Abstract

On-policy distillation (OPD) adapts diffusion models by querying a teacher along trajectories generated by the current student, but how it should behave under classifier-free guidance (CFG), a default component of modern diffusion systems, remains poorly understood. Existing OPD methods naturally extend velocity matching to the CFG-composed prediction, directly matching teacher and student guided velocities. We show that this objective is under-identified at the branch level: positive- and negative-branch errors can compensate in the guided prediction. Through two contrasting cases, we find that naive matching remains effective under shared negative conditioning, where both branch errors decrease jointly. When the model’s native CFG schema retains privileged information in the teacher’s negative branch that is unavailable to the student, however, this joint reduction breaks down and the composed objective induces antagonistic branch-error dynamics, reducing the positive-branch error while increasing the negative-branch error. We term this failure mode Negative Branch Asymmetry (NBA). To address NBA, we introduce Positive–Direction Matching (PDM), a branch-aware OPD objective that separately constrains the positive prediction and the CFG conditional direction. We apply PDM to dense-to-sparse video control, where naive guided matching is highly sensitive to inference guidance scales, while branch-aware supervision enables more robust and effective knowledge transfer.

1 Introduction

Classifier-free guidance (CFG) (Ho and Salimans, 2022) drives nearly every modern diffusion model (Labs, 2025; Esser et al., 2024; Wan et al., 2025), yet the velocity it denoises with is never produced by the network directly. Instead, CFG evaluates the model twice: a positive branch under the target text condition and a negative branch under the model’s null or negative text condition. It then composes the resulting velocity predictions as , where the guidance scale is a deployment knob chosen at inference, often long after training.

On-policy distillation (OPD) adapts a diffusion model by letting the student generate a denoising trajectory with its current policy, evaluating teacher and student at the same student-visited states, and updating the student to match the teacher’s local velocity (Jiang et al., 2026; Fang et al., 2026; Li et al., 2026b). The combination of on-policy state coverage and dense per-step supervision makes OPD an appealing alternative to offline distillation and scalar-reward optimization (Agarwal et al., 2024; Zhong et al., 2026; Wang et al., 2026b).

Faced with a guided teacher, diffusion distillation can handle CFG in different ways. Some methods absorb a CFG-defined teacher field into a single student prediction, thereby internalizing the guidance strength used to construct the target (Luo et al., 2023; Yin et al., 2024b; Zhou et al., 2026). In the setting considered here, however, both teacher and student retain the standard CFG interface of the underlying diffusion model and produce separate positive and negative predictions (Fang et al., 2026; Li et al., 2026b). A natural extension of OPD is then to match their CFG-composed velocities, Because the two branches remain available, the student can still be evaluated with different guidance scales at inference; however, the training loss constrains only their composition at the training scale.

This composed objective is under-identified at the branch level. Let and denote the positive- and negative-branch errors. Guided matching constrains only , allowing the two errors to compensate without changing the composed prediction. Branch ambiguity alone does not imply failure. Under shared negative conditioning, shared-parameter updates may reduce both branch errors jointly. Under privileged negative conditioning, however, our experiments show that this joint reduction can break down, exposing the compensation freedom of the composed objective.

To examine how negative-branch conditioning affects OPD optimization, we track the positive- and negative-branch errors throughout training in two image-domain distillation settings. In text-rendering distillation (Li et al., 2026b), both errors decrease jointly and naive matching remains effective. In reference-conditioned distillation (Jiang et al., 2026), where the teacher’s negative branch receives privileged information, naive matching instead reduces the positive-branch error while increasing the negative-branch error, inducing antagonistic branch-error dynamics. We term this failure mode Negative Branch Asymmetry (NBA).

NBA can remain hidden at the guidance scale used for training because the opposing branch errors compensate in the composed prediction. Once the guidance scale changes at inference, the branches are recomposed with different weights and the learned compensation no longer holds. Guidance-scale sensitivity is therefore a direct observable consequence of NBA: a student can closely match the teacher at yet drift when evaluated at another guidance scale. Figure Rethinking Classifier-Free Guidance in On-Policy Diffusion Distillation illustrates this branch ambiguity and its effect under guidance-scale changes.

The remedy is to supervise before composition. Our primary objective, Positive–Direction Matching (PDM), separately constrains the positive prediction and the CFG conditional direction . Zero PDM loss forces both branch errors to zero, preventing the composed objective from improving one branch at the expense of the other. As a foil, we also study Independent Branch Matching (IBM), which directly matches the positive and negative branches. Both objectives remove the compensation freedom of guided-only matching, while weighting branch-level supervision differently.

