Equilibrium Forcing: Adaptive Video Generation Without Noise Conditioning

Hansen Jin Lillemark; Alex Rojas; Zachary Novack; Runqian Wang; Yilun Du; Yian Ma; Taylor Berg-Kirkpatrick; Rose Yu

cs.CVAug 11, 2026

Equilibrium Forcing: Adaptive Video Generation Without Noise Conditioning

Authors: Hansen Jin Lillemark, Alex Rojas, Zachary Novack, Runqian Wang, Yilun Du, Yian Ma, Taylor Berg-Kirkpatrick, Rose Yu

Organizations: UC San Diego · MIT · Harvard University

Abstract

Standard autoregressive video generation algorithms based on Diffusion and Flow Matching rely on rigid training objectives and static sampling schedules, limiting inference procedures from adapting to the data. We introduce Equilibrium Forcing (EqF), a simplified framework for video denoising generative models without noise level conditioning. EqF pioneers modular training- and inference-time designs for noise-unconditional generation that decouple learning the denoising field from sampling. This flexibility allows for inference-time algorithms that operate in a closed loop by adapting to feedback from the sample, improving video quality and consistency on challenging autoregressive video generation benchmarks. Extensive analysis elucidates exactly how removing the noise level conditioning enables EqF's data-dependent inference properties to surpass the performance of standard noise level-conditional denoising video methods.

Figures & tables

Figure 1: Equilibrium Forcing Overview. EqF is trained with a simple unmodulated equilibrium denoising objective (left), which can be shaped at inference time through the $\eta$ warp (middle). The sampling landscape here is shaped to be an attractor, with the magnitude decreasing as the sample descends and converges (right).

Figure 2: Left: FM follows externally-defined noise schedule conditioning, which diverges from the true denoising field. Center: By training without explicit noise level conditioning, EqF learns a correct denoising field everywhere by estimating the noise level internally. Right: EqF leverages the internal noise level estimate for adaptive autoregressive video generation inference.

Panel of Figure 3 — Figure 3: Left : Absolute noise conditioning error between scheduled $\sigma^{(i)}$ and the predicted $\tilde{\sigma}^{(i)}\approx g_{\phi}(x^{(i)})$ increases over 256 autoregressive rollouts. Right : FVD worsens over 256 autoregressive rollouts with FM due to externally prescribed noise conditions. Conditioning on estimated noise levels (dotted) helps slightly. Removing the noise condition altogether ( EqF ) performs best.

Figure 5: Budget-adaptive inference results. EqF with budget-adaptive sampling achieves the lowest FVD across Minecraft, Re10K, and Droid.

Method	Sampler	Inference Warp	FVD $\downarrow$	VBench $\uparrow$
EqF (Ours)	NAG, $\mu=0.3$	$c$ -function	$64.34\pm 1.78$	$0.7733\pm 0.0008$
EqM ( Wang and Du, 2025 )	NAG $\mu=0.1$	–	$77.02\pm 5.21$	$0.7679\pm 0.0009$
EqF	GD	$c$ -function	$77.63\pm 3.31$	$0.7721\pm 0.0005$
FM	Euler	$c$ -function	$104.13\pm 4.33$	$0.7703\pm 0.0012$
NU-FM ( Sun et al., 2025 )	GD	–	$101.16\pm 3.57$	$0.7698\pm 0.0011$
Diffusion	DDIM	–	$106.00\pm 1.22$	$0.7681\pm 0.0008$

Table 1: Autoregressive Minecraft 300-frame rollout results across 5 seeds. EqF with NAG sampling achieves the best FVD and VBench scores.

Figure 6: Visualizations of autoregressively generated RealEstate10K videos using EqF -FT and FM-FT finetuned models from Wan 2.1.

Figure 7: Generated videos from the Droid dataset using EqF -FT finetuned from Wan 2.2.

