Action-Scaled CFG for Diffusion Guidance

• Action-Scaled Classifier-Free Guidance is a family of methods that adaptively modulates guidance strength based on action magnitude or control signals.
• It addresses limitations of fixed guidance by introducing synthetic negative actions and dynamically scaling the guidance parameter in diffusion processes.
• The approach integrates into various diffusion frameworks—including video generation and language modeling—balancing control effort with output fidelity through adaptive mechanisms.

Action-Scaled Classifier-Free Guidance denotes a family of modifications to classifier-free guidance in which guidance strength is not treated as a fixed scalar throughout sampling. In trajectory-conditioned video diffusion, it dynamically modulates guidance strength in proportion to action magnitude and replaces the unconditional branch with a synthetic negative action; in discrete diffusion LLMs, it treats the guidance scale itself as a control action selected during generation; and, in a geometric control interpretation of diffusion guidance, Auto-MOG can be read as an action-scaled rule that balances instantaneous control effort in a Riemannian metric rather than the ambient Euclidean norm (Kim et al., 29 Sep 2025, Zhou et al., 8 May 2026, Jia et al., 12 Mar 2026).

1. Formal scope and canonical formulations

Setting	Scaling signal	Guided update
Trajectory-to-video diffusion	$$\omega_t(a) = \lambda \lVert a\rVert_2 \cdot 1_{t > T/2}$$	$$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$
Discrete diffusion LLMs	learned block action $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$	$$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$
Geometry-aware diffusion guidance	energy-balanced $\beta_{\mathrm{auto}}(t)$	$s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$, with $u = M_t^{-1}\Delta s$

The literature therefore does not present a single universally standardized algorithm under this label. Instead, the phrase has been used for technically distinct constructions that share a common move: the CFG coefficient is made dependent on an action variable, where “action” may mean physical robot action magnitude, a decision variable in an MDP, or control effort measured by a manifold metric. Taken together, these formulations suggest a shift from static guidance to adaptive control.

2. Action magnitude as the scaling variable in trajectory-to-video diffusion

In trajectory-to-video generation, the problem setting is: given an initial frame $I_1$ and a sequence of robot actions $a_{1:N-1}$, a diffusion-based model synthesizes the next $N-1$ frames $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$0 that visually depict the result of executing the actions from $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$1. In the formulation reported for IRASim built on DiT, actions are injected as conditioning via AdaLN layers in the DiT architecture (Kim et al., 29 Sep 2025).

The starting point is the standard noise-space CFG rule

$$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$2

where $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$3 is a guidance scale. In action-conditioned video generation, however, classic CFG is reported to be problematic for two reasons. First, “dropping” actions is semantically ill-defined: a zero action denotes no motion, not a neutral prior. Second, fixed guidance weights miscalibrate steering: they are too strong for small actions, producing oversteering and texture artifacts, and too weak for large actions, producing understeering and motion attenuation.

Action-Scaled CFG addresses both issues by replacing the unconditional branch with a “negative” action condition $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$4 and introducing an action-dependent guidance scale. With action vector $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$5 and magnitude $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$6, the update is

$$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$7

with

$$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$8

The reported default is $$\hat{\epsilon}_t(x_t, a) = \epsilon_\theta(x_t, a) + \omega_t(a)\big[\epsilon_\theta(x_t, a) - \epsilon_\theta(x_t, -a)\big]$$9, and the guidance is applied only in the first half of the denoising trajectory. The stated intuition is explicit: for small actions, weak guidance minimizes unintended motion and preserves texture; for large actions, stronger guidance enhances motion intensity and trajectory coherence; restricting guidance to early steps steers global, low-frequency structure while leaving late steps to refine textures without oversteering.

This formulation is architecture-agnostic at the sampler level. The same conditional pathway is used for $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$0 and $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$1, producing $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$2 and $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$3. The method can be inserted into DDPM, DDIM, or DPMSolver samplers in noise space, and in per-video-frame generation the schedule resets per frame, using $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$4 when generating the frame associated with $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$5.

3. Sampling integration, empirical behavior, and the relation to Action-Scaled Noise Truncation

The reported implementation for per-frame AS-CFG sampling is straightforward. For each future frame, one optionally samples an initial latent with Action-Scaled Noise Truncation, then iterates from $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$6 to $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$7, computes $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$8 and $\tilde{a}_j \in \{0.0, 0.25, \ldots, 3.0\}$9, sets $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$0 for $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$1 and $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$2 otherwise, forms

$$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$3

and applies a standard sampler step. Batching the two conditionings in one forward pass is recommended to avoid doubling latency per step; if a baseline does not use CFG, the expected cost is roughly $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$4 denoiser compute, mitigated by batching. AS-NT adds negligible overhead because it affects initial sampling only (Kim et al., 29 Sep 2025).