Having isolated when NBA occurs, we apply branch-aware OPD to dense-to-sparse video control on Wan-VACE (Jiang et al., 2025). The teacher observes dense per-frame control, whereas the student receives only sparse keyframes. In this practical setting, naive guided matching degrades sharply when the inference guidance scale departs from its training value, while PDM and IBM remain stable. PDM also improves control fidelity across pose, depth, and scribble modalities, demonstrating that branch-aware supervision enables more robust and effective knowledge transfer beyond the image-domain case study.

• •

  We show that CFG-composed OPD is under-identified at the branch level and identify when this ambiguity becomes harmful. It remains benign under shared negative conditioning, but produces NBA when privileged negative conditioning breaks joint branch-error reduction and induces antagonistic branch-error dynamics.

• •

  We introduce Positive–Direction Matching (PDM), a branch-aware OPD objective that supervises the positive prediction and the CFG conditional direction separately, preventing cross-branch error compensation and improving robustness across inference guidance scales. We include Independent Branch Matching (IBM) as a branch-aware foil.

• •

  We apply branch-aware OPD to dense-to-sparse video control and provide quantitative evidence across pose, depth, and scribble modalities. Naive matching exhibits severe guidance-scale sensitivity, while branch-aware supervision transfers dense control knowledge more reliably.

2 Preliminaries

2.1 On-Policy Distillation for Diffusion Models

Diffusion on-policy distillation (OPD) trains a student model using states sampled from its own evolving generation process (Jiang et al., 2026; Fang et al., 2026; Li et al., 2026b). Let

(1)

denote a noisy state visited along a trajectory generated by the current student. At this state, the teacher and student define local denoising transitions conditioned on and , respectively. The teacher may have access to privileged information unavailable or only partially available to the student, and therefore and need not be identical.

Existing diffusion OPD formulations (Jiang et al., 2026; Fang et al., 2026; Li et al., 2026b) minimize the discrepancy between teacher and student transitions at student-visited states. Although they differ in their derivations and optimization procedures, their transition-level objectives reduce, up to a timestep-dependent weighting factor, to matching the corresponding model predictions:

(2)

where and denote the teacher and student velocity predictions, and absorbs the parameterization- and solver-dependent weighting. We use velocity prediction throughout the paper, while the same formulation applies to equivalent noise, score, or flow parameterizations.

2.2 Diffusion OPD with Classifier-Free Guidance

We next consider diffusion models that use classifier-free guidance (CFG) with guidance scale . The velocity used for denoising is

(3)

where and denote the positive and negative branch predictions, respectively. We preserve the CFG schema prescribed by each model’s original training and inference pipeline. In many models, the negative branch changes the text condition while retaining auxiliary inputs such as reference images or other control signals.

Define the positive- and negative-branch discrepancies as

(4)

Substituting these discrepancies into the CFG-composed matching objective gives

(5)

Existing branch-retaining OPD settings (Fang et al., 2026; Li et al., 2026b) are primarily studied in text-to-image distillation, where teacher and student share the same null-text conditioning on the negative branch. Such symmetry is not guaranteed in OPD with privileged information, where the teacher may receive reference or control information unavailable or only partially available to the student. Because the model’s native CFG schema may retain this information in the negative branch, privileged negative conditioning arises naturally in practical knowledge-transfer settings. We analyze its consequence next.

3 Negative Branch Asymmetry and Branch-Aware OPD

3.1 Negative Branch Asymmetry

Under privileged negative conditioning, the teacher’s negative target cannot be directly reproduced from the student’s negative input. Nevertheless, Eq. 5 constrains only the CFG-composed discrepancy. At any supervised state, matching the guided predictions requires only

(6)

or equivalently,

(7)

This condition admits infinitely many non-zero branch-error pairs, allowing the two errors to compensate without changing the guided prediction.

Equation 7 establishes the branch ambiguity but does not determine its optimization dynamics. We therefore investigate when this ambiguity becomes harmful empirically in Section 4.1. Across two controlled image-domain cases, we observe joint branch-error reduction under shared negative conditioning, but antagonistic branch-error dynamics under privileged negative conditioning.

An absolute performance drop under a guidance-scale change is not by itself evidence of NBA, since the teacher may intrinsically rely on CFG. The relevant signature is excess degradation introduced by naive distillation: the student departs from the teacher’s guidance-scale behavior or degrades more strongly than its branch-aware counterpart. Section 4.1 tests these predictions empirically.

3.2 Branch-Aware OPD

To prevent cross-branch error compensation, we supervise the predictions before CFG composition. Let denote a pointwise distillation loss evaluated at a student-visited state and timestep . Its corresponding OPD objective is

(8)

Positive–Direction Matching.

For a model , define its CFG conditional direction as

(9)

Our primary objective, Positive–Direction Matching (PDM), separately matches the positive prediction and the conditional direction:

(10)

where controls the direction-matching strength. The first term anchors the positive prediction, while the second preserves the CFG conditional direction. Zero PDM loss requires , eliminating the compensation freedom of guided-only matching.