	Minecraft		Re10K		Droid
Method	FVD $\downarrow$	VBench $\uparrow$	FVD $\downarrow$	VBench $\uparrow$	FVD $\downarrow$	VBench $\uparrow$
EqF Adaptive NAG	$\mathbf{91.45\pm 0.92}$	$0.771\pm 0.000$	$\mathbf{127.69\pm 1.57}$	$\mathbf{0.761\pm 0.000}$	$\mathbf{107.38\pm 0.82}$	$\mathbf{0.812\pm 0.002}$
EqF NAG	$92.08\pm 0.30$	$\mathbf{0.774\pm 0.000}$	$166.73\pm 2.98$	$0.759\pm 0.000$	$113.58\pm 3.51$	$0.810\pm 0.002$
FM	$135.37\pm 1.74$	$0.769\pm 0.000$	$145.42\pm 5.93$	$\mathbf{0.761\pm 0.000}$	$108.69\pm 3.71$	$0.809\pm 0.000$

Table 3: Comparison of FVD and VBench at 50 sampling steps across Minecraft, RealEstate10K, and Droid datasets using the budget-adaptive EqF algorithm. NAG

\mu=0.1

Table 12

Appendix figures & tables16 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 12: Pearson Correlation convergence across training of the Re10K FM and EqF models.

Dataset	# Samples	FM/ EqF Field MSE	Validation $v$ -Loss		Relative Field MSE $(\%)$	Pearson Correlation
		$\mathbb{E}\\|f_{\textrm{FM}}-f_{\textsc{EqF}}\\|_{2}^{2}$	$\mathbb{E}\\|f_{\textrm{FM}}-\mathbf{v}\\|_{2}^{2}$	$\mathbb{E}\\|f_{\textsc{EqF}}-\mathbf{v}\\|_{2}^{2}$
Minecraft	$2{,}084$	$0.0425\pm 0.00505$	$0.576\pm 0.00270$	$0.576\pm 0.00271$	$7.378$	$0.984$
Re10K	$4{,}096$	$0.00347\pm 0.00003$	$0.142\pm 0.00146$	$0.143\pm 0.00147$	$2.432$	$0.999$
Droid	$1{,}417$	$0.0135\pm 0.000385$	$0.307\pm 0.00972$	$0.318\pm 0.00993$	$4.325$	$0.996$

Appendix

Table 6: Empirical agreement between trained FM and EqF denoisers. All quantities are evaluated on matched held-out samples using the same clean inputs, noise levels, and Gaussian noise. Relative field MSE denotes the magnitude of

\mathbb{E}\|f_{\textrm{FM}}-f_{\textsc{EqF}}\|_{2}^{2}

normalized by

\tfrac{1}{2}\bigl(\mathbb{E}\|f_{\textrm{FM}}\|_{2}^{2}+\mathbb{E}\|f_{\textsc{EqF}}\|_{2}^{2}\bigr)

. Across all three domains, the trained fields have small normalized discrepancy and high Pearson correlation despite EqF receiving no explicit noise-level condition.

Figure 13: Noise level readout across sampling steps. Ideally, sampling ends at noise level $0$ , but Flow Matching samples terminate at a significant, nonzero noise level, which is a potential contributing factor to autoregressive error accumulation. The right shows a zoomed view of the red box from the left plot.

Figure 14: Noise conditioning error introduced artificially, with the loss calculated only on the active sampling horizon. Left: horizon only. Right: gain from adding context corruption. Noise conditions are clamped to $[0,1]$ , and errors are standardized with respect to $\delta\in[-0.07,0.07]$ .

Method	Sampler	Inference Schedule	Conditioning	FVD $\downarrow$
Flow Matching	Euler	Identity	$\sigma^{(i)}$	$126.633$
Flow Matching	Euler	Identity	$\tilde{\sigma}^{(i)}\approx g_{\phi}(x^{(i)})$	$121.145$
Flow Matching	Euler	$c$ -Function	$\sigma^{(i)}$	$103.610$
Flow Matching	Euler	$c$ -Function	$\tilde{\sigma}^{(i)}\approx g_{\phi}(x^{(i)})$	$94.488$
Flow Matching	NAG, $\mu=0.2$	$c$ -Function	$\sigma^{(i)}$	$1045.633$
Flow Matching	NAG, $\mu=0.2$	$c$ -Function	$\tilde{\sigma}^{(i)}\approx g_{\phi}(x^{(i)})$	$81.193$

Appendix

Table 7: Flow Matching autoregressive generation results under different inference schedules and conditioning choices. Conditioning on the inferred noise level

g_{\phi}(x^{(i)})

substantially improves FVD, especially when combined with NAG under the

c

Function inference schedule.