The companion method, Action-Scaled Noise Truncation, is motivated by the claim that trajectory-to-video generation seeks a faithful realization of a specific trajectory more than diversity. Its scaling rule is

$$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$5

with $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$6, $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$7, and $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$8 the dataset mean of $$\ell_{\mathrm{CFG}}(x) = \ell_{\mathrm{incond}}(x) + (1+\tilde{a}_j)\big(\ell_{\mathrm{cond}}(x) - \ell_{\mathrm{incond}}(x)\big)$$9. AS-CFG is described as directional control, whereas AS-NT is variance control.

Quantitatively, short-trajectory generation shows consistent gains for AS-CFG over the IRASim baseline. On RT-1, the baseline reports PSNR 26.024, SSIM 0.833, and Latent L2 0.2100, while +AS-CFG reports 26.198, 0.837, and 0.2068. On Bridge, the baseline reports 25.340, 0.834, and 0.1939, while +AS-CFG reports 25.398, 0.835, and 0.1938. On LanguageTable, the baseline reports 28.794, 0.888, and 0.1663, while +AS-CFG reports 29.021, 0.890, and 0.1653. In long-trajectory autoregressive generation, RT-1 improves from 21.729, 0.760, and 0.2408 to 21.984, 0.763, and 0.2355; Bridge from 21.536, 0.769, and 0.2306 to 21.601, 0.771, and 0.2302; and LanguageTable from 24.861, 0.852, and 0.1730 to 24.920, 0.853, and 0.1719.

Ablations directly compare action scaling with fixed guidance. On RT-1, fixed $\beta_{\mathrm{auto}}(t)$0 yields 26.052/0.832/0.2112, whereas AS-CFG yields 26.198/0.837/0.2068. On Bridge, fixed $\beta_{\mathrm{auto}}(t)$1 degrades to 25.175/0.830/0.1950, whereas AS-CFG improves to 25.398/0.835/0.1938. On LanguageTable, fixed $\beta_{\mathrm{auto}}(t)$2 slightly helps, but AS-CFG is best at 29.021/0.890/0.1653. The reported qualitative findings are improved motion intensity controllability, fewer artifacts, better small object preservation, and closer resemblance to ground-truth trajectories.

4. Guidance scale as a learned control action in diffusion LLMs

A second usage of the term emerges in discrete diffusion language modeling, where the guidance scale is explicitly recast as a sequential decision variable. In this setting, continuous CFG is first recalled in the standard form

$\beta_{\mathrm{auto}}(t)$3

and the discrete analogue is expressed in logit space as

$\beta_{\mathrm{auto}}(t)$4

with $\beta_{\mathrm{auto}}(t)$5. The central claim is that a fixed $\beta_{\mathrm{auto}}(t)$6 is structurally mismatched to diffusion language generation because the optimal guidance strength depends on noise regime, task, and generation stage (Zhou et al., 8 May 2026).

The resulting Action-Scaled CFG formulation models guidance selection as an MDP. The state $\beta_{\mathrm{auto}}(t)$7 includes timestep ratio $\beta_{\mathrm{auto}}(t)$8, mask ratio, task progress, previous CFG scale, and model confidence, with all features normalized to approximately $\beta_{\mathrm{auto}}(t)$9. The action is a discrete guidance scale from

$s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$0

selected at decision points and held constant for $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$1 consecutive diffusion sub-steps. The reward is sparse and terminal: $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$2 for $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$3 and $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$4. A categorical policy $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$5 and a separate value function are trained with PPO and GAE. The reported implementation uses separate actor/critic MLPs with two hidden layers, 128 units, LayerNorm, ReLU, orthogonal initialization, and 30 effective decision points through action repetition.

Integration into generation is described for LLaDA-8B-Instruct, a masked ddLM. At each decision block, the policy selects $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$6, and for the next $s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$7 sub-steps the model computes conditional and unconditional logits, applies

$s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$8

fills masked tokens deterministically, and remasks low-confidence positions. The base ddLM remains frozen during RL.

The empirical results emphasize controllability–fluency tradeoffs rather than physical motion. At 60 steps, RL-MEAN reaches keyword coverage 74.6% with PPL 56.2, versus fixed CFG at 71.4% and 61.3; RL-FREQ reaches coverage 74.2% with PPL 54.6. For length control, RL-MEAN reports 92.8% accuracy, 91.8% content preservation, and PPL 205.6, compared with fixed CFG at 76.0%, 90.4, and 301.9; RL-FREQ reports 92.2%, 91.7%, and 211.0. For sentiment pos$s_{\mathrm{GUIDE}} = s_0 + \beta_t\,u$9neg, RL-MEAN lowers PPL to 145.2 versus 184.7 fixed while maintaining 99.4% accuracy, and RL-FREQ reaches 99.6% accuracy. For the harder neg$u = M_t^{-1}\Delta s$0pos direction, RL-FREQ reports 40.6% accuracy, +7.8pp over fixed 32.8, with content 76.1%, +7.4pp, and PPL 106.6 versus 137.2. The learned trajectories are reported as interpretable and task-dependent: keywords and length produce hump-shaped schedules, while sentiment produces monotone decreasing schedules.