Baseline: Independent Branch Matching.

To separate the benefit of branch-level supervision from the particular design of PDM, we include Independent Branch Matching (IBM) as a baseline:

(11)

IBM retains the per-branch weights of the expanded naive objective but removes its cross-branch interaction term. Like PDM, it has a unique branch-level zero-loss solution for , but directly matches the two branches rather than preserving the positive prediction and conditional direction. We compare the empirical behavior of these two branch-aware formulations in Table 2.

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Method
Teacher	75.24	92.91	94.16	94.43	94.09
OPD (Naive)	73.87	92.72	94.52	94.43	94.11
OPD (PDM)	74.48	93.73	93.99	94.02	94.38

3.3 Efficient Supervision for Dense-to-Sparse Video Control

Full-trajectory OPD is particularly expensive for video because it requires a teacher evaluation at every denoising state. For our dense-to-sparse video application, we independently find that supervising only an early portion of the student trajectory substantially reduces this cost while maintaining performance. A related observation is reported concurrently by DanceOPD (Zhou et al., 2026).

Let denote the states visited by the student in denoising order. We supervise only the first states:

(12)

The student still completes the full denoising rollout, but teacher supervision is computed only for these states. Here recovers full-trajectory supervision, while smaller reduces training cost. This design is used only for the dense-to-sparse video experiments; the image-domain case studies follow their respective standard supervision protocols. We study the effect of in Section 4.3.2.

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Pose-Control	MPJPE		PCK@0.2		PCK@0.1		Quality
Method	All	Key	All	Key	All	Key	FID	FVD
Teacher	3.03	2.82	96.02	96.46	91.15	92.23	14.13	56.01
Student	5.92	4.10	86.78	91.89	69.97	82.53	15.81	81.41
SFT	5.02	3.31	90.36	94.77	76.72	88.55	14.11	63.90
Off-policy	5.14	3.44	89.78	94.09	75.46	87.48	14.49	68.50
OPD (Naive)	4.43	3.14	91.84	95.25	80.28	89.35	13.49	65.12
OPD (IBM)	4.20	2.88	92.93	96.11	82.27	90.95	13.26	65.72
OPD (PDM)	4.13	2.83	92.98	96.12	82.48	91.03	13.52	62.77
Depth-Control	CORR		RMSE		SI-RMSE		Quality
Method	All	Key	All	Key	All	Key	FID	FVD
Teacher	96.98	97.58	7.50	6.36	6.19	5.23	11.02	36.89
Student	83.21	91.27	16.87	11.13	14.36	9.37	15.03	71.33
SFT	88.39	96.17	13.83	7.80	11.96	6.52	12.87	58.13
Off-policy	88.25	96.01	13.98	8.00	12.10	6.64	12.66	59.35
OPD (Naive)	90.58	96.56	12.39	7.47	10.69	6.16	12.08	72.20
OPD (IBM)	91.14	96.91	12.03	7.11	10.37	5.85	11.76	60.38
OPD (PDM)	91.24	97.13	11.95	6.91	10.31	5.68	11.64	60.60
Scribble-Control	Recall		Precision		F1		Quality
Method	All	Key	All	Key	All	Key	FID	FVD
Teacher	93.26	94.40	94.26	95.27	93.73	94.81	9.56	24.22
Student	64.20	82.93	65.50	83.78	64.70	83.24	12.29	69.13
SFT	67.23	89.03	69.52	90.66	68.27	89.79	10.69	50.56
Off-policy	70.98	91.55	72.15	91.73	71.49	91.60	11.60	52.90
OPD (Naive)	74.78	90.77	75.38	91.34	75.00	90.99	10.53	59.95
OPD (IBM)	75.92	92.23	76.47	92.70	76.13	92.43	10.12	52.67
OPD (PDM)	76.42	93.03	76.13	92.86	76.22	93.03	10.34	50.53

4 Experiments

We first investigate when the branch ambiguity of CFG-composed matching develops into NBA. We then evaluate branch-aware OPD in dense-to-sparse video control and ablate its main design choices.

4.1 When Does NBA Emerge?

4.1.1 Experimental Setup

We contrast two image-domain distillation settings with different negative conditioning. In text-rendering distillation, we follow DiffusionOPD (Li et al., 2026b) and use an SD3.5-Medium-based (Esser et al., 2024) OCR teacher specialized for visual text rendering. Teacher and student receive the same prompt on the positive branch and the same null-text condition on the negative branch:

(13)

Models are trained at and evaluated on 1,018 held-out prompts.

In reference-conditioned distillation (Jiang et al., 2026), we conduct experiments with FLUX-2-klein-base-4B (Labs, 2025), with the teacher observing a reference image unavailable to the text-only student:

						(14)

The teacher therefore receives privileged information on its negative branch. Models are trained at and evaluated on held-out prompts across inference guidance scales.

