  • Local PF-ODE training is accurate only at small steps, as larger steps make discretization error dominate.The paper argues that the objective should therefore allow flexible step sizes.Source: §1 · p. 2
  • Few-step endpoint objectives lack an approximate semigroup, so extra steps can change the path, cause schedule sensitivity, and lead to early saturation.The proposed alternative calls for trajectory consistency so intermediate steps refine one trajectory.Source: §1 · p. 2
  • TiM learns transitions from any state to a previous state for arbitrary intervals, parameterizing state-to-state transitions along the PF-ODE trajectory.The paper describes this as learning the generative process’s solution manifold rather than approximating a differential equation or statistic map.Source: §1 · p. 2

2. Related Work

Prior approaches trade iterative quality for few-step efficiency, and text-to-image distillation relies on teacher-based pipelines. TiM is presented as a from-scratch model for arbitrary-step sampling with quality that improves as sampling increases.

2. Related Work

  • Diffusion models iteratively solve a PF-ODE or SDE with many function evaluations, while Consistency Models use direct few-step mappings but saturate and have complex training requirements.FlowMap and MeanFlow train CM-like models from scratch but are described as inheriting stagnation with more steps.Source: §2 · p. 2
  • Text-to-image distillation methods either match a teacher’s output distribution or mimic its generation path, while hybrid methods combine the two.The cited examples include SD-Turbo and DMD for distribution distillation, and LCM and PCM for trajectory distillation.Source: §2 · p. 2
  • Figure 2 contrasts local-vector-field learning and fixed-endpoint maps with TiM’s arbitrary state-to-state transitions, which unify few-step and many-step generation.The paper associates this approach with learning the solution manifold of the generative process.Source: Figure 2 · p. 3
  • TiM is presented as the first text-to-image generator trained from scratch for arbitrary-step sampling, with strong few-step results that improve monotonically with more compute.The paper contrasts this with few-step distillation methods that require a large pre-trained teacher and costly pipelines.Source: §2 · p. 3

3. Transition Models

Transition Models generalize diffusion’s local PF-ODE supervision to state transitions over arbitrary intervals, learning the generative process’s solution manifold. This supports sampling from large leaps to fine-grained iterative refinement.

3.1. Limitation of PF-ODE Supervision

  • PF-ODE supervision constrains training to local dynamics, so numerical solvers use small steps or high-order substeps, inducing large NFE counts.Source: §3.1 · pp. 3–4

3.2. State Transition

  • The State Transition Identity enforces path consistency across composed steps; derivative supervision smooths the solution manifold for coherent large steps and stable small-step refinement.Source: §3.2 · p. 4

3.3. Scalability and Stability in TiM Training

  • DDE uses forward-pass finite differences, is about 2× faster than JVP, and is FSDP-compatible; short-interval weighting addresses loss spikes from large transitions.Source: §3.3 · p. 5

3.4. Improved Architectures

  • Separate encoders distinguish absolute time from interval, while Interval-Aware Attention conditions spatial query, key, and value computations on interval magnitude.The design targets coarse restructuring for large steps and local refinement for small ones.Source: §3.4 · p. 5
  • TiM offers any-step generation on GenEval, with strong few-step performance and consistent, stable quality improvements as NFE increases.The table caption defines 1-NFE as one sampling step and 8-NFE as four steps with CFG.Source: Table 2 · p. 6

4. Experiments

TiM is evaluated on text-to-image generation across sampling budgets and in ablations of its objective, architecture, and training strategy. The reported results cover GenEval, MJHQ30K, and ImageNet-256.

4.1. Setup

  • The 865M-parameter text-to-image model is trained from scratch on 33M public-dataset images using native-resolution strategies and resolution-dependent timestep shifting.Sampling supports arbitrary step counts; the text encoder is Gemma3-1B-it.Source: §4.1 · pp. 6–7

4.2. Text-to-Image Generation

  • TiM achieves an SOTA FID of 5.25 on MJHQ30K, beats 8-NFE distilled models at 1-NFE on GenEval, and improves monotonically with NFE.Its 128-NFE quality rivals closed-source models, and its 8-NFE performance on DPGBench exceeds 100-NFE baselines such as SDXL.Source: §4.2 · p. 7

4.3. Ablation Studies

  • On ImageNet-256, the TiM objective reduces 1-NFE FID by over 6× versus the SiT objective, while DDE is more scalable than JVP.The comparison uses a 131M-parameter model trained for 80 epochs; the reported reduction is 309.5 → 49.91.Source: §4.3 · p. 7
  • Combining Decoupled Time Embedding and Interval-Aware Attention lowers 8-NFE FID from 33.08 to 29.21, outperforming either addition alone.Both components individually improve performance across sampling steps.Source: §4.3 · p. 7
  • Interval weighting consistently improves the best architecture, yielding FID scores of 47.46 / 24.62 / 17.10 at 1, 8, and 50 NFEs.The study reports these as the final and best scores across the three sampling budgets.Source: §4.3 · p. 7

5. Conclusion and Limitations

The conclusion presents TiM as a flexible model that improves quality with more sampling steps and scales to high resolutions. It also identifies content safety, controllability, fine detail, and some high-resolution outputs as limitations.

