# FlowMo: Variance-Based Flow Guidance for Coherent Motion in Video Generation

## Paper ID #12093

## Supplementary Material

Abstract

Text-to-video diffusion models are notoriously limited in their ability to model temporal aspects such as motion, physics, and dynamic interactions. Existing approaches address this limitation by retraining the model or introducing external conditioning signals to enforce temporal consistency. In this work, we explore whether a meaningful temporal representation can be extracted directly from the predictions of a pre-trained model without any additional training or auxiliary inputs. We introduce FlowMo, a novel training-free guidance method that enhances motion coherence using only the model's own predictions in each diffusion step. FlowMo first derives an appearance-debiased temporal representation by measuring the distance between latents corresponding to consecutive frames. This highlights the implicit temporal structure predicted by the model. It then estimates motion coherence by measuring the patch-wise variance across the temporal dimension, and guides the model to reduce this variance dynamically during sampling. Extensive experiments across multiple text-to-video models demonstrate that FlowMo significantly improves motion coherence without sacrificing visual quality or prompt alignment, offering an effective plug-and-play solution for enhancing the temporal fidelity of pre-trained video diffusion models.

## Qualitative Comparison: FlowMo vs. the Base Model (Wan2.1-1.3B, CogVideoX-5B)

As mentioned in the paper, FlowMo is a novel training-free guidance method that enhances motion coherence. In this section, we provide an apples-to-apples qualitative comparison showing the impact of FlowMo on the base model (Wan2.1-1.3B, CogVideoX-5B). The comparisons are conducted with the same random seed on diverse prompts that capture a variety of motion types. Use the arrows to navigate through the results.

### Wan2.1-1.3B

A boy with glasses flying a kite in a grassy field.
A woman performing a challenging exercise.
A dolphin jumping out of ocean waves.
A ninja flipping through a bamboo fores.
A person rowing a boat across a misty lake.
A roulette wheel in a dimly lit room or casino floor.
A senior couple dancing at sunset on a pier.
A woman in a flowing dress dancing in a field.
A child jumping on a trampoline.
A helicopter flying over a forest.
Pikachu with Charmander at a campfire.
A painter creating a landscape on canvas.

### CogVideoX-5B

A violinist performing a solo on stage.
A pair of flamingos wading through shallow water.
A ballerina leaping through the air.
A deer leaping over a fallen log.
A potter shaping clay on a spinning wheel.
A teenager skateboarding down a handrail.
A falcon swooping down.
A golfer following through on a perfect swing.
A bee collecting pollen from a vibrant flower.
A chef flipping vegetables in a wok with dramatic flames.

## Qualitative Comparison: FlowMo vs. FreeInit

As mentioned in the paper, we compare FlowMo with FreeInit, a method originally designed for UNet-based DDPM/DDIM models that suffer from temporal artifacts due to signal-to-noise ratio (SNR) discrepancies between training and inference. These artifacts often result in inconsistencies across frames (e.g., identity or background shifts). In contrast, FlowMo operates on modern Transformer-based models trained with Flow Matching (FM), which offer greater temporal consistency due to stronger architectures and training on large-scale data. For a fair comparison, we adapted FreeInit to FM-based DiT models by applying its re-noising strategy to initialize low-frequency components. To provide a fair comparison, we adapted FreeInit for use with FM-based DiT models. This involved re-noising a denoised latent and combining this re-noised latent with random noise to initialize the low-frequency components, before repeating the denoising process, as per FreeInit's methodology. Here are some of the results from our qualitative comparisons between FlowMo and our adapted FreeInit. Use the arrows to navigate through the results.

Athletic man doing gymnastics on a horizontal bar.
Young adult male doing a handstand on the beach.
A small dog playing with a red ball on a hardwood floor.
A man jumping rope on a dark stage.
A young woman doing stretches on the beach.
A close-up of a person's feet as they walk through flowers.
A person lifts one knee high in a marching motion.
A young woman practicing boxing in a gym.
A female kayaker paddling through white water rapids.
An origami bird transforming into a real dove and taking flight.

## Motivation for FlowMo

FlowMo arose from the observation that videos with coherent and incoherent motion exhibit separation in a measure we defined as Patch-Wise Variance. Given a tensor, we first compute the ℓ1-distance between consecutive latent frames to eliminate their common appearance information and get a debiased motion representation. We then compute patch-wise temporal variance, and finally take its mean value across channels.
Patch-Wise Variance of a Latent Video
After examining the patch-wise variance of the model's prediction when generating videos with coherent and incoherent motion, we found that the model's predictions for coherent motion consistently exhibited lower patch-wise variance compared to those for incoherent motion, as seen in the figure below. Intuitively, in videos with smooth and consistent motion, object trajectories evolve gradually, resulting in lower temporal variance. In contrast, incoherent motion introduces abrupt changes, manifesting as larger fluctuations and higher patch-wise variance in the latent predictions.
Patch-Wise Variance of a Latent Video
We have therefore proposed to use this measure to guide the model to reduce the patch-wise variance during sampling, thus encouraging it to produce a prediction which is more likely to demonstrate coherent motion. After each timestep of the first 12 timesteps, FlowMo minimizes the maximum patch-wise variance of the model's prediction, which results in an adjusted latent for the next timestep. We chose the first 12 timesteps because we found that coarse spatial information is determined in the first steps (0-4) and motion is determined at around steps 5-8 (and refined later), as seen in the figures below.