To diagnose branch coupling, we train naive matching, PDM, and a positive-only ablation (), and track both branch errors throughout training. The positive-only ablation isolates how updates toward the positive target affect the negative-branch error. It is used only for this optimization diagnostic; generation comparisons use naive matching and PDM under the same training protocol. Full implementation details are provided in Appendix 7.1.

4.1.2 Branch-Error Dynamics

Figure 2 reveals two distinct optimization regimes. In text-rendering distillation, positive-only training reduces both branch errors, showing that positive-branch updates also improve the negative branch. Naive matching and PDM exhibit the same joint error reduction, indicating a benign regime.

Reference-conditioned distillation exhibits the opposite behavior. Positive-only training reduces the positive-branch error but substantially increases the negative-branch error, showing that positive-branch updates no longer benefit the negative branch under privileged conditioning. Naive matching follows the same antagonistic pattern, decreasing the positive error while increasing the negative error. PDM instead reduces the positive error while preventing sustained negative-error growth. The antagonistic trajectory under naive matching is the optimization signature of NBA, while PDM restores joint branch-level supervision.

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	MPJPE		PCK@0.2		PCK@0.1		Quality
Method	All	Key	All	Key	All	Key	FID	FVD
Naive ()	4.62	3.22	91.35	95.01	79.39	89.54	14.05	67.44
Naive ()	4.94	3.31	90.23	94.53	77.92	88.22	22.66	134.09
Naive ()	8.98	6.23	80.08	87.42	69.14	81.57	78.20	507.70
IBM ()	4.28	2.91	92.67	95.95	81.69	91.03	12.99	53.83
IBM ()	4.42	3.04	92.09	95.53	81.41	90.81	13.69	56.85
IBM ()	4.91	3.43	90.92	94.69	80.66	89.98	18.00	71.17
PDM ()	4.27	2.75	92.71	96.38	82.12	91.66	13.83	58.65
PDM ()	4.17	2.73	92.81	96.61	82.27	91.81	13.46	55.85
PDM ()	4.48	2.90	92.14	95.64	81.72	91.15	15.25	60.97

4.1.3 Intrinsic and Distillation-Induced CFG Sensitivity

The branch-error trajectories above distinguish benign joint reduction from NBA during optimization. We next examine how these regimes manifest under inference-time guidance shifts. An absolute performance drop away from the training guidance scale is not sufficient evidence of NBA, since the teacher itself may intrinsically rely on CFG. Table 1 shows that, in text-rendering distillation, both students closely track the teacher throughout the guidance sweep. At , the teacher, naive student, and PDM student obtain OCR rewards of , , and , respectively, and all improve similarly as guidance increases. Thus, neither objective introduces substantial sensitivity beyond the teacher’s intrinsic CFG dependence.

Reference-conditioned distillation exhibits a different pattern. Figure 3 shows that the teacher preserves the reference-supplied style across guidance scales and that PDM closely tracks this behavior. Naive matching instead departs from the teacher, producing visual distortion and style drift that become most pronounced at , where CFG reduces to the positive prediction. This excess degradation relative to both the teacher and PDM isolates the sensitivity introduced by naive distillation. Together with the branch-error trajectories in Figure 2, these results show that NBA induces guidance-scale sensitivity beyond the teacher’s intrinsic reliance on CFG.

4.2 Application to Dense-to-Sparse Video Control

4.2.1 Experimental Setup

We apply branch-aware OPD to dense-to-sparse video control using Wan-VACE (Jiang et al., 2025). The teacher receives a dense control sequence , while the student observes only sparse keyframes :

						(15)

We construct a benchmark from OpenHumanVid (Li et al., 2025) containing 600 test clips and evaluate pose, depth, and scribble control under the dense-to-four-keyframe setting. Baselines include the unadapted sparse-control student, SFT on data-derived diffusion states, and off-policy teacher matching; all methods use the same student architecture and training budget.

Unless otherwise specified, PDM uses and supervises the first student-visited states. Main results use joint training over all three control modalities. Guidance-scale and hyperparameter studies use pose-only models to reduce repeated training cost; results from the two protocols are therefore not directly comparable. Complete data, metric, and implementation details are provided in Appendix 7.1.

4.2.2 Main Results

Table 2 reports results at the training guidance scale . PDM provides the most consistent control-fidelity improvements across pose, depth, and scribble, while IBM also outperforms naive matching on most control metrics. The performance of IBM supports the benefit of removing cross-branch compensation, while the stronger overall results of PDM support its positive–direction parameterization.

These matched-scale results establish the practical value of branch-aware OPD independently of guidance-scale shifts. At , PDM improves control fidelity over naive OPD, SFT, and off-policy distillation across all three modalities. Thus, branch-aware on-policy supervision improves dense-to-sparse knowledge transfer itself, rather than merely correcting off-scale degradation.