5. Conclusion and Limitations

  • Table 6 evaluates resolution generation on GenEval, including six listed aspect ratios, and treats scores below 0.10 as failure to generalize.Source: Table 6 · p. 8
  • TiM’s 865M-parameter model is reported to outperform multi-billion-parameter models, improve monotonically from one step to many, and scale to ultra-high resolutions.The paper frames this as evidence for a unified generative model that is efficient and scalable.Source: §5 · pp. 7–8
  • Content safety and controllability remain open challenges; fidelity can degrade on fine details such as text and hands, with occasional high-resolution artifacts likely tied to autoencoder bias.The artifact example is 3072 × 4096.Source: §5 · p. 8

Appendix

  • The appendix provides the State Transition Identity derivation, training and sampling algorithms, method comparisons, implementation details, and additional results.Source: Appendix · p. 13

A. Transition Model Framework

  • The Transition Model Framework section derives the TiM identity equation, presents training and sampling algorithms, and analyzes connections to existing methods.Source: A. Transition Model Framework · p. 13

A.1. TiM Identity Equation Derivation

The derivation uses symmetry between two equations to obtain the TiM identity. It decomposes coefficients and substitutes the resulting expressions into an earlier equation.

A.1. TiM Identity Equation Derivation

  • For Eqs. (18) and (19), the derivation uses Ct,r as a simplified denominator for At,r and Bt,r when calculating each term.Source: §A.1 · p. 13
  • Symmetry between the preceding equations is identified as key to the TiM identity, which follows by combining Eqs. (16), (17), and (21).Source: §A.1 · p. 13
  • The derivation decomposes the coefficients of x and ε in Eq. (23) before substituting Eqs. (23)–(25) into Eq. (7).Source: §A.1 · p. 14

A.2. TiM Training Algorithm

TiM trains a transition function for arbitrary time intervals and samples by repeatedly applying such transitions. Its objective generalizes diffusion training, recovering the diffusion target in the infinitesimal-interval limit.

A.2. TiM Training Algorithm

  • TiM is trained from scratch, with its training procedure specified in Algorithm 1.The supplied algorithm passages show noisy-state construction and a transition target, but do not provide enough intact text to summarize further steps.Source: §A.2 · p. 14, §A.3 · p. 15

A.3. TiM Sampling Algorithms

  • For multi-step sampling, TiM can add stochasticity to the sampling process to improve diversity, with a scaling factor used to balance stochasticity and stability.The sampling discussion relates this option to an SDE diffusion process.Source: §A.3 · pp. 14–15

B.1. Connections with Diffusion Models

  • TiM’s training objective generalizes the standard diffusion objective, reducing to the diffusion identity as t→r; the diffusion target itself lacks state-to-state transitions.The section identifies this missing transition modeling as a limit on arbitrary-step generation.Source: §B.1 · p. 16

B. Connections with Existing Methods

  • TiM shares diffusion-model parameters and time distributions but learns a different objective, whose identity target becomes the diffusion target as t approaches r.The section also supplies transport-specific time-distribution details in Table 8.Source: §B.1 · p. 16, Table 8 · p. 16

B.2. Connections to Other training Methods

TiM relates its continuous-time transition objective to several consistency and flow-based training strategies. Its architecture adds decoupled time embeddings and interval-aware attention to DiT, with cross-attention for text conditioning.

B.2. Connections to Other training Methods

  • TiM’s objective reduces to the continuous-time consistency-model objective when r = 0.The supplied comparison specifies the squared-distance loss setting for this reduction.Source: §B.2 · p. 17
  • TiM generalizes discrete state-to-state transitions in consistency trajectory, phased consistency, and Shortcut models to continuous time.Its identity equation specifies transitions between arbitrary states.Source: §B.2 · p. 18
  • For CTM and PCM, the target is an intermediate state; PCM learns the identity independently on each trajectory segment, and CTMs coincide with Shortcut models under a stated timestep condition.The condition is tn−1 = (tn+r)/2.Source: §B.2 · p. 19
  • TiM’s objective also reduces to the MeanFlow objective under the OT-FM transport setting.The section gives the corresponding OT-FM parameterization.Source: §B.2 · p. 19

C.1. Model Architecture

  • The DiT architecture uses decoupled time embeddings and interval-aware attention with LoRA-AdaLN, and incorporates text caption features through cross-attention.LoRA-AdaLN avoids increasing model size, according to the passage.Source: §C.1 · p. 19

C.2. Text-to-Image Training Details

The text-to-image setup combines native-resolution training, resolution-dependent timestep shifting, and model-guidance training. The accompanying additional-results tables cover transport, DDE ϵ, timestep-sampling, and time-weighting ablations.

