At the nuclear periphery, interactions of chromatin with the nuclear lamina via lamina-associated domains (LADs) confer structural stability to the genome. We have examined the dynamics of lamin B1 LADs in the first 72 h of adipocyte differentiation in relation to changes in developmental gene expression and chromatin states. We show a repositioning of whole stand-alone LADs and of LAD edges as a nuclear structural feature of early adipogenesis. Adipogenic genes are either already in inter-LADs before differentiation, or are released from variable (v)LADs, while vLADs sequester genes involved in non-adipogenic lineages. LAD repositioning only partly concurs with transcriptional changes. In addition, we identify differentially expressed genes in constitutive LADs (cLADs), which reside in H3K9me3-depleted, euchromatic pockets of low lamin B1 contact frequency. There, active histone modifications (H3K4me1, H3K4me3 and H3K27ac) already established in adipose stem cells predict the post-differentiation LAD vs. inter-LAD fate of these genes. GeneHancer, ECHi-C and FISH data show that enhancers of expressed cLAD genes reside i) within the cLAD active pockets, ii) outside LADs, or iii) in LADs and are released from the lamina to approach their cLAD target genes. Thus, LADs and local euchromatic pockets within LADs emerge as determinative structural features of adipose nuclear architecture. At a higher-order level of spatial organization, FISH analysis of Chr.1p reveals that LADs form clutches at the nuclear periphery while interspersed inter-LADs adopt a looser configuration. Depletion of lamin A/C or B1 does not affect LAD clutches but results in the aggregation of multiple inter-LADs together, suggesting that chromatin tension operates to spatially segregate LADs from inter-LADs. Downregulation of CBX5/HP1a in lamin A/C or B1-depleted cells de-compacts both LAD and inter-LAD clutches, suggesting that lamins and CBX5/HP1a together impose mechanical constraints on chromatin to physically segregate LADs from inter-LADs.