4.2.3 Guidance-Scale Generalization

Table 3 evaluates pose-only models trained at and tested at different guidance scales. Naive matching degrades sharply as the inference scale moves away from training, reaching its largest drop at . In contrast, PDM and IBM remain stable across the sweep, showing that branch-aware supervision prevents the excess guidance sensitivity induced by composed matching. PDM provides the most consistent control fidelity across the evaluated scales.

Figure 4 qualitatively illustrates the excess guidance-scale sensitivity of naive OPD expected under NBA. Additional qualitative comparisons on pose, depth, and scribble-controlled generation are provided in Appendix 7.2.

4.3 Ablation Studies

4.3.1 Effect of the Direction-Matching Weight

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	MPJPE		PCK@0.2		PCK@0.1		Quality
Method	All	Key	All	Key	All	Key	FID	FVD
PDM ()	4.24	2.81	92.71	96.24	81.80	91.05	13.97	59.72
PDM ()	4.27	2.75	92.71	96.38	82.12	91.66	13.83	58.65
PDM ()	4.36	2.95	92.08	95.77	81.25	90.39	13.33	61.79
PDM ()	4.40	3.00	92.27	95.96	80.89	90.75	12.97	56.85
PDM ()	4.49	3.07	91.60	95.35	80.21	89.93	12.96	56.91

Table 4 studies the direction-matching weight in PDM. When , PDM reduces to positive-only matching. We find that provides the best overall control fidelity, including the lowest keyframe MPJPE and the highest PCK@0.1. Larger values improve some distributional-quality metrics but weaken control accuracy. We therefore use as the default.

4.3.2 Effect of the Supervision Horizon

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	MPJPE		PCK@0.2		PCK@0.1		Quality		Time
Method	All	Key	All	Key	All	Key	FID	FVD	s/step
PDM ()	4.33	2.98	92.53	95.68	81.19	90.57	13.70	54.41	23
PDM ()	4.45	3.11	92.18	95.57	80.78	90.51	13.89	60.63	38
PDM ()	4.27	2.86	92.59	95.98	81.71	91.13	13.58	57.08	69
PDM ()	4.27	2.75	92.71	96.38	82.12	91.66	13.83	58.65	132
PDM ()	4.65	3.14	91.34	95.25	80.81	90.09	13.91	61.95	790

Table 5 studies the number of supervised states in the dense-to-sparse video application. Increasing raises training cost from 23 seconds per step at to 790 seconds under full-trajectory supervision (). Among the evaluated settings, provides the strongest control fidelity while remaining substantially more efficient than full-trajectory supervision. We therefore use for the main video experiments.

5 Related Work

5.1 Diffusion Model Distillation

Although our goal is not few-step generation, prior diffusion distillation provides the closest context for understanding how teacher supervision and classifier-free guidance are typically transferred to a student. Most existing methods focus on reducing the number of denoising steps required at inference. Progressive Distillation recursively compresses multiple teacher steps into a single student step (Salimans and Ho, 2022). Consistency-based methods, including Consistency Models (Song et al., 2023; Kim et al., 2024) and Latent Consistency Models (Luo et al., 2023), train a model to produce consistent outputs across states along the same probability-flow trajectory, enabling one- or few-step generation. Distribution Matching Distillation (DMD) matches the student distribution to the teacher through their score functions (Yin et al., 2024b), while other approaches further combine diffusion supervision with adversarial training (Sauer et al., 2024; Yin et al., 2024a).

Many of these methods also distill classifier-free guidance into the student. Rather than retaining separate positive and negative branches at inference, they use the CFG-composed teacher prediction as the distillation target, thereby baking the effect of guidance into a single student prediction (Luo et al., 2023; Yin et al., 2024b; Wu et al., 2026; Huang et al., 2025). This design improves sampling efficiency by avoiding two model evaluations for CFG and, more broadly, transfers the strongly guided teacher distribution into a compact few-step generator.

Our setting differs in both objective and purpose. We do not primarily seek to compress a multi-step guided teacher into a CFG-free few-step student. Instead, we study diffusion OPD in which the teacher and student each construct their own guided prediction from positive and negative branches. Matching only their final guided predictions is under-identified at the branch level. This ambiguity becomes harmful when the teacher’s negative branch contains privileged information unavailable to the student, preventing the two branch errors from being reduced jointly.

