Goal Force: Teaching Video Models To Accomplish Physics-Conditioned Goals

1. Introduction

• Text can be too abstract for complex physical tasks, while specifying a target image can be burdensome or infeasible.The paper uses a soccer kick as an example: intent includes the force and precision imparted to the ball, not merely scoring.Source: §1 · p. 1
• Goal Force defines goals through desired forces and intermediate dynamics, aiming to make them precise for physics-based planning and intuitive for users.This approach is motivated by how people decompose abstract tasks into concrete sub-goals with spatial and motion properties.Source: §1 · pp. 1–2
• The framework conditions video generation on explicit force vectors and trains on paired videos with a multi-channel signal for goal forces, direct forces, and mass.Training uses synthetic causal primitives such as elastic collisions and falling dominos; inference requires no simulator.Source: §1 · pp. 2–3
• Despite training on simple synthetic collisions and dominos, the model generalizes zero-shot to force-propagation chains, golf-club use, and picking roses by their stems.The authors characterize it as an implicit neural physics simulator.Source: §1 · pp. 2–3
• The authors release training and evaluation code, model weights, synthetic training data, and benchmark datasets.The project page is identified as the release location.Source: §1 · p. 3

Video generative models and controllable video generation

• Video generators render plausible complex dynamics [7] [18] [22] [45], but text/image conditioning and trajectory-heavy controls [59] lack precise causal-action interfaces.Controllable approaches also use camera control [46] [65], drag editing [54] [59], trajectory specification [12] [40], and optical-flow guidance [31] [41] [44].Source: §2 · p. 3

Controllable video generation

• Sparse motion prompting [16] and force prompting specify motion or immediate interventions, whereas Goal Force plans causal force chains toward a force on a target object.For example, a direct force topples a block, while a goal force prompts a pendulum swing that knocks it over.Source: §2 · p. 3, Figure 3 · p. 4

Physics simulators and hybrid approaches

• Explicit physics methods [2] [11] [24] [28] [35] [36] [50] [63] often require 3D geometry, while hybrid models [33] [37] [47] depend on inference-time simulators.Unlike prior work focused on local physical properties or simulated-data tasks [29] [50], Goal Force trains the generator as an approximate neural simulator for causal interactions without an inference-time physics simulator.Source: §2 · p. 3

Interactive world models

• Interactive world models have focused mainly on games [9] [10] [48], while real-world interaction [1] [4] typically offers text prompts or camera navigation rather than goal-force control.Goal Force supports reasoning about antecedent actions, including tool use and multi-object collisions, to achieve a specified physical goal.Source: §2 · p. 3

Planning with videos

• Video models support decision-making as reward functions [15] [23], dynamics models [48] [56], and pixel planners [3] [27] [67]; Goal Force adds goal forces to visual planning for robotic actions.UniPi [14] and Adapt2Act [38] use text-conditioned video models to predict visual plans that inverse dynamics models convert into actions.Source: §2 · pp. 3–4

3. Method: Prompting with Goal Force

• Given a starting frame and text prompt, Goal Force asks the model to generate a plausible antecedent causal chain that produces the specified force on a target object.For example, the desired effect may be a ball moving right, achieved by another ball striking it.Source: §3 · p. 4

3.1. Multi-Channel Physics Control Signal

• The 3-channel control tensor encodes direct force as cause, goal force as effect, and optional object mass using Gaussian blobs; force and mass values are relative to each synthetic dataset.Direct and goal forces use moving blobs whose trajectories and durations scale with the force vector; mass uses a static blob whose radius scales with mass.Source: §3.1 · p. 4

3.2. Goal Reaching via Implicit Planning

• Training data spans domino and ball collision chains and swaying flowers, with 3k domino videos, 6k rolling-ball videos, and 3k PhysDreamer carnation videos.The ball set includes 4.5k collision and 1.5k miss cases; the flower sequences teach non-rigid dynamics.Source: §3.2 · pp. 4–5
• Figure 4 contrasts prior force-conditioned methods, including PhysGen [37], PhysDreamer [63], and Force Prompting [17], with Goal Force generation of causes; Tora [64] is conditioned on trajectories.Prior methods apply the provided force directly to the target, whereas Goal Force prompts for the desired effect and generates its causes.Source: Figure 4 · p. 5
• Randomly masking either direct force or goal force teaches the model both to infer antecedent actions from goals and to simulate outcomes from actions.Ball and domino collision data provide ground-truth pairs of direct force and resulting goal force; non-collision scenes receive only direct-force conditioning.Source: §3.2 · p. 5
• Randomly masking the mass channel teaches the model to use supplied physical information when available and estimate properties such as mass from appearance otherwise.Text sets semantic context and guides the video distribution, but leaves the low-level causal plan unspecified so the model must plan a plausible antecedent action for the goal.Source: §3.2 · pp. 5–6

3.3. Architecture and Training Details

• The model uses Wan2.2 [49] with a ControlNet trained on the high-noise expert, cloning its first 10 DiT layers and forwarding outputs to the frozen base model.Training ran for 3,000 steps with effective batch size 4 on four 80GB A100s; videos were 81 frames at 16 FPS.Source: §3.3 · p. 6