Figure 15: Comparison of the noise level that sampling terminates at across FM, NU-FM, EqF , and EqF with NAG. Ideally, sampling ends at a noise level of $0$ . Closed-loop sampling with EqF terminates at a lower noise level, and NAG accelerates the schedule and ends at an even lower noise level. The right shows a zoomed view of the red box from the left plot.

Figure 16: Early Stopping on Minecraft with EqF . The early stopping algorithm using noise level readouts optimizes the compute/performance tradeoff. Each value of $\mu$ is evaluated with stopping thresholds $\sigma_{\text{thresh}}=0.1,0.2,0.3,0.5,0.7$

Inference Mode	Sampler	Stopping Noise Level $\sigma_{\text{thresh}}$	$N$	FVD $\downarrow$
Adaptive Early Stopping	EqF GD	0.7	$27.7$	$161.67$
		0.5	$38.9$	$94.87$
		0.3	$49.8$	$86.70$
		0.2	$55.4$	$89.88$
		0.1	$67.6$	$94.75$
Adaptive Early Stopping	EqF NAG $\mu$ =0.1	0.7	$26.0$	$161.59$

Appendix

Table 8: Adaptive early stopping experiments on Minecraft with EqF . For adaptive runs, the stopping noise level induces an empirical number of function evaluations

N

. Higher setting of

\mu

for NAG makes the adaptive stopping condition trigger sooner. All runs use

c

-function as the

\eta

warp. These are the values plotted in Figure 16 .

Table 21

Config	Minecraft	Re10K	Droid
Training
Effective Batch Size	8	8	16
Learning Rate	2e-4 (Linear Warmup)	1e-4 (Linear Warmup)	1e-5 (Linear Warmup)
Warmup Steps	2,000	2,000	2,000
Weight Decay	1e-3	1e-3	1e-3
Training Steps	580k	100k	60k

Appendix

Table 12: Training settings for Minecraft, Re10K, and Droid across models. The Rectified Flow schedule is from Liu et al. (2023) and the Cosine schedule is from Nichol and Dhariwal (2021) . Minecraft is trained from scratch. For Re10K, we finetune Wan T2V 1.3B ( Wan et al., 2025 ) . For Droid, we finetune Wan TI2V 5B.

Table 23

Figure 17: Re10K Validation Loss and FVD across equilibrium finetuning steps.

Figure 18: Training loss for noise level estimation. The readout predictor $h_{\omega}$ , trained on EqF activations, converges substantially faster than the framewise predictor $g_{\phi}$ trained directly from noisy data.

Panel of Figure 19 — Figure 19: Marginalized residuals of noise level estimates from the framewise noise level predictor $g_{\phi}$ trained directly on noisy data (left) and the readout predictor $h_{\omega}$ trained on EqF activations (right). Both predictors are accurate, but $h_{\omega}$ is especially accurate near the low-noise boundary.

Figure 20: Conversions between noise level, discretized solver time, and induced warp. a) Conversion between $\sigma$ and update multiplier under different choices of the warp function $\eta$ . b) Induced conversion between solver time $s$ and noise level $\sigma$ through the trajectory $\rho$ . Equally sized steps in solver time can correspond to different changes in noise level. c) Warp multiplier as a function of solver time through the composition $\eta(\rho(s))$ . Due to the vanishing update multiplier for attractor-style choices of $\eta$ , equally sized steps in solver time take increasingly smaller steps as the sampler approaches data.

Figure 21: Online replanning on Minecraft. The replanning threshold $\tau$ controls when the retained future horizon is discarded and regenerated. $\tau=\infty$ never replans, while $\tau=0$ always replans. Intermediate thresholds trade off reuse of the current plan against responsiveness to new observations.

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