5.2 On-Policy Distillation for Diffusion Models

Recent work extends on-policy distillation to diffusion and flow models by querying the teacher on states sampled from the current student. D-OPSD performs on-policy self-distillation using privileged context, allowing a student to learn from a stronger teacher evaluated along the student’s own denoising trajectory (Jiang et al., 2026). Flow-OPD distills task-specialized flow-matching teachers into a unified student through on-policy sampling and dense per-step supervision (Fang et al., 2026). DiffusionOPD formulates this process through transition-level KL divergence and shows that it reduces to prediction matching under standard diffusion transitions (Li et al., 2026b). Concurrently, DanceOPD treats generative capabilities as velocity fields and internalizes operator-defined fields such as CFG into a single student prediction through on-policy field matching (Zhou et al., 2026). Unlike the branch-retaining setting studied here, such a student no longer exposes separate positive and negative predictions at inference.

Despite differences in derivation and optimization, these methods share the same central principle: the student generates the trajectory, while the teacher provides dense local supervision at student-visited states. Their studied configurations, however, either collapse CFG into a single student prediction or retain separate branches while sharing the same negative conditioning between teacher and student. In the latter case, the negative-branch error need not be exactly zero, but shared conditioning allows the two branch errors to be reduced jointly. Existing work therefore does not examine how privileged information in the teacher’s negative branch changes the optimization of a branch-retaining student.

Our work studies this missing regime. We show that CFG-composed matching permits cross-branch error compensation and identify when this ambiguity becomes harmful: under shared negative conditioning, both branch errors can decrease jointly, whereas privileged negative conditioning can induce antagonistic branch-error dynamics. We term this failure mode NBA. We further introduce branch-aware OPD objectives, with PDM as the primary formulation, to prevent such error compensation and improve robustness across inference guidance scales.

6 Conclusions and Limitations

We show that CFG-composed OPD is under-identified at the branch level, but that this ambiguity does not always cause failure. Under shared negative conditioning, the positive- and negative-branch errors can decrease jointly. When the teacher’s negative branch contains privileged information unavailable to the student, however, joint error reduction can break down and naive matching induces antagonistic branch-error dynamics. We identify this failure mode as Negative Branch Asymmetry (NBA). To address it, we introduce Positive–Direction Matching (PDM), which separately supervises the positive prediction and CFG conditional direction. Contrasting image-domain studies validate when NBA emerges, while dense-to-sparse video control demonstrates that branch-aware supervision improves knowledge transfer and robustness across inference guidance scales.

Despite these results, the relative behavior of branch-aware objectives remains incompletely understood. PDM and IBM share the same branch-level zero-loss solution under non-degenerate weights, so PDM’s observed advantage is currently empirical rather than theoretical. Future work may characterize their different optimization behavior and extend NBA analysis to other guidance mechanisms and teacher–student conditioning asymmetries.

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7 Appendix

7.1 Additional Experimental Details

7.1.1 Text Rendering Distillation

Models.

The base model is Stable Diffusion 3.5-Medium (Esser et al., 2024). Both the teacher and the student are LoRA adapters (Hu et al., 2022) of rank and scale , applied to the query/key/value and output projections of every self- and cross-attention block in the MM-DiT transformer; all other weights are frozen. We use the same OCR teacher model used in DiffusionOPD (Li et al., 2026b); the student is initialized from the base model (identity adapter) and is the only module updated during distillation.

Objectives.

We compare, under identical rollouts and hyper-parameters, the naive CFG-composed objective, Positive-Direction Matching with and the positive-only ablation. Only the pointwise objective differs across methods. The positive- and negative-branch errors reported in Figure 2 are per-transition norms in transition-mean space, averaged over the supervised timesteps and logged every optimizer step.

Optimization.

We use AdamW (, , , weight decay ) with a constant learning rate of and gradient clipping at norm , keeping an EMA of the trainable parameters (decay , updated every steps). Training runs on H100 GPUs in fp16 mixed precision with a per-GPU sampling batch of prompts, one image per prompt, and sampling batches accumulated per update, giving an effective batch of trajectories ( transitions) per step. Each round performs a single optimizer update; we train for updates with seed .

Data and reward.

Prompts are drawn from the OCR text-rendering set ( train / test) used in DiffusionOPD (Li et al., 2026b), where the target string to be rendered is given in quotes. For evaluation, we read the text from the generated image with PaddleOCR (Cui et al., 2025) and score

(16)

where is the Levenshtein (edit) distance between the two strings—the minimum number of single-character insertions, deletions, or substitutions to turn into —and denotes string length. A score of means the rendered text is read back exactly; means no characters match.

Evaluation.

Unless noted, models are evaluated on the full -prompt test set with denoising steps in fp16. For the guidance-scale generalization study we sweep the inference guidance while keeping the training configuration fixed.

7.1.2 Reference-Conditioned Distillation

Data and task construction.