4.1. Comparison to Text-Only Baselines

• The 75-scene benchmark tests increasing generalization across two-object and multi-object collisions, human-object interaction, and tool-object interaction.Forty Prolific participants assessed goal-force adherence, realistic motion, and visual quality; scenes were curated from permissively licensed web sources and generative models.Source: §4.1 · p. 6
• Goal Force outperforms both text-only baselines on goal-force adherence, with minimal degradation in visual quality and motion realism.The comparison uses a 2AFC human study on the new 75-scene benchmark.Source: §4.1 · p. 6

4.2. Comparison to Prior Methods

• PhysGen [37], PhysDreamer [63], and Force Prompting treat goal-force prompts as direct pokes rather than planning antecedent causes, while ToRA can violate event order.The passage also states that Goal Force can perform direct Force Prompting.Source: §4.2 · p. 6
• Table 2 reports high success in selecting a physically valid force initiator across diverse, complex scenes.The table covers visual planning accuracy across scenes.Source: Table 2 · p. 7

5.1. Visual Plans are Accurate

• In 22 natural-blocker scenes, Goal Force selected the correct initiator in 98% of valid pool trials, versus a random-baseline ceiling of 33.3%; failures mostly involved spontaneous target motion.The model’s physically grounded planning also generalizes to other natural scenarios, including those shown in Figure 2.Source: §5.1 · p. 7, Figure 5 · p. 8

5.2. Visual Plans are Diverse

• Across 26 random seeds, Goal Force scored 0.6577 on diversity metric δ(p), above the deterministic baseline’s 0.3900 on the 5-domino task.The metric is normalized so uniform sampling across five targetable dominos scores 1.0, while complete mode collapse scores approximately 0.39.Source: Table 3 · p. 7, §5.2 · p. 7

5.3. Visual Plans Leverage Privileged Physics

• In ball-collision scenarios, Goal Force adjusts projectile speed to account for changed object masses and achieve the desired force magnitude in both in-distribution and out-of-distribution settings.A heavier target requires a stronger impact to achieve a specific goal force.Source: Figure 6 · p. 8, §5.3 · p. 8

• Training on simple synthetic causal primitives enables Goal Force to plan backward from a user-defined goal and generate a physically plausible antecedent causal chain.The model functions as an implicit neural physics planner.Source: §6 · p. 8
• Goal Force shifts generative video control from specifying a direct force as the cause to declaring a desired goal force as the effect.Source: §6 · p. 8
• The planning capability generalizes to complex out-of-domain scenarios involving tool use and human-object interactions.The work points toward interactive world models that plan actions to achieve desired physical outcomes, beyond simulating physical reactions.Source: §6 · p. 8

7.1. Comparison to Prior Works: Direct Force Prompting Quantitative Comparison

• The comparison evaluates direct force prompting against PhysGen [37], Force Prompting, and PhysDreamer [63] using a 2AFC human study.The study included N = 10 participants recruited on Prolific.Source: §7.1 · p. 12
• The goal force prompt is encoded in the second control-signal channel, while the direct force prompt is encoded in the first.Source: §7.1 · p. 12
• The evaluation uses two benchmarks: four PhysGen scenes and three PhysDreamer scenes highlighted on their respective project pages.Source: §7.1 · p. 12
• On the PhysGen benchmark, the model is compared with PhysGen [37] and Force Prompting.Source: §7.1 · p. 12
• On the PhysDreamer benchmark, the model is compared with PhysDreamer [63] and Force Prompting.Source: §7.1 · p. 12
• The cited benchmarks cover differing modeled phenomena: PhysGen models rigid body mechanics, whereas PhysDreamer models oscillations.Source: §7.1 · p. 12

7.2. Synthetic Data Generation

• 3D forces and object properties are projected into 2D pixel coordinates using camera parameters to create the multi-channel control signal ˜π.This projection is used across all synthetic datasets to model physical interactions in video frames.Source: §7.2 · p. 12

7.2.1. Dominos Dataset

• The domino dataset contains 3k Blender videos of force-initiated chains, with randomized domino counts, layouts, directions, visuals, and force magnitudes.Counts range from 3 to 10 and force magnitude from 0 to 1; JSON files record contact dominos and their 2D coordinates across frames.Source: §7.2.1 · p. 12

7.2.2. Rolling Balls Dataset

• The rolling-balls dataset contains 6k Blender videos: 4.5k collision cases and 1.5k misses, with varied ball properties, scenes, and forces.Collision cases include evenly split straight-on and indirect strikes, with collision forces based on projectile mass, target distance, and randomized collision time; JSON files record coordinates and physics parameters, plus trajectories for indirect collisions and miss cases.Source: §7.2.2 · pp. 12–13

7.2.3. Plants Dataset

• The plant dataset uses PhysDreamer [63] to generate non-rigid plant-sway videos after direct forces, varying initial conditions, contact points, force angles, and magnitudes.Force magnitudes range from 0 for a gentle poke to 1 for a strong impulse.Source: §7.2.3 · p. 13

7.3.1. How important is the mass channel?

• Masking the mass channel and relying on text for mass leads to worse performance than the result reported in Figure 6.Source: §7.3.1 · p. 14

7.3.2. How important is the direct force channel?

• Masking the direct-force channel causes failures on some complex, out-of-domain causal chains, including human-object interactions.Source: §7.3.2 · p. 14

7.3.3. How specific does the text prompt need to be?

• Action wording can be generic, while unspecified sources defer to pretrained priors that may choose invisible forces; source and interaction type can be specified for embodiment and high-level planning without prescribing low-level dynamics.Source: §7.3.3 · p. 14