5. Geometry-aware and control-theoretic reinterpretation

A third line of work does not use robot actions or reinforcement learning, but it provides an explicit mapping from action-scaled CFG heuristics to a manifold-aware control formulation. The starting point is standard CFG in score form,

$u = M_t^{-1}\Delta s$1

where $u = M_t^{-1}\Delta s$2 is the unconditional score, $u = M_t^{-1}\Delta s$3 is the conditional score, and $u = M_t^{-1}\Delta s$4. High guidance scales are diagnosed as failing because Euclidean extrapolation ignores the manifold geometry of the data distribution $u = M_t^{-1}\Delta s$5, driving trajectories off the high-density data manifold and producing oversaturation, harsh textures, and collapse (Jia et al., 12 Mar 2026).

The geometric correction is encoded in a local Riemannian metric

$u = M_t^{-1}\Delta s$6

with $u = M_t^{-1}\Delta s$7 penalizing normal motion. The Manifold-Optimal Guidance update is

$u = M_t^{-1}\Delta s$8

Using the tangent/normal decomposition,

$u = M_t^{-1}\Delta s$9

so tangential components pass with gain $I_1$0 and normal components are strongly attenuated by $I_1$1.

The action-scaled connection appears in Auto-MOG. The local quadratic transport cost

$I_1$2

is interpreted as a natural instantaneous action density, with cumulative action $I_1$3. Auto-MOG sets

$I_1$4

and measures guidance effort under the manifold metric:

$I_1$5

Its energy-balance rule is

$I_1$6

yielding the closed-form schedule

$I_1$7

The paper’s explicit interpretation is that Auto-MOG is an action-scaled guidance rule measured in the correct Riemannian metric, not the ambient Euclidean norm. Compared to Euclidean action-scaled CFG, exemplified by $I_1$8, Auto-MOG replaces $I_1$9 by $a_{1:N-1}$0 and uses the geometry-aware direction $a_{1:N-1}$1 rather than $a_{1:N-1}$2 itself.

6. Empirical significance, misconceptions, and limitations

The three formulations share the objective of improving the controllability–quality tradeoff, but they do so with different assumptions and failure modes. In image generation, Auto-MOG reports broad gains over guidance baselines. On DiT-XL/2 for ImageNet-256, Auto-MOG reaches FID 8.78 versus CFG++ 12.45 and APG 9.34. On EDM2-XXL for ImageNet-256, Auto-MOG reports FID 4.30 versus APG 4.94. On FLUX.1 for COCO-512, it reports FID 17.84, HPSv2 30.88, and CLIP 36.37. On SD-XL at high scale $a_{1:N-1}$3, it reduces Saturation from 0.28 to 0.17 and Contrast from 0.24 to 0.16, while reporting HPSv2 29.00, CLIP 34.20, and best FID 21.60; in a blind paired comparison with $a_{1:N-1}$4, Auto-MOG achieves Overall 62.0%, Color 61.6%, Realism 60.6%, and Texture 58.5%, with $a_{1:N-1}$5 (Jia et al., 12 Mar 2026).

In trajectory-conditioned video, a common misconception is that AS-CFG is merely fixed CFG with a different constant. The defining differences are the synthetic negative action $a_{1:N-1}$6, the magnitude-dependent scale $a_{1:N-1}$7, and the early-steps-only schedule. The method is described as modality-agnostic in concept, but the “negative-condition” trick relies on an action’s antisymmetry, so in domains without meaningful negation the paper advises caution. Reported failure modes include noisy or poorly scaled actions, time misalignment between $a_{1:N-1}$8 and the generated frame, and extreme action magnitudes; the listed mitigations are normalization per DoF, clipping $a_{1:N-1}$9, and smoothing $N-1$0 across time (Kim et al., 29 Sep 2025).

In diffusion LLMs, a parallel misconception is that action-scaled guidance must be tied to physical actions. Here the “action” is a discrete control decision over the CFG scale. The limitations are correspondingly different: dependence on reward models and metric choice, computational burden from many full diffusion episodes, discrete action granularity, and the sparse-reward long-horizon problem. The reported mitigations include action repetition, advantage normalization, small discrete action sets, and deployment through deterministic RL-MEAN or RL-FREQ trajectory aggregation (Zhou et al., 8 May 2026).

Taken together, these results indicate that the term “Action-Scaled Classifier-Free Guidance” names a broader methodological pattern rather than a single formula. One branch scales guidance by physical action magnitude, one learns guidance as a sequential control policy, and one reinterprets action scaling as metric-aware control effort. This suggests that the central research question is no longer whether guidance should be used, but how the guidance coefficient should respond to state, action, geometry, and task objective throughout the diffusion trajectory.