Following the style-learning experiment in Jiang et al., we construct a style-distillation setting spanning six distinct visual styles, denoted by the placeholders [A]–[F]. For each style we provide four training demonstrations (Wu et al., 2026; Wang et al., 2026a), each pairing a text prompt with a reference image that exposes the target style to the teacher, yielding training demonstrations in total. The demonstrations are organized by style: every demonstration for style [A] shares the same target appearance, and likewise for [B]–[F]. We train the LoRA for gradient steps, drawing a batch of sampled records per gradient step; different visits use independently sampled initial noise and denoising states, so repeated exposure to a demonstration still yields stochastic training observations. For qualitative evaluation, we construct held-out test prompts that invoke the same style placeholders while changing the surrounding content, composition, or interactions. The goal is to test whether the LoRA can distill the style knowledge exposed by the seen demonstrations into its weights and, at inference, transfer a learned style to unseen text prompts. The resulting evaluation tests whether the text-only student internalizes the reference-supplied style through OPD rather than reproducing any particular training scene.

Model and conditioning.

We use the multi-step FLUX.2-klein-4B-base model (Labs, 2025) at resolution. Each reference image is converted to RGB, bicubically resized to cover the target canvas, center-cropped, and normalized to before VAE encoding. The student follows the original text-to-image interface and receives only the prompt. The teacher uses the same diffusion backbone in its image-editing interface: it receives the student-visited noisy latent together with the encoded reference-image latents, and its text condition appends the instruction “Make the overall style consistent with the reference image.” For the teacher’s negative prediction, we replace the text with the null prompt while retaining the reference-image latents. The student’s negative prediction uses the same null prompt without reference latents.

Parameterization and teacher update.

We freeze the VAE, text encoder, and base diffusion-transformer weights and optimize LoRA adapters with rank 64 and scaling parameter . The adapters are applied to the query, key, value, and output projections of the self- and context-attention modules, together with the corresponding feed-forward projections in each transformer block. We maintain separate student and teacher adapters initialized from the same weights. After each student update, we update the teacher adapter with exponential moving average decay . Teacher predictions are evaluated without gradients.

On-policy objectives.

For each batch, the student initializes a trajectory from Gaussian noise under the text-only condition. We use the native FLUX.2-klein (Labs, 2025) scheduler with a 30-step denoising grid. At every supervised state, the teacher and student construct their own positive and negative predictions. The student rollout uses its CFG-composed velocity at , while the teacher is evaluated at the same student-visited state. We implement naive OPD by matching the teacher and student after CFG composition. PDM instead matches the teacher’s positive prediction and the CFG conditional direction separately, with . All compared objectives use the same base model, reference–prompt pairs, student rollout states, and optimization budget.

Optimization.

We train with AdamW using learning rate , , , zero weight decay, and gradient-norm clipping at 1.0. Training uses eight processes with a per-process batch size of 2 and no gradient accumulation, giving a global batch size of 16. We use bfloat16 mixed precision for the trainable model and VAE, gradient checkpointing, and DeepSpeed ZeRO-2.

Inference and qualitative evaluation.

At inference, we discard the teacher adapter and reference image; the student receives only the held-out text prompt. We generate images with 40 denoising steps and evaluate guidance scales . For a given evaluation prompt, all objectives and guidance scales use the same initial noise, isolating changes caused by the training objective and CFG composition. We assess the resulting images qualitatively by inspecting whether they preserve the defining visual knowledge while following the changed context of the evaluation prompt and maintaining generation quality. This experiment is an illustrative qualitative case study; we do not interpret it as an aggregate estimate of performance.

7.1.3 Dense-to-Sparse Video Benchmark

Our dense-to-sparse video benchmark is derived from OpenHumanVid (OHV) (Li et al., 2025). Starting from the 12-part OHV release (K clips with DWPose annotations), we first filter clips according to minimum length and motion magnitude. We then split videos into non-overlapping 81-frame clips at resolution while preserving pixel alignment between RGB and control streams.

Difficulty stratification.

To reduce evaluation bias toward easier samples (Li et al., 2026a), we compute a motion score based on frame-to-frame differences of rendered DWPose skeletons. The clips are divided into six difficulty buckets according to this score, and we randomly sample 100 clips from each bucket to form the 600-clip test set. The remaining clips are used for training and validation. Please refer to Table 6 for more details.

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Bucket	Motion score	#Test	#Train
diff1.5-2.0
diff2.0-2.5
diff2.5-3.5
diff3.5-5.0
diff5.0-7.0
diff7.0+
Total			K

7.1.4 Sparse Keyframe Control

All video experiments target the dense-to-sparse setting: the teacher receives the control signal at every frame, while the student receives it only at a sparse set of pixel-space keyframes. Following the masked video-to-video (MV2V) interface of the VACE (Jiang et al., 2025) base model, the student input frame stack and mask (over frames at , in the range) are built as

• •

  = the reference image (appearance anchor), with (given, not generated);

• •

  = the control frame at each pose keyframe ;

• •

  all remaining frames are blank (), with (to be synthesized).