C.2. Text-to-Image Training Details

  • Native-resolution training resizes images to dimensions divisible by 32, groups equal-size images into buckets, and supports resolutions up to 4096 × 4096 with batch size 1.The stated resizing example maps 1025 × 513 to 1024 × 512 while preserving resolution and aspect ratio as much as possible.Source: §C.2 · p. 19
  • Timestep shifting maps sampled timesteps across resolutions, using 1024 × 1024 pixels as the base resolution.The passage motivates this adjustment by noting that higher-resolution images require stronger corruption than lower-resolution images.Source: §C.2 · pp. 19–20
  • The 865M-parameter TiM-T2I model is trained from scratch for about 30 days on 16 NVIDIA-A100 GPUs, and uses model-guidance training with CFG scale ω = 1.75 after 100K iterations.The passage also specifies a constant learning rate of 4 × 10−4.Source: §C.2 · p. 20

D. Additional Results

  • The additional-results tables cover ablations of transport, DDE ϵ, timestep sampling, and time-weighting functions.Their captions specify these topics but do not provide the table values.Source: Table 9 · p. 20, Table 10 · p. 21, Table 11 · p. 21

D.1. Additional Ablations

The ablations examine transport choice, DDE finite-difference step size, timestep sampling, and time weighting. They report preferred settings for the first three and a result for the tested time-weighting combination.

Transport Comparison

  • OT-FM and TrigFlow yield the best convergence among tested transports, EDM is slightly worse, and VP-SDE performs worst; the authors use OT-FM.The transport choice is assessed in an ablation study.Source: §D.1 · p. 21

Differential Derivation Equation Calculation

  • ϵ ∈ [0.001, 0.01] gives high numerical precision in the DDE calculation, and the authors use ϵ = 0.005 for training stability.The comparison concerns the finite-difference quantity used to calculate the network time derivative.Source: §D.1 · p. 21

Timestep Sampling

  • 50% of samples with t = r and 10% with r = 0 give the best timestep-sampling results in the TiM-B/4 ablation.These settings correspond to diffusion training and consistency training, respectively.Source: §D.1 · p. 21

Time Weighting

  • The reported time-weighting combination slightly surpasses the best results in Table 4, though the supplied passage truncates its full expression.The ablation compares transformations and reciprocal, Soft-Min-SNR, square-root, and square weighting functions.Source: §D.1 · p. 21

D.2. Class-Guided Image Generation

TiM-XL shows strong performance-efficiency trade-offs on class-guided ImageNet generation at 256 × 256 and 512 × 512. It competes with few-step consistency models at low NFE and matches or surpasses many multi-step diffusion models at higher NFE.

Setup

  • Evaluation uses SD-VAE for ImageNet-256 × 256 and DC-AE for ImageNet-512 × 512, reporting FID, sFID, IS, Precision, and Recall.The XL model has 664M parameters and is trained for 750K iterations, or 300 epochs.Source: §D.2 · p. 21

Performance Analysis

  • At 1 to 4 × 2 NFEs, TiM-XL competes with few-step consistency models; at higher NFEs, it matches or surpasses many multi-step diffusion models in FID.The comparisons cover ImageNet-256 × 256 and ImageNet-512 × 512 class-guided generation.Source: §D.2 · pp. 22–23, Table 13 · p. 22, Table 14 · p. 23
  • TiM demonstrates stable gains in generation quality as the NFE increases.Source: §D.2 · p. 23

E. Qualitative Results

Figure 6 shows TiM generations at 128 NFEs, including resolutions up to 4096 × 4096 and multiple aspect ratios.

E. Qualitative Results

  • Figure 6 presents TiM high-resolution and multi-aspect generations at 128 NFEs.Source: Figure 6 · p. 24
  • TiM attains resolutions up to 4096 × 4096 in the shown generations.Source: Figure 6 · p. 24
  • The examples include 1024 × 4096 and 2560 × 1024 aspect ratios.Source: Figure 6 · p. 24
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