We use the uniform layout pixel_kf throughout: index is reserved for the reference image, so the model is conditioned on pose at three interior keyframes out of frames. Keyframes are indexed in pixel space; under the VACE VAE ( temporal, spatial compression) this maps non-linearly to latent frames, so all masks are constructed in pixel space and then compressed. This same sparse construction is used both inside the on-policy rollout during training and at inference; the teacher instead receives the dense per-frame control.

7.1.5 Evaluation Metrics

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Base model & adapter
Base model	Wan2.1-VACE-1.3B (frozen)
Adapter	LoRA, rank ,
LoRA target	self/cross-attn , ffn per VACE block
Precision	bf16 autocast, gradient checkpointing
Optimization
Optimizer	AdamW, , wd ,
Learning rate	(constant)
Training steps
Devices / batch	GPUs (DDP), per-GPU batch
Diffusion & rollout
Solver / schedule	UniPC, steps, shift
OPD rollout	active steps (“-of-”)
Guidance scale
Data
Resolution / length	, frames
Keyframes	pixel (0 = reference)
Train / val / test	K / / clips

All methods are evaluated independently on the 600-clip test set. Scores are computed per clip and averaged over the dataset.

Control fidelity (per modality).

For each control modality we re-extract the control signal from the generated video with the corresponding annotator and compare it to the control that was fed in.

• •

  Pose. We run DWPose (Yang et al., 2023) on the generated video and use the body joints, in normalized image coordinates. A joint is counted only when both the GT and predicted confidence exceed ; frames with fewer than valid joints are skipped. We report MPJPE (mean per-joint error in normalized coordinates) and PCK@ for , where a joint is correct if its error is below and is the per-frame bounding-box size of the GT skeleton. Metrics are reported over all frames and over the keyframe subset separately.

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  Depth. We re-extract depth from the generated frames with DPT-Hybrid (MiDaS) (Ranftl et al., 2020) and compare against the dense depth control (same annotator). Since these are relative depths, we remove the scale/shift ambiguity with a closed-form least-squares affine alignment and report the affine-invariant SI-RMSE (primary), the raw RMSE, and the Pearson correlation.

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  Scribble. We re-extract neural line-art from the generated frames with the VACE scribble annotator and compare against the dense line-art control. Line pixels are binarized as deviations from the per-frame median (/), and we report a tolerant boundary F1 (precision/recall) with a dilation tolerance of pixels.

Distributional quality.

Independent of control adherence, we measure perceptual and temporal realism against the GT distribution: FID (clean-fid, InceptionV3 features, frames per clip) captures per-frame appearance, and FVD (I3D pretrained on Kinetics-400, frames linspace-sampled per clip) captures spatio-temporal consistency.

7.1.6 Implementation and Hyperparameters

All methods fine-tune the same Wan2.1-VACE-1.3B (Jiang et al., 2025) base model with LoRA (Hu et al., 2022) adapters (the base weights are frozen), so differences are attributable to the training objective alone. LoRA (rank , ) is applied to the query/key/value/output projections of both self- and cross-attention and the two feed-forward linears within every VACE block. We train with AdamW (, , no weight decay) for steps on GPUs (DDP, per-GPU batch ), under bf16 mixed precision with gradient checkpointing. Inference and the on-policy rollout use the UniPC solver (Zhao et al., 2023) on a -step schedule (shift). All models are distilled and deployed at classifier-free guidance scale . Videos are frames at . Table 7 lists the full configuration.

Off-policy distillation baseline.

The off-policy baseline uses the same teacher–student prediction-matching loss as OPD but evaluates it on standard data-derived diffusion states. Given a ground-truth video latent , we sample and and construct . While SFT matches the student prediction at this state to the ground-truth velocity target, the off-policy baseline replaces that target with the teacher prediction under dense control. The student is evaluated at the same state under sparse control. It therefore differs from OPD only in the state distribution, using noised ground-truth latents instead of student-visited states.

7.2 More Qualitative Results

Figures 5 and 6 provide additional qualitative evidence of distillation-induced CFG sensitivity under privileged conditioning. In reference-conditioned distillation, PDM more closely follows the teacher and preserves the reference-supplied style across guidance scales, whereas naive matching exhibits appearance drift and visual artifacts. In dense-to-sparse video control, PDM likewise maintains subject appearance and controlled structure as the inference scale changes, while naive matching degrades substantially. These results further demonstrate the excess guidance sensitivity associated with NBA.

Figures 7, 8 and 9 extend the qualitative comparison to pose, depth and scribble control under the default guidance scale. Across all three modalities, PDM follows the sparse structural conditions more faithfully while maintaining coherent visual content. These results show that the benefit of branch-aware supervision is consistent across different forms of conditioning